# Understanding microwave backscattering of bare soils by using the inversion of surface parameters, neural networks and genetic algorithm

код для вставкиСкачатьDepartement de Geographie et Teledetection Faculte des lettres et sciences humaines Universite de Sherbrooke UNDERSTANDING MICROWAVE BACKSCATTERING OF BARE SOILS BY USING THE INVERSION OF SURFACE PARAMETERS, NEURAL NETWORKS AND GENETIC ALGORITHM (COMPREHENSION DE LA RETRODIFFUSIONDES MICRO-ONDES SUR LE SOL NU EN UTILISANTL’INVERSIONDES PARAMETRES DE SURFACE, LES RESEA UXDE NEURONES E T L ’ALGORITHME GENETIQUE) MAHMOD REZA SAHEBI These presentee pour l’obtion du grade de Philosophiae Doctor (Ph.D.) en teledetection Sherbrooke Aout 2003 Reproduced with permission of the copyright owner. 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Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. L'auteur conserve la propriete du droit d'auteur qui protege cette these. Ni la these ni des extraits substantiels de celle-ci ne doivent etre imprimes ou aturement reproduits sans son autorisation. Canada Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Composition du jury: Prof. Ferdinand Bonn, directeur de these Prof. Goze Bertin Bertie, evaluateur interne Prof. H ardy Granberg, evaluateur interne Prof. Gerard Ballivy, Evaluateur exteme President; M. Bernard Chaput, doyen Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. To the great loves o f my life: to my parents Mehri and Manouchehr to my wife Sudabeh and to my daughter Saghar Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RESUME L’estimation des parametres physiques de la surface du sol, notamment de l’humidite et de la rugosite, est importante pour les Etudes hydrologiques et agricoles, car ils constituent deux parametres majeurs dans la precision du ruissellement au niveau d’un bassin versant en milieu agricole. Le radar offre un potentiel eleve pour la mesurer des parametres de la surface du sol par teledetection. Une image radar est produite par un systeme actif ou un signal hyperfrequence est emis vers le sol et sa reflexion au capteur (retrodiffusion) est mesuree. Les variations de l’intensite du signal retrodiffuse produisent une variation du niveau de gris des pixels de 1’image. Les progres technologiques des demieres annees dans le domaine du radar ont mis en evidence la complexity des mecanismes regissant la retrodiffusion d’un signal par une cible visee. En effet, ces mecanismes sont bien souvent dependants a la fois de l’instrumentation et de la cible. L’information contenue dans le signal hyperfrequence retrodiffuse par une cible visee, reflete d’une fa?on globale, la geometrie, la nature et les proprietes dielectrique de cette cible; de plus, cette information re<?ue a l’antenne, traitee par l'ordinateur du systeme de reception, doit etre interpretee en tenant compte de la polarisation et de la frequence de l'onde incidente, de la geometrie de visee. De nombreuses etudes ont deja ete realisees sur le potentiel de la teledetection radar a retrouver l’humidite et la rugosite du sol. En particulier, l’etude de la reponse de la retrodiffusion radar d’un sol nu constitue un champ important dans le domaine de la teledetection a cause de sa capacite d’extraire les parametres physiques appropries de la surface. L’humidite du sol peut etre definie comme la quantite de precipitation stockee temporairement a l’interieur de la couche superficielle de la terre qui est generalement limite par la zone d’aeration. Elle est definie aussi comme un rapport, exprime en pourcentage, de poids d’eau Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. liquide par poids de sol sec. La sensibilite du radar a l’humidite du sol est definie comme le taux de variation de la retrodiffusion du signal radar avec le contenu en eau du sol. Pour des parametres de radar constants (frequence, angle d’incidence, polarisation), le coefficient de retrodiffusion d’un sol nu dont la rugosite est constante varie en fonction de son humidite et. Ceci est en fait du a une variation de sa constante dielectrique. En regie generate les milieux dont la constante dielectrique est elevee constituent habituellement des surfaces hautement reflechissantes. Done, plus notre cible contient d’eau plus notre coefficient de retrodiffusion sera eleve. La rugosite de surface d’un sol est la variation statistique et aleatoire de la hauteur de la surface par rapport a une surface de reference. Elle est caracterisee par la dimension verticale (l'ecart-type des hauteurs ou rms hauteurs) et aussi dans certains cas, la dimension horizontale (la longueur de correlation de surface). La rugosite de la surface affecte le coefficient de retrodiffusion et masque la reponse de la constante dielectrique. Plus une surface est rugueuse et plus le signal de retrodiffusion sera intense parce que la partie speculaire du signal reflechi diminue et la partie diffusee de fa<?on lambertienne, augmente. Souvent, la grande difficulty de l'observation radar de l’etat des surfaces naturelles est le caractere indissociable de la rugosite avec l'humidite sur la retrodiffusion et l'extraction de l'un des parametres necessite la connaissance de l'autre. L’objectif de ce travail est d’evaluer et d’inverser les modeles de coefficient de retrodiffusion permettant de choisir la meilleure approche pour extraire les parametres de surface rugosite et humidite a partir des images radar. Pour separer les effets des differents parametres sur le signal acquis au-dessus d’une zone complexe, les concepts multi-techniques (multi-polarisation, multi-angulaire, multi-capteurs, multi-frequence, et multi-temporel) offrent les meilleures possibilites de solutions. A partir d’une etude theorique (simulation), trois configurations differentes, la multi polarisation, la multi-frequence et la multi-angulaire, sont verifiees a fin d’evaluer la Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. configuration optimale pour un capteur a bord d'un satellite radar permettant de choisir la meilleure approche pour extraire la rugosite de surface. Une etude de simulation utilisant les modeles theoriques et experimentaux permet d'estimer la sensibilite du coefficient de retrodiffusion a la variation relative des parametres du sol en termes des caracteristiques des radars. Les simulations ont ete effectuees a l’aide des quatre modeles theoriques (SPM, POM, GOM et IEM) et deux modeles empiriques (modele de Dubois et modeles de Oh). C’est la configuration multi-angulaire qui donne les meilleurs resultats. Base sur ce resultat, le travail a ete poursuivi comportant les cinq phases suivantes : Phase 1) Un nouvel indice normalise de la retrodiffusion radar (Normalized radar Backscatter soil Roughness Index-NBRI) utilisant 1’approche multi-angulaire est propose. Cet indice presente une relation logarithmique entre les coefficients de retrodiffusion et l'ecart-type des hauteurs de la surface (rms hauteurs) qui peut estimer et classifier la rugosite de surface des zones agricoles a partir de deux images radar avec differents angles d’incidence. II est tres sensible de changement des conditions de la surface, par exemple si les deux images ne portent pas les meme valeurs de l’humidite, les resultats peuvent ne pas etre fiables. Phase 2) Un nouveau modele empirique lineaire a ete presente pour estimer l’humidite du sol en utilisant les donnees de RADARSAT-1. Ce modele est base sur le modele lineaire de CLOUD mais il est capable de rendre compte l’influence des effets de Tangle incidence et de la rugosite de la surface qui sont deux parametres tres importants pour estimer Thumidite de surface. Le modele propose est capable d’estimer Thumidite de surface en reduisant les erreurs d’estimation, comparativement aux autres modeles lineaires. Phase 3) Inversion des parametres de surface a l’aide des modeles non-lineaires classiques. Dans ce cas, la methode numerique de Newton-Raphson a ete utilisee dans le modele d’extraction pour resoudre le probleme d’inversion. Cette inversion est capable d’estimer les deux parametres de surface (la rugosite et Thumidite) simultanement en utilisant des modeles de coefficient de retrodiffusion bases sur une approche multi-angulaire. Trois differents modeles ont ete choisis selon le domaine de validite des modeles et les conditions de surface, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. il s’agit des modeles GOM, Oh et MDM. Le MDM qui est developpe pour les sites du Quebec a donne les meilleurs resultats. Phase 4) Dans cette phase, un reseau de neurones avec une methode dynamique d’apprentissage a ete mis au point pour inverser les parametres de surface a partir des donnees radar. Un algorithme rapide d’apprentissage a ete utilise pour entrainer les reseaux de neurones multicouches a l’aide de la technique filtre du Kalman. Pour l’etape d’apprentissage, deux bases de donnees differentes (les donnees simulees et empiriques) ont ete utilisees. Chaque base de donnees a ete configuree sous forme d’ensemble simple et d’ensemble multi-angulaire servant comme donnees d’entree, compatibles avec une et deux images respectivement. Toutes les configurations sont entrainees et ensuite evaluees avec les donnees RADARSAT-1 et les donnees simulees. Pour le site d’etude, la base de donnees empirique (donnees mesurees) ayant la configuration basee sur 1’ensemble multi-angulaire donne les resultats des plus precis. L’avantage de l’approche multi-angulaire avec des donnees mesurees est clairement etabli. Phase 5) Finalement, une methode novatrice a ete developpee base sur la mise au point d’un algorithme genetique (AG) pour estimer les parametres de surface. Cette technique est basee sur la Theorie de revolution de Darwin. A partir des donnees du probleme, on cree (generalement aleatoirement) une "population" de solutions possibles. Les caracteristiques de chaque solution represented ses genes. Puis, on evalue chacune des solutions. On elimine une partie infime de celles qui se sont montrees inutiles ou desastreuses, et on recombine les genes des autres afin d'obtenir de nouveaux individus-solutions. Selon la theorie evolutionniste, cette nouvelle generation sera globalement plus adaptee au probleme que la precedente. On itere alors le procede jusqu'a la naissance d'ime solution que l'on jugera satisfaisante. Done, l’algorithme genetique a ete engage pour l’inversion des parametres de surface a partire des images radar en utilisant des modeles de coefficients de retrodiffusion. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V Cette partir de l’etude s’appuie sur cinq campagnes de mesures realisees en France : Orgeval 94, Alpilles 97, et Pays de Caux 98-99, et sur deux campagnes realisees au Canada (province du Quebec): Brochet 99 et Chateauguay 99 avec les images de RADARSAT et ERS. Ainsi, dans cette partie nous avons utilise un etalonnage empirique du modele de retrodiffusion IEM. Cette calibration a ete realisee en utilisant des configurations radar variees en incidence, polarisation et longueur d’onde. Basees sur plusieurs bases de donnees, des relations entre le parametre de calibration et la rugosite de surface ont ete retrouvees pour chaque configuration radar. La version calibree du modele IEM a par la suite ete validee sur une autre base de donnees experimentale independante. Cette calibration s'avere etre robuste et generalisable, puisqu’elle est independante de la base de donnees et du capteur utilises. Cette etude a demontre que 1’algorithme genetique peut presenter une bonne estimation de l’humidite et de la rugosite de surface, simultanement, a partir d’une seule image radar. Cette approche avec sa bonne precision peut etre plus utile pour les regions ayant un risque de precipitation ou de gel du sol pendant la periode separant 1’acquisition des images RADARSAT multi-angulaire. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SUMMARY Estimates of the physical parameters of the soil surface, namely moisture content and surface roughness, are important for hydrological and agricultural studies, as they appear to be the two major parameters for runoff forecasting in an agricultural watershed. Radar has high potentiality for the remote measurement of soil surface parameters. In particular, the investigation of the radar backscattering response of bare soil surfaces is an important issue in remote sensing because of its capacity for retrieving the desired physical parameters of the surface. The objective of this study is to formulate and to constrain a methodology for solving the inverse problem for the operational retrieval of soil surface roughness and moisture. To separate the effects of the different parameters on the measured signal over complex areas, multi-technique concepts (multi-polarization, multi-angular, multi-sensor, multi-frequency, and multi-temporal) are the main solution. In this work, based on a simulation study, three different configurations, multi-polarization, multi-frequency and multi-angular, are compared to obtain the best configuration for estimating surface parameters and the multi-angular configuration gives the best results. Based on these results, this study was continued according to five different phases: Phase 1) A new index, the NBRI (Normalized radar Backscatter soil Roughness Index), using the multi-angular approach was presented. This index can estimate and classify surface roughness in agricultural fields using two radar images with different incidence angles. Phase 2) A new linear empirical model to estimate soil surface moisture using RADARSAT-1 data was proposed. This model can provide soil moisture with reduced errors of estimation compared to other linear models. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Phase 3) Inversion of the surface parameters using nonlinear classical methods. In this case, the Newton-Raphson method, an iterative numerical method, was used in the retrieval algorithm to solve the inverse problem. Phase 4) In this phase, the neural network technique, with a dynamic learning method, was applied to invert the soil surface parameters from the radar data. The results were obtained through performance testing on two different input schemes (one and two data series) and two different databases (theoretical and empirical). The advantage of the multi-angular set with measured data is apparent. These results are the best in this study. Phase 5) Finally, a novel genetic algorithm (GA) was developed to retrieve soil surface parameters. In this study, it is shown that the genetic algorithms, as an optimization technique, can estimate simultaneously soil moisture and surface roughness from only one radar image. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. viii Table of content Resume Summary Table of content Figures Tables Preface Acknowledgement i vi viii xiv xxii xxiv XXV Chapter 1: Introduction Importance of soil surface parameters Definitions and system parameters Radar sensor characteristics affecting backscatter Synthetic aperture radar (SAR) Incidence angle (0) Frequency / Wavelength Polarization Sigma nought (ct°) RADARSAT Influence of target parameters on microwave backscatter Backscatter from bare soil Soil roughness Surface roughness parameters Dielectric properties of soil Scope of the work Problem definition Objectives Hypotheses Methodology References 1 1 2 2 2 3 4 5 7 8 12 12 13 15 18 20 20 21 22 22 25 Chapter 2: A comparison of multi-polarization and multi-angular approaches for estimating bare soil surface roughness from spacebome radar data Abstract / Resume Introduction Objectives Radar observation of soil roughness Modeling approach 28 29 29 30 30 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ix Methods Study area Data description Results and discussion Simulation results Comparison to satellite configurations Application to RADARSAT data NBRI and soil roughness relationship for very rough surfaces Conclusion References 32 32 32 33 33 36 37 38 39 39 Transition between chapters 2 and 3 Chapter 3: Estimation of the moisture content of bare soil from RADARSAT-1 SAR using simple empirical models Abstract Introduction Study area Data Ground data Satellite SAR data Testing and fitting the models A new linear model Interpretation and discussion Conclusions References 41 Transition between chapters 3 and 4 Chapter 4: An Inversion method based on multi-angular approaches for estimating bare soil surface parameters from RADARSAT-1 data Abstract Introduction Study site and Data description Methodology Model descriptions Inversion method Evaluation of the results Discussion and Results analysis Surface parameters mapping Conclusion References Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 43 43 44 44 44 45 45 46 46 49 49 51 53 54 54 56 59 60 62 64 65 72 79 80 X Transition between chapters 4 and 5 C hapter 5: Neural Networks for the inversion of soil surface parameters from SAR satellite data Abstract / Resume Introduction Network Properties Network architecture Training algorithm Backpropagation Extended Kalman filter Surface parameter inversion Data descriptions Study area Ground data Satellite data Network data descriptions Model descriptions Databases for network training and simulation Input configurations Results and discussions Surface parameters mapping Conclusion References Appendix 1 Backscattering models description Transition between chapters 5 and 6 C hapter 6: Bare soil moisture content and surface roughness estimation with SAR data using genetic algorithms Abstract Introduction Genetic algorithms Model descriptions Study areas and data descriptions Study areas Satellite data Ground data Genetic algorithms to retrieve soil surface parameters GA evaluation Model evaluation Conclusion References Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 85 86 87 88 88 90 90 92 93 94 94 94 96 97 97 97 98 98 107 113 113 117 121 123 124 125 126 126 131 131 132 132 134 143 145 146 147 xi Chapter7: Conclusions and future research directions Summary and conclusions Prospects and recommendations for future research APPENDIX A: Spaceborne observation of catchment surface changing conditions generating excess runoff, erosion and flood risk downstream Abstract Introduction and background C-band SAR mapping of surface roughness of bare soils Introduction Methodology and data acquisition Data analysis Classification of roughness classes Conclusion for roughness mapping with RADARSAT Optical observation of crop residue cover as a way to control erosion and runoff Crop residues are an efficient way to reduce erosion and runoff Mapping of crop residues is possible with optical sensors operating in the SWIR spectral range References 150 150 154 155 156 156 157 157 157 158 159 159 160 160 160 161 APPENDIX B; A multi-angular RADARSAT based C-band backscattering model for estimation of bare soil surface roughness Abstract Introduction Study site and data description Study area Ground data Satellite data Methodology Results and discussion Simulation results Comparison of satellite configurations Definition of a multi-angular backscatter index using RADARSAT data NBRI and soil roughness relationship for very rough surfaces Conclusions References 162 163 163 164 164 164 164 164 165 165 165 167 167 167 169 APPENDIX C: A RADARSAT-1 based multi-angular approach to separate and map moisture and surface roughness components of the radar signal backscattered by bare soils Abstract 170 171 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. xii Introduction Methodology Study site Data Ground data Satellite data Discussion and Results analysis Conclusion References 172 173 175 175 175 176 177 177 180 APPENDIX D: In-situ measurements Soil moisture Instrument Sampling methods Calibration Data verification Surface roughness Definitions rms height The profilometer Photograph analysis Problems and alternative methods Soil texture References 183 184 184 185 185 186 189 189 196 190 191 192 192 195 APPENDIX E: Optimization using non-linear Least square method 197 APPENDIX F: Newton-Raphson method for nonlinear systems of equations 201 APPENDIX G: Semi-empirical calibration of the IEM backscattering model using radar images and moisture and roughness field measurements Abstract Introduction Databases Study areas Satellite data Field data Modelling the radar signal Integral equation model (IEM) backscattering model IEM results Semi-empirical calibration of the IEM 204 205 205 208 208 209 210 211 211 213 220 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. xiii Validation of the IEM calibration Effect of radar frequency on calibration Conclusions References Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 238 243 246 247 xiv Figures Chapter 1 Figure 1. Schematic diagrams of system (la) and local (lb) incidence angle (0) 4 Figure 2. Components of an electromagnetic wave. The plane of polarization is defined by the electric field 6 Figure 3. Definition of surface area used to derive reflectivity parameters for distribution surface scatters. 0 j: incidence angle; A ;: illuminated area in the plane of the wave; AL : illuminated area on the ground; R : range from the radar’s position at pulse transmission 7 Figure 4. RADARSAT imaging modes, (a) RADARSAT-1; (b) RADARSAT-2 12 Figure 5. Specular and diffuse components of radiation scattered at (a) perfect plan, (b) slightly rough, (c) very rough surfaces. 0! and 02 are the incidence angle and scattering angle respectively 14 Figure 6. Two configurations of height variations: (a) random height variations superimposed on a periodic surface; (b) random height variations superimposed on a flat surface 15 Figure 7. Measured height profile of a slightly rough surface 17 Figure 8. The corresponding autocorrelation function of a slightly rough surface. The correlation length of 12 cm corresponds to the displacement £ for which p(£)=l/e 17 Figure 9. Measured dielectric constant for soil types as a function of volumetric soil moisture at 5 GHz 20 Chapter 2 Figure 1. Location of study area. 33 Figure 2. Comparison between multi-polarization and multi-angular approaches: simulation by the SPM with a correlation length of 2 cm 34 Figure 3. Comparison between multi-polarization and multi-angular approaches: simulation by the POM with a correlation length of 10 cm 34 Figure 4. Comparison between multi-polarization and multi-angular approaches: simulation by the POM with a correlation length of 15 cm 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XV Figure 5. Comparison between multi-polarization and multi-angular approaches: simulation by the IEM with a correlation length of 2 cm 35 Figure 6. Comparison between multi-polarization and multi-angular approaches: simulation by the IEM with a correlation length of 6 cm 35 Figure 7. Comparison between multi-polarization and multi-angular approaches: simulation by the Oh model 36 Figure 8. Comparison between multi-polarization and multi-angular approaches: simulation by the Dubois model 36 Figure 9. Multi-angular approaches: simulation by the GOM with a correlation length of 10 cm 36 Figure 10. Relation between rms height and backscattering coefficient simulated by the Dubois model 37 Figure 11. Relationship between theoretical roughness index (NBRI) and soil roughness; simulation by the GOM 38 Figure 12. Relationship between roughness index (NBRI) measured from RADARSAT data and soil roughness on 10 parcels of land 38 Chapter 3 Figure 1. Location of study area 44 Figure 2. Relationship between measured and estimated backscatter coefficients calculated using the Ji model. Recalculated values show a slight increase accuracy 47 Figure 3. Relationship between measured and estimated backscatter coefficients calculated using the Champion model. Recalculated values show a marked increase accuracy 48 Figure 4. Relationship between measured and estimated backscatter coefficients: calculated using the proposed new model 48 Chapter 4 Figure 1. Location of study area 57 Figure 2. Location of the parcels 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. xvi Figure 3. Correlation between the dielectric constant measured and estimated by MDM 66 Figure 4. Correlation between the dielectric constant measured and estimated by OM 66 Figure 5. Correlation between the dielectric constant measured and estimated by GOM 67 Figure 6. Correlation between rms height measured and estimated by MDM 67 Figure 7. Correlation between rms height measured and estimated by OM 68 Figure 8. Correlation between rms height measured and estimated by GOM 68 Figure 9 Variation of the dielectric constant as a function of rms height for two different incidence angles for OM 70 Figure 10 Variation of the dielectric constant as a function of rms height for two different incidence angles for MDM 71 Figure 11 rms height map in pixel scale 74 Figure 12 Volumetric humidity map in pixel scale 75 Figure 13 rms height map in homogeneous zone scale 76 Figure 14 Volumetric humidity map in homogeneous zone scale 77 Figure 15 Flowchart of homogeneous zone calculation 78 Chapter 5 Fig. 1. Multilayer perceptron architecture 89 Fig. 2. Location of study area 95 Fig. 3. Relationship between measured and estimated soil surface parameters. Single set, simulated data 101 Fig. 4. Relationship between measured and estimated soil surface parameters. Single set, measured data 102 Fig. 5. Relationship between measured and estimated soil surface parameters. Multiangular set, simulated data 103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XVII Fig. 6. Relationship between measured and estimated soil surface parameters. Multiangular set, measured data constant 104 Fig. 7. Comparison between soil surface parameters simulated by the neural network and inversion of the traditional backscattering models 106 Fig. 8. rms height map at pixel scale 109 Fig. 9. Dielectric constant map at pixel scale 110 Fig. 10. rms height map at homogeneous zone scale 111 Fig. 11. Dielectric constant map at homogeneous zone scale 112 Chapter 6 Figure 1. Relationship between measured and estimated soil surface parameters. Data 1 137 Figure 2. Relationship between measured and estimated soil surface parameters. Data 2 137 Figure 3. Relationship between measured and estimated soil surface parameters. Data 3 138 Figure 4. Relationship between measured and estimated soil surface parameters. Data 4 138 Figure 5. Relationship between measured and estimated soil surface parameters. Data 5 139 Figure 6. Relationship between measured and estimated soil surface parameters. Data 6 139 Figure 7. Relationship between measured and estimated soil surface parameters. Radar configuration: C-hh 20-21 ° 141 Figure 8. Relationship between measured and estimated soil surface parameters. Radar configuration: C -w 23-24° 141 Figure 9. Relationship between measured and estimated soil surface parameters. Radar configuration: C-hh 25-27° 142 Figure 10. Relationship between measured and estimated soil surface parameters. Radar configuration: C-hh 35-40° 142 Figure 11. Relationship between measured and estimated soil surface parameters for (a) rms height roughness and (b) dielectric constant. Radar configuration: C-hh 45-47° 143 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 12. Relationship between desired and estimated soil surface parameters based on a theoretical simulation Figure 13. Relationship between measured o° and estimated o° using the calibrated IEM for all data APPENDIX A Figure 1. a) Initiation of an erosion rill caused by excess runoff in Normandy, b) Remains of a sealing crust on bare soil compared to a recently harrowed section with a greater roughness. Figure 2. Variation of the satellite backscattering coefficient <r° as a function of mean surface heights (rms) at 39° for the Normandy site. Figure 3: Segment of RADARSAT image and the corresponding classified image. Image dimension is 4.7 km (horizontal) by 6.2 km (vertical). Figure 4: a) Note the difficulty to separate visually the residue colour from the bare soil, b) Reflectance spectra of bare soil and cereal residue. Lignine and cellulose absorption bands help to discriminate residues from bare soil. APPENDIX B Figure 1. Localization of study area Figure 2. Comparison between multi-polarization, multi-frequency and multi-angular approaches for 0^=18%; simulation by the Oh model Figure 3. Comparison between multi-polarization, multi-frequency and multi-angular approaches for 0^=28%; simulation by the Oh model Figure 4. Multi-angular approaches; simulation by GOM with a correlation length of 10 cm. Figure 5. Relationship between theoretical roughness index (NBRI) and soil roughness; simulation by the GOM Figure 6. Relationship between measured roughness index (NBRI) and soil roughness on 10 field plots Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. xix APPENDIX C Figure 1. Location of study area. 175 Figure 2. Correlation between the dielectric constant measured and estimated by MDM 178 Figure 3. Correlation between the dielectric constant measured and estimated by ODM 178 Figure 4. Correlation between rms height measured and estimated by MDM 179 Figure 5. Correlation between rms height measured and estimated by ODM 179 APPENDIX D Figure 1. The dielectric Thetaprobe measuring the volumetric soil moisture 184 Figure 2. 2m (134 samples) profilometer used for measuring surface height values 190 Figure 3. Examples profile recorded for the Chateauguay and the Pike River watersheds 191 APPENDIX G Figure 1. IEM-simulated backscattering coefficient (with L measured) as a function of the backscattering coefficient measured from radar images. Exponential, fractal, and Gaussian correlation functions were used: (a), (b), and (c) ERS W 2 3 0/24° 215 (d), (e), and (f) RADARSAT HH21724725726° 216 Figure 2. IEM-simulated backscattering coefficient (with L measured) as a function of the backscattering coefficient measured from radar images. Exponential, fractal, and Gaussian correlation functions were used: (a), (b), and (c) RADARSAT HH357397400 217 (d), (e), and (f) RADARSAT HH45747747.5747.7° 218 Figure 3. IEM behaviour as a function of correlation length for an exponential correlation function. Surface characteristics are defined as mv=30% and rms=1.7 cm. The radar configuration used is C-HH240. 221 Figure 4. Calibration parameters Loptl and Lopt2 for VV237VV24° (ERS) as a function of surface height, for exponential, fractal, and Gaussian correlation functions. 223 Figure 5. Calibration parameters Loptl and Lopt2 for HH21724725726° (RADARSAT) as a function of surface height, for exponential, fractal, and Gaussian correlation functions. 224 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XX Figure 6. Calibration parameters Loptl and Lopt2 for HH35°/39°/40° (RADARSAT) as a function of surface height, for exponential, fractal, and Gaussian correlation functions. 225 Figure 7. Calibration parameters Loptl and Lopt2 for HH45747747.5°/47.7° (RADARSAT) as a function of surface height, for exponential, fractal, and Gaussian correlation functions. 226 Figure 8. Comparison between calibration parameters and measured correlation length, for an exponential correlation function: (a) and (e) C -W 237240 - (b) and (f) C-HH21724725726° 227 (c) and (g) C-HH35°/39740° - (d) and (h) C- HH45747747.5°/47.7° 228 Figure 9. IEM behaviour as a function of rms surface height, using the analytical expressions of Loptl and Lopt2: (a) C-W 23°, mv=40%, Loptl extracted from C-W 23724° (b) C-HH23°, mv=40%, Loptl extracted from C-HH21724725726° (c) C-W 23°, mv=40%, Lopt2 extracted from C-W 237240 (d) C-HH23°, mv=40%, Lopt2 extracted from C-HH247257260. 230 Figure 10. IEM behaviour as a function of rms surface height, using the analytical expressions o f Loptl and Lopt2: (a) C-HH38°, mv=40%, Loptl extracted from C-HH39°/40° (b) C-HH47°, mv=40%, Loptl extracted from C-HH47°/47.5747.7° (c) C-HH38°, mv=40%, Lopt2 extracted from C-HH35°/39°/40° (d) C-HH470, mv=40%, Lopt2 extracted from C- HH45°/47747.5747.7° 231 Figure 11. Effect of incidence angle and polarization on calibration parameter Lopt2. 232 Figure 12. Comparison between the backscattering coefficient simulated by the calibrated IEM and the backscattering coefficient measured from radar images. Exponential, fractal, and Gaussian correlation functions were used: (a), (b), and (c) ERS W 23724° 234 (d), (e), and (f) RADARSAT HH21724725726° 235 Figure 13. Comparison between the backscattering coefficient simulated by the calibrated IEM and the backscattering coefficient measured from radar images. Exponential, fractal, and Gaussian correlation functions were used: (a), (b), and (c) RADARSAT HH35°/39740° 236 (d), (e), and (f) RADARSAT HH45°/47747.5747.7° 237 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. xxi Figure 14. Backscattering coefficient simulated by the uncalibrated IEM as a function of the backscattering coefficient measured by the ERASME sensor. Exponential, fractal, and Gaussian correlation functions were used: 239 (a), (b), and (c) C-HH250 240 (d), (e), and (f) C-W 25° Figure 15. Backscattering coefficient simulated by the calibrated IEM as a function of the backscattering coefficient measured by the ERASME sensor. Exponential, fractal, and Gaussian correlation functions were used: 241 (a), (b), and (c) C-HH25° 242 (d), (e), and (f) C -W 25° Figure 16. Behaviour o f the calibration parameter Lopt2 for X-band radar data (Orgeval 94 database) with configurations W 45°/480/520/550/57° (SIR-C). Exponential, fractal, 244 and Gaussian correlation functions were used Figure 17. Calibration parameter Lopt2 as a function of rms for L- and C-band radar data (Orgeval 94 database), HH polarization, and incidence angles between 44° and 51°. 245 Exponential, fractal, and Gaussian correlation functions were used Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. xxii Tables Chapter 1 Table 1. Radar bands and frequencies 5 Table 2. RADARSAT-1 imaging modes 10 Table 3. RADARSAT-2 imaging modes 11 Chapter 2 Table 1. Surface parameters measured in the field 33 Table 2. The simulation parameters 33 Table 3. Relationship between rms heights and simulated backscattering coefficients 33 Chapter 3 Table 1. Acquisition parameters of the RADARSAT SAR images 45 Table 2. The values of constant coefficients for the Ji model 46 Table 3. The values of constant coefficients for the Champion model 46 Table 4. Statistical results of comparison between measured and calculated backscattering coefficients using the Ji, Chapman and the new model 49 Chapter 4 Table 1 Coefficient of performance (CP'A) for surface parameters obtained by inversion approach 65 Chapter 5 Table 1. Acquisition parameters of the RADARSAT images 96 Table 2. Summary of inversion results using neural network 99 Table 3. Statistical results of comparison between measured and simulated soil surface parameters using the neural network, the Oh model (OH) and the modified Dubois model (MDM) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 107 xxiii C hapter 6 Table 1. The values of a and p for calculation £optbased on an exponential correlation 131 Table 2. Data description. 133 Table 3. Statistical results of the comparison between measured and calculated rms height and dielectric constant for the study areas. 136 Table 4. Statistical results of the comparison between measured and calculated rms height and dielectric constant for different radar configurations. 140 APPENDIX D Table 1. Results of volumetric soil moisture (readings from the Thetaprobe and standard laboratory method) and rms height for the Pike River site 187 Table 2. Results of volumetric soil moisture (readings from the Thetaprobe and standard laboratory method) and rms height for the Chateauguay site 188 Table 3. Soil analysis results of particle size for Chateuguay watershed 194 APPENDIX G Table 1. Description of the database 210 Table 2. Comparison of uncalibrated IEM simulations and radar data for the available ERS and RADARSAT (IEM-radar) configurations. Exponential, fractal, and Gaussian correlation functions were used 214 Table 3. Comparison of calibrated IEM simulations and radar data for the available ERS and RADARSAT (IEM-radar) configurations. Exponential, fractal, and Gaussian correlation functions were used 233 Table 4. Calibration validation using ERASME W -2 5 ° and ERASME HH-25° (Pays de Caux 94) data. The mean and the standard deviation of the difference between IEM <r° and radar cj° were calculated before and after calibration 238 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. xxiv PREFACE The following studies have been published, accepted for publication or submitted and form the basis for chapters two, three, four, five and six of this thesis which constitute the main body of this thesis. This thesis is the format of a thesis by article. Appendixes A to F provide more detailed information in the direction of the main chapters. Two important points have to be noted: - First, according to the individuality of each paper, some parts such as study area or data descriptions had to be explained in each paper expressing the fact that these sections are repeated in some chapters. - Each paper or manuscript was formatted based on the different Journals’ instructions. Therefore, the layout and formatting of the chapters can be vary. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XXV ACKNOWLEDGEMENT First and foremost, I would like to express my gratitude to my supervisor Professor Ferdinand Bonn who has been a constant source of inspiration and guidance. I would especially like to thank G. Benie, Q. H. J. Gwyn and G. Ballivy for their fruitful, invaluable help and contribution. I am grateful to P. Gagnon and the anonymous reviewers for their corrections and suggestions. I want to thank all the colleagues of CARTEL specially, J. Angles, P. Cliche, M. Lambert, and J. Smyth have provided an excellent working environment. My special thank to my beloved wife Sudabeh for giving me the encouragement to go on to graduate work when I needed it. I am grateful to the Ministry of Science, Research and Technology of Iran for granting me a scholarship and financial support. This work also was partly supported by FCAR (Action Concertee RADARSAT) and NSERC (Grant RGP 6043 and Canada Research Chair of F. Bonn). Some of the data used in the work have been provided by the Canadian Space Agency under the RUDP program and by the partners of the European FLOODGEN project. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 Chapter 1 INTRODUCTION 1. Importance of soil surface parameters Remote sensing offers watershed researchers a type of data which is very different from those they have traditionally worked with. These data provide a new tool for use in scaling and in extrapolating point measurements to represent areas. The spatial nature of remote sensing data for different scale areas is their most unique characteristic, especially when considering that all hydrologic data are obtained from point measurements (King and Delpont, 1993; Blyth, 1993). Indeed, remote sensing presents entirely new measurements, such as rainfall over ocean, snow water content, and surface temperature, which are not traditionally available to hydrologists. Remote sensing can provide measurements for several hydrologic variables used in modeling, either as direct measurements comparable to traditional forms, as surrogates of the traditional forms, or as entirely new data (Blyth, 1993). This study focuses on the estimation of soil surface parameters using radar remote sensing data, on how some commonly available models will perform with a data set and on how this performance can be improved using different novel approaches. The measurement of soil surface parameters (soil moisture and surface roughness) is important for understanding hydrological, environmental and agricultural conditions (Boisvert et al., 1995). Soil surface parameters are useful across the different scales. For example, on a global scale, they are important as boundary conditions for hydrologic and climate models. On a regional scale, they are important for agricultural assessments (crop yield models, drought prediction, erosion, etc.), flow hydraulics and infiltration (Govers et al., 2000). A number of environmental disasters including floods, flash floods, droughts, and landslides, are closely linked to soil surface parameters. Better measurements of these parameters and simulation based on these would help in reducing the potential for damage from such events (Bindlish and Barros, 2000). As important as it may seem to our understanding of hydrology, soil surface parameters as descriptors of hydrological models have not had widespread application in modeling (Engman Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 and Gurney, 1991). This omission can be explained by two important facts. First, soil surface parameters are difficult to measure on a consistent and spatially comprehensive basis. Second, the understanding of the roles of these parameters in hydrology and ecosystem processes has been developed from point measurements where the emphasis has been on the temporal variability of soil surface parameters. Therefore, most hydrological models (empirical and semi-empirical) have been designed around available point data, and do not describe the influence of spatial variability (Bindlish and Barros, 2000). Traditional methods, based on in-situ soil surface parameter measurements, are sparse, point measurements and each value is representative of only a very small area for the time period of measurement. However, remote sensing data with sufficient accuracy would provide truly significant wide-area soil surface parameters data for hydrological and environmental studies across global and regional regions (Engman and Gurney, 1991). 2. Definitions and system parameters Several parameters affecting the backscatter microwave signal from bare soils have already been mentioned in the literature (Ulaby et al., 1982, 1996; Dobson and Ulaby, 1986; Engman and Wang, 1987; Oh et al, 1992; Fung and Chen, 1992; Dubois et al., 1995; Boisvert et al., 1995). The most important of them are relatable to the radar sensor configuration and the target parameters. The radar configuration is characterized by its incidence angle, frequency and polarization. The radar emits a microwave signal at a given configuration and measures the signal backscattered that contains information on the target (surface parameters). Holms (1990) and Boisvert et al. (1995) reviewed the effect of most of these parameters on the radar signal for agricultural applications. This section briefly explains the most important parameters be addressed, when extracting accurate bare soil surface parameters. 2.1. Radar sensor characteristics affecting backscatter 2.1.1. Synthetic aperture radar (SAR) Conventional radar (radio detection and ranging) imaging is a technique in which a target is illuminated with electromagnetic waves of microwave configuration and the reflected signal is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 used to deduce information about the target (Elachi, 1988). The all-weather, transmit-andreceive, radar imaging remote sensing technique uses the round-trip travel times and amplitude of the signal reflected from multiple targets on the ground to determine the distances to the targets, and to generate a rough two-dimensional image of the target area as the radar sweeps the area of interest. Real aperture radar (RAR) would have a resolution of about 5-10 km, limited by the power and size of the footprint of the radar beam, and thus a RAR’s pattern resolution is set by the width of the antenna. Synthetic aperture radar (SAR), most commonly used today, combines signal processing techniques with satellite orbit information to produce a resolution much smaller than the antenna pattern width (Elachi, 1988). SAR processing significantly improves the resolution of point targets in both the cross-track (range) and along-track (azimuth) direction by focusing on the raw radar echoes (Elachi, 1988; Curlander and McDonough, 1991). Fine resolution in the cross-track direction is achieved by using a radar signal of high bandwidth, which improves the differentiation of radar echoes from closely spaced targets in the range direction. 2.1.2. Incidence angle Incidence angle (0) is defined as the angle between the radar line-of-sight and the local vertical (Figure 1) with respect to the geoid (Ulaby et al., 1982). Incidence angle can be incorporated by look angle (<p) and the curvature of the earth that assumes a level terrain or constant slope angle (a) (Figure la). In contrast, as illustrated in Figure lb, incidence angle can be incorporated as the local incidence angle and takes into account the local slope angle (a) (NASA, 1989). In general, reflectivity from distributed scatterers decreases with increasing incidence angles. For example, over a bare soil, the backscattering coefficient decreases when the local incidence angle increases. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 SAR DEPRESSION ANGLE LOOK''' ANGLE TRAP'S INCIDENT ANGLE AZIMUTH ANGLE (a) INCIDENT ANGLE SURFACE NORMAL VERTICAL RADAR WAVE LOCAL INCIDENT ANGLE SLOPE ANGLE (a) V' SCATTERING SURFACE (b ) F ig u re 1. Schematic diagrams of system (la) and local (lb) incidence angle (0) From NASA, 1989). 2.1.3. Frequency / Wavelength Radar wavelength and frequency are inter-related as seen in Equation 1: j ~ _c_ f (1) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 where c is the speed of light (3x1010 cms_1) ,/ is the frequency in terms of hertz (Hz) and X is the wavelength in centimeters (cm). Table 1 presents the value of X and/ for radar bands. The definition and nomenclature for these radar bands, although now adopted as convention, are arbitrary (having been established by the US military during World War II for security reasons). Other classification systems were established outside of the United States; however, the system presented below appears to be the most widely used. In bare soils, the penetration depth and backscatter coefficient change as a function of frequency. Table 1. Radar bands and frequencies (From Waite, 1976) Wavelength (X) Frequency (f) (in cm) 136-77 100 - 30 30-15 15-7.5 7.5 - 3.75 3.75 - 2.40 2.40-1.67 1.67-1.18 1.18-0.75 (in MHz) 220 - 390 300-1000 1000-2000 2000 - 4000 4000 - 8000 8000-12500 12500-18000 18000-26500 26500 - 4000 Radar frequency band P UHF L S c X Ku K Ka 2.1.4. Polarization Propagating electromagnetic radiation (EMR) has three vector fields that are mutually orthogonal. The direction of propagation is one vector; electric and magnetic fields make up the other two vector fields (Figure 2). Active microwave energy, as well as other frequencies of EMR, have a polarized component defined by the electric field vector of the radiation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 E (Electric Field) H (Magnetic Field) Direction Figure 2. Components of an electromagnetic wave. The plane of polarization is defined by the electric field. (From Waite, 1976). Linear polarized radar systems operate using horizontally or vertically polarized microwave radiation as shown in Figure 2. When the electric vector field is parallel to the X-axis (vertical), the wave would be vertically polarized (V). Conversely, if the electric vector field was parallel to the Y-axis (horizontal), the wave would be designated horizontally polarized (H). In radar systems, energy is both transmitted and received. Therefore, the linear polarizations can be mixed and matched to provide the four linear polarization schemes (Wait, 1976). A radar can be designed to measure the radar response for VV, HH, HV or VH, where the first letter denotes the polarization of the receive antenna and the second letter denotes the polarization of the transmit antenna; however, the response for HV and VH are identical (Ulaby etal., 1981). Champion (1996) demonstrated that the value of angular dynamics of the radar response, over a bare soil, is larger at HH than at VV and both of them larger than at HV. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 2.1.5. Sigma nought fa0) As illustrated in Figure 3, sigma nought or backscattering coefficient represents the average reflectivity of a horizontal material sample, normalized with respect to a unit area AL on the horizontal ground plane (Cosgriff et al., 1960). It is a fraction which describes the amount of (average) backscattered energy compared to the energy of the incident field. The Backscattering coefficient depends on the target properties (physical and electrical) and on the radar configuration such as frequency, polarization, and incidence angle. It also depends on the local surface slope towards the radar (Ulaby et al., 1981). A dR dz fol dR sin 0t dR Figure 3. Definition of surface area used to derive reflectivity parameters for distribution surface scatters. 0 i: incidence angle; A ;: illuminated area in the plane of the wave; A l : illuminated area on the ground; R : range from the radar’s position at pulse transmission (Modified from Cosgriff et al., 1960) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 In most references, a 0 is the favored descriptor for scene reflectivity. Most of the related discussions of this thesis conform to this convention. The backscattering coefficient, which is a unitless quantity representing the radar cross-section (in m2) of a given pixel on the ground per unit (physical) area of the pixel (in m2), is akin to the optical reflectivity responsible for the intensity recorded by an optical imaging system. Often, because a 0 may exhibit a wide dynamic range, it is expressed in decibels (dB): cr0(dB) = 10xlogcr0(m2m"2) (2) 2.1.6. RADARSAT The information concerning RADARSAT-1/2 presented in this section has its origin at the Canadian Space Agency Web site: www.space.gc.ca . RADARSAT-1, Canada's first Earth resources remote sensing satellite was launched November 4, 1995, and was designed for five years of service in orbit. The only imaging instrument is a SAR operating in C-band, HH polarization. A variety of resolution, image swath width, and incidence angle parameters are available that may be selected through ground command. The designated agency responsible for RADARSAT is the Canadian Space Agency (CSA). The mission is the result of more than a decade of work and initiative by the Canada Centre for Remote Sensing (CCRS) and the data distribution is done commercially by RADARSAT international (RSI). RADARSAT-1 was designed in response to user requirements that demand a variety of incidence angles (from about 20° to 50°) in the standard imaging modes. An antenna with electronic elevation beam steering is part of the baseline RADARSAT design. Although this enables user requirements to be met, it does add further complexity to the entire system. In order to provide a reasonably constant ground range resolution over the range of incidence angles, three different pulse bandwidths are needed. Signal-to-noise ratio and data rate considerations in these modes are comparable to those of the standard beams. Extended modes result from selection of beams outside of the nominal 500 km accessibility region, either closer to nadir (steeper incidence), or further away (more shallow or grazing incidence angle). RADARSAT-1 is the first operational satellite radar Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 system to implement the ScanSAR technique (Moore et al., 1981; Raney et al., 1991), which provides a continuous image swath of either 300 km or 500 km width. ‘T o be launched in 2004, RADARSAT-2 will be lighter, cheaper, more capable, and will assure data continuity well into the new millennium. Its enchanced capabilities include additional beam modes, higher resolution, multi-polarization, more frequent revisits, and an increased downlink margin enabling reception of data from lower-cost receiving antenna systems.” “RADARSAT-2 will carry a C-band remote sensing radar with a ground resolution ranging from 3 to 100 metres. Swath widths may be selected in a range from 20 to 500 kilometres.” Imaging modes for RADARSAT-1/2 include several modes presented in Figure 4 and Tables 2 and 3. In each mode, data are collected continuously along a swath parallel to the sub satellite path. Swath length is limited only by the duration of continuous radar operation, and may be thousands of kilometers long. Swath widths and positions are determined by the antenna elevation beam patterns and the radar range gate control. For RADARSAT-2, “additional modes are generated by appropriate choices of antenna beam and range pulse bandwidth. The fine resolution mode, for example, is achieved by selecting the widest available bandwidth, and using a narrow beam in elevation at angles of incidence larger than approximately 45°. A narrow swath results from the requirement to minimize beamwidth in order to maintain good signal-to-noise ratio, and also from the necessity to maintain data rates consistent with downlink channel capacity. Wide swath modes require wider antenna elevation beamwidths than normal, and the smallest available range pulse bandwidth. These compromises allow a larger land area to be covered with about the same number of pixels, which of course implies a coarse r ground range resolution.” “Representing a significant evolution from RADARSAT-1, the design of RADARSAT-2 will be the first commercial SAR satellite to offer multi-polarization — an important tool increasingly used to identify a wide variety of surface features and targets.” Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 RADARSAT-1 compatible beam modes are also available ensuring data continuity for existing users. Other key features of RADARSAT-2 include the ability to select all beam modes in both left and right looking modes (Figure 4b), high downlink power, secure data and telemetry, solid-state recorders, on-board GPS (Global Position System) receiver and the use o f a high-precision attitude control system. TABLE 2. RADARSAT-1 imaging modes (Modified from www.space.gc.ca) Resolution Mode Width Incidence (km) (degrees) Looks1 (R1xA, m) Standard 25x28 4 100 20-49 Wide (1) 48-30x28 4 165 20-31 Wide (2) 32-25x28 4 150 31-39 Fine resolution 11-9x9 1 45 37-48 ScanSAR (N) 50x50 2-4 305 20-40 ScanSAR (W) 100x100 4-8 510 20-49 Extended (H) 22-19x28 4 75 50-60 Extended (L) 61-28x28 4 170 10-23 1 Nominal; ground range resolution varies with range. 2 Nominal; range and processor dependent. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 TABLE 3. RADARSAT-2 imaging modes (Modified from www.space.gc.ca) Resolution Width Incidence (RxA, m) Swath coverage (km) (km) (degrees) Standard 25x28 250-750 100 20-49 Fine 10x9 525-750 50 36-48 Low Incidence 40x28 125-300 170 16.5 High Incidence 20x28 750-1000 70 49-60 Wide 25x28 250-650 150 20-45 ScanSAR (N) 50x50 250-600 300 20-47 ScanSAR (W) 100x100 250-720 500 20-47 Fine (Quad-Pol) 11x9 400-600 25-50 30-41 Standard (Quad-Pol) 25x28 250-600 25-50 20-41 Ultra-Fine (N) 3x3 400-550 10 30-40 Ultra-Fine (W) 3x3 400-550 20 30-40 Triple-Fine 11x9 400-750 50 30-49 Mode Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4. RADARSAT imaging modes a) RADARSAT-1; b) RADARSAT-2 (Modified from www.space.gc.ca) 2.2. Influence of target parameters on microwave backscatter 2.2.1. Backscatter from bare soil It has long been known that soil can play an important role in backscatter measurements of crops or forest. The entire scope of the parameters influencing backscatter from soil is not Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 understood yet, but soil moisture content, soil roughness and vegetation cover (if present) are known to be three of the most important factors (Ulaby et al, 1982). A good synthesis of these phenomena is given in Ulaby et al. ("1982), Wagner (1998) and Company-Remond (1996), and the sections below are adapted from it. When an electromagnetic wave with an incidence angle, other than normal incidence, makes an impact on a soil surface (not perfectly smooth), the incidence power is scattered in many directions, including the backscatter direction (Figure 5). The component scattered in the backscatter direction provides the relation between the energy received by radar and the characteristic of the soil medium. The rest of the energy is transmitted (penetrates) through the layers of different densities. The depth of penetration and absorption depend on the wavelength and soil characteristics (Ulaby et al., 1982; Wagner, 1996). For example, the depth of absorption losses can vary from 0.5 to 10 cm for a radar signal in C-band. Normally, this thickness is 0.5 to 5 cm (Ulaby et al., 1982). Therefore, the crucial patterns of the target in determining the backscatter response of a bare soil surface are the dielectric constant (the upper layer of soil depending on wavelength) the geometrical properties of soil surface roughness, soil properties (texture, bulk density, etc.) and geographic conditions (topography and local slopes) (Dobson and Ulaby, 1986). 2.2.2. Soil roughness Soil roughness is expressed by describing disturbances or irregularities in the soil surface at a scale which is generally too small to be detected by a conventional topographic map or survey (Govers et al., 2000). Romkens and Wang (1986) make a distinction between four types of roughness: (i) microrelief variations, which are due to individual grains or micro-aggregates, (ii) random roughness, which is related to soil clodiness, (iii) oriented roughness, which describes the systematic variations in topography due to farm implements and (iv) higher order roughness, representing elevation variations at the field, basin or landscape level. Roughness is one of the most important target parameters that influence radar backscattering. For incident microwaves, when a surface is smooth (specular), the impinge energy is reflected away from the surface. As shown in Figure 5a, the angle of reflection is equal to the angle of incidence (0i=02). This radiation-reflection is governed by Snell’s Law (Jackson, 1986). When Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 a surface is slightly rough (or isotropic), the incidence energy is scattered in many directions (incoherent component), including the backscatter direction (coherent component) and specular direction (Figure 5b).When the surface gets rougher, the incidence energy is scattered in many directions. In other words, the reflected energy becomes more diffuse and less described by Snell’s Law (Figure 5b) until the surface becomes really rough (Ulaby et al., 1982; Wagner, 1998). As the surface is truly rough, the reflected energy diffuses in all directions (Figure 5c). In this case, the energy is independent of incidence angle and the surface is considered diffuse and the signal Lambertian (Ulaby et al., 1982). Specular reflector Reflected wave Incident wave > Smooth surface (a) Mixed scatterer Backscattered com ponent *tr (b) V u T r ^ * 'o ^ Slightly rough ssurface aw rv J ^ T n V o 5 ,,° a ■r u - „ u . JX Diffused scatterer . ^ _ Rough surface (C) Figure 5. Specular and diffuse components of radiation scattered at (a) perfect plan, (b) slightly rough, (c) very rough surfaces. 0j and 02 are the incidence angle and scattering angle respectively. (From Trevett, 1986) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 2.2.3. Surface roughness parameters In agriculture zones, a surface profile may generally consist of two height variations: i) a random component with certain statistical properties, and ii) a deterministic component, such as the periodic pattern shown in Figure 6a (Ulaby et al., 1982). The random component is defined relative to a reference surface, which may exist as periodic component (Figure 6a) or as Mean (flat) surface (only random variation, as in Figure 6b). Random Surface Component Periodic (Reference) Surface Mean (Reference) S u rfa c e ^ Figure 6. Two configurations of height variations: (a) random height variations superimposed on a periodic surface; (b) random height variations superimposed on a flat surface (From Ulaby et a l, 1982). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 The statistical variation of a random surface can be characterized by its rms height (s), which is a measure of vertical roughness, its correlation length (£), which is a measure of the horizontal roughness and its correlation function p(£,), which presents the distribution of the surface roughness. Figure 7 shows the height variation z(x) for a typical random surface as a function of x, the horizontal distance across the mean surface. In general the height z is a function of both x andy, but if z(x,y) is statistically independent of the azimuth angle in the x-y plane, it is then sufficient to use z(x) alone to characterize the statistical properties of the surface. Classically, according to Ulaby et al. (1982), rms height is calculated by: (3) where z is the mean surface height and z2 is the second moment of height. According to Ulaby et al. (1982) and Company-Remond (1996), the surface autocorrelation function can be expressed as a measure of the degree of correlation between the height z(x) at a point x and the height z(x+Q at a point t, distant from x: P (0 = (4) | z 2(x)dx with the limits of integration extending over the overlapping segment of the profiles z(x) and z(x+t). In the discrete case the integral is replaced by summation. Figure 8 displays the computed autocorrelation function p(£) of the random surface shown in Figure 7. The correlation function of a surface is defined as the displacement t, for which p(£) is equal to e'1 (Ulaby et al, 1982; Company-Remond, 1996): P ( 0 = e -' (5) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17 Figure 8 illustrates this autocorrelation. A surface with a rapidly varying height profile has a short value for £, whereas for a perfectly smooth surface for which any point is perfectly correlated with every other point, £ is infinite (Ulaby et al., 1982). Surface Profile O • f- l :r- 2 Distance (cm) Figure 7. Measured height profile of a slightly rough surface (From Ulaby et al., 1982). Autocorrelation M/e 20 40 60 Displacement x 1 (cm) 80 90 100 Figure 8. The corresponding autocorrelation function of a slightly rough surface. The correlation length of 12 cm corresponds to the displacement £, for which p(£)=e'' (From Ulaby et al., 1982). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 In this study, the correlation length is not really used, because first, this factor does not have an important role in hydrological studies and second, as explained in Appendix F, measuring the correlation length is a problem because of the substantial instability of agricultural soils and therefore, the classical method can not give an accurate estimation of this factor and introduces important errors in results. 2.2.4. Dielectric properties o f soil As mentioned before, the radar backscattering coefficient depends on soil moisture because the larger the dielectric constant of the soil the stronger the scattered radiation is as compared with the radiation entering the sub-surface medium (Schanda, 1987). In other words, the dielectric properties of moist soils are major factors in determining the microwave scattering from a bare soil (Holmes, 1990). Soil is a heterogeneous mixture of solid particles (mineral and organic matter), air and water. Soil moisture measurement using microwave remote sensing is based on the large contrast between the dielectric properties of water and dry soil (Engman and Chauhan, 1995). The complex dielectric constant (e) presents the dielectric properties of the soil medium. This constant is given as (Ulaby et al., 1982): s - s '+je" j = V-T (6) where e’ is the real part of the dielectric constant or permittivity and e" is the imaginary part of the dielectric constant or loss factor. Dry soil exhibits a narrow range in s’ between about 2 and 4, whereas that of water is about 81 (Hallikainen et al., 1985). The dielectric constant of soil is therefore a function of the water content of the soil and the dielectric constant increases with increasing water content. In nature, the s' range of soil is from about 3 to 30 (Holmes, 1990). Also, both s' and s" vary with frequency, permittivity increasing with increasing wavelength and the loss factor decreasing with increasing wavelength (Ulaby et al., 1982; Holmes, 1990). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 s' and e" depend on environment temperature. Both of them decrease with decreasing temperature below 0°C (Hallikainen et al., 1985) Dielectric properties of soil medium depend upon soil moisture, soil density, soil texture and fluid chemistry. However, these dependencies exhibit characteristic behavior as a function of frequency and temperature; there exists a potential to infer such bulk characteristics from radar backscatter (Koorevar et a l, 1983; Henderson and Lewis, 1998). Hallikainen et al. (1985), also reported by Wagner (1998), showed that the dielectric constant (e) of soil moisture is a function of its volumetric soil moisture content (mv) and of the soil texture characteristics. As volumetric soil moisture content increases both components of the complex dielectric constant (s' and s") increase (Figure 9). Also Hallikainen et al. (1985) aimed to establish an accurate empirical model (as a polynomial expression) for different frequencies and different soil types. Concentrating on the frequency used in this study (Cband), the results of their experiments are presented in Figure 9. Equation 7, Adapted by Wagner from the original Hallikainen et al. (1985), also presents the polynomial expressions for C-band (frequency = 6 GHz): s' = (1.993 + 0.002Sa + 0.015CI) + (38.086 - 0.176Sa - 0.633CI) x m v +(10.720+1.256Sa+1.522Cl) x m v2 (7a) s" = (-0.123 + 0.002Sa + 0.003CI) + (7.502 - 0.058Sa - 0.U6CI) x m v + (2.942 +0.452Sa+0.543CI) x mv2 (7b) where Sa and Cl are the clay and sand components of soil (presented by weight) respectively. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 1 - Sandy Loam ~ 3 - Silt Loam 4 - Silt Loam 5 -Si l t y Clay Frequency: 5 GHz o 0.0 0.1 0.6 0.5 0.4 12 13 Volumetric Moisture m v (g C I7I'3 ) Figure 9. Measured dielectric constant for five soil types as a function of volumetric soil moisture at 5 GHz (From Hallikainen et al., 1985). 3. Scope of the work 3.1. Problem definition Due to the relationships between the backscattering coefficient (a0) and surface characteristics (soil roughness, soil moisture, and vegetation), many studies have shown the possibility of inferring land surface parameters from active microwave data (Dobson and Ulaby, 1986; Dubois et al., 1995; Engman and Wang, 1987; Fung and Chen, 1992; Oh et al., 1992; Ulaby et al., 1978, 1982, 1996). However, these studies mainly showed that radar backscattered signal Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 could be related to soil moisture, but with the following caveat: perturbating factors, mainly surface roughness (on a bare soil) are important and have to be taken into account. Because surface roughness as well as soil moisture affect radar backscatter on bare soils, any practical application of radar must be able to account for these two target features. Thus, if one were interested in monitoring soil moisture over complex areas, the effects of roughness would have to be subtracted from the measured backscatter in order to isolate the soil moisture effects. This is not a practical solution. However, by changing some sensor parameters (frequency, incidence angle and polarization) it is possible to decrease the influence of the soil parameters on radar backscatter. This study addresses the problem of the estimation of bare soil surface parameters (roughness and moisture) and applies algorithms to this estimation based on remotely sensed data. Separating roughness and soil moisture is however of very high importance, because these parameters have opposite hydrological effects: high roughnesses (s) will slow down runoff, while high moisture (mv) will increase runoff. 3.2. Objectives The overall objective of this research project concerns the development of a consistent methodology for the inversion of the soil surface parameters (roughness and moisture) from SAR data especially RADARSAT-1 images. Therefore, it is necessary to go beyond the empirical approaches tested so fax, by combining them with backscattering coefficient models and more sophisticated approaches. Consequently, the main objective is divided into the following objectives ranked by increasing sophistication: 1) Finding the best configuration (i.e. incidence angle, frequency and polarization) of satellite data for the extraction of soil surface parameters based on the multi-technique approach. 2) Evaluating the potential of simple linear models to estimate bare soil surface parameters. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 3) Using a numerical inversion approach based on the traditional backscatter models using RADARSAT-1 data to estimate the soil surface parameters. 4) Testing a neural network technique, as a new concept, for the inversion of soil surface parameters from RADARSAT-1 images. 5) Using a genetic algorithm optimization method for the inversion of soil surface parameters from only one radar image. 3.3. Hypotheses The proposed work will try to verify the following hypotheses: General hypothesis: It is possible to obtain the surface parameter values of a soil from radar images using the inversion approaches; in other words, separating the soil moisture and soil surface roughness signals from the radar signal. Sub hypothesis: > The multi-angular configuration gives the best results for inversing the surface parameters on a bare soil agricultural field. > Backscattering models can be improved locally by adaptation. > Inversion of the soil surface parameters by the neural network method with selflearning capability may generate more precise results than the approach obtained by traditional models. > Estimation of soil moisture and surface roughness simultaneously from only one radar image can be realized using an accuracy optimization approach (such as the genetic algorithm) and backscattering models. 3.4. Methodology As explained, the radar backscatter coefficient (ct°) of a bare soil surface is determined by three attributes: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 1) the geometry of the air-soil boundary, commonly known as surface roughness can be presented by rms height (5) or rms height and correlation length (s and £); 2) the microwave dielectric properties of the soil medium can be presented by volumetric soil humidity (mv) or dielectric constant (e); 3) theoretical or empirical models define the relationship between the radar backscatter coefficient (ct°) and soil surface parameters according to radar configuration. It is important to note that in this study only rms height represents surface roughness and the influence of correlation length is considered as negligible (Company-Remond, 1996). Thus, theoretically, we have one equation (model) with two unknowns (e and s). To resolve this problem, two solutions are presented. First, the rms height (s) or dielectric constant (e) is presented as known and the other is presented as unknown. This value can be obtained by field measurement or from some databases. Second, both s and e are presented as unknowns therefore, we need two equations to find these unknowns and solve these as a set of equations. Three equations should be used if we take into account the correlation length (£). This means using two or three images with two or three different conditions for example, using the images with different incidence angles, different frequencies or different polarizations that can give two (or three) different backscattering coefficients for the same target. In this study we used the second solution. Based on the above explanations, this work is divided into five phases: 1- Comparison of the multi-angular, multi-polarization and multi-frequency approaches to obtain the best configuration for estimating surface parameters. A simulation study using theoretical and empirical backscattering models has permitted the estimation of the backscattering coefficient's sensitivity to a relative variation in soil parameters in terms of radar characteristics. This work forms the first paper, published in the Canadian Journal of Remote Sensing. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 2- Retrieval of the soil surface parameters using the linear classical methods based on the cloud model (Attema and Ulaby, 1978). This is the theme of the second paper, published in the International Journal of Remote Sensing. 3- Inversion of the surface parameters using the nonlinear classical methods. In this case, the Newton-Raphson method, an iterative numerical method, is used in the retrieval algorithm to solve the inverse problem. This approach is the third paper submitted to the Journal of Hydrology. The paper is conditionally accepted after corrections. 4- Inversion of the surface parameters using a dynamic learning neural network by: i) one series of data; ii) two series of data. In this case, two different databases (theoretical and empirical) are tested for network learning. This approach has been submitted to the Canadian Journal of Civil Engineering. 5) The genetic algorithm optimization method is used to estimate the soil surface parameters by only one set of radar data (one image). This novel approach was based on the use of an international dataset (France & Canada) for testing its universality and obtaining better validation. It has been submitted to Photogrammetric Engineering and Remote Sensing. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 4. References: Attema E. P. and Ulaby, F. T. (1978) Vegetation modeled as water cloud. Radio Science, Vol. 13, No. 2, pp. 357-364. Bindlish, R. and Barros, A. P. (2000) Multifrequency soil moisture inversion from SAR measurements with the use of IEM. Remote Sensing o f Environment, Vol. 71, pp. 67-88. Blyth, K. (1993) The use of microwave remote sensing to improve spatial parameterization of hydrological models. Journal o f Hydrology, Vol. 152, pp. 103-129. Boisvert, J. B., Pultz, T. J., Brown, R. J., and Brisco, B. (1995) Potential of synthetic aperture radar for large-scale soil moisture monitoring: a review. Canadian Journal o f Remote Sensing, Vol. 21, No. 1, pp. 1-13. Boisvert, J. B., Gwyn, Q. H. J., Chanzy, A., Major, D. J., Brisco, B. and Brown R. J. (1997) Effect of surface soil moisture gradients on modelling radar backscattering from bare fields. International Journal o f Remote Sensing, Vol. 18, No. l,pp. 153-170. Company-Remond, A. (1996) Observation radar et modelisation d'un parametre du ruissellement. These de doctorat, Universite de Bourgogne, Dijon, 258 p. Cosgriff, R. L., Peake, W. H., and Taylor, R. C. (1960) Terrain scattering properties for sensor system design, Terrain handbook II, Engineering Experiment Station, The Ohio State University, Columbus, OH. Curlander, J. C. and McDonough, R. N. (1991) Synthetic aperture radar systems and signal processing. Wiley-Intersci., New York, 647 pp. Dobson, M. C. and Ulaby, F. T. (1986) Active microwave soil moisture research. IEEE Transactions on Geoscience and Remote Sensing, Vol. 24, No. 1, pp. 23-36. Dubois, P. C., van Zyl, J., and Engman, T. (1995) Measuring soil moisture with imaging radars. IEEE Transactions on Geoscience and Remote Sensing, Vol. 33, No. 4, pp. 915-926. Elachi, C. (1988) Spacebome radar remote sensing: Application and techniques, IEEE press, New York, 255 p. Engman, E. T. and Wang J. R. (1987) Evaluation roughness models of radar backscatter. IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-25, No. 6, pp. 709-713. Engman, E. T. and Gurney, R. J. (1991) Remote sensing in hydrology. Chapman and Hall, 225 p. Engman, E. T. and Chauhan, N. (19951) Status of microwave soil moisture measurements with remote sensing. Remote Sensing o f Environment, Vol. 25, pp. 709-713. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 Fung, A. K. and Chen K. S. (1992) Dependence of the surface backscattering coefficients on roughness, frequency and polarization states. International Journal o f Remote Sensing, Vol. 13, No. 9, pp. 1663-1680. Govers, G., Takken, I. and Helming, K. (2000) Soil roughness and overland flow. Agronomie, Vol. 20, pp. 131-146. Halikainen, M. T., Ulaby, F. T., Dobson, M. C., El-Rays, M. A., and Wu, L. (1985) Microwave dielectric behavior of wet soil - Part I - Empirical models and experimental observations. IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-23, No. 1, pp. 25-34. Henderson F. M. and Lewis, A. J. (1998) Principles and applications of imaging radar. (Chapter 8), Third Edition, Vol. 2, John Wiley & Son Inc., New York, 866 p. Holmes, M. G. (1990) Application of radar in agriculture, (Chapter 19) Application of remote sensing in agriculture, Steven, M. D. and Clark, J. A., Butterworths, pp. 307-330. Jackson, R. D. (1986) Soil water modelling and remote sensing. IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-24, No. 4, pp. 510-516. King, C. and Delpont, G. (1993) Spatial assessment of erosion: contribution of remote sensing, a review. Remote Sensing Reviews, Vol. 7, pp. 223-232. Koorevar, P., Menelik, G. and Dirksen, C. (1983) Elements of soil physics. Developments in soil science 13, Elsevier Science, Publisher, B.V., Amsterdam, 228 p. Moore, R. K., Claasen J. P. and Lin Y. H. (1981) Scanning spacebome synthetic aperture radar with integrated radiometer. IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-17, No. 3, pp. 410-421. NASA (1989) Instrument panel report, SAR: synthetic aperture radar (Earth Observation System, Vol: Ilf), Earth science & applications division, NASA, Washington, D.C., 233 p. Oh, Y., Sarabandi, K. and Ulaby, F. T. (1992) An empirical model and inversion technique for radar scattering from bare soil surfaces. IEEE Transactions on Geoscience and Remote Sensing, Vol. 30, No. 2, pp. 370-381. Raney, R. K., Luscombe, A. P., Langham, E. J. and Ahmed, S. (1991) RADARSAT. Proceedings o f the IEEE, Vol. 79, No. 6, pp. 839-849. Romkens, M. J. M. and Wang, J. Y. (1986) Effect of tillage on surface roughness. Transactions on ASAE, Vol. 29, pp. 429-433. Schanda, A. (1987) On the contribution of volume scattering to the microwave backscattered signal from wet snow and wet soil. International Journal o f Remote Sensing, Vol. 8, No. 10, pp. 1489-1500. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 Ulaby, F. T., Batlivala, P. P. and Dobson M. C. (1978) Microwave dependence on surface roughness, soil moisture and soil texture: Part I - Bare soil. IEEE Transactions on Geoscience and Remote Sensing, Vol. 16, No. 4, pp. 286-295. Ulaby, F. T., Moore, R. K. and Fung A. K. (1981) Microwave remote sensing active and passive. Vol. I: Microwave remote sensing and fundamentals and radiometry, AddisonWesley, Reading, MA, pp. 1-457. Ulaby, F. T., Moore, R. K. and Fung A. K. (1982) Microwave remote sensing active and passive. Vol. II: Radar remote sensing and surface scattering and emission theory, AddisonWesley, Reading, MA, pp. 457-1064. Ulaby, F. T., Dubois, P. C., and van Zyl, J. (1996) Radar mapping of surface soil moisture. Journal o f Hydrology, Vol. 184, pp. 57-84. Wagner, W. (1998) Soil moisture retrieval for ERS scatterometer data, Ph. D. Thesis, Vienna University of Technology, Vienna, 167 p. Waite, W. P. (1976) Historical development of imaging radar, in Geoscience applications of imaging radar systems. RSEMS, Lewis, A. J. (ed.), Association of American Geographers, Vol. 3, No. 3, pp. 1-22. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 CHAPTER 2 A COMPARISON OF MULTI-POLARIZATION AND MULTIANGULAR APPROACHES FOR ESTIMATING BARE SOIL SURFACE ROUGHNESS FROM SPACEBORNE RADAR DATA Mahmod Reza SAHEBI, Joel ANGLES and Ferdinand BONN Canadian Journal o f Remote Sensing, 2002, Vol. 28, No. 5, pp. 641-652. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 Can. J. Remote Sensing, Vol. 28, No. 5, pp. 641-652, 2002 A comparison of multi-polarization and multi-angular approaches for estimating bare soil surface roughness from spacebome radar data Mahmod R. Sahebi, Joel Angles, and Ferdinand Bonn Abstract. Soil surface roughness and moisture content both have a significant effect on microwave backscatter to the satellite. Hie purpose of this work is to evaluate the optimum sensor configuration for existing radar satellites to quantify soil surface roughness. A simulation study using theoretical and empirical models permits the estimation of the sensitivity of the backscatter coefficient to relative variations in soil parameters in terms of radar characteristics. Two different configurations for estimating surface roughness were tested, multi-polarization (co-polarizations) and multi-angular, and the results of the multi-angular configuration provided the best results. A normalized radar backscatter soil roughness index (NBRI) is presented for estimating soil roughness from a multi-angular approach using sensors such as RADARSAT-1. This index was tested using the geometric optics model (GOM) and RADARSAT data. Coefficients of determination of 99% and 83%, respectively, were obtained for each simulation. Resumd. La rugosity et l’humiditd d'une surface de sol nu ont un effet significatif sur le coefficient de rdtrodiffusion enregistrd par le capteur satellitaire RSO. L’objectif de ce travail est d’dvaluer la configuration optimale pour un capteur & bord d’un satellite radar permettant de choisir la meilleure approche pour extraire la rugosity de surface. Une dtude de simulation utilisant les modules thdoriques et expdrimentaux permet d’estimer la sensibility du coefficient de rdtrodiffusion h la variation relative des paramdtres du sol en termes des caract&istiques des radars. Pour la rugosity, deux approches diffdrentes sont vdrifides, la configuration multi-polarisation (co-polarisations) et la configuration multi-angulaire. Cette demidre donne les meilleurs rdsultats. Un indice normalisd de la rdtrodiffusion radar pour la rugositd du sol (normalized radar backscatter soil roughness index, NBRI) est proposd pour estimer la rugositd de surface 4 partir de l’approche multiangulaire comme celle de RADARSAT-1. Cet indice a dtd testd par le meddle GOM (Geometric Optics Model) et les donndes de RADARSAT. Les coefficients de ddtermination sont respectivement de 99% et 83% pour chacune des simulations. Introduction Estimates of the physical parameters of the soil surface, including moisture content and surface roughness, are important for hydrological and agricultural studies, as they appear to be the two major parameters for forecasting runoff in an agricultural watershed (Bates et al., 1997). Soil surface roughness is also a factor that controls the erosive power of runoff water, by reducing the velocity of surface flow, and thus the ability to erode and transport solid particles. A reduction in roughness can increase erosion, and thus an adequate mapping of soil surface roughness can be used in erosion-hazard modeling. Combined, distributed runofif-erosion models require roughness inputs, either in terms of Manning coefficients as in the Hydrotel/GIBSI model (Fortin et al., 1991) or as arbitrary roughness classes such as in the STREAM model (Le Bissonais, 1990). The latter model has been used in the European FLOODGEN project (King et al., 1998) to map excess runoff risk in Upper Normandy (France) and to guide the establishment of agro-environmental protection measures. Research with active microwave sensors to provide soil conditions on a quantitative basis has been conducted by several authors (Oh et al., 1992; Blyth, 1993; Chanzy et al., 1995; Ulaby et al., 1996). The important parameters that significantly influence the radar response of soils can be classified into two categories: (i) the target parameters such as moisture, roughness, and vegetation cover (if present); and (u) the sensor parameters such as frequency, polarization, and incidence angle. Radar scattering by a bare soil surface is determined by the geometry of the soil surface, commonly known as surface roughness, and the dielectric properties of the soil, which depend on the soil characteristics such as moisture, particle-size distribution, and mineralogy. Remotely sensed synthetic aperture radar (SAR) data can provide spatial and multi-temporal estimates of moisture and Received 2 April 2001. Accepted 1 May 2002. M.R. Sahebi, J. Angles, and F. Bonn.1 CARTEL, University de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada. ‘Corresponding author (e-mail: fbonn@courrier.usherb.ca). © 2002 CASI Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 641 30 Vol. 28, No. 5, October/octobre 2002 surface roughness depending on the sensor configuration and field conditions. Several studies were conducted over the last 20 years to study the relationship between the backscattering coefficient and soil parameters (Dubois et al., 1995; Fung, 1994; Prdvot et al., 1993; Fung and Chen, 1992; Oh et al., 1992; Engman and Wang, 1987; Dobson and Ulaby, 1986a; 1986b; Ulaby et al., 1978; 1982; 1996). Most of the research work was oriented towards the estimation of soil moisture and the development of algorithms for mapping soil moisture distribution. Estimation of surface soil moisture was usually obtained by using an empirical relationship to convert the measured backscatter coefficient (o°) to volumetric soil moisture (n ty ) (Dobson and Ulaby, 1986a; Prdvot et al., 1993; Ulaby et al., 1996). For example, Ulaby and Batlivala (1976) and Ulaby et al. (1978) reported from their analyses of early ground-based scatterometer measurements over bare soils that there is a positive correlation between 0 ° in the frequency range of 1 12 GHz and soil moisture. At incidence angles greater than 20°, an increase in surface roughness increases the radar backscatter. These results received confirmation more recently by Wang et al. (1986) and Champion (1996). The backscattering coefficient can vary over a 20 dB range with surface roughness height changes from ~0 to 4 cm (Wang et al., 1997). Thus, to estimate soil moisture from radar backscatter measurements over bare soils, the effects of surface roughness have to be taken into consideration. Objectives This paper addresses the estimation of surface roughness and applies some algorithms developed to estimate this parameter using remotely sensed data. The main objectives of this research are to ( 1 ) find the best radar configuration for estimating surface roughness, (2 ) present an approach for estimating surface roughness using the best configuration obtained by simulated results, and (3) test the developed approach (presented in objective 2) with actual RADARSAT data and in situ measured surface parameters (roughness and soil moisture). To reach objective 1, two radar configurations, multi-angular and multi-polarization, were compared using the backscatter coefficient simulated by some existing backscattering coefficient models. The small perturbation model (SPM), the physical optics model (POM), the geometric optics model (GOM), the integral equation model (IBM), the Dubois model, and the Oh model are used in this study. It is important to note that this study focuses on the actual SAR satellite data, which is why the multi-polarization approach is presented only as co-polarizations (HH or VV). Radar observation of soil roughness Surface roughness is usually described by two parameters, root mean square (rms) height (s) and correlation length (/)- The statistical variation of a random surface is characterized by the autocorrelation function of surface p(£), where § is the displacement of height variations of the surface. Several mathematical forms have been used in the literature to describe p(£) of natural surfaces, including the Gaussian form p(^) = e x p j^ - j (1) and the exponential form p© = e x p j= ^ j (2 ) According to Oh et al. (1992), the exponential autocorrelation function is adapted to smooth surfaces and the Gaussian autocorrelation function is adapted to rough surfaces. In practice, estimation of surface roughness can be defined as a quadratic correlation between the radar backscatter coefficient (o°) and the roughness parameters (s and I). Assuming soil moisture is known, we have one equation with two unknowns. There are two solutions to this problem. First, the influence of correlation length can be assumed to be negligible, and thus correlation length, which shows the horizontal distribution of surface roughness, is not estimated. Alternatively, the relationship with s and I can be established through two equations based on backscatter acquired by two different radar configurations. Using data acquired at two different incidence angles or polarizations, the equations can be solved for both s and I. In this study, we used the second solution with two different approaches, multi-polarization and multi-angular, to determine the best configuration for estimating surface roughness and develop a new index for estimating surface roughness using radar. Modeling approach The aim of this study was to compare the ability of multi polarization and multi-angular approaches for estimating bare soil surface roughness. The comparison was carried out using existing theoretical and empirical models. The theoretical models tested included the SPM, POM, GOM, and IEM. The empirical models examined were the Dubois model and the Oh model. Small perturbation model (SPM) (Ulaby et al., 1982) The SPM is intended to simulate scattering from a relatively smooth surface with ks < 0.3, kl < 3, and m < 0.3, where k is the wave number (k = litfk, where K is the wavelength) and m is the rms slope of the surface (m = s [p'(O) ] 0 5, where p*(0) is the second derivative of p © evaluated at %= 0). According to the SPM, the backscattering coefficient (a^,) for any transmitreceive polarization (pp) can be calculated as follows: a£p(0) = 0 ^ ( 0 ) + 0 ^ (0 ) 642 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (3) © 2002 CASI 31 Canadian Journal of Remote Sensing / Journal canadien de t§!6d6tection where 6 is the incidence angle; o^,h is the coherent component, which becomes negligibly small for observation angles 0 > 1 0 ° (Henderson and Lewis, 1998); and is the noncoherent component given by According to this model the backscattering coefficient can be calculated as follows: ojp = —1/ppPexpf-4 * 2* 2 cos2 e)V (4 fc2 ^cos 2 8 )" w„(2*sin 0O) 2 oSk = 4k 4s 212 cos4 ( ffpP|2 {exp[-(Wsin 0 )2]} (4) »=i "! +—ReC/pjjFpp)exp{-3k2s1cos2 6 )V (2 *sin0 ,0 ) (7) 2 «-i "! (*2 J2C O S 2ey I / -> t2.2_2m^ + --(fpp|exp(-2 i 2 j 2 cos2 0 ) £ t W" (2 *sin 0 ,0 ) where Rpp can be presented as n! Rbh= ^er - s in 2 0 er cos 0 i , > *vv= + yer - s i n 4 0 er cos 0 cos 0 cos 0 ^er - sin2 0 I + yer - s n r 0 - with ft,h = and e,. is the real part of the dielectric constant. Physical optics model (POM) (Ulaby et al., 1982) The POM, also known as the Kirchhoff approach under the scalar approximation, was developed for slightly rough surfaces satisfying the condition 0.06k2/2 > ks,kl > 6 , and m < 0.25. The coefficient o °, is given by Equation.(3), where o®,h becomes negligibly small for observation angles 0 > 1 0 ° (Henderson and Lewis, 1998), and a ^ . is given by 2 COS0 /w = -COS0 sin20 COS0 gin2 0 COS0 For a Gaussian autocorrelation function, /.e x p jV k /^ ' 0 ^ ( 6 ) = (*/)2 [|*pp|2a + sin2 0 ) + R e ^ R ^ > sin 2 0 ] x exp (-A cos 2 0 ) £ n=l h co s 2 n !n 0 exp (kl sinO) 2 WB(2 k sin 0 0 ) = (5) where h = 41c1s2, and R*w is the complex conjugate of Rpp. Geometric optics model (GOP) (Ulaby et al., 1982) The GOM, also known as the Kirchhoff method under the stationary phase approximation, is intended to characterize scattering by rough surfaces, with 0.06k2/2 > k s ,k l> 6 , and (2ks cos 0) 2 > 10. This model predicts that 0 ^,(0 ) = a?v(0) at all incidence angles. The expression for die co-polarized backscattering coefficient is given by c pp(® = \RrM2 2 m 2 cos4 exp 0 tan2 2 n Oh model (Oh et al., 1992) Because of the inadequate performance of theoretical models for predicting the backscatter response of random surfaces, Oh et al. (1992) developed an empirical model based on experimental data acquired at L, C, and X bands (1.50, 4.75, and 9.50 GHz, respectively). This model was designed for surfaces with various roughnesses (from slightly smooth to very rough) and moisture conditions. This model does not incorporate correlation length. The valid surface conditions cover the following ranges: 0.1 < ks < 6.0,2.6 < kl < 19.7, and 9 < nty < 31%. The backscattering coefficients for this model can be written as follows: 0 2m2 where /?pp(0 ) is the surface reflectivity from normal incidence. Integral equation model (IEM) (Fung and Chen, 1992) The IEM is a backscattering model applicable to a dielectric rough surface. This model is based on an approximate solution of a pair o f integral equations for typical agricultural soils. It can be applied to complex anisotropic surfaces, and its continuous applicability ranges from smooth to rough surfaces. The validity range of the IEM given by Fung (1994) is defined such that ks < 3, cos20[(fcy)2/(O.46fc/)O5]exp {-[2 x 0.46k/(l sin 0 )]0'5} « 1 , and k/'x ks < p (|er|)0-5, where p. is a constant (equal to 1.6 and 1.2 for the Gaussian and exponential autocorrelation functions, respectively). ag,. = g 4 p cos 3 0 [ / U 0 ) + R ^ m ( 8 a) agv = ^ ^ [/?vv(0) + JRhh(0)] ( 8 b) where 1 exp(-ks) and g = 0.7{1 - exp[-0.65(fcs)18]}. © 2002 CASI Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 643 32 Vol. 28, No. 5, October/octobre 2002 Dubois model (Dubois et al., 1995) The Dubois model (Dubois et al., 1995) was developed using scatterometer data and is based on an empirical model for smooth and medium-rough surfaces. The model is optimized for bare surfaces and requires radar channels at a frequency between 1.5 and 11.0 GHz. It gives best results for ks < 2.5,0 > 30°, mv < 35%, and normalized difference vegetation index (NDVI) less than 0.4. This model does not incorporate correlation length. The HH- and VV-polarized backscattering cross sections were found to follow Equations (9a) and (9b): CT&, = 10- 2 -7 5 a ° v = 10" 2 -3 5 C--S^5 .e iOa 0 2 8 taneEr(fa sinO) 1-4 ^ su r0 su re io aM6t” ter(ks sin0)u XQ 7 7 (9a) (9b) Methods The models described in the previous sections are used to simulate backscatter coefficients for estimating surface roughness of bare soils. The simulation was carried out using a C-band frequency (wavelength equal to 5.6 cm), two polarizations (HH and W ) , and two incidence angles (20° and 40°). These radar parameters were selected to represent the RADARSAT-1 and European remote sensing (ERS-1/2) radar satellite sensors. In this study, to obtain the best comparison possible, the following elements were considered: (1) According to experimental results obtained by McNaim et al. (1996) at C band, HH is more sensitive than VV or HV to surface roughness, and Beaudoin et al. (1990) and Coppo et al. (1995) concluded that with incidence angles greater than 30° the sensitivity of the backscattering coefficient to soil moisture decreases but sensitivity to roughness increases. Therefore, in this study the incidence angle was kept constant ( 6 = 40°) to test the multi-polarization approach, and the polarization was kept constant (HH polarized) when testing the multiangular approach. (2) Two different indicators were chosen to evaluate the two approaches. The first indicator was the a ° / a ° ratio. This ratio is defined as crgj, /ogv in the multi-polarization approach and O4 o°/(?2 0 ° *n Oie multi-angular approach. If this ratio approaches 1 (og = a°), we conclude that the proposed approach was not sensitive enough to extract the necessary information for estimating surface roughness (Autret et al., 1989). The second indicator was presented as lo g -o g l to show the absolute difference value of the backscattering coefficient. This difference was represented by |agh - ogv| in the multi-polarization approach and by |ogo°- ° 2 0 °l i*1 the multi-angular approach, where and o%° represent the backscatter coefficient for incidence angles of 40° and 20°, respectively. (3) To obtain the best results, the validity range of each model was respected. (4) To estimate surface roughness using the multi-angular approach, a new roughness index (normalized radar backscatter soil roughness index, NBRI) is proposed. The index, calculated from two different values of backscattering coefficients obtained by two different radar incidence angles for one target, allows us to calculate and classify surface roughness from radar data. (5) To validate the theoretical approach, field data from the St. Lawrence Lowlands area of Quebec, Canada, and data from RADARSAT-1 are used. Study area The agricultural sites chosen for this study are the Chateauguay River (45°19'N, 73°46'W) and Pike River (45°08'N, 72°54'W) watersheds, which are located on the south shore of the St. Lawrence River, southeast of Montreal, Quebec, Canada (Figure 1). D ata description Roughness and moisture measurements were carried out over 27 parcels of land on the same days as those when the images were acquired. To calculate rms height, six 2 m long (with 1 cm sampling interval) surface profiles (three parallel and three perpendicular to the soil furrows) were investigated for each parcel. These profiles were photographed and then digitized. The method for extracting and modeling the roughness parameters has been described in detail by Beaulieu et al. (1995). A reflectometry instrument was used to measure the surface moisture. Fifteen samples were taken in each parcel and measurements were carried out for soil depths of 0 -5 cm with a Thetaprobe soil moisture sensor. Using the equation presented in the Thetaprobe soil moisture user manual (Delta Devices Ltd., 1996), the direct outputs (DC voltage in mV) were converted to soil water content (m 3 -m-3) and dielectric constant. To evaluate the results obtained by this method, five soil samples for each parcel from soil depths of 0 -5 cm were transferred to our laboratory. Wet and dry weights were used to determine gravimetric soil water content. The soil water contents (in m 3 mr3) obtained using these two methods were compared, and a mean relative difference of 1 2 % (equivalent to 1 .8 % volumetric soil moisture) between the two methods was observed. The satellite data used in this study correspond to a RADARSAT image pair. The first image was acquired on 12 November 1999 in the standard-1 ascending (SI) mode, with incidence angles ranging from 20° to 25°, and the second image was acquired on 18 November 1999 in the standard-7 ascending (S7) mode, with incidence angles ranging from 40° to 49°. The RADARSAT DN values are converted to o° according to Shepard (1998). An average backscatter 644 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. © 2002 CASI 33 Canadian Journal of Remote Sensing / Journal canadien de t§!6d6tection Figure 1. Location of the study area coefficient (in dB) was assigned to each parcel of land, corresponding to a 20-30 pixel area. The roughness and moisture of the surface were measured in situ on 12 and 18 November (the same dates as the satellite images were acquired). Between the periods of data acquisition, however, the weather was stable and surface moisture had not changed significantly because of the low evaporation and temperature at that time of the year. Average temperatures were 2.3°C, and there was no recorded rainfall between the two acquisition dates. To completely satisfy the conditions of this study, however, only 1 0 parcels of land were chosen that had exactly the same moisture and roughness for the two dates. Table 1 shows the measured rms height and soil moisture for these 1 0 parcels. Results and discussion Table 1. Surface parameters measured in the field. Parcel No. 2 5 7 8 14 17 105 108 109 117 November 18 rms Soil height moisture (cm) (%) 4.91 21.89 29.94 2.28 4.29 20.85 3.26 23.46 4.17 20.13 3.14 23.74 3.20 13.30 5.13 16.63 4.11 27.14 2.68 15.06 Table 2. Simulation parameters. Simulation results This section evaluates the applicability of the two proposed approaches for the estimation of surface roughness. Generally, a large range of surface rms heights (0 . 1 0 < 5 < 6 . 0 0 cm) was chosen to simulate backscatter; however, for each model only the results within its region of validity are presented. Therefore, to be able to cover a large domain of possible surface conditions, four different values for correlation lengths and two different soil moistures were chosen, depending on the region of validity of each model. Table 2 shows the parameters used for the simulations. Figure 2 shows the simulated results from the SPM for a correlation length (/) equal to 2 cm and an exponential November 12 rms Soil height moisture (cm) (%) 5.01 21.26 2.39 30.45 4.49 21.12 3.77 23.93 4.51 20.60 3.29 23.16 3.82 13.93 5.46 17.05 26.65 4.03 2.84 15.18 Model SPM POM IEM KM GOM Oh Dubois rms height (cm) 0.10-0.25 0.10-2.00 0.10-1.80 0.10-0.70 2.20-6.00 0.10-6.00 0.10-2.00 Volumetric soil moisture (%) 18, 28 18, 28 18, 28 18, 28 18, 28 18, 28 18, 28 Correlation length (cm) 2 15 2 6 10 — — ' autocorrelation function. Figure 2 clearly shows the advantage of the multi-angular approach for estimating the roughness of smooth surfaces. © 2002 CASI Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 645 34 Vol. 28, No. 5, October/octobre 2002 n. Multi-pelarization, m , «■18% m . = 18% 10. ’—■*—'Multi-angular, Multi-potartzation, m , • 28% ' X -Multi-angular, m , *■28% »• § 8 -| 23 — Multi-polarization, m, a 10% ■» ■Mutti-angnlar, m , c 18% — Multl-polarizatian, m, - 28% ' X ■Multi-angular, m, « 28% -X (a) S'18-I §tj, o" ^13 o’ (b) «5 ■ 1.0 035 0.10 0.15 030 035 030 035 0.05 0.10 0.15 rms height (cm) 030 035 030 035 rms height (an) Figure 2. Comparison between multi-polarization and multi-angular approaches: simulation by the SPM with a correlation length of 2 cm. (a) Indicator of / o f . (b) Indicator (of J. Hie ratio indicator o f /o f for the multi-polarization and multi-angular approaches varies from 19 to 43% and increases with higher rms values, and the difference indicator |of - a§| varies from 55% (3.00 dB) to 74% (3.40 dB). This can also be observed in the results of the POM and IEM for smooth surfaces (Figures 3-6). In both models, the superiority of the multi-angular approach is shown. For the POM, values of o f / o f are almost equal to 1.00 for the multi-polarization approach, but are between 1.30 and 6.12 for the multi-angular approach. This difference is less for the IEM, with o f / o f values between 1.00 and 1.60 for the multi-polarization approach compared with 1.20 to 8.50 for the multi-angular approach. In both models, however, these values decrease with higher rms (in die medium surface roughness range) and increase again, thus displaying a sinusoidal form. This phenomenon may be explained by the model behavior. For a large range of rms heights (smooth and medium surface roughness) for both models (POM and IEM), the relation between Oy, and rms height has a curvilinear form (logarithmic or polygonal of more than 2°). This curve form depends on die incidence angle, and there is a gap between the curve for 20° and that for 40°. For example, for the POM model, these curves are so close in rms height at 1.50 cm that the values of o f /o f and |of - o f | decrease until the rms height is 1.50 cm and then reach a minimum (1.00 and 3.30 dB, respectively) before increasing again (Figures 4a, 4b). This phenomenon is also observed in the IEM model (Figures 5a, 5b). In addition, the POM model predicts that 0 ^ / 0 ^ with increasing rms, a result that is contrary to experimental observations (Oh et al., 1992). The indicator |of - o f| has a linear form for both approaches for smooth surfaces (Figures 2b, 3b). This means that the o° versus rms height curves for the SPM model are parallel and the differences between o f and o f are constant The empirical models (Oh and Dubois models) also verify the increase of o f /o f with smooth surfaces for the multiangular approach; however, contrary to the POM and IEM, this increase continues and the empirical model curves do not have a completely sinusoidal form. For the Oh model this increase changes to a stable value (a line parallel to the horizontal axis). For the Dubois model, the values of o f / o f are almost equal to 1.00 (between 1.00 and 1.14) for the multi-polarization approach; however, they are between 1.55 and 11.50 for the multi-angular approach. In the Oh model, contrary to the other models, the indicator o f /o f is approximately the same for a very smooth surface but decreases in the case of multi- 7 14 ■ -t—- M ulti-polarlzatioii, m,= 18% 6 a 'M nlti-angolar, m , = 18 % — Multi-polarization, m , x 28% 8 'M ulti-angular, m , = 28% 4 12 - 10 - 5 <? 2 1 0 0 0.1 03 03 0.4 03 rms height (cm) 0.6 0.7 03 0.9 0 0.1 03 03 0.4 03 0.6 0.7 03 0.9 rms height (cm) Figure 3. Comparison between multi-polarization and multi-angular approaches: simulation by the POM with a correlation length of 10 cm. (a) Indicator of/of. (b) Indicator |of - off 646 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. © 2002 CASI 35 Canadian Journal of Remote Sensing / Journal canadien de t§l6d6tection 6 — Midti-pola ■* ■ »MulH angular, m T» 1 8 % —*— Multi-potari*«tkH»,»T*2 8 % » J# ’Mura-angolar, m Ta 28% 5 —*— Majti-polarimtloii, ra , «18% • ■ ■Multi-«ngutar, m , x 18% —*—Mutti-poMrizatfon, m , =>28% >)M -MuIti-ingaUr, m , = 28% 10 4 as, S' 3 2 1 0 0 1.0 0 15 23 15 2.0 ran height (cm) mis height (cm) Figure 4. Comparison between multi-polarization and multi-angular approaches: simulation by the POM with a correlation length of 15 cm. (a) Indicator of/a®, (b) Indicator |af - o f f 33 . —*— Matti-pelaifoatioii, m« * 18% - ■ •M altl-«uinii8^nv= 18% —*— Midti^MirintioD, mr ■ 28% - X 'M idti-aiipUuvni, = 28% 3J» - M olli'polaiiatioo, mr ■ 18% ■ ’Molti-angnUr, m* = 18% M aM -potaintion, mr » 28% - M *Mnlti-aiigalar,n»v»28% 15 ■ S I*® ■a £13-| **13 OS 0 1.0 ID rms height (cm) rms height (cm) Figure 5. Comparison between multi-polarization and multi-angular approaches: simulation by the IEM with a correlation length of 2 cm. (a) Indicator a®/a®. (b) Indicator [of - o§ j. 7 6 (a) * 35 — 4 — M atti-polarization, my * 18% - • »MmM ■BgnlT,iav » I 8 % —*— M altt-paUriw rtoti) ■ 28% • * •MnttMmgotar, * 28% 30 S'25 ■u e«20 j-15 i2 ,4' €3^ o 21 —o— M ulti-polarization, raT=*18% - ■ -Multi-angobuv raT«18% —*— Midti-poUrbHitioii, m , » 28% - X •MaHl*iiigBlar,iBTB28% (b) * V ms* * _ m 1 _ mS« * ....................... I I * ! - ' 10-1 5 ■ I " “T~ 0 0.1 on 03 on 03 0.6 0.7 03 rms height (cm) 0.1 on 03 I on 03 0.6 0.7 03 rms height (cm) Figure 6. Comparison between multi-polarization and multi-angular approaches: simulation by the IEM with a correlation length of 6 cm. (a) Indicator of/o®. (b) Indicator \af - cr®|. polarization and becomes equal to 1 . 0 0 in a medium-roughness surface zone; however, for the multi-angular approach this indicator increases to 1.50 and 1.70 for mv = 18 and 28%, respectively. The difference between indicator la® - a°| for both approaches in the Dubois model is greater than that for the Oh model (Figures 7, 8 ). According to the GOM, a|Jh is equal to a ° v, which means that the indicator of/a® is always equal to 1 . 0 0 for rough and very rough surfaces and therefore this approach is not efficient for the estimation of surface roughness. This is also observed in the results of the Oh model (Figure 7a). As shown in Figure 9, for rough surfaces (rms heights less than 3.50 cm). © 2002 CASI Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. . 647 36 Vol. 28, No. 5, October/octobre 2002 2.0 ■ 5 —*— M atti.polarlzatlon, ra , ■ 18% - » -Multi-angular, ra , -18% —*— Multl-polarixatkm, mT- 28% * I t 1Multt^mgulur, n t, 28 % -•— M olU-poUrizaUon, m,= 18% ] ■ ‘M ulti-angular, in , = 18% -*— M ulti-polarization, m , =28 % * ■M oltl-angiilar, m . - 28% 4 t? tT' 1.0 ■ 1 0 0 4.5 2 6.0 3 4 rms height (cm) rms height (cm) Figure 7. Comparison between multi-polarization and multi-angular approaches: simulation by the Oh model, (a) Indicator crf/a®. (b) Indicator |a? - o^j. 10 - -•— M ulti-polarization, m , * 18% • ■M uitteugutar, m , = 18% ■*—M uW -potariatkm , m , ■ 28% St -M ulw ngiilar, m , e 28% 12 ■ — MuHH . . ■ -Multl-angular, m , * 18% . -a— Molti-pobu'teatioii, St, a 28% K •Multi-angular, m , = 28% 10 . l 0 0JS 1.0 2.0 0 1.0 ra n height (cm ) 2.0 rm s height (cm ) Figure 8. Comparison between multi-polarization and multi-angular approaches: simulation by die Dubois model, (a) Indicator cr?/ crjj. (b) Indicator |a? - <r§|. the |<t? —<j§t indicator is greater than 1 .0 0 , whereas for very rough surfaces this value is equal to 1.00. This phenomenon may be explained by the behavior of microwave scattering, because when the surface is very rough it behaves like a Lambertian surface and the incidence signals are scattered in all directions almost uniformly, independent of the incidence angle. Another important parameter is the influence of soil moisture (mv) on the results obtained. The simulation results with indicators la? - a ° | and a ? /a ? suggest that differences between these indicators for multi-polarizations with my = 18 and 28%, respectively, are not very large; however, these differences are often uniform (the curves or the lines are parallel). Conversely, these differences are important in the multi-angular approach. This may be explained by the variation in the sensitivity to soil moisture with varying incidence angles. According to the literature, radar backscattering is more sensitive to soil moisture at small incidence angles, and therefore a backscatter coefficient obtained with a 2 0 ° incidence angle is more sensitive to soil moisture than in the case of a 40° incidence angle. 6 - ■ -Multi-lingular, m* = 18% • H -Multi-angular, raT= 28% 5 4 3 2 1 0 2 3 4 6 5 rms height (cm) Figure 9. Multi-angular approaches: simulation by the GOM with a correlation length of 10 cm. C o m p a riso n to sa te llite c o n fig u ra tio n s As described earlier, the simulation parameters in this study were chosen (HH and VV for multi-polarization and 20° and 648 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. © 2002 CASI 37 Canadian Journal of Remote Sensing / Journal canadien de t6!6d6tection o° • 6.0822ln(s) -14.506 R2*1 >10 I -20 -30 0 24 1.S rms height (cm) Figure 10. Relationship between rms height and backscattering coefficient simulated by the Dubois model. liable 3. Relationship between rms heights and simulated backscattering coefficients. Model SPM POM IEM GOM Oh Incidence angle (°) 40 40 40 40 40 rms height range (cm) 0.10-0.30 0.10-1.00 0.10-1.00 3.00-6.00 0.10-0.30 40° for multi-angular) close to the parameters of the RADARSAT-1 and ERS-1/2 radar satellite sensors. This comparison assesses the capability of these satellites for estimating surface roughness and can also be used to simulate the capabilities of RADARSAT-2 and ENVISAT. The results obtained in the previous section show that the multi-angular approach gives a satisfactory estimation of surface roughness, whereas the results of the multi-co-polarization approach are questionable. Therefore, with the capability .of acquiring data at different incidence angles, we conclude that using the RADARSAT-1 satellite alone can provide the necessary images to estimate surface roughness. Application to RADARSAT data Definition of a multi-angular backscatter index The simulated results suggest a relationship between the backscatter coefficient and soil roughness (rms height) for the same target conditions (soil roughness and soil moisture are constant for the two pairs of data). The simple relationship between multi-angular backscatter and soil roughness can be presented by Equation obtained o° = 8.6350 ln(j) - 6.242 0 ° = 8.5910 ln(s) - 13.725 o° = 21.3420 ln(r) - 15.409 0 ° = -5.4527 ln(f) + 3.200 o° = 5.0580 ln(j) - 4.308 Correlation coefficient (R2) 1.0000 0.9997 0.9983 0.9859 0.9120 s = ap(af,ojj) + b (1 0 ) where j is the surface roughness, p(a°, o§) is the relationship between two different backscatter coefficients obtained using two different incidence angles, and a and b are linear coefficients. To determine this relationship, we plotted the values of the simulated backscattering coefficients for different rms heights and obtained a strong logarithmic relationship between these values. Figure 10 provides the results for the Dubois model, and Table 3 shows the results of this analysis for different models. Regarding this relation, pfaf.a-j) can have the form p(o?,o§) = ln(NBRI) (11) where NBRI = 2 l± 4 of-»2 © 2002 CASI Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (12) 649 38 Vol. 28, No. 5, October/octobre 2002 1.80 y»0.0762x + 1.3802 R2 - 0.9935 1.88 1J0 1.78 2.83 5.03 3J3 9 ii Figure 11. Relationship between theoretical roughness index (NBRI) and soil roughness; simulation by the GOM. y -0 .S S 2 8 x + 1.1004 R2« 0.831 2.5 2i 3.0 3.5 Figure 12. Relationship between roughness index (NBRI) measured from RADARSAT data and soil roughness on 10 parcels o f land. The normalized radar backscatter soil roughness index (NBRI) can be used to generate soil roughness maps over large areas with C-band SAR data. NBRI and soil roughness relationship for very rough surfaces Based on the knowledge of field conditions (very rough surface), the proposed approach was tested using simulated and actual backscatter values. To simulate backscatter coefficients, the GOM was chosen with the following parameters: 3 £ s < 6 cm, e = 8 , and 1 = 4 cm. Figure 11 shows the results obtained using simulated backscatter values, and a correlation coefficient higher than 99% was derived. This approach was tested with the backscatter coefficients obtained from the RADARSAT images (Figure 12) and a coefficient of 650 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. © 2002 CASI 39 Canadian Journal of Remote Sensing / Journal canadien de t6!6d6tection determination (R2) greater than 83% was obtained, which is a strong relationship for actual satellite data. Conclusions Two radar configurations (multi-polarization and multiangular) were proposed for estimating surface roughness using C-band SAR satellite imagery. The values of the backscatter coefficients were calculated using six existing theoretical and empirical models (SPM, POM, IEM, GOM, Oh, and Dubois) for different roughness and moisture conditions (0 . 1 0 5 rms < 6.00 cm, 2 < / < 15 cm, and mv = 18 and 28%). The simulation results indicate that the multi-angular approach is mote sensitive to surface roughness conditions than the multi polarization (co-polarization) approach. Based on these results, it was concluded that the RADARSAT-1 satellite with its capability of acquiring data at different incidence angles could be used for estimating surface roughness. Based on our results, we propose a new index, the normalized radar backscatter soil roughness index (NBRI), using the multi-angular approach. This index estimates and classifies surface roughness in agricultural fields using two radar images with different incidence angles. Roughness dominates the radar signal at high incidence angles, and moisture dominates the radar signal at low angles. A relatively simple NDVI-like approach should be easier to implement for operational users when compared to a sophisticated model inversion method or a neural network approach, even if the latter methods can be slightly more accurate. The NBRI was tested using simulated data (from the GOM) and measured data (from RADARSAT images), and correlation coefficients (R2) of 99 and 83%, respectively, were obtained for each te st Work is continuing towards extending the multi-angular approach for providing an estimation of surface roughness and to separate roughness from soil moisture using RADARSAT images. In this case, it is possible to invert the soil surface parameters using the multi-angular approach. For this purpose, bare soil surface parameters are extracted from two or three RADARSAT images acquired at different incidence angles. Acknowledgements This study was partly supported by the Fonds pour la formation de chercheurs et l’aide k la recherche (FCAR) (Actions Concertdes RADARSAT et IRDA), the FLOODGEN project (CSA-RUDP), and the Natural Sciences and Engineering Research Council of Canada. The authors want to thank all the colleagues of CARTEL, especially P. Gagnon, P. Cliche, F. Charbonneau, G.B. Bdnid, S. Foucher, and J. Smyth, and J.P. Fortin from INRS-Eau and the MCHE o f Iran for granting a scholarship and financial support to M. Sahebi. References Autret, M„ Bernard, R., and Vidal-Madjar, D. 1989. Theoretical study of the sensitivity of the microwave backscattering to the soil surface parameters. International Journal'of Remote Sensing, Vol. 10, No. 5, pp. 171-179. Bates, P.D., Horritt, M.S., Smith, C.N., and Mason, D. 1997. Integrating remote sensing observations of flood hydrology and hydrologic modelling. Hydrological Processes, Vol. 11, pp. 1777-1795. Beaudoin, A., Le Tban, T., and Gwyn, Q.HJ. 1990. SAR observations and modeling of the C-band backscatter variability due to multiscale geometry and soil moisture. IEEE Transactions on Geoscience and Remote Sensing, Vol. 28, No. 5, pp. 886-895. Beaulieu, N., Leclerc, G., and Moisan, Y. 1995. Determination de la rugositd de surface par des mdthodes accessibles. Canadian Journal o f Remote Sensing, Vol. 21, No. 2, pp. 198-203. Blyth, K. 1993. The use of microwave remote sensing to improve spatial parameterization of hydrological models. Journal o f Hydrology, Vol. 152, pp. 103-129. Champion, 1 .1996. Simple modelling of radar backscattering coefficient over a bare soil: variation with incidence angle, frequency and polarization. International Journal o f Remote Sensing, Vol. 17, No. 4, pp. 783-800. Chanzy, A., Bruckler, L., and Perrier, A. 1995. Soil evaporation monitoring: A possible synergism of microwave and infrared remote sensing. Journal o f Hydrology, Vol. 165, No. 1, pp. 235-261. Coppo, P., Luzi, G., and Schiavon, G. 1995. Understanding microwave backscattering of bare soil by comparing models and experimental data collected during two different airborne campaigns. In Proceedings o f the 1995 International Geoscience and Remote Sensing Symposium, IGARSS'95, 10-14 July 1995, Firenze, Italy, pp. 1346-1348. Delta Devices Ltd. 1996. Thetaprobe soil moisture sensor. User manual MUUM-2, Delta Devices Ltd., Cambridge, U.K. 18 pp. Dobson, M.C., and Ulaby, F.T. 1986a. Active microwave soil moisture research. IEEE Transactions on Geoscience and Remote Sensing, Vol. 24, No. 1, pp. 23-36. Dobson, M.C., and Ulaby, F.T. 1986b. Preliminary evaluation of the SIR-B response to soil moisture, surface roughness, and crop canopy cover. IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-24, No. 4, pp. 517-526. Dubois, P.C., Van Zyl, J., and Engman, T. 1995. Measuring soil moisture with imaging radars. 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Further reproduction prohibited without permission. 651 40 Vol. 28, No. 5, October/octobre 2002 Henderson, F.M., and Lewis, A.J. 1998. Principles and applications o f imaging radar. Chapter 8. 3rd ed. John Wiley & Son Inc., New York. King, C., Hill, J., Bonn, F., Caloz, R., et al. 1998. FLOODGEN 2nd progress report to the European Commission. Report ENV4 CT96 0368, BRGM Report R40088. Bureau de Recherches Geologiques et Minieres, Orleans, France. Le Bissonais, Y. 1990. Experimental study and modelling of soil surface crusting processes. Catena Supplement, Vol. 17, pp. 13-28. McNairn, H., Boisvert, J.B., Major, D.J., Gwyn, Q.H.J., Brown, R.J., and Smith, A.M. 1996. Identification of agricultural tillage practices from Cband radar backscatter. Canadian Journal o f Remote Sensing, Vol. 22, No. 2, pp. 154-162. Oh, Y., Sarabandi, K., and Ulaby, F.T. 1992. An empirical model and inversion technique for radar scattering from bare soil surfaces. IEEE Transactions on Geoscience and Remote Sensing, Vol. 30, No. 2, pp. 370-381. Pr6vot, L., Champion, I., and Guyot, G. 1993. Estimating surface soil moisture and leaf area index of a wheat canopy using a dual-frequency (C and X bands) scatterometer. Remote Sensing o f Environment, Vol. 46, pp. 331339. Shepard, N. 1998. Extraction erf beta nought and sigma nought from RADARSAT CDPF products. Report AS97-5001, ALTRIX Systems, Ottawa, Ont. 12 pp. Ulaby, F.T., and Batlivala, P.P. 1976. Optimum radar parameters for mapping soil moisture. IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-14, No. 2, pp. 81-93. Ulaby, F.T., Batlivala, P.P., and Dobson, M.C. 1978. Microwave dependence on surface roughness, soil moisture and soil texture: part I — bare soil. IEEE Transactions on Geoscience Electronics, Vol. 16, No. 4, pp. 286-295. Ulaby, FT., Moore, R.K., and Fung, A.K. 1982. Microwave remote sensing active and passive. Vol. II: radar remote sensing and surface scattering and emission theory. Artech House, Ann Arbor, Mich. Ulaby, F.T., Dubois, P.C., and van Zyl, J. 1996. Radar mapping of surface soil moisture. Journal o f Hydrology, Vol. 184, pp. 57-84. Wang, J., Hsu, A.Y., Shi, J., O'Neill, P.E., and Engman, E.T. 1986. Microwave backscatter from agricultural fields observed by shuttle imaging radar. IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-24, No. 4, pp. 510-516. Wang, J., Hsu, A.Y., Shi, J., O’Neill, P.E., and Engman, E.T. 1997. A comparison of soil moisture relatival model using SIR-C measurements over the Little Washita River watershed. Remote Sensing o f Environment, Vol. 59, pp. 308-320. 652 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. © 2002 CASI 41 TRANSITION BETWEEN CHAPTERS 2 AND 3 Chapter 2 has presented a method for evaluating multi-technique approaches to estimate soil surface parameters from SAR data. The first section provides a description of the backscattering models. It is followed by a comparison of the multi-angular and multi polarization approaches and the results show that the multi-angular approach performs significantly better than multi-polarization. This section is further developed in Appendix B where this comparison is carried out using three radar configurations (multi-angular, multi polarization and multi-frequency), and again the multi-angular shows the best results. This important conclusion guides the rest of this study. Indeed, the continuity of the thesis is based on the estimation of soil surface parameters using the multi-angular approach. The second section presents a novel approach for estimating soil surface roughness referred to as the NBRI (Normalized radar Backscatter soil Roughness Index). The NBRI can estimate soil surface roughness, however knowledge of soil moisture is needed and the NBRI is not capable of giving any information relating to soil moisture. As explained before, the global aim of this thesis is to estimate both soil surface roughness and moisture and therefore, the presence of an approach for estimating soil moisture seems to be needed for supporting the NBRI to wards reaching this aim. The following chapter presents a new empirical model to retrieve soil moisture content. This linear model, like the NBRI, is very easy and fast to use and it can be a good complement to the NBRI, which is a rapid and simple approach. This model can be used only for estimating soil surface moisture or both surface parameters. To develop this new model, first two linear models (Ji and Champion models) were tested and recalculated, then, based on their formulation the new linear model is executed. Appendix E gives some more information concerning the Least Square method used in Chapter 3. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 Chapter 3 ESTIMATION OF THE MOISTURE CONTENT OF BARE SOIL FROM RADARSAT-1 SAR USING SIMPLE EMPIRICAL MODELS Mahmod Reza SAHEBI, Ferdinand BONN and Q. Hugh J. GWYN International Journal o f Remote Sensing, 2002, Vol. 24, No. 12, pp. 2575-2582. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. INT. J. REMOTE SENSING, 2003, VOL. 24^ NO. 12, 2575-2582 Estimation of the moisture content of bare soil from RADARSAT-1 SAR using simple empirical models M. R . SAHEBI*, F. BONN and Q. H. J. GW YN Centre duplications et de recherches en teledetection (CARTEL), Universite de Sherbrooke, Sherbrooke, QC, J1K 2R1, Canada (Received 13 May 2002; in final form 25 November 2002) Abstract. Synthetic Aperture Radar (SAR) provides a remote sensing tool to estimate soil moisture. Mapping surface soil moisture from the grey level of SAR images is a demonstrated procedure, but several factors can interfere with the interpretation and must be taken into account. The most important factors are surface roughness and the radar configuration (frequency, polarization and incidence angle). This Letter evaluates the influence of these variables for estimation of bare soil moisture using RADARSAT-1 SAR data. First, the parameters of two linear backscatter models, the Ji and Champion models (Ji et al. 1995, Champion 1996), were tested and the constants recalculated, rms error based on the backscattering coefficient was reduced from 6.12 and 6.48 dB to 4.28 and 1.68 dB for the Ji and Champion models respectively. Secondly, a new model is proposed which had an rms error of only 1.21 dB. The results showed a marked increase in accuracy compared with the previous models. 1. Introduction Microwave remote sensing techniques are o f prim ary interest for m onitoring soil m oisture, due to their all-weather capabilities, ability to penetrate m any natural media and sensitivity to surface variables (such as w ater content) th at are difficult to estim ate using optical sensors. Surface soil moisture content has usually been estimated with an empirical relationship to convert the m easured backscatter coefficient (ct°) into volumetric soil m oisture (mv) (Dobson and Ulaby 1986, Prevot et al. 1993, Ulaby et al. 1996). The objective o f this Letter is to make use of RADARSAT-1 Synthetic Aperture R adar (SAR) d ata for soil moisture content estim ation. To reach this goal, the selected models (Ji et al. 1995, Cham pion 1996) were first evaluated, then their coef ficient constants were recalculated for the study area using RADARSAT-1 SAR data. Following this, a new model is presented to increase the accuracy o f soil moisture estimation. The linear model proposed in this Letter is a function o f soil moisture, rms height o f the surface roughness and incidence angle. All three variables have a multiplicative effect on the radar signal expressed as a backscatter coefficient (dB). ‘Corresponding author; e-mail: ferdinand.bonn@usherbrooke.ca International Journal o f Remote Sensing ISSN 0143-1161 print/ISSN 1366-5901 online © 2003 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/0143116031000072948 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 M. R Sahebi et al. 2576 2. Study area The agricultural sites chosen for this study are the Chateauguay (73° 4 6 'W, 45° 19'N) and Pike River (72° 5 4 'W, 45° 0 8 'N ) watersheds, which are located on the south shore o f the St Lawrence River, south-east o f M ontreal, C anada (figure 1). The areas consist mainly o f agricultural fields on a rather flat, relief plateau with a homogeneous soil texture com posed o f about 36% clay, 42% silt and 22% sand. The ground surveys were m ade on rectangular agricultural parcels o f about 0.6 ha th at were considered as hom ogeneous spatial units. The parcels were furrowed with rough to very rough surfaces. 3. Data 3.1. Ground data Roughness and m oisture measurem ents were carried out on 27 parcels in the C hateauguay area and 11 parcels in the Pike River watershed, on the same day as the SAR image acquisitions. To calculate rm s heights, the param eter used to quantify roughness, six 2 m long (1.5 cm sampling interval) surface profiles (three parallel and three perpendicular to the soil furrows) were m easured for each parcel. The profiles were photographed and then digitized. The m ethod for extracting and modelling the roughness param eters has been described in detail by Beaulieu et al. (1995). T o measure the surface moisture, a Thetaprobe soil moisture instrum ent which measures the apparent dielectric constant o f the soil was used. Fifteen samples were taken at each parcel. These measurem ents were carried out for soil at 0-5 cm depth, n Hb*r Figure 1. Location of study area. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45 Remote Sensing Letters 2577 corresponding to the length o f the Thetaprobe needles. Using the equation presented in the Thetaprobe soil moisture user m anual (Delta T Devices Ltd 1996), the direct outputs (D C voltage in mV) were converted to soil w ater content (m 3 m -3 ) and dielectric constant. Field measurements were m ade on 12, 15, 18 and 23 November, the same dates as the SA R image acquisitions. 3.2. Satellite SAR data F our RADARSAT-1 SAR images were acquired during the ground surveys as described in table 1. All four images cover the Chateauguay watershed but only two images (standard-1 and standard-7 ascending) cover the Pike River watershed. T he parcels were identified on the images, which had been georeferenced and geometrically corrected using reference points identified by a global positioning system (GPS). The image digital num ber (DN ) values were converted to a tr° using coefficients by Shepard (1998). In order to include spatial variability and to avoid problem s related to georeferencing o f individual pixels o f the parcels in the study area, an average a° (dB) was assigned to each parcel (approximately 20-30 pixels). The SAR and ground data o f the Chateauguay site were used first to calculate the coefficients and constants o f the Ji and Cham pion models. The Pike River data were then used for the com parison and evaluation between these models and the proposed new model. 4. Testing and fitting the models Previous research w ork has described the relationship between <r° (dB) and volumetric soil surface m oisture (m„) as linear (Attem a and Ulaby 1978): (7 ° = C + Dmv (1 ) where C is the backscatter coefficient o f a dry soil and D = da®Idm v is the radar sensitivity to soil m oisture th at varies with the radar configuration. The backscattering coefficient varies with the sensor param eters (frequency, polarization and incidence angle) and the target param eters (roughness and m oisture for a bare soil). In equation (1), for a given frequency and polarization, soil m oisture is related to D, in which case C can be expressed as a function o f roughness and incidence angle. In this study, two models based on equation (1) are used. The first m odel (Ji model; Ji et al. 1995) expresses equation (1) as: a0 = C '+ A 's+ Dmv (2) where A' and C are the constants for a given rad ar configuration and s is the rms height o f surface roughness (cm). The values used for a configuration o f C-band, H H polarization are presented in table 2. Table 1. Acquisition parameters of the RADARSAT SAR images. Date 12 November 15 November 18 November 23 November 1999 1999 1999 1999 RADARSAT-1 mode Incidence angle (°) Pixel spacing (m) Orbit Standard-1 Standard-3 Standard-7 Standard-7 20-25 34-40 45-49 45-49 12.5 12.5 12.5 12.5 Descending Ascending Ascending Descending Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 2578 M. R Sahebi et al. Table 2. The values of constant coefficients for the Ji model. Original values Recalculated values using Chateauguay data A' C’ D 0.364 0.221 -17.67 -16.51 0.125 5.43 Table 3. The values of constant coefficients for the Champion model. Original values Recalculated values using Chateauguay data c. c2 c3 D -29.2 27.2 18.46 2.8 0.34 17.42 2.22 -27.45 The second m odel (Cham pion model; Cham pion 1996) is: a° = Ci + C2 cos{d)c , + D m v (3) where 0 is the incidence angle and C\ , C2 and C3 are constant coefficients (table 3). T o obtain results from these models, the following procedure was applied. 1. To evaluate the accuracy o f the model outputs, the backscatter coefficients were simulated using the measured in situ variables. The coefficients were then com pared with the backscatter coefficients obtained from the images of the Pike River watershed (figures 2 and 3). 2. To increase the predictive accuracy o f the two models in the study area, the constants o f each model were recalculated using the Chateauguay watershed data. The constants were recalculated using the nonlinear least-squares m ethod o f Colem an and Li (1996). The results of this analysis are presented in tables 2 and 3 for the Ji and Cham pion models respectively. 5. A new linear model According to equations (2) and (3), it would appear th at neither o f these models could represent all the variables th at have an influence on the radar response. The Ji m odel depends on the roughness; however, it is not sensitive to incidence angle. On the other hand, the C ham pion model depends on the incidence angle but it does not take into account the roughness. To solve this problem, we propose a new model using the rms height roughness and incidence angle as follows: er°(dB) = A \ + A 2 cos(0 ) ' 43 + / 4 4 ln (s)+ D m v (4) The constants A \, A2, A 3 , A 4 and D were calculated for a configuration o f C-band, H H polarization using the nonlinear least-squares method. The following values were obtained for the Chateauguay and Pike River sites: A\ = -2 7 .1 4 , A 2 = 17.50, A 3 = 0.25, A 4 = -0 .3 1 and Z>== 1.85. 6. Interpretation and discussion Figures 2, 3 and 4 present the relationship between the measured and calculated backscattering coefficient values for the Ji, the Cham pion and the new model respectively. T ab le4 also presents the statistical results for these models. Based on the statistical results for the comparison presented in table 4, the correlation between the measured c° and the <r° calculated from original coefficients for both Ji Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 2579 Remote Sensing Letters CQ ■o a ■ Original values A Recalculated values -5- b ^ -10- E i UJ -20 -20 -15 -10 5 0 Measured o-° (dB) Figure 2. Relationship between measured and estimated backscatter coefficients calculated using the Ji model. Recalculated values show a slight increase in accuracy. and Cham pion models was not strong and there were large errors. However, as was expected, the adaptation o f the Cham pion and Ji models with new local coefficients significantly increased the accuracy o f the models for estimating soil surface m oisture. Figures 2 an d 3 show th at <x° obtained from recalculated values (triangular points) are closer than tfi calculated from the original values (rectangular points) to the ideal 1 : 1 regression line (where all points would be situated on the line). This increase is more apparent for the Cham pion model. In figure 2 , the recalculated points were slightly closer than the original points to the ideal 1:1 line; however in figure 3, the recalculated data were considerably closer than the original data to the ideal 1 : 1 line. Linear empirical models can be applied only within the region where they were initially developed. Their coefficients have to be recalculated to take into account different soil characteristics and agricultural practices when they are to be used in other regions. Furtherm ore, the values related to the new model show further decrease o f the rms error in comparison with the Ji and Cham pion models (table 4). According to the indicators, presented in table 4, the new model reduces the error m argin noticeably in all cases. This means th at the new model can provide the surface soil m oisture in relation to the backscatter coefficient with reduced errors. The new model was tested at an incidence angle o f about A T over rough surfaces, which are generally unfavourable conditions for soil m oisture surface estimation. The results are still more accurate in com parison with the results using Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 2580 M. R Sahebi et al. CO T3 ■ A °b +o-> (0 E *3 W LU Original values Recalculated values -10- ill*1 -15- -20 -20 ■■ -1 5 -10 5 0 M e asu red a 0 (dB) Figure 3. Relationship between measured and estimated backscatter coefficients calculated using the Champion model. Recalculated values show a marked increase in accuracy. -5 - 00 T3 o b ■o 1 0 0) +-I - - to E -15- -20-I -20 - 15 -10 M easu red 5 ct° 0 (dB) Figure 4. Relationship between measured and estimated backscatter coefficients calculated using the proposed new model. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 2581 Remote Sensing Letters Table 4. Statistical results of comparison between measured and calculated backscattering coefficients using the Ji, the Champion and the new model. Indicator Model Champion (original) Champion (recalculated) Ji (original) Ji (recalculated) New model Mean absolute error (dB) RMS error (dB) Variance of error Maximum error (dB) 6.24 6.48 1.81 9.17 1.42 5.96 4.10 1.05 1.68 6.12 0.93 1.42 1.25 0.61 2.94 7.84 5.77 1.85 4.28 1.21 the o th er models. However, the new m odel should be adapted for all RADARSAT-1 acquisition m odes and for a range o f agricultural surfaces. C om parison o f the results o f the original and im proved models (table 4) shows th at the effect o f incidence angle cannot be neglected and m ust be taken into account by the models. However, the influence o f roughness on linear models is less noticeable. 7. Conclusions This study has determ ined the relationship between RADARSAT-1 backscatter (for C -band, polarization H H ) an d the volum etric soil m oisture o f bare soil surfaces using linear backscattering models. The simple m odel, described in this Letter, estimates the soil m oisture content for all ra d ar configurations, even fo r incidence angles near 50° and over rough surfaces. However, when applying the m odel in another region o r w ith other sensor configurations (i.e. polarization an d frequency), it will be necessary to recalculate the model coefficients. Acknowledgments This study was partly supported by F C A R (Action Concert 6 e R A DARSAT), and N S E R C grant 006042 and the M inistry o f Science, Research and Technology o f Iran provided a scholarship and financial support to M. Sahebi. The authors want to th an k all the colleagues o f C A R TEL especially P. G agnon, J. Angles, P. Cliche an d M . Lam bert. References A t t e m a , E . P., and U l a b y , F. T., 1978, Vegetation modeled as water cloud. Radio Science, 13, 357-364. B e a u li e u , N., L e c l e r c , G., and M o is a n , Y., 1995, Determination de la rugosite de surface par des methodes accessibles. Canadian Journal of Remote Sensing, 21, 198-203. C h a m p io n , I., 1996, Simple modelling of radar backscattering coefficient over a bare soil: variation with incidence angle, frequency and polarization. International Journal of Remote Sensing, 17, 783-800. Coleman, T. F., and Li, Y., 1996, An interior, trust region approach for nonlinear minimization subject to bounds. SIAM Journal on Optimization, 6, 418-445. Delta T Devices Ltd 1996, Thetaprobe Soil Moisture Sensor. User manual, Mll-UM-2. Delta T Devices Ltd, Cambridge, UK. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 2582 Remote Sensing Letters D o b s o n , M. C ., a n d U l a b y , F . T ., 1986, A ctiv e m icro w av e soil m o istu re research. IEEE Transactions on Geoscience and Remote Sensing, 24, 23-36. Ji, J., S k r i v e r , H., and G u d m a n d s e n , P., 1995, Estimation of soil moisture from the MAESTRO-1 SAR data of Flevoland. Proceedings of Sensor and Environmental Applications of Remote Sensing, 1995, edited by J. Askne (Rotterdam: A. A. Balkema), pp. 103-110. P r B v o t, L ., C h a m p io n , I., and G u y o t , G ., 1993, Estimating surface soil moisture and leaf area index of a wheat canopy using a dual-frequency (C and X bands) scatterometer. Remote Sensing of Environment, 46, 331-339. S h e p a r d , N., 1998, Extraction of beta nought and sigma nought from RADARSAT CDPF products. Report No. AS97-5001, ALTRIX Systems, Ontario, Canada. U l a b y , F. T., D u b o is , P. C., and v a n Z y l , J., 1996, Radar mapping of surface soil moisture. Journal o f Hydrology, 184, 57-84. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51 TRANSITION BETWEEN CHAPTERS 3 AND 4 In Chapters 2 and 3, two independent methods (NBRI and new linear) are presented for estimating soil surface roughness and soil moisture content. The NBRI (Chapter 2) is strictly developed based on the multi-angular approach, but the new linear model (Chapter 3) is not necessarily executed for the multi-angular approach; however, it can be used in the context o f multi-angular data. In this case, at first, the rms height should be calculated using NBRI (Chapter 2) as: s = ax]n(N BRl)+ b £T° +£T° where NBRI = —^ i s (1) the relationship between two different backscatter coefficients (a°i and a°2) obtained using two different incidence angles, and a and b are linear coefficients that must be calculated for each region independently. Then, the volumetric soil surface moisture (mv) can be given by: Tx - A4 ln(s) = —------— — D or T2 - Aa ln(s) = —-------—— D (2) h and T2 are expressed as: Tx = a x - A x- A 2 cos(dx)Ai and T2 = a ° - A x- A2 cos(8 2)A' where Aj, A2, A 3 , A 4 and D are constant coefficients related to the sensor characteristics; a°i and a° 2 (in dB) represent the backscattering coefficients from images with incidence angles 61 and Q2 respectively. This new linear model integrates the influence of rms height and incidence angle simultaneously within the relationship between the backscatter coefficient and soil moisture content for a given frequency and polarization. However, it has to be noted that the constant Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52 coefficients were calculated for the study area and this suggests that the model should be used with caution in other regions and if necessary, they have to be recalculated. In spite of the simplicity o f these modes, it is evident that linear models are based on several observations (purely empirical). There is no reason to accept this fact as an inconvenience; however, it is assured that its results must be compared with the results obtained from more complex models (theoretical and semi-empirical models). The next chapter presents a methodology for inverting the theoretical and semi-empirical backscattering models for retrieving soil surface parameters (soil surface roughness and soil moisture content simultaneously) in the concept of the multi-angular approach. These inversions were made using analytical and numerical (Newton-Raphson) methods. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 Chapter 4 AN INVERSION METHOD BASED ON MULTI-ANGULAR APPROACHES FOR ESTIMATING BARE SOIL SURFACE PARAMETERS FROM RADARSAT-1 DATA Mahmod Reza SAHEBI, Joel ANGLES and Ferdinand BONN Journal o f Hydrology, submitted on September, 2002 This paper has been evaluated and has been modified according to the journal reviewers’ comments. The new corrected version has been resubmitted on August 2003 and replaces the preceding version. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 AN INVERSION METHOD BASED ON MULTI-ANGULAR APPROACHES FOR ESTIMATING BARE SOIL SURFACE PARAMETERS FROM RADARSAT-1 DATA Abstract The radar signal recorded by earth observation (EO) satellites is known to be sensitive to soil moisture and soil surface roughness, which influence the onset of runoff. This paper focuses on the inversion of these parameters using a multi-angular approach based on RADARSAT-1 data with incidence angles of 35° and 47° (in mode S3 and S7). This inversion was done based on three backscatter models: Geometric Optical Model (GOM), Oh Model (OM) and Modified Dubois Model (MDM), which are compared in order to obtain the best configuration. For roughness expressed in rms of heights, mean absolute errors of 1.23 cm, 1.12 cm and 2.08 cm, and for dielectric constant, mean absolute errors of 2.46, 4.95 and 3.31 were obtained for the MDM, GOM and the OM simulation, respectively. This means that the MDM provided the best results with minimum errors. According to this, the inversion algorithm was applied on the images and the final results are presented in two different maps showing pixels and homogenous zones. KEYWORDS: Remote sensing, RADARSAT, multi-angular, soil moisture, soil roughness, inversion. 1. Introduction Synthetic Aperture Radars (SAR) are active microwave sensors that have the potential to acquire data under almost any meteorologic condition and without an external source of illumination. It is, therefore, possible to collect information on a regular over an area often covered by cloud at either day or night. This advantage over sensors operating in the visible and infrared portion of the electromagnetic spectrum improves the capability to monitor dynamic phenomena. The potential of SAR data has been demonstrated for monitoring the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 earth's surface (Ulaby et al, 1978, 1982, 1996; Dobson and Ulaby, 1986a, 1986b; Engman and Wang, 1987; Oh et al, 1992; Fung and Chen, 1992; Fung, 1994; Dubois et al, 1995). However, it is sometimes difficult to separate land cover information using a single channel o f SAR data. A multi-technique approach, using SAR data, is thus seen as essential in environmental studies. In the scope of this paper, the monitoring of land surface parameters is defined as the estimation of soil surface roughness and moisture status over a large area. Mapping of soil surface roughness and moisture over a large scale regularly or at critical times (floods, droughts, landslides, etc.) is useful for agronomists and hydrologists. It provides an overall view of land surface parameters on a spatial scale. It allows the detection of dry and wet areas, as well as smooth and rough areas and the identification of areas of potential hydrological or agronomic problems. Mapping of surface characteristics can be done either from point measurements or estimated values from models and remote sensing. Soil moisture obtained from remote sensing instruments is derived by converting the detected dielectric constant. The remote sensing data are not as accurate as the ground point data because of the resolution and the algorithms or models that have to be applied to the signal in order to obtain the soil moisture estimate. However, they do provide information on the spatial variability (Benallegue et a l , 1998) and the derived values provide a map of an area without having to interpolate data as with point measurement. Based on simulation results, Sahebi et al. (2001 & 2002) indicated that a multi-angular approach is better adapted to the separation of moisture and roughness signals than multi polarization and multi-frequency approaches. Therefore, the RADARSAT-1 satellite with its capability of acquiring data at different incidence angles could be used for estimating soil moisture and surface roughness. However, it is necessary to develop a method adapted to RADARSAT-1 data for estimating these parameters. The objective of this paper is to formulate and define a transformation approach to solve the inverse problem for the operational retrieval and mapping of soil surface roughness and moisture. The strategy consists in formulating the inverse problem in the context of multi- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 angular RADARSAT-1 data. We study the relation between the C-band radar response and soil parameters, specifically soil dielectric constant (e) and rms height (s), which are used as constraining target parameters in the Geometric Optics Model (GOM) (Ulaby et al., 1982), the Oh Model (OM) (Oh et al., 1992) and the Modified Dubois Model (MDM) (Angles, 2G01). According to results obtained from the MDM, a roughness and a moisture maps for the Chateauguay watershed (Quebec, Canada) were produced. 2. Study site and data description The agricultural site chosen for this study is part of the Chateauguay watershed (73°46' W, 45° 19' N), located on the south shore of the St. Lawrence River, southeast of Montreal, Canada (Figure 1). The area consists mainly of agricultural fields on a rather flat relief plateau with homogenous texture composed of about 36% clay, 42% silt and 22% sand. During the ground surveys the parcel surfaces were rough to very rough. Roughness and moisture measurements were carried out over 27 agricultural parcels, simultaneously with the image acquisitions (Figure 2). Roughness measurements were made using a homemade needle profilometer measuring 2 meters in length. To calculate rms height, six 2 m long (1.5 cm sampling interval) surface profiles (three parallel and three perpendicular to the soil furrows) were investigated for each parcel. These profiles were photographed and then digitized. The method for extracting and modeling the roughness parameters has been described in detail by Beaulieu et al. (1995). To measure the surface moisture a time domain reflectometry (TDR) instrument was used. These measurements were carried out with a Thetaprobe soil moisture sensor for soil depths of 0-5 cm corresponding to the length of the Thetaprobe needles. Fifteen samples were taken in each parcel of land. Using the equation presented in the Thetaprobe soil moisture User Manual (Delta Devices Ltd., 1996), the direct outputs (DC voltage in V) were converted to soil moisture content (m3.m'3) and dielectric constant. Also, to evaluate the results obtained by this method, five 0-5 cm soil samples for each parcel were transferred to our laboratory. Wet and dry weights were used to determine gravimetric and volumetric soil moisture content. The soil moisture content (m3.m‘3) obtained by these two Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 methods were compared and a mean relative difference of 12 % (equivalent to 1 .8 % in volumetric soil moisture) was observed between the two methods. \ VIctertaxHlle? rummon 7 / STUDY AREA Montreal ;8herbrook-e-._ s h a te a u g u a Couiansville U.S.A Figure 1. Location of study area Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission. Figure 2. Location of the parcels (Airborne photography over Chateauguay watershed) The satellite data used in this study correspond to a RADARSAT-1 image pair. The first image was acquired on November 15, 1999 in S3 (Standard-3 Ascending) mode with incidence angles ranging from 30 to 35° and, the second image was acquired on November 18, 1999 in S7 (Standard-7 Ascending) mode with incidence angles ranging from 45 to 49°. The RADARSAT DN values were converted to G° according to Shepard (1998). In order to include the spatial variability and to avoid problems related to georeferencing of individual pixels of the parcels in the study area (homogeneous soil structure, bare soil, homogeneous ploughing), an average o° (dB) was assigned to each parcel (approximately 20 to 30 pixels). The roughness and moisture of the surface were measured in-situ on November 15 and 18 (the same dates as the satellite image acquisitions). Between the periods of data Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 acquisition, the weather was stable and surface moisture had not changed significantly because of the low evaporation and temperature at that time of the year. According to local observation and Environment Canada, average daily temperatures were 2.3 °C (with minimum value of 1.5° and maximum value of 7°) and there was no recorded rainfall nor soil freezing between the two acquisition dates. However, to completely satisfy the conditions of this study, 20 parcels that had nearly the same moisture and roughness for the two dates were chosen for the analysis. 3. Methodology The important parameters that significantly influence the soil surface radar response may be classified into two categories: 1) the target parameters such as moisture, roughness and vegetation cover (if present) and, 2) the sensor parameters such as frequency, polarization and incidence angle. Usually in remote sensing applications, the sensor parameters are known; however, the relationship between die target and the measured signals have to be investigated. Estimation of soil surface parameters was usually obtained by using theoretical or empirical relationships to convert the measured backscatter coefficient (a0) into soil surface roughness and moisture (Dobson and Ulaby, 1986a; Pr6vot et al., 1993; Ulaby et al., 1996). Thus for each target, we had one equation with two unknowns, or three if the model incorporates the correlation length. As a consequence, the use of radar data acquired with single configuration does not generally permit the estimation of these soil surface variables. Therefore, to simultaneously estimate the surface parameters over complex areas, multi-technique concepts (multi-polarization, multi-angular, multi-sensor, multi-frequency, and multi-temporal) are the main solution. From a ground based experiment (Chanzy et a l, 1998) and a theoretical study (Sahebi et al., 2001, 2002), it was demonstrated that the multi-angular configuration is the best one to estimate bare soil surface parameters. For this reason, the multi-angular configuration is used for the inversion of backscattering models to estimate for roughness and soil moisture from RADARSAT-1 data acquired at two different incidence angles. It has to be noted that this approach was tested with different RADARSAT-1 images acquired at different Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60 incidence angles (between 20 and 49 degrees) and the presented images gave the optimal results. 3.1. Model descriptions As mentioned before, the aim of this study is to estimate bare soil surface parameters using multi-angular approaches. This process was carried out using existing theoretical and empirical backscatter models that introduce the relationship between backscatter coefficient and surface parameters (roughness and dielectric constant). Considering the study sites profile that contain very rough surfaces, the comparison the mentioned backscattering models is carried out using simulations by GOM (Geometric Optics Model; Ulaby et al., 1982), OM (Oh Model; Oh et al., 1992) and MDM (Modified Dubois Model; Angles, 2001). Geometric Optics Model (GOM) The Geometric Optics Model (GOM) also known as the Kirchhoff method under the stationary phase approximation intended to express scattering by rough surfaces with, 0.06Ar2^ 2>ks, k£> 6 and (2 ks.cos 0 )2> 10 where ■£ is the correlation length, k is the wave number (k=2 n/A, where A is the wavelength), s is the root mean square (rms) height and 6 is the incidence angle. This model predicts that a°hh(0)=crOvv(0), at all incidence angles. The expression for the co-polarized backscattering coefficient is given by: 0) where Rpp(0) is the surface reflectivity from normal incidence and m is the rms slope of the surface (m= s [p"(0 ) f 5 where p"(0 ) is the second derivative of autocorrelation function of surface p(£) evaluated at £=0). Several mathematical forms have been used in the literature to describe p(£) of natural surfaces, including the Gaussian and the exponential forms. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 According to Oh et al. (1992), the exponential function is adapted to smooth surfaces and Gaussian autocorrelation function is adapted to rough surfaces. Based on the study area descriptions (rough to very rough surfaces) the Gaussian autocorrelation function was chosen for calculating m values. Oh Model (OM) Because of the inadequate performance of theoretical models for predicting the backscatter response of random surfaces, Oh et al. (1992) developed an empirical model based on experimental data acquired in L- C- and X-bands (1.5,4.75 and 9.5 GHz respectively). This model was designed for surfaces with various moisture conditions and roughnesses, from slightly smooth to very rough and does not incorporate the correlation length. The valid surface conditions cover the following ranges: 0.1 < ks < 6.0, 2.6 < < 19.7 and 9% < mv <31% , where mv is the volumetric soil moisture. The backscattering coefficients for this model can be written in hh polarized: ufth = g-Jp cos3 G[Rw(0) + Rhh{9)\ where -Jp = 1 - (“ ) (2) ^x exp(- ks) and g^O.T^-exp^-O.bS^)1'8)] Modified Dubois Model (MDM) The empirical model developed by Dubois et al. (1995) was initially developed in order to separate moisture and roughness using a bipolarization approach. This model is limited to ks < 2.5, 6 > 30° and moisture contents mv < 35%. This model was tested over the study area by the researchers of the University de Sherbrooke (Angles, 2001; Angles et al., 2002) and the results presented an important difference between simulated and desired values. The method that Dubois et al. (1995) have been following has been used for adapting the Dubois model into measured data over the Quebec agricultural area. To overcome this discrepancy, the RADARSAT-1 data (band-C, hh-polarized and incidence angles between 20° and 50°) and measured ground data (soil surface roughness, soil moisture and soil texture) were used. This modification is presented as a new model named Modified Dubois Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Model (MDM). It expresses the backscattering coefficient for this model is described by Equation 3 that can be applied to bare agricultural surfaces of Quebec with cm< s <6 cm and 14%< mv <32% (Angles, 2001). x(fa.sin^)0'883x2 07 (3) where k is the wave number (k=2 n/%) and X is the wavelength. Applying this model to RADARSAT-1 data acquired at two different incidence angles of the same target with a short time interval, this approach generates a two equation system with two unknowns, which can be resolved to obtain s and e. However, for validation progress, this model may be tested in other regions with different conditions. 4. Inversion method Let us suppose that we have backscatter coefficients (o V in this case) measurements for a given surface at the given incidence angles 0j, 02 and 03 (if applicable). From these measurements, it is possible to compute the land-surface parameters using the above models. As explained, three models are chosen. The MDM is analytically invertible. Equations 4 and 5 show the inversion of this model to calculate land-surface parameters using the multiangular approach for hh-polarization: Sr los M 0.112 x (tan 0 i - tan 0 i) j=i-x 0.883I1 03'67xcxm(0i)x (4) tan(ft)-tan( 0 2 ) (5) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 where a°hh (@i) and a°hh ( 6fe) are the backscatter coefficients measured at Oj and 62 respectively, and: cr&/(ft)xsin4 n 7(ft)xcos1'5(ft) crJW(&)xsin4 117( 0 2 ) x c o s u (& ) The OM and GOM are not invertible by this way. For these models, the Newton-Raphson method (Ortega and Rheiriboldt, 1970), a numerical iterative method, is used in the retrieval algorithm to solve the inverse problem. Based on Newton-Raphson method, the variable matrices (the unknown variables) are s and Er for OM and s, £r and £ for GOM. The known parameters in the model are die backscatter coefficients at two or three different incidence angle. The algorithm can be summarized as follows: Step 1. Presentations of the zeroed functions (/*) are issued by using GOM and OM based on the multi-angular approach. For example these functions for OM are: f\ = crlh((h) - gyfp cos #l[Rw($) + Rkh($\j\ - 0 (6 -a) f i —<y\h{6 i) —g jp cos &[Rw(#2) + Rhh(8 i)]= 0 (6 -b) (p and g functions are already explained in Eq. 2). Step2. Computation of the error matrix based on an initial guess of the variables ( 5 . and s for OM; Sr, s and £ for GOM). In this study, the initial values were: s-=10, j =3 cm and £= 5 cm. Step3. Computation of the matrix ay which is the relation between the backscatter coefficient and the soil-surface parameters. Equations 7 and 8 present this matrix for OM and GOM respectively: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dfi dfi dfi ds dsr d l a _ dffi dfi_ ds dsr 81 for GOM (8) dfi dfi dfi ds dsr d l . Step 4. Calculation o f the error {Sx.fi in the estimation o f land surface properties. This matrix can be solved by the LU (Lower and Upper triangular) decomposition method (Westlake, 1968). Step 5. Correction o f the error in the estimation o f soil surface parameters by Sxj for the next iteration. Step 1 through 5 are repeated until convergence is reached; that is, S = 10'5 in this case. 4.1. Evaluation of the results Evaluation o f the errors requires comparisons between predicted and measured surface parameters. All comparisons between measured in-situ and predicted surface parameters obtained by RADARSAT-1 images are presented on an even basis for rms heights and surface dielectric constants (separately). They are carried out using the coefficient of performance CP'a (James and Burgess, 1982): (13) where O(i) is the ith observed parameter, Oavg is the mean value o f the observed parameter, S(i) is the ith predicted parameter using radar images and n is the total number o f events. The coefficient o f performance approaches zero as observed and predicted values get Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65 closer. This coefficient can show the efficiency o f each model for estimating surface parameters. In this study, the mean total absolute error for the results o f each model is also calculated. 5. Discussion and Results analysis Figure 3 to 8 present a comparison between the value o f surface parameters estimated from the inversion o f radar data and those measured in-situ. For rms height, the results with minimum error are given by GOM with a mean absolute error o f 1.12 cm, followed by MDM (with a mean error equal to 1.23 cm) and OM (with a mean error equal to 2.08 cm). However, for the dielectric constant, MDM definitely has the best estimation with an error equal to 2.46 followed by OM (with an error equal to 3.35) and GOM (with an error equal to 4.59). As explained, to be able to compare these results, we also used the coefficient o f performance {CP'a). Table 1 presents the values o f this coefficient These results show that the inversion o f MDM gives the best results for estimating the soil surface parameters. Table 1. Mean absolute error and coefficient o f performance {CP’a) for surface parameters obtained by inversion approach Errors Models CP'A Height rms Dielectric Dielectric Height rms Total (cm) constant constant M DM 1.23 2.46 2.26 1.7 1.98 GOM 1.12 4.59 2.03 6.28 4.16 OM 2.08 3.35 6.30 3.59 4.95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66 16 14 2 0 0 2 4 6 8 10 12 14 16 Measured dielectric constant Figure 3. Scatter plot o f dielectric constant measured and estimated by MDM 16 14 810 O :5 88 s> "•o O 9<0 6 i a4 2 0 0 2 4 6 8 10 12 14 16 M anured dielectric constant Figure 4. Scatter plot o f dielectric constant measured and estimated by OM Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 16 14 E12 8c 810 •g Is a 0 1a 6 £ 2 0 0 2 4 6 6 10 Measured dielectric constant 14 12 16 Figure 5. Scatter plot of dielectric constant measured and estimated by GOM ?5 0 1 2 3 4 5 6 7 Measured rms height (cm) Figure 6 . Scatter plot of rms height measured and estimated by MDM Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68 0 1 2 4 3 6 5 7 Measured rms height (cuf Figure 7. Scatter plot of rms height measured and estimated by OM 7 6 i Io 5 JC 4 £ 1 ill 2 1 0 0 1 2 3 4 5 6 7 Measured rms height (cm) Figure 8 . Scatter plot of rms height measured and estimated by GOM Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 For MDM and OM, the estimation of the dielectric constant is more exact than the estimation o f rms height. Contrarily, the rms height estimated by GOM is more exact. On the other hand, for GOM, total value of CPU, for the dielectric constant is greater than those for rms height (Tablel). This sensitivity to roughness may be explained by the behavior of GOM. According to this model, the statistical variation of surface roughness is characterized by its rms height, correlation length and correlation function that is represented by rms slope (m). Therefore, the precision of roughness estimation also depends on the estimation of correlation length. However in MDM and OM, roughness is characterized only by rms height. This study presents an approach to estimate surface parameters derived from SAR satellite data with reduced estimation errors, comparative to other studies. However, there are still errors in the estimation of soil surface parameters. Further investigations are needed to understand this drawback, but several hypotheses can already be given: - Failure of the models to present a real relationship between radar signal properties and target parameters: Unfortunately, none of the backscatter models provide results in good agreement with experimental observations for all of the polarization configurations and over a wide range of incident angles, even when confined to its presumed validity range (Henderson and Lewis, 1998). - Behavior of the models in the multi-angular approach context to find an exact solution: Consider the case o f two dimensions, where we want to simultaneously solve: f1- f a ,X £>s) = 0 ft- 0 = (13) An example of this case is presented by equation 6 a & b for OM. Each o f the functions has zero regions where their respective functions are positive to negative. Unfortunately, according to model behavior, the functions f l and f2 are not dependent to each other. Note further that the zero contours consist of a number of disjoint closed curves. Figure 9 showing the curves s vs. s for parcel no 120 (a°i = -10.07 dB and ct°2 = -10.77 dB for 0i = Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 35° and 02 = 47.4° respectively) simulated by OM is an example of this situation. The solution obtained from these data was the point with the coordinate s = 2.32 cm and £ = 5 that was the closest point between the two curves. This phenomenon was also observed in some cases in the inversion with GOM. Figure 10 shows the same curves simulated by MDM. These curves intersect exactly at s= 3.25 cm and e = 11.75 which is the exact solution of the system of equations. - Incompatibility between ground measurements and estimated parameters: As explained, the ground data for each parcel are issued by some point measurements and their mean are presented as rms height and dielectric constant of the parcel. These measurements were random and numerous enough to calculate a good mean value, but generally, can this method present the real characterization of surface parameters? Unfortunately, no better method for this measurement has yet been presented. 10 9 . 6 = 47.7° 8 C l o s e s t p o i n t b e t w e e n th e c u rv e e 7 6 5 4 3 0 1 2 3 4 5 6 7 rms heigh t ( c m ) Figure 9. Variation of the dielectric constant as a function of rms height for two different incidence angles for OM Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 19 17 IN TERSECTIO N c <0 < o 15 c o o 13 o .£ ■o 11 9 7 0 1 2 3 4 5 6 7 rms height (cm) Figure 10. Variation of the dielectric constant as a function of rms height for two different incidence angles for MDM - Error in the estimation of the backscatter coefficient for parcels. To present the backscatter coefficient of each parcel, we calculate a mean of the pixels that were within the parcels. The pixel values vary sometimes with considerable variance. This operation increases errors. - Influence of tillage direction and look direction: The orientation of mechanical labor, which can be related to roughness measurements, has an influence on backscattering signals (Remond et al., 1999; Smyth et al., 2000). However, the backscatter models do not enable to simulate this influence directly. Also, the use of images acquired from different orbits (ascending and descending) is sometimes inevitable in temporal studies with SAR data. The look direction accounted for 1.5 dB difference in o° for ERS-1 images by Gauthier et al. (1998). Unfortunately, this investigation is not yet done for RADARSAT-1 images. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 - Influence of speckle and climatic conditions on radar signals. Discussion of these problems is not the aim of this paper. However, these phenomena can produce some errors when calculating backscatter coefficients from satellite images. 6. SURFACE PARAMETERS MAPPING The inversion algorithm is applied on two RADARSAT-1 images of the studied watershed. Two important points should be noted, first, the forest and urban areas are masked in the maps; second, the humidity maps are presented in term of volumetric soil moisture (m3.m'3) obtained by inverting the empirical model of the dielectric constant developed by Halikainen et al. (1985). This application was carried out in two different scales namely pixel scale and homogenous zone scale. In pixel scale (Figures 11 and 12) the inversion is applied directly on the two images pixel by pixel. The speckles of the images were reduced using the Lee filtering (Lee, 1981). The pixel scale maps are more accurate, however the pixel values vary and are also difficult to use, so that is difficult to have a general idea of the surface parameters distribution on the watershed. To solve this problem, we used the homogenous zones scale. Each homogenous zone on a radar image presents a minimal variance in the backscatter coefficients. Furthermore, within a homogenous zone the physical characteristics of the soil surface is almost the same. This kind of presentation allows us to have a general vision of the distribution of surface parameters (Figures 13 and 14). Creating an homogeneous zone contents four steps: 1) Improving the image contrast: this contrast is only for better viewing the images and does not touch the pixel values. This step helps to better view the images, specially, for manual digitalization (step 3). 2) Noise reducing: this step is carried out using the despeckle filters. Generally, the adaptative filters like Lee or Frost filters reduce notably the noise. In this study the Lee filter and a Low-pass filter was tested. As expected, the filter reduced the speckles better than Low-pass filter, but it modifies the values of the pixels that changed the final results. Contrarily, the Low-pass filter reduced the noises less than the Lee filter but the values of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 the pixels did not change significantly. However the final results (homogeneous zone maps) were approximately the same. Therefore the best filter should be chosen in each case. For this study, it was the low-pass filter. 3) Edge detection of homogeneous zone: in this step two filters were used to limit the homogeneous zones based on the minimal variance of o° in each zone (Angles, 2001), and then the edge of each zone was detected using an edge detection filter. For a few zone the polygonal of edge was not correctly closed. This problem was corrected manually. 4) Averaging: In the last step, the average of the o°s in each zone was calculated and presented as the o° value of the homogeneous zone. Figure 15 presents the methodological flowchart for homogenous zone calculation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 Figure 11. rms height map in pixel scale Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 45*14 31" N / 73r'42l41" W Figure 12. Volumetric humidity map in pixel scale Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 45°22 00" N ( 7 y ^ 3 0 3 ‘ VI m 6 cm 3 cm o 1000m 4 5 14 31 N / 73= 4 2 41" W Figure 13. rms height map in homogeneous zone scale Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 14. Volumetric humidity map in homogeneous zone scale Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78 Mean of the RADAR Images (two or more images) Improve the IMAGE-1 contrast Low-pass filtering Bomogenizaiicii of the minimal variances zones filtering Edge detedi ©a filtering on IMAGE-2 IMAGE-3 Correction of the homogenous zones (manual digitalization) IMAGE-4 Calculation mem of fcacfcscatter coefficient Introduce to main program for soil surface estimation Figure 15. Flowchart of homogeneous zone calculation Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 7. Conclusion This work has demonstrated the possibility of using the multi-angular approach to derive soil moisture and surface roughness from satellite remote sensing data. In spite of some errors, this estimation derived from satellite radar data is a useful tool for estimating the soil surface parameters over extended areas. These errors can be produced either by some essential averaging or by the behavior of the backscattering models or the incompatibility of the ground measurements and the results obtained using satellite images. However, in this paper, we demonstrated that using the right approach (multi-angular), it is possible to decrease these types of errors and derive acceptable results for the whole area in the watershed. To minimize the influence of backscatter models, we used the Modified Dubois Model (MDM) developed for agricultural sites in Quebec and presenting minimum errors. This result is obtained by comparing the same results calculated by GOM, MDM and OM. For an application point of view, the final products of this investigation are the maps of soil surface parameter. These maps were illustrated following two different scales that can serve for many applications like hydrological models, agricultural or environmental management, etc. For example, the pixel scale maps of moisture and roughness can easily serve in hydrological models based on pixel like units AGNPS (Young et al., 1987) or ANSWERS (Beasley et al., 1980). However the homogeneous zone maps represent the soil surface distribution in a large area and can be used in agricultural or hydrological management at the subcatchment scale by hydrological response units. Acknowledgements This study was partly supported by FCAR (Action Concertee RADARSAT) and NSERC. The authors want to thank all the colleagues of CARTEL, especially P. Gagnon, R. Magagi and D.C. He, for their editing work and the MCHE of Iran for granting a scholarship and financial support to M. Sahebi. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 8. References Angles, J. (2001) “Separation de l’humidite et de la rugosite dans le signal retrodiffus6 des images RSO selon une approche multi-angle”. Memoire de Maitrise, Dep. de geographie et teledetection, Universite de Sherbrooke, QC, CANADA, 82 p. Beasley, D. B., Huggins, L. F., and Monke, E. J. (1980) “ANSWERS: A model for watershed planning”. Transactions o f theASAE, Vol. 23, No. 4, pp. 938-944. Beaulieu, N. Leclerc G. and Moisan Y. (1995) “Determination de la rugosite de surface par des methodes accessibles”. Canadian Journal o f Remote Sensing, Vol. 21, No. 2, pp. 198203. Benallegue, M., Taconet, O. Vidal-Madjar, D. and Normand, A. (1998) “The use of radar backscattering signals for measuring soil moisture and surface roughness”. Remote Sensing o f Environment, Vol. 53, pp. 61-68. Chanzy, A. King, C. Pr6vot, L. and Remond, A. (1998) “Comparison of ERS and RADARSAT measurements on bare soils: first results”. Second Int. Workshop on Retrieval ofBio-&Geo-physical Parameters from SAR Data, ESTEC, The Netherlands, pp. 471-477. Delta Devices Ltd (1996) “Thetaprobe Soil moisture sensor, user manual”. Mll-UM-2; Delta Devices Ltd, Cambridge, U.K. 18 p. Dobson, M. C. and Ulaby, F. T. (1986a) “Active microwave soil moisture research”. IEEE Transactions on Geoscience and Remote Sensing, Vol. 24, No. 1, pp. 23-36. Dobson, M. C. and Ulaby, F. T. (1986b) “Preliminary evaluation of the SIR-B response to soil moisture, surface roughness, and crop canopy cover”. IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-24, No. 4, pp. 517-526. Dubois, P. C., van Zyl, J. and Engman, T. (1995) “Measuring soil moisture with imaging radars”. IEEE Transactions on Geoscience and Remote Sensing, Vol. 33, No. 4, pp. 915926. Engman, E. T. and Wang, J. R. (1987) “Evaluation roughness models of radar Backscatter”. IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-25, No. 6 , pp. 709-713. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81 Fung, A. K. and Chen, K. S. (1992) “Dependence of the surface backscattering coefficients on roughness, frequency and polarization states”. International Journal o f Remote Sensing, Vol. 13, No. 9, p. 1663-1680. Fung, A. K. (1994) “Microwave scattering and emission models and their applications”. Norwood: Artech House, 573 p. Gauthier, Y., Bernier, M., and Fortin, J.-P. (1998) “Aspect and incidence angle sensitivity in ERS-1 SAR data”. International Journal o f Remote Sensing, Vol. 19, No. 10, pp. 20012006. Halikainen, M. T., Ulaby, F. T., Dobson, M. C., El-Rays, M. A., and Wu, L. (1985) “Microwave dielectric behavior of wet soil - Part I - Emperical models and experimental observations”. IEEE Transactions on Geoscience Electronics. Vol. GE-23, No. 1, pp. 2534. Henderson F. M. and Lewis, A. J. (1998) “Principles and applications of imaging radar”. Chapter 8 . Third Edi. John Wiley & Son Inc. 1074 p. James, L. D. and Burgess, S. J. (1982) “Selection, calibration and testing of hydrologic models”. In Hydrologic Modeling o f Small Watersheds, eds. C.T. Hann, H.P. Johnson and D.L. Brakkensiek. ASAE, St. Joseph, Mich. p. 437-472.Lee, J. S. (1981) “Refined filtering o f image noise using local statistics”. Computer Graphics and Image Processing. Vol. 15. pp. 380-389. Oh, Y., Sarabandi, K. and Ulaby, F. T. (1992) “An empirical model and inversion technique for radar scattering from bare soil surfaces”. IEEE Transactions on Geoscience and Remote Sensing, Vol. 30, No. 2, pp. 370-381. Ortega, J. M. and Rheinboldt W. C. (1970) “Iterative solution of nonlinear equations in several variables”, New York: Academic Press Inc, 572 p. Pr6vot, L., Champion, I. and Guyot, G. (1993) “Estimating surface soil moisture and leaf area index of a wheat canopy using a duai-frequency (C and X bands) scatterometer”. Remote Sensing o f Environment, Vol. 46, pp. 331-339. Remond, A., Beaudoin, A. and King C. (1999) “SAR imagery to estimate roughness parameters when modelling runoff risk”. International Journal o f Remote Sensing, Vol. 20, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82 No. 13, pp. 2613-2625. Sahebi, M. R., Angles, J. and Bonn F. (2001) “A multi-angular Radarsat based C-band backscattering model for estimation of bare soil surface roughness”. Proceedings o f the 23rd Canadian Symposium on Remote Sensing, August 21-24, 2001, Ste-Foy (Quebec), Canada, pp. 865-871. Sahebi, M. R,, Angles, J. and Bonn F. (2002) “A comparison of multi-polarization and multi-angular approaches for estimating bare soil surface roughness from spacebome radar data”. Canadian Journal o f Remote Sensing, Vol. 28, No. 5, pp. 641-652. Shepard, N. (1998) “Extraction of beta nought and sigma nought from RADARSAT CDPF products”. Report No: AS97-5001, ALTRIXSystems, Ontario, Canada, 12 p. Smyth, J., Bonn, F., Hardy, S., R 6 mond, A. and Clement, P. (2000) “Potential retrieval of tillage direction as a runoff indicator using RADARSAT data”. Remote Sensing in Hydrology 2000, AIHS Red book 267, pp. 368-370. Ulaby, F. T., Batlivala, P. P. and Dobson, M. C. (1978) “Microwave dependence on surface Roughness, soil moisture and soil texture: Part I - Bare soil”. IEEE Transactions on Geoscience Electronics, Vol. 16, No. 4, pp. 286-295. Ulaby, F. T., Moore, R. K. and Fung A. K. (1982) “Microwave remote sensing active and passive; Vol. II: Radar remote sensing and surface scattering and emission theory”. Artech House, Ann Arbor Ltd., pp. 457-1064. Ulaby, F. T., Dubois, P. C. and van Zyl, J. (1996) “Radar mapping of surface soil moisture”. Journal o f Hydrology, Vol. 184, pp. 57-84. Westlake, J. R. (1968) “Handbook of numerical matrix inversion and solution of linear equations”, New York: John Wiley & Son Inc., 171 p. Young, R. A., Onstad, C. A., Bosch, D. D. and Anderson, W. P. (1987) “Agricultural nonpoint-source pollution model (AGNPS) I and II Model documentation”, St. Paul: Minn. Pollution Control Agency, Washington, D.C., USDA-NRS>, 77 p. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 TRANSITION BETWEEN CHAPTERS 4 AND 5 The previous chapter described a method for inverting the backscattering models. This inversion allows the estimation of both soil surface roughness and moisture content based on the multi-angular approach. Based on the description of the soil surface measurements and the limitations of backscattering models (explained in Chapter 2), three models, GOM, OM and MDM, were selected for this inversion. Two important results may be derived from this chapter as: i) The possibility of retrieving soil surface parameters simultaneously, based on the multiangular approach. In other words, a demonstration is made on how the multi-angular can be executed for soil surface parameter estimation. Furthermore, the proposed method is applied on radar images and the results are illustrated in the form of roughness and soil moisture maps. ii) Comparing different models quantitatively. This comparison not only showed the performance of each model but also gives a global idea about the accuracy of backscattering models. The second result confirms that backscattering models may not always be robust enough to give accurate results. Therefore, to guide this study towards more precise soil surface estimation, a new approach is needed. The neural network technique is presented as a possible solution for this problem. Neural network algorithms have been shown to be powerful techniques for remote sensing inversion problems. The neural network is a complicated technique to use and many parameters have to be defined clearly such as the number of hidden layers, the number of nodes, the training method, etc. These parameters can completely change the output results. Therefore, this technique can not be used blindly and its features must be chosen carefully. However, several studies have proven that the neural network is a strong tool and provides good accuracy if these features are chosen correctly. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The following chapter outlines the neural network technique for the retrieval of soil surface parameters from RADARSAT data and in-situ measurements. To eliminate the influence of backscattering models on the results, these models are replaced by a neural network structure. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 85 Chapter 5 NEURAL NETWORKS FOR THE INVERSION OF SOIL SURFACE PARAMETERS FROM SAR SATELLITE DATA Mahmod Reza SAHEBI, Ferdinand BONN, Goze B. BENIE Canadian Journal o f Civil Engineering, Submitted on October, 2002 This paper has been evaluated and modified, then resubmittedfor the first time on January 2003. A second revision asked fo r additional changes. This new version is now presented here. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 86 NEURAL NETWORKS FOR THE INVERSION OF SOIL SURFACE PARAMETERS FROM SAR SATELLITE DATA Abstract: This paper presents an application of neural networks to the extraction of bare soil surface parameters such as roughness and soil moisture content using SAR satellite data. It uses a fast learning algorithm for training a multilayer feedforward neural network using the Kalman filter technique. Two different databases (theoretical and empirical) were used for the learning stage. Each database was configured as single and multi-angular sets of input data (data acquired at two different incidence angles) which are compatible with data from one and two satellite images respectively. All the configurations are trained and then evaluated using RADARSAT-1 and simulated data. The empirical (measured) database with the multi-angular set o f input data configuration had the best accuracy with a mean error of 1.54 cm for root mean square (rms) height of the surface roughness and 2.45 for soil dielectric constant in the study area. Based on these results the proposed approach was applied on RADARSAT-1 images from the Chateauguay watershed area (Quebec, Canada) and the final results are presented in the form of roughness and humidity maps. Key words: Neural networks, Kalman filter, RADARSAT, SAR, soil roughness, soil moisture. Resume: Cet article prdsente une application des reseaux de neurones pour l’extraction des param&res de surface des sols nus tels que la rugosite et l’humiditd en utilisant les donnees issues de capteurs satellitaires RSO. Un algorithme rapide d’apprentissage a ete utilise pour entrainer les reseaux de neurones multicouches a l’aide de la technique du filtre Kalman. Pour l’etape d’apprentissage, deux bases de donnees differentes (donnees simulees et donndes empiriques) ont ete utilisees. Chaque base de donndes a dte configurde sous forme d’ensemble simple et d’ensemble multi-angulaire (donnees acquises a partir de deux angles d’incidence differents) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 87 servant comme donnees d’entr6 es, compatibles avec une et deux images respectivement. Toutes les configurations sont entrainees et ensuite evaluees avec les donnees RADARSAT-1 et les donnees simulees. Pour le site d’etude, la base de donnees empiriques (mesurdes) ayant la configuration basee sur l’ensemble multi-angulaire donne les resultats les plus precis avec une erreur de 1,54 cm pour la hauteur rms de la rugosite et de 2,54 pour la constante didlectrique du sol. Sur la base de ces rdsultats, l’approche proposee a 6t 6 appliquee sur les images RADARSAT-1 du bassin versant de la riviere Ch&teauguay (Quebec, Canada) et les resultats finaux sont presentes sous la forme de cartes de rugosit6 et d’humiditd. Mots cles: Rdseaux de neurones, filtre du Kalman, RADARSAT, RSO, rugositd du sol, humidite du sol. Introduction Microwave remote sensing is of primary interest for monitoring land surfaces because of its all weather capability, its signal penetration depth through natural media and its sensitivity to surface variables (such as water content) which are difficult to estimate using optical remote sensing sensors. With its weather-independent capability and sensitivity to the soil dielectric constant, Synthetic Aperture Radar (SAR) presents a unique advantage. As it provides its own energy, it can operate day and night. Several research projects have demonstrated the feasibility of deriving soil surface parameters from SAR. Most of them were oriented towards the estimation of soil moisture and the development of algorithms for mapping soil moisture distribution, by investigating the relation between the backscattering coefficient and soil parameters (Oh et al. 1992; Prevot et al. 1993; Fung 1994; Dubois et al. 1995; Ulaby et al. 1996). Estimation of soil surface moisture was usually obtained by using an empirical relationship to convert the measured backscatter coefficient (a0) into volumetric soil moisture (/nv). Results showed that the radar specifications for optimum soil moisture detection with minimum soil roughness influence were determined to be the C-band with HH polarization and an incidence angle around 10-12° (Benallegue et al. 1998; Boisvert etal. 1997). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 88 The SAR incidence angles of present and future satellite missions start around 20° (23° for ERS1/2, 38° for JERS-1, 15-55° for SIR-C and 20-50° for RADARSAT 1/2). This means that the incidence angles of operational SAR systems are quite different from the 10-12° optimum angle for moisture and that radar results are expected to depend on both soil water content and roughness. In addition, the influence of soil roughness on the radar signal cannot be neglected. Bindlish et al. (2000) and Sahebi et al. (2003b) investigated numerical methods to invert soil surface parameters using multi-configuration approaches and backscattering models. These results are interesting, however errors introduced by the backscattering models to present a real relationship between radar signal properties and target parameters decreased the accuracy of these results. Based on a theoretical study, Chen et al. (1995) used a dynamic learning neural network to invert the soil surface parameters. Their results were accurate and interesting but it is necessary to validate them based on measured satellite data. Therefore, the objective of this paper is to make better use of satellite SAR data for estimating soil surface parameters. We focus on the development of a consistent methodology for soil surface parameter inversion from RADARSAT-1 data using neural networks. Network Properties Network architecture The multilayer perception architecture is an outgrowth of the perception, which was first studied by Rosenblatt (1959). The term perception was coined by Rosenblatt to cover a variety of architectures designed by him while trying to model the human brain. Today, the use of the term perception generally refers to a single node. The term multilayer perception means more than one layer of nodes fully interconnected between layers. This paper will deal strictly with multilayer perceptions. Figure 1 shows the structure of a multilayer perception. Each of the disks in the diagram represents a node, which performs a weighted sum of the inputs and applies a nonlinearity function. The network shown has one hidden layer, that is, one layer that is neither input nor output. The network has M inputs, H nodes in the hidden layer, and N outputs. A short-hand Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 89 notation for describing this architecture is M-H-N. Superscripts are used to indicate the layer with which the variable is associated. The layers are numbered from the first layer of nodes performing the nonlinear function of the weighted sum of the inputs. In other words, the inputs to the network are not counted as a layer. The first hidden layer of the network is Layer 1. Outputs w. M2 Inputs Fig. 1. Multilayer perceptron architecture. A remaining problem with the application of multilayer perceptrons to various problems lies in architecture determination. Unfortunately, in the literature no practical way to determine the number of nodes required for a given problem is outlined. There has been some preliminary work in this area for determining the number of hidden nodes required (Huang and Huang Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 1991). Techniques that may allow automatic pruning of the size of a network (LeCun et a l 1990) have been developed. The combination of these techniques with some basic rules of thumb for sizing a network should provide effective methods for automatically architecting a multilayer perceptron. This paper will not deal with the automatic sizing issue. The architectures of the networks are determined using heuristic rules based on past experience in training these networks. In order to make such networks useful, a method for determining interconnection weights is required. Algorithms for setting weights are called learning rules or training algorithms and will be discussed in the next section. Training algorithm Backpropagation Many researchers have worked in the area of adaptive systems during the 1960's using perceptions. The single-node perception was a popular architecture for which the learning rule had been shown to converge when a solution existed (Nilsson 1965, pp. 82-87). However, in 1969, Minsky and Papert published their book that showed that a single node perception could not perform the simple Boolean function exclusive-OR (Minsky and Papert 1969). The book discouraged many researchers from further work in the area. From that time until the early 1980's, neural network research was not vigorously pursued. Since this period, it has been shown that a simple two-layer network can perform the exclusive-OR problem (Rumelhart et al. 1986). In fact, Rosenblatt had developed some algorithms that could train multilayer networks (Rosenblatt 1959) although convergence of these training procedures could not be proved. The lack of an effective training rule for multilayer networks has been cited by many researchers as the primary reason for the demise of neural network research in the 1970's. There are now many training algorithms available for multilayer perceptions. Some algorithms have been developed for multilayer networks where the nodes have hardlimiter nonlinearities. However, the most popular architecture uses sigmoidal nonlinearities on the nodes. The sigmoid is differentiable, which makes it possible to implement weight update rules based on the gradient of the error with respect to the weights in the network. The best known rule for Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91 training weights in a multilayer perceptron is the backpropagation training algorithm. This technique was popularized by Rumelhart etal. (1986), although it was first derived by Werbos (1982) and rederived by Parker (1982). It has been suggested by White (1989) that the stochastic approximation techniques developed by Robbins and Monro (1951) subsume backpropagation. Backpropagation is a gradient descent method for training weights in a multilayer perceptron. For a given problem, there is a set of training vectors X such as, for every vector x e X, there is an associated desired output vector d e D, where D is the set of desired outputs associated with the training vectors in X. Let the instantaneous error Ep be defined as: [1] Ep = U d p - z p)r (dp - z p) = l ' Z ( d k>p- z kp)2 Z Z *=1 where T signifies the transpose of a matrix, dk,p is the Ath component of the pth desired output vector dp, and z*,p is the Ath component of the actual output vector zp when the pth training exemplar Xp is input to the multilayer perceptron. Let the total error ETbe defined as follows: [2] S r -IX P=l where P is the cardinality of X. Note that E t is a function of both the training set and the weights in the network. The backpropagation learning rule is defined as follows: [3] 8E b Vw(0 = - 7 — —+ aVM t -1) dw where tj, the learning rate, is some small positive number; a, the momentum factor, is also a small positive number, and w represents any single weight in the network. In the above equation, Vw(t) is the change in the weight computed at time t. When the momentum term is used (a * 0 ), the training rule is called the momentum method; otherwise, it is the backpropagation method. The algorithm (eq. [3] with a = 0) is often called instantaneous backpropagation because it computes the gradient based on a single training vector. Another Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 variation is batch backpropagation, which computes the weight update using the gradient based on the total error E t when training results are presented. In this case, instantaneous backpropagation is the method used. Extended Kalman filter The extended Kalman filter approach to training a multilayer neural network considers weights in the network as the states of a system to be estimated. Since the weights do not have any dynamics this becomes a static estimation problem. The state and measurement equations for this system can be written as (Ruck et al 1992; Singhal and Wu 1989): [4] w(t +1) = w{t) [5] d (t) = h[w(t), x(t), t]+ v(0 where w is the weight vector comprising all the weights in the network, x is the input vector, d is the vector comprising the desired outputs of the network, v(t) is a white Gaussian noise sequence with zero mean and a covariance of d and t is the time index. h[...] is the nonlinear function that maps the states to outputs i.e., it describes the network. The standard form o f the extended Kalman filter equations for the system described by eq. [4] and [5] are (Ruck et al. 1992; Stengel 1986): + K \d , - z , ] [6 ] *, [7] K , = P „ tH ?[ H ,P ,_ ,H f+ el Y ' [8] P,=P,-AK,H,P,-i] where wh wt-i are the estimates of the w (state) vector at time t, t-1 respectively, Kt is the Kalman gain matrix, Ht is the gradient matrix resulting from linearization of the network with respect to w evaluated at wt-i, and Pt is the state covariance matrix. zt is the actual output at time t i.e., z, = h(wt-i, xt.i) and dt - zt is the so called innovation or residual term (Stengel 1986). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 93 This difference is what drives the correction to the weights in the network. The entries in the gradient matrix are: [9] H» = t , where i is the number of outputs and j is the number of weights in the network. Surface parameter Inversion Generally, estimation of land surface parameters, as targets, is obtained using a relationship to convert them into backscattering coefficients (ct°) from SAR data according to the sensor parameters (frequency, polarization and incidence angle). In traditional approaches, this relationship is expressed as backscattering models. Unfortunately, none of the backscatter models provide results in good agreement with experimental observations for all o f the polarization configurations and over a wide range of incident angles, even when confined to its presumed validity range (Henderson and Lewis 1998). This study proposes to define a relationship using neural networks in order to decrease the errors introduced by backscattering models. In this study, the soil surface parameters presented are soil surface roughness (expressed by rms height of the surface in cm) and soil dielectric properties (expressed by the dielectric constant). Dielectric properties of soil medium depend upon soil moisture, soil density, soil texture and fluid chemistry. However, these dependencies exhibit characteristic behavior as a function of frequency and temperature; there exists a potential to infer such bulk characteristics from radar backscatter (Henderson and Lewis 1998). Hallikainen et al. (1985) showed that the dielectric constant (e) of soil moisture is a function o f its volumetric soil moisture content (mv) and of the soil texture characteristics. As volumetric soil moisture content increases the dielectric constant increases. The authors also aimed to establish an accurate empirical model (as a polynomial expression) for different frequencies and different soil types. Equation 10, adapted from the original Hallikainen et al. (1985) paper, presents the polynomial expressions for C-band: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94 [10] s = (1.993 + 0.0025a + 0.015C7) + (38.086 - 0.1765a - 0.633C/) x » + (10.720 +1.2565a +1.522C/) x m 2v where 5a and Cl are the clay and sand components of soil (presented by weight) respectively. In this case, the dielectric constant can be presented as a moisture property of the soil surface. Data descriptions Study area The agricultural sites chosen for this study are the Chateauguay (73° 46' W, 45° 19' N) and the Pike River (72° 54' W, 45° 08' N) watersheds, located on the south shore of the St. Lawrence River, southeast of Montreal, Canada (Fig. 2). The study areas extend over a total area of about 9 by 9 km2 for the Chateauguay and 5 by 5 km2 for the Pike River watershed. They consist mainly of agricultural fields on a rather flat relief plateau with homogenous texture composed of about 36% clay, 42% silt and 22% sand. The ground surveys were made on rectangular agricultural parcels of about 0 .6 ha area. Ground data Field measurements were made on 12, 15, 18 and 23 November, 1999(the same dates as the satellite image acquisitions). Roughness and moisture measurements were carried out over 27 parcels of land in the Chateauguay area and 11 parcels of land in the Pike River watershed, the same day as image acquisitions. To calculate rms heights, six 2 m long (1.5 cm sampling interval) surface profiles (three parallel and three perpendicular to the soil furrows) were measured for each parcel using a home made needle profilometer. The profiles were photographed and then digitized. The method for extracting and modeling the roughness parameters has been described in detail by Beaulieu et al. (1995). The parcels were ploughed, displaying rough to very rough surfaces, with an average rms height of approximately 3.6 cm. The minimum measured rms height was 1.4 cm and the maximum was 5.3 cm. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95 STUDY AREA M M ii: Fig. 2. Location of study area. To measure surface moisture, a reflectometry instrument (TDR Thetaprobe soil moisture sensor) was used. Fifteen measurements were made in each parcel of land for soil depths of 05 cm. Using the equation presented in the Thetaprobe soil moisture User Manual (Delta-T Devices Ltd., 1996) the direct outputs (DC voltage in mV) were converted to soil water content (mv) and dielectric constant (e). The soil moisture contents range from 0.11 to 0.26 cm" 3.cm'3 with average of about 0.17 for both watersheds. Also, to evaluate the results obtained by this method, five soil samples for each parcel for soil depths of 0-5 cm were transferred to our laboratory. Wet and dry weights were used to determine gravimetric and volumetric soil water content. The volumetric soil water content (in m 3.m"3) obtained by these two methods were compared and a mean relative difference of 12 % (equivalent to 1 .8 % volumetric soil moisture) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 96 between the two methods was observed. Between the data acquisition periods, the weather was stable and surface moisture had not changed significantly because of the low evaporation and temperature at that time of the year (November). Average temperatures were 2.3 °C and there was no recorded rainfall between the two acquisition dates. Satellite data Four RADARSAT-1 images were acquired during the ground surveys as described in Table 1. All four images cover the Chateauguay watershed but only two images (SI and S7 ascending) also cover also the Pike River watershed. The parcels were identified on the images, which had been georeferenced Mid geometrically corrected using reference points identified by GPS. The RADARSAT digital number (DN) values were converted to a 0 using coefficients by Shepard (1998). In order to include spatial variability and to avoid problems related to the georeferencing of individual pixels of the parcels in the study area (homogeneous soil structure, bare soil, homogeneous ploughing), an average ct° (dB) was assigned to each parcel (approximately 20 to 30 pixels). The Chateauguay watershed data (SAR image and ground truth) were used for network training. The Pike River data were then used for the comparison and evaluation of the simulated results. Table 1. Acquisition parameters of the RADARSAT images Date RADARSAT Mode Incidence angle Pixel size (m) Orbit 12-11-1999 Standard-1 (SI) 20°-25° 12.5 descending 15-11-1999 Standard-3 (S3) 34°-40° 12.5 ascending 18-11-1999 Standard-7 (S7) 450-490 12.5 ascending 23 -11-1999 Standard-7 (S7) 450 . 4 9 ° 12.5 descending Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97 Network data descriptions Model descriptions To increase the performance of the neural network, it is vital to use a database spanning a wide range o f soil surface parameters, with different ranges of soil moisture content and soil surface roughness. Obtaining this kind of data based on measured ground data is not always possible, because, first, establishing the data involves several images, study areas with different conditions and field measurements that are sometimes expensive and that require a lot of time and energy for processing the data, and second, in spite of voluminous data acquisitions, often the principle of obtaining a wide range of soil surface parameters is not always guaranteed. Therefore, using backscattering models that simulate the theoretical radar signal according to various sensor configurations and soil surface parameters can represent a good solution. To evaluate the performance of this hypothesis, the results of theoretical and measured data (for the training phase) are compared in this study. To create a training neural network database based on theoretical (simulated) data, two surface scattering models are used. The IEM (Integral Equation Model) is used for smooth to rough surfaces (Fung and Chen 1992) and the GOM (Geometric Optics Model) is used for rough and very rough surfaces (Ulaby et al. 1982); therefore, the combination of these models can cover a very wide range of surface roughnesses. The description of these models is given at Appendix 1. Databases for network training and simulation To train the neural network, two different datasets are applied. > The first set is the simulated data. These data are produced using IEM and GOM since they cover a wide range of surface roughness as well as soil moisture for the C-HH band. Thus, a rather wide range of surface conditions is taken into account during the training process. > The second data set is the measured data. As explained, all the Chateauguay watershed data are used for this database. The backscattering coefficients are obtained from RADARSAT-1 images and the soil surface parameters are selected from ground data. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98 In the two above cases, after the training process, the Pike River data (RADARSAT-1 images and ground truth) were used for simulation. The data from SI and S7 ascending images are considered as input data and the surface parameter results from the network simulation (as output data) are compared with measured ground data for result validation. Input configurations The input configurations of the neural network are considered as adapted various measurement datasets. The input data are the backscattering coefficient (a0) and the incidence angle (0). The outputs of the network are rms height (s) and dielectric constant (e). The inputs to the network are determined according to the following schemes: 1) single set: in this scheme, the inputs to the network are incidence angle and backscatter coefficients with a total of two input nodes. 2) multi-angular set: based on simulation results, Sahebi et al. (2001 & 2002) indicated that a multi-angular approach is better adapted to the separation of moisture and roughness signals than multi-polarization and multi-frequency approaches. Therefore, the backscattering coefficients of two incidence angles are simultaneously fed into the network in this scheme. Therefore, there are four input nodes (<A, <A. &i and 62 ). Results and discussions To obtain the best neural network architecture parameters, many different networks with different node positions (number of nodes in the hidden layers) were tested, and then the optimal network configuration was chosen. Table 2 shows the best results obtained for different databases and different input configurations. In the first column in this Table, the number of optimal nodes for the first and second hidden layers is presented respectively. The second and third columns present the optimal training cycle and the training error respectively. The training error is the mean square error between the network outputs and the target outputs. The four last columns show the mean absolute error (M.A.E.) and the standard deviation of error (Std.E.) for estimating rms height and soil dielectric constant. The M.A.E. and Std.E. present the absolute average and standard deviation of the difference between the simulated Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99 values (from the neural network) and the ground measured values over the Pike River watershed parcels respectively. Table 2. Summary of inversion results using the neural network Hidden Single set Simulated data Single set measured data Multi-angular set Simulated data Multi-angular set measured data Figures 3 to 6 Training Training layer nodes cycle error 70-70 6000 70-70 Mean absolute Standard error deviation of error s (cm) s s (cm) e 0.52 3.4 3.6 1.0 3.0 6000 0.61 2.1 3.2 0.8 2.1 90-50 1800 HT6 1.9 3.1 0.8 1.3 90-50 2000 10* 1.2 2.4 0.2 0.6 show the retrieval of soil surface parameters versus their corresponding reference (ground measurements). From table 2, it can be seen that the single sets do not perform as well as the multi-angular sets and both errors for training and estimation are considerable. Comparing the standard deviation of errors for all sets shows that the errors obtained by single sets have a higher standard deviation than multi-angular sets that present a weaker performance for single sets. This fact can also be observed in Fig. 3 to 5, since both M.A. error and Std.E. have minimum values for both soil surface parameters (Table 2). This conclusion was also obtained when the traditional approaches were used to invert the same surface parameters from SAR data (Sahebi et al. 2003b). This is logical because, for each target, we had one equation explaining the relationship between ct° and soil surface parameters with at least two unknowns (roughness rms height and soil dielectric constant). In addition, in one case involving single sets, negative value was obtained for the dielectric constant, which is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 not acceptable. According to the results of the multi-angular sets, it can be concluded that this configuration with measured data gives the best results in this study. In addition, training with the simulated database performs faster than in the case of the measured database.. The threshold of training error set at 10"6 was reached after 1800 and 2 0 0 0 cycles for the simulated and measured databases respectively (Table 2). It can therefore be concluded that the data used for the training phase do not behave exactly as the data used for the network simulation (Fig. 4). In other words, the errors in the backscattering models have an influence on the network results. These errors are introduced by the inaccuracy of the backscattering models in presenting the relationship between the radar signals received and the bare soil surface parameters (Sahebi et a l, 2003b). The best performance was obtained when measured data, based on the multi-angular set, were used for training (Table 2 and Fig. 6 ). Based on the accuracy and the limitations of satellite SAR images, this result is acceptable and is suggested by this study. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 101 (a) 9 8 7 Measured values Simulated values 5.01 3.12 2.39 5.01 449 3.77 4.02 4.75 4.31 4.03 329 1.90 7.51 621 0.65 2.14 8.15 1.11 3.34 6.95 0.87 7.93 6 5 4 3 2 1 0 3 4 5 6 7 Measured rms height (cm) (b) 26 24 22 20 18 16 14 12 10 8 6 4 Measured values Simulated values 112 15.62 1723 14.06 1128 13.46 9.59 7.77 1345 14.75 13.98 16.14 2424 1622 11.78 9.75 12.81 520 -1.12 1420 9.11 15.63 2 0 -2 14 Measured dielectric constant Fig. 3. Relationship between measured and estimated soil surface parameters. Single set, simulated data, (a) rms height; (b) dielectric constant. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102 (a) 6 5 4 3 2 ♦ ♦ 1 M.A.E. = 2.1 Std.E. =0.8 Measured values Simulated values 5.01 3.12 2.39 5.01 449 3.77 4.62 4.75 4.51 4.03 3.29 3.70 0.78 6.03 3.15 2.10 1.07 5.50 2.23 5.72 1.12 148 Measured values Simulated values 11.3 15.62 17.23 14.06 1128 1346 9.59 7.77 1345 14.75 13.98 1323 1225 12.32 9.05 1425 12.55 1044 6.81 1140 7.32 9.32 o 2 3 4 5 Measured rms height (cm) (b) 20 18 16 14 12 10 8 6 M.A.E. = 3.2 Std.E. = 2.1 4 2 0 4 6 8 10 12 14 16 18 20 Measured dielectric constant Fig. 4. Relationship between measured and estimated soil surface parameters. Single set, measured data, (a) rms height; (b) dielectric constant. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 103 (a) 7 6 5 Measured Simulated values 4 5.01 5.12 2.39 5.01 449 3.77 4.62 4.75 4.51 44)3 3429 6.39 2.02 4.45 4.10 6.32 1.15 2.11 24)7 1.15 4.87 1.13 Maaaurad values Simulated values 11.3 15.62 17.23 14.06 1138 13.46 94)9 7.77 1345 14.75 13.98 14.90 1040 1930 11.78 9.35 935 5.50 9.85 1430 10.70 1730 3 2 M.A.E. = 1.9 Std.E. - 0.8 1 0 7 Measured rms height (cm) (b) 20 £ 10 M AE. a 3.1 Std.E. = 1.3 0 2 4 6 8 10 12 14 16 18 20 22 Measured dielectric constant Fig. 5. Relationship between measured and estimated soil surface parameters. Multi-angular set, simulated data, (a) rms height; (b) dielectric constant. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104 (a) 7 6 5 Measured values simulated 4 5.01 3.12 2.39 501 4.49 3.77 4.62 4.75 4.51 4.03 309 4.09 4.49 1.31 3.52 3.41 2.32 301 6.72 3.13 3.16 24)2 11.3 15.62 17.23 14.06 11.28 13.46 9.59 7.77 13.45 14.75 13.98 13.78 3 2 1 0 0 7 6 2 3 4 5 Measured rms height (cm) 1 (b) 20 18 16 14 12 a■D 10 8 6 55 4 12.83 15.28 11.34 9.03 10.51 7.20 10.47 10.58 12.21 13.16 2 0 0 2 4 6 8 10 12 14 16 18 20 Measured dielectric constant Fig. 6 . Relationship between measured and estimated soil surface parameters. Multi-angular set, measured data, (a) rms height; (b) dielectric constant. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105 In fact, as explained above, the training with measured data allows us to eliminate the inaccuracy in the traditional backscattering models. To give an idea of the advantages of soil surface retrieval by neural networks (measured data and multi-angular set), its results were compared with of soil moisture and surface roughness retrieval using traditional models. In this case, the inversion method using the Newton-Raphson method, based on the multi-angular approach (Sahebi et al. 2003b), was carried out. According to the Pike River profile containing rough to very rough surfaces, and the validity range of the backscattering models, three models could be validated for this comparison: the GOM (Geometric Optics Model; Ulaby et al. 1982), OM (Oh Model; Oh et al. 1992) and MDM (Modified Dubois Model; Angles 2001) (Index A). The GOM uses the correlation length in its formulation. Therefore, to invert this model, three images are required. Since the simulation phase of the neural network were obtained using two images covering all of the Pike River, therefore the OM and MDM were carried out for this comparison. Figure 7 shows the relationship between measured and simulated rms height and dielectric constant. The figure demonstrates that s and e obtained from the neural network are closer than the same parameters calculated from the traditional methods to the ideal 1:1 regression line. Table 3 presents the statistical results for comparing the measured and the simulated surface parameters for the Pike River data. In all the statistical indicators presented in the table, the advantage of neural network is evident. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 (a) 6 5 4 • Neural network A MDM OOM 3 2 <0 1 0 0 1 2 Measured rms height |cm) 5 6 (b) 20 16 *A 12 • Neural network AOM OMDM « 8 E 3 4 0 0 4 Measure! dielectric constant16 20 Fig. 7. Comparison between soil surface parameters simulated by the neural network and inversion of the traditional backscattering models (die Oh model and the modified Dubois model), (a) rms height; (b) dielectric constant. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 107 Table 3. Statistical results of comparison between measured and simulated soil surface parameters using the neural network, the Oh model (OH) and the modified Dubois model (MDM) Mean Absolute Model Error s (cm) 8 RMS Error Variance of Maximum Error Error s (cm) e s (cm) 8 s (cm) e Neural network 1.19 2.41 0.22 0.60 1.21 2.47 1.49 2.95 MDM 2.42 3.50 1.39 1.25 2.74 3.70 4.18 6.46 OM 2.70 4.39 0.96 1.35 2.85 4.58 3.75 7.19 This approach gives a good estimation of the soil surface parameters based on SAR satellite data with reduced estimation errors. However, there are still errors in this estimation that can be introduced by: errors in ground measurements; errors in representing all surface conditions; errors in the estimation of the backscatter coefficient for parcels of land and errors due to the influence of tillage direction, speckle and climate conditions on the radar signal (Sahebi et al., 2003b). Surface parameter mapping The proposed network is applied on two RADARSAT-1 images (S3 and S7 ascending) of the Chateauguay watershed. It should be noted that forests, rivers and urban areas are masked in the maps. This application was carried out using two different scales namely pixel scale and homogeneous zone scale. At pixel scale (Fig. 8 and 9), the network is applied directly on the two images pixel by pixel. The pixel scale maps are exact, however the pixel values vary and are also difficult to use, making it difficult to have a general idea of the surface parameter distribution in the watershed. To solve this problem, we used the homogeneous zones scale Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 108 (Angles 2001; Sahebi et al. 2003b). Each homogeneous zone on a radar image presents a minimal variance in the backscatter coefficient. Furthennore, within an homogeneous zone the physical characteristics of the soil surface are almost the same. This kind of representation allows us to have a general view of the distribution of the surface parameters (Fig. 10 and 11). These maps are useful for many domains i.e. hydrological models, agricultural applications or environmental management, etc. For example, the pixel scale maps of moisture and roughness can easily serve in hydrological models based on pixel units such as AGNPS (Young et al. 1987) or ANSWERS (Beasley et al. 1980). However, they still display a spatially noisy image. On the other hand, the homogeneous zone maps represent the soil surface distribution in a large area and can be used in agricultural or hydrological management at the subcatchment scale by hydrological response units that are less noisy spatially, but their accuracy at a given point may be lower. According to the structure of soils and following extensive experimentation over the study area, when farmers plough profoundly, die surface becomes rougher hence water is more infiltrated and evaporation increases thus, the surface becomes drier. This fact is clearly shown in Fig. 8 to 11, when rms height is important, soil moisture is low and when rms height is small, surface moisture is high. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 109 Fig. 8. rms height map at pixel scale. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 110 Fig. 9. Dielectric constant map at pixel scale. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ill 14 12 10 8 6 * % 4 2 A 0 1000m Fig. 10. rms height map at homogeneous zone scale. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 112 Fig. 11. Dielectric constant map at homogeneous zone scale. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 Conclusion In this study, the neural network was used as a mapping function where the domain is the set o f measured values (a0) and the range is the set of surface scattering parameters. The aim of this study is to apply the neural network to invert the surface parameters such as roughness rms heights and dielectric constant. The neural network learning process is designed to adjust the network weights to adapt them to the selected training data. The learning algorithm makes use o f the Kalman filtering technique to update the network weights, in the sense that the stochastic characteristics of input data sets are implicitly incorporated into the network. Two different databases for network training with two different configurations were tested and the multi-angular set configuration with measured data seems to show minimum errors in estimating soil surface parameters. However, a more complete database covering a larger range o f humidity and soil roughness for the training phase could decrease errors in the network simulation. From an application point of view, the final outputs of this work are soil surface parameter maps. These maps were illustrated following two different scales that can serve for many applications such as hydrological models, agricultural or environmental management, etc. Acknowledgments This study was partly supported by FCAR (Action Concertee RADARSAT), and NSERC grant 006042 and the Ministry of Science, Research and Technology of Iran provided a scholarship and financial support to M. Sahebi. The authors want to thank all the colleagues at CARTEL especially J. Angles, P. Gagnon, Q.H.J. Gwyn, P. Cliche and M. Lambert. References Angles, J. 2001. Separation de Phumidite et de la rugosite dans le signal retrodiffuse des images RSO selon une approche multi-angle. Mdmoire de Maitrise, Dep. de geographie et teledetection, University de Sherbrooke, QC, Canada, 82 pp. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 114 Beasley, D. B., Huggins, L. F., and Monke, E. J. 1980. ANSWERS: A model for watershed planning. Transactions of the ASAE, 23(4): 938-944. Beaulieu, N., Leclerc, G. and Moisan, Y. 1995. Determination de la rugosite de surface par des methodes accessibles. Canadian Journal of Remote Sensing, 21 (2), 198-203. Benallegue, M., Taconet, O., Vidal-Madjar, D. and Normand, A. 1998. The use of radar backscattering signals for measuring soil moisture and surface roughness. Remote Sensing of Environment, 53: 61-68. Bindlish, R. and Barros, A. P. 2000. Multifrequency soil moisture inversion from SAR measurements with the use of IEM. Remote Sensing of Environment, 71: 67-88. Boisvert, J. B., Gwyn, Q. H. J., Chanzy, A., Major, D. J., Brisco, B. and Brown, R. J. 1997. Effect of surface soil moisture gradients on modelling radar backscattering from bare fields. International Journal of Remote Sensing, 18(1): 153-170. Chen, K. S., Kao, W. and Tzeng, Y. 1995. Retrieval of surface parameters using dynamic learning neural networks. International Journal of Remote Sensing, 16(5): 801-809. Delta-T Devices Ltd. 1996. Thetaprobe Soil Moisture Sensor. User manual, Mll-UM-2, Delta Devices Ltd., Cambridge, U.K. Dubois, P. C., van Zyl, J., and Engman, T. 1995. Measuring soil moisture with imaging radars. IEEE Transactions on Geoscience and Remote Sensing, 33(4): 915-926. Fung, A. K. and Chen, K. S. 1992. Dependence of the surface backscattering coefficients on roughness, frequency and polarization states. International Journal of Remote Sensing, 13(9): 1663-1680. Fung, A. K. 1994. Microwave scattering and emission models and their applications. Artech House Inc., Boston, Mass. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 115 Henderson, F. M. and Lewis, A. J. 1998. Principles and applications of imaging radar. Chapter 8 . 3rd ed. John Wiley & Son Inc., New York. Huang, S. C. and Huang, Y. F. 1991. Bounds on the number of hidden neurons in multilayer perceptrons. IEEE Transactions on Neural Networks, 2: 47-55. Le Cun, Y., Denker, J. S. and Solla, S. A. 1990. Optimal brain damage, in Advances in Neural Information. Processing systems 2 (D. S. Touretzky, Ed.). San Mateo, CA; Morgan Kaufinann, pp. 598-605. Minsky, M. L. and Papert, S. A. 1969. Perceptrons. MIT Press, Cambridge, MA. Nilsson, N. J. 1965. Learning Machines. McGraw-Hill, New York. Oh, Y., Sarabandi, K. and Ulaby, F. T. 1992. An empirical model and inversion technique for radar scattering from bare soil surfaces. IEEE Transactions on Geoscience and Remote Sensing, 30 (2): 370-381. Parker, D. B. 1982. Leaming-logic. Invention Rep. 581-64. Stanford University, Stanford, CA, Oct. 1982. Pr6vot, L., Champion, I. and Guyot, G. 1993. Estimating surface soil moisture and leaf area index of a wheat canopy using a dual-frequency (C and X bands) scatterometer. Remote Sensing of Environment, 46: 331-339. Robbins H. and Monro, S. 1951. A stochastic approximation method. Annals of Mathematics and Statistics., 22:400-407. Rosenblatt, A. 1959. Principles of neurodynamics. Spartan Inc., New York. Ruck, D. W., Rogers, S. K., Kabrisky, M., Maybeck, P. S. and Mills, J. P. 1992. Comparative analysis of backpropagation and the extended Kalman filter for training multilayer perceptrons. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(6): 691. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 686- 116 Rumelhart, D. E., McClelland, J. L. and the PDP Research Group. 1986. Parallel distributed processing, vol. 1: Foundations, MIT Press, Cambridge, MA. Sahebi, M. R., Angles, J. and Bonn, F. 2001. A multi-angular RADARSAT based C-band backscattering model for estimation of bare soil surface roughness. Proceedings of the 23rd Canadian Symposium on Remote Sensing, August 21-24,2001, Ste-Foy (Quebec), Canada, pp. 865-871. Sahebi, M. R., Angles, J. and Bonn, F. 2002. A comparison of multi-polarization and multiangular approaches for estimating bare soil surface roughness from spacebome radar data. Canadian Journal of Remote Sensing, 28(5): 641-652. Sahebi, M. R., Bonn, F. and Gwyn, Q. H. J. 2003a. Estimation of bare soil surface moisture from RADARSAT using simple empirical models. International Journal of Remote Sensing, 24(12): 2575-2582. Sahebi, M. R., Angles, J. and Bonn, F. 2003b. An inversion method based on multi-angular approaches for estimating bare soil surface parameters from RADARSAT-1 data. Journal of Hydrology (under revised). Shepard, N. 1998. Extraction of beta nought and sigma nought from RADARSAT CDPF Products. Report No:AS97-5001, ALTRIX Systems, Ottawa, Ont. Singhal, S. and Wu, L. 1989. Training multilayer perceptrons with the extended Kalman algorithm, in Advances in Neural Information Processing Systems 1 (D. S. Touretzky, ed.). San Mateo, CA: Morgan Kaufinann, pp. 133-140. Stengel, R. F. 1986. Stochastic optimal control. John Wiley, New York. Ulaby, F. T., Moore, R. K. and Fung, A. K. 1982. Microwave remote sensing active and passive, Vol. II : Radar Remote Sensing and Surface Scattering and Emission Theory, Artech House, Ann Arbor, Mich. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 117 Ulaby, F. T., Dubois, P. C., and van Zyl, J. 1996. Radar mapping of surface soil moisture. Journal of Hydrology, 184, 57-84. Werbos, P. J. 1974. Beyond regression: new tools for prediction and analysis in the behavioral sciences. Ph,D. thesis, Harvard University, Cambridge, MA. White, H. 1989. Learning in artificial neural networks: A statistical perspective. Neural Computation, 1: 425-464. Young, R. A., Onstad, C. A., Bosch, D. D. and Anderson, W. P. 1985. Agricultural nonpointsource pollution model (AGNPS) I and II Model documentation. St. Paul: Minn. Pollution Control Agency, Washington, DC.: USDA-ARS. Appendix 1 Backscattering models description Integral Equation Model (IEM) The IEM (Fung and Chen 1992) is a backscattering model applicable to a dielectric rough surface. The model is based on an approximate solution of a pair of integral equations for typical agricultural soils. It can be applied to complex anisotropic surfaces and its continuous applicability ranges from smooth to rough surfaces. The validity range of IEM given by Fung (1994) is defined such that: ks < 3, Cos2^ - ^ ^ ^ . e x p ( - A/2 x 0A6k£ (l- s i n 6 ) ) « 1 and k i.k s < { i^ £ r \ where k is the wave number (k=2m'JI where X is the wavelength), er is dielectric constant, s is the root mean square (rms) height, £ is the correlation length, which is a measure of the horizontal roughness, 6 is the incidence angle and // is a constant (equal to 1.6 and 1.2 for Gaussian and exponential autocorrelation functions respectively). According to this model the backscattering coefficient for any transmit-receive polarization (pp) can be calculated as follows: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 118 k 2 l s |2 - aj 2 2 2 (4k 2 s 2 cos2 0 )n n r n ( r % 1 . Q(.\ \fpp\ exp(-4fts cos 0 ) 2 ,- --------------- — W (2ksm0,O) n\ n= 1 P/» [Al] + y Re(f*pFpp) exp(-3fcV cos2 0 ) ^ ^ „=i +oo / / _ 2 + |Fp/) |exp(- 2 £ 2s 2 cos2 0 ) g (A: 5 °°S ^ »•' .IF”(2A:sin0,0) 2 - A p 2 /j\fl .IF” (2A:sin 0,0) 5 where: CO S0 Fhh= 2 sin 2 0 CO S0 COS0 4R m, - M 0 +R» )2 8r y s. - _ . sin 2 0 V cos2 0 F = 2 ------- f i - e•( 1 - R J + COS0 -sin 2 0 / Rpp is the Fresnel coefficient at horizontal and is given by: D J\hh cos0-V ^ -sin20 D ""J---- 9 XVyy cos0+v*~sin 0 £t cos “ 0 —- ^ £ t - sin2 0 I ■ I..... £r cos 0 + ^ — - sin2 0 where Sr is the real part of the dielectric constant. £n2 exp (-M s in 0 ) 2 For a Gaussian autocorrelation function: JFn(2A:sin0,O) = Geometric Optics Model (GOM) The Geometric Optics Model (Ulaby e* a/. 1982) also known as the KirchhofF method under the stationary phase approximation is intended to characterize scattering by rough surfaces Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 119 with, 0.06kl£ 2>ks, k£> 6 and (2 fo.cos 0) 2> 10. The model predicts that <^hh(0) =cPvv( 0), at all incidence angles. The expression for the co-polarized backscattering coefficient is given by: R [A2] < > (*) = PP (0) xexp (2 m 2 cos &) tan 2 0 2m where Rpp(0 ) is the surface reflectivity from normal incidence and m is the rms slope given by: Rhh.wCO) 1 —-J^r l + yjs' Oh Model (OM) Because of the inadequate performance of theoretical models for predicting the backscatter response of random surfaces, Oh et al. (1992) developed an empirical model based on experimental data acquired in L- C- and X-bands (1.5, 4.75 and 9.5 GHz respectively). This model was designed for surfaces with various moisture conditions and roughnesses, from slightly smooth to very rough and does not incorporate correlation length. The valid surface conditions cover the following ranges: 0.1 < ks < 6.0, 2.6 < k t < 19.7 and 9% < m v < 31%, where mv is the volumetric soil moisture. The backscattering coefficients for this model can be written: [A3] < r l = g j p cos3 0[Rn (0) + Rhh(0)] [A4] 0 -w = where -Jp - I - o g cos3 0 J i U ? ) + * * (? )] f 2 0 ^ mRlv(0’0^ r / VI — x ex p (-ks) and g = 0.7|l-exp(-0.65(&s)18)J \7 Z ) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 Modified Dubois Model (MDM) The model developed by Dubois et al. (1995) was initially developed in order to separate moisture and roughness using a bipolarization approach. This model is limited to ks < 2.5, 6 > 30° and moisture contents mv < 35%. This model was tested over study area by the researchers of the University de Sherbrooke (Angles 2001) and the results presented an important difference between simulated and desired values. As the Dubois Model is an empirical model based on the theoretical models and scatterometer signal responses. The method that Dubois et al. (1995) had been followed for adapting the Dubois model into measured data over the Quebec agricultural area. The data content the RADARSAT-1 and measured ground data (soil surface roughness, soil moisture and soil texture) were used. In the case of the RADARSAT-1 sensor configuration (band-C, HH-polarized and incidence angles programmable between 20° and 50°) an attempt was made to modify this model with 1 cm< 5 <6 cm and 14%< mv <32% (Angles 2001). This modification presented as a new model named Modified Dubois Model (MDM). The backscattering coefficient for this model is described by Equation 3 that can be applied to all bare agricultural surfaces of Quebec. [A5] <r“ =10-3i7x ^ ? ^ x l 0 0" 2 “ " x (f e .s in « )“ sin 5 0 x /’ where k is the wave number (k=2 jtfX) and X is the wavelength. When used with RADARSAT data from two different incidence angle of the same target with a short time interval, this approach generates a two equation system with two unknowns, which can be resolved to obtain s and e. However, this model may be tested in other regions with different conditions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 121 TRANSITION BETWEEN CHAPTERS 5 AND 6 For estimating soil moisture content and soil surface roughness in a multi-angular approach environment, Chapters 4 and 5 present two inversion methods based on traditional models and neural network respectively. According to the nature of radar satellite images (resolution, precision, speckle, etc.), both methods give acceptable results. In the previous chapter, a multi-layer perceptron neural network was developed with two hidden layers and trained by the Kalman filter method. This algorithm showed a very good relationship between the soil surface parameters and the backscattering coefficients. Furthermore, this chapter showed the advantage of the multi-angular set with ground measured data. To improve the results, a new image acquisition with terrain campaigns was considered. Unfortunately, both data set acquisitions in the fall of 2001 and spring of 2002 were unusable. This failure was due to changing soil surface conditions between image acquisitions. In other words, there were precipitations between data acquisitions; hence, soil moisture contents changed between the two image pairs which is contrary to the basic hypothesis of the multi technique approaches including the multi-angular one. This phenomenon can be considered as a practical limitation for using multi-technique approaches. This limitation is less important for regions with less precipitation (like arid or semi-arid regions). Chapter 6 outlines a new solution for this problem. This solution uses only one image and presumes the optimal answers based on optimisation theories. These optimal answers can be as exact as the soil surface parameters obtained by other methods. In this case, a genetic algorithm, considered as one of the most powerful optimization methods, was used. The genetic algorithm is a numerical iterative optimization method, which is capable of solving either simple or complex problems. Due to its process (encoded into a gene, which is a binary representation), the genetic algorithm tries several possible solutions to find the best fit answer. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 122 What the help of an international collaboration which gave us access to a better and more universal database, two new concepts are discussed in the following chapter. First, a new backscattering model (calibrated Integral Equation Model) is used for retrieving soil surface parameters. The detail of this model is found in Appendix F. Second, the data used in this chapter were extended. The set of data contains 6 databases obtained from different sites in Canada and France. The images were acquired by the RADARSAT and ERS radar satellites with different configurations. This data set gives a more reliable validation, with a better generalization potential. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 123 Chapter 6 BARE SOIL MOISTURE CONTENT AND SURFACE ROUGHNESS ESTIMATION WITH SAR DATA USING GENETIC ALGORITHMS Mahmod R. SAHEBI, Ferdinand BONN, Nicolas BAGHDADI, Mehrez ZRIBI, Joel ANGLES and Christine KING Photogrammetric Engineering & Remote Sensing, Subm itted on August, 2003 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 124 BARE SOIL MOISTURE CONTENT AND SURFACE ROUGHNESS ESTIMATION WITH SAR DATA USING GENETIC ALGORITHMS Abstract The retrieval of soil surface parameters such as roughness and soil moisture content using satellite radar data is of considerable importance in many areas, including agriculture, hydrology and environment. The inversion technique for retrieving soil roughness and soil moisture from radar observation has been investigated in several research works. Genetic algorithms (GAs), as a novel optimization technique, are capable of providing a very good estimation of multi-parameters function roots. In this study, a GA is proposed to estimate the unknown parameters (rms height roughness and dielectric constant) of the backscattering models. The objective of this study is to develop a GA approach for the retrieval of soil surface parameters from SAR image data over bare soils. The calibrated integral equation model (IEM) was employed for computation of the cost function. Good agreement was observed between approach outputs and ground measurements. The fact that the proposed inversion algorithm can be executed using only one radar image is the most important advantage. Key words: Genetic algorithm, Integral equation model (IEM), SAR, Soil surface roughness, Soil moisture, Inversion. Introduction There have been significant research efforts based on remote sensing techniques to estimate bare soil surface parameters (roughness and soil moisture content) in the past two decades. Recent advances in active microwave remote sensing have proved the relationship between the radar backscattering coefficient (a0) and the soil surface parameters (Oh et al., 1992; Fung, 1994; Dubois et al., 1995; Ulaby et al., 1996; Boisvert et al., 1997). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 125 In order to extract reliable information concerning soil surface roughness from radar imagery, it is necessary to understand the behaviour of the radar signal over a bare soil that is mathematically expressed by backscattering models. Many theoretical and empirical forward backscattering models for the study of soil surfaces have been reported in the literature (Ulaby et al., 1982; Fung and Chen, 1992; Oh et al., 1992; Dubois et al, 1995). These models simulate the microwave radar backscattering coefficient using various physical and geometrical parameters such as rms soil roughness and soil moisture. Most of the models, however, have an intrinsic limitation. Moreover, none of the existing models provide consistently good agreement with the measured data (Rakotoarivony et al., 1996; Zribi et al, 1997; Baghdadi et al., 2002a and Sahebi et al., 2003a). The deviation between simulations and measurements can reach several decibels, which renders the inversion results inaccurate. In this study, the IEM (Fung and Chen 1992), which is one of the most widely used models, is utilized to express the relationship between the backscattering coefficient and soil surface parameters. The success of the IEM can be partly attributed to its applicability to a wide range of roughness scales. Recently, Baghdadi et al. (2003) proposed a semi-empirical calibration of the IEM for enhancing the agreement between model simulation and observed data. This calibration presents a new function for correlation length in order to correct the imperfection of the IEM behavior. The reliability of this calibration was validated using databases acquired over different sites and good overall agreement was observed between measured and calculated data. Accordingly, this calibration is applied in this study. Backscattering models express the value of a° in relation to the radar sensor parameters (frequency, polarization and incidence angle) and target parameters (soil surface roughness, soil moisture content and if present, vegetation cover). From the point of view of applications, radar sensor parameters are known and ct° can be extracted from radar image however, for a bare soil, soil surface roughness and soil moisture have to be estimated. The inversion algorithm, then, is required for this estimation. On the other hand, estimation of surface soil parameters is obtained by using a theoretical or empirical relationship to convert the measured backscatter coefficient (a0) into soil surface roughness and soil moisture. However, this inversion is very difficult to implement. This is largely due to the mathematical complexity of the inverse problem. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 126 Recently, different algorithms such as numerical methods based on multi-configuration approaches (Bindlish et a l, 2000; Sahebi et a l, 2002 & 2003a) or neural networks (Baghdadi et al., 2002b; Sahebi et a l, 2003b) have been investigated for inverting soil surface parameters. These results are interesting, in spite of the fact that in all cases, two or more images are requested. This study tries to present an approach that can invert soil surface parameters using only one radar image. This paper presents a genetic algorithm developed to estimate the optimal parameters of the soil surface from the radar satellite backscattering coefficient. To reach this objective, the IEM backscattering model was inversed. The simulated surface parameters compare well with the ground data measurements and the results are discussed. Genetic algorithms Over the last decade, genetic algorithms (GAs) have been extensively used as search and optimization tools in various problem domains, including the sciences, commerce and engineering. The primary reasons for their success are their broad applicability, ease o f use and global perspective. The concept of a genetic algorithm was first conceived by Holland (1975) based on the concept of the optimal selection of natural evolutionary processes. The GAs are search and optimization procedures that are motivated by the principles of natural genetics and used artificially to construct search algorithms that are robust and require minimal problem information. Not only do GAs provide an alternative method for solving problems but also, they consistently outperform other traditional methods in most o f the problem links. Many of the real world problems involve finding optimal parameters, which prove difficult for traditional methods but ideal for GAs (Deb, 2001). GAs are initialised with a population of guesses (multiple points), rather than by beginning with a single point within the search space, which is the set of solutions within which the desired solution resides. These are usually random and will be spread throughout the search space. A typical algorithm then uses three operators, selection, crossover and mutation, which are chosen in part by analogy with the natural world, to direct the population (over a series of time steps or generations) towards convergence at the global optimum (Coley, 1999). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 127 Typically, these initial guesses are held as binary encodings (or strings) of the true variables, although an increasing number of GAs use "real-valued" (i.e. base-10) encodings, or encodings that have been chosen to mimic in some manner the natural data structure o f the problem. This initial population is then processed by the three main operators (Goldberg, 1998). Selection, corresponding to the survival of the fittest, attempts to apply pressure upon the population in a way similar to that of natural selection found in biological systems. This means giving preference to better individuals, allowing them to pass on their genes to the next generation. Poorer fitting individuals are weeded out and better fitting individuals have a greater than average chance of promoting the information they contain within the next generation of population. Crossover allows solutions to exchange information in a way similar to that used by a natural organism undergoing sexual reproduction. This operator randomly chooses pairs of individuals promoted by the selection operator and exchanges the subsequences before and after that locus (point) between two individual binary strings to create two new offsprings (individuals). Mutation is used to randomly change (flip) with a small probability some of the single bits within individual strings (chromosomes). Mutation is typically used very sparsely. After selection, crossover and mutation have been applied to the initial population, a new population will have been formed and the generational counter is increased by one. This process of selection, crossover and mutation is continued until a fixed number of generations have elapsed or some form of convergence criterion has been met. On a first encounter, it is far from obvious that this process is ever likely to discover the global optimum, let alone form the basis of a general and highly effective search algorithm. However, the application of the technique to numerous problems across a wide diversity of fields has shown that it does exactly this. The ultimate proof of the utility of the approach possibly lies with the demonstrated success of life on Earth (Deb, 2001). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 128 After selection of the GA parameters (population size, crossover probability, mutation probability,...), the algorithm can be summarized as follows: 1) Randomly initialize population (t). 2) Determine fitness of population (t). 3) Repeat: i. select parents from population (t) ii.perform crossover on parents creating population (t+ 1) iii. iv. perform mutation on population (t+ 1) determine fitness of population (t+ 1) 4) Until best individual is good enough. Model descriptions The model used here is the IEM (Fung and Chen, 1992). The IEM is a backscattering model applicable to a dielectric rough surface. This model is based on an approximate solution o f a pair of integral equations for typical agricultural soils. It can be applied to complex surfaces and its continuous applicability ranges from smooth to rough surfaces. The validity range of IEM given by Fung (1994) is defined such that: ks < 3, cos26>-^L=r.exp(-J2 x o.46ke (1-sinfl))« l J0A6M ' and M.ks<uJ&\ where k is the wave number 1 (k=2 n/A where X is the wavelength), s is the root mean square (rms) height, £ is the correlation length, 0 is the incidence angle and p is a constant. According to this model the backscattering coefficient for any transmit-receive polarization (pp) can be calculated as follows: <*°rr = y | / „ | 2 raj>(-4*V + cos2 + cos1 ff) ' w , R e ( /; F „ ) exp( - 3 * V cos2 Z n=l \FppIexp(-2A:2s 2 cos2 S °°S ^ W. W n(2k sin^,0) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (J) 129 where * denotes complex conjugate, Re means real part, and: ffu, = ------ 2 Rhh f =■ — anda f,„, cos# cos# , sin 2 # Fhh = 2 4 R ,* cos# F - O Si n20 ' (i+ R j2 et cos2 # ^ • £r - s in 2# 1- ( i- R y v ) 2 + V (1 + R yv) 2 - er W* (n, v) = i - Jf p* ( f , O e-**"* >< W Rpp is the Fresnel coefficient at horizontal or vertical polarization, and is given by: D XUtA—- ry c o s # - - s i n 2# r—— 5 £r c o s # - ^ - s i n 2# I----------------- 9--- W ~~ £r cos 9 + ■ yj£ I - sin # cos#+v^-sin # where ^ is the real part of the dielectric constant. The statistical variation of a random surface is characterized by the autocorrelation function of surface p(£) where % is the displacement of height variations of the surface. Several mathematical forms have been used in the literature to describe p(£) of natural surfaces, including the Gaussian form P(4) = exp (- ¥ (2) the exponential form: P it) = exp (3) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 130 and the fractal form (Zriby et a l, 1998): /?(£) = exp - p (4) with t = -1.67D + 3.67 where D is the fractal dimension. Many research works have revealed a poor agreement between IEM simulations and measured data (Rakotoarivony et a l, 1996; Zribi et al, 1997; Baghdadi et al., 2002a). Deviations of as much as several decibels have been found, which renders the inversion results inaccurate. Baghdadi et al (2002c) proposed a semi-empirical calibration of the IEM to improve its performance, with consideration of several radar configurations based on different databases acquired by different groups on many study areas. The discrepancy between the measured and simulated backscattering coefficients is assumed to be directly related to the poor accuracy of the correlation length measurements, considering that the other IEM input parameters (rms height roughness, soil moisture and sensor parameters) are relatively accurate. Baghdadi et a l (2 0 0 2 c) thus proposed an empirical calibration parameter 0 opt2 ), which integrates the true correlation length and the imperfections of the IEM (the shape for the correlation function is considered as exponential). This parameter depends on rms surface height and radar sensor configuration (frequency, polarization and incidence angle). The results reveal two trends for the behaviour of S opt2 - the first is characterized by lower rms heights and an approximately constant £opt2 , and the second by higher rms heights and a £ o p t2 that increases with rms height according to an exponential relationship (Baghdadi et al, 2003). According to this approach, the correlation length is dependent on rms height. The expressions were adjusted empirically for $ opt2 as a function of rms height which was modeled by an exponential function (for C-band) given by: ZoPa(.s ’ 0 >PP) = a x s f > (5) The values of a and f3 are presented in Table 1. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 131 Table 1. The values of a and p for calculation £ o p t2 based on an exponential correlation Radar configuration a P 0 pp 21 hh 65.46 1.2723 23 w 24.78 1.5845 24-26 hh 26.61 1.5660 35-40 hh 17.50 1.4500 45-47 hh 11.63 1.5836 Study areas and data descriptions Four measurement campaigns were carried out in France (Orgeval 94, Alpilles 97, and Pays de Caux 98-99) and two in Canada (Pike River 99 and Chateauguay 99, in the Quebec Province). The study sites consisted of agricultural fields on low-relief plateaus. Fieldworks were made at the same day as satellite radar overpasses and provided descriptions of the soils and their dielectric and structural properties (roughness and moisture). Data descriptions are presented in Table 2. Study areas Data 1 & 2: The first study area was in the Pays de Caux, in Normandy, France (long. 0°50'W, lat. 49°47N). It was selected as a study area for the European FLOODGEN project (FLOOD risk reduction by spacebome recognition of indicators of excess runoff GENerating areas) (King, 2001). Soil composition at this site is about 67% silt, 13% clay, and 17% sand. Fieldwork was carried out in 1994, 1998, and 1999 to describe the roughness and moisture parameters in a few reference plots. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 132 Data 3: The second study area was in the Rh6 ne valley in southern France (the Alpilles; long. 4°45'E, lat. 43°47'N). It was chosen as part of the European RESEDA project (Baret, 2000). Soil composition is 54% silt, 40% clay, and 6 % sand. Fieldwork was carried out in 1997. Data 4\ The third study area was the Orgeval site, 70 km east of Paris (long. 3°07'E, lat. 48°51rN). Soil composition is about 78% silt, 17% clay, and 5% sand. Fieldwork was carried out to measure soil moisture and roughness (Zribi et al., 1997). Data 5 & 6 : Two study areas in Canada were also used, the first in the CMteauguay River basin south of Montreal (long. 73°46'W, lat. 45°19'N) and the second in the 650 km2 basin of the Pike River (long. 72°54'W, lat. 45°08rN), a tributary of Lake Champlain on the borders of Quebec, Vermont, and New York State. The soil texture is composed o f about 36% clay, 42% silt and 22% sand. The ground surveys were made on rectangular agricultural plots of about 0.6 ha that were considered as homogeneous spatial units (Angles, 2001; Sahebi et al., 2002). Satellite data Satellite data were obtained from the various study areas using ERS and RADARSAT (Cband) sensors. Image characteristics are described in Table 2. The radar data are available in hh and w polarizations, with incidence angles between 23° and 47°. The radar images underwent various types of pre-processing in order to retrieve calibrated and georeferenced radiometric information. The average backscattering coefficient was calculated for each reference plot. Ground data During the measurement campaigns, reference plots were visited and physical parameters (moisture and surface roughness) were measured on the same days as radar data were acquired. The main characteristics of the data sets used are shown in Table 2. Roughness measurements were made using laser and needle profilometers (1 and 2 m long and with 0.5, 1, and 2 cm sampling intervals). Four to twelve roughness profiles were established for each training field. From these measurements, the standard deviation of surface height Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 133 (rms) was calculated for presenting soil surface roughness. The surface was assumed to be isotropic and the autocorrelation function was fitted to an exponential function. The rms values depend on the agricultural practices used and the aggressive effects of rain on bare soil surfaces; lower values correspond mainly to sowed fields and higher values to recently ploughed fields. The volumetric water content at field scale was assumed to be equal to the mean value estimated from several samples (4 to 15 per plot) collected from the top 5 cm of soil using the gravimetric method and a TDR (Time Domain Reflectometry) probe (Delta Devices Ltd., 1996). The standard deviation of the measured volumetric water content is about 5%. The empirical model developed by Hallikainen et al. (1985) was used to link the volumetric water content to the corresponding complex dielectric constant. This model uses the sand and clay composition of the soil. Table 2. Data description Data Description Field data Radar configuration Radar data (roughness, moisture) Data 1 Data 2 Data 3 Data 4 Data 5 Data Pays de Caux 98 BRGM «F98» Pays de Caux 99 BRGM «F99» Alpilles 96-97 BRGM «RES» 45 plots 18 plots 16 plots Orgeval 95 CETP «095» CARTEL «CHA» CARTEL «BRO» ERS-2, C-w-230 RADARSAT-1 C-hh-39°, 47° ERS-2 C-w-23 ° RADARSAT-1 C-hh-23°, 39° ERS-2 C-w-23 ° RADARSAT-1 C-hh-23°, 40° C-w-230 plots ERS-2 21 plots RADARSAT-1 plots RADARSAT-1 Pike River 99 6 incidence) 11 Chateauguay 99 8 (frequency, polarization, C-hh-25°, 35°, 47.5°, 47.7° C-hh-21°, 45° ................... ................... Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 134 Genetic algorithms to retrieve soil surface parameters Using optimal correlation length in the IEM, not only increases the accuracy of the model, but also decreases the number of unknown parameters to estimate. As explained in Equation 5, -8 opt2 is expressed by rms height surface roughness, therefore the IEM depends on only two target parameters (dielectric constant, e, and rms height roughness, s), which have to be estimated. Then these two parameters are coded into the genes to be optimized. A set of [s, s] composes a population. A set of [0 % , 0, A,], obtained from radar images for each parcel of land, is introduced into the IEM as input data. From trial solutions of chromosomes (here, two sets of chromosomes compose a population) in the GA, the simulated backscattering coefficients were calculated using the IEM then the cost function was constructed as: C (d S )= |Cr,"-<r2| (6 ) where a°s presents the simulated backscattering coefficients and a°m presents the measured backscattering coefficients obtained from the radar images. Fitness that can be expressed by the best estimation of the unknown parameters measured by the cost function C. The best fitness is reached when the value of the cost function is the lowest. A common selection approach assigns a probability of selection, Pj, to each individual, j , based on its fitness value. A series of N random numbers (in this study N -30 ) is generated and compared against the cumulative probability (Equation 7) of the population: CP, = £ pj (7) j=l The appropriate individual, i, is selected and copied into the new population if: Ci.1 < U ( 0 ,l) < C i. The cost function of the new population is calculated again. Then j least-fitting chromosomes are replaced by j new chromosomes. The operators are used to create new solutions based on existing solutions in the population. As explained, there are two basic types of operations: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 135 i) the pair of individuals selected undergoes crossover with probability p c. Crossover generates a random number Rc from a uniform distribution in the range 0-1 and creates two new individuals (x' andy1) according to equation 8 ; j x „ if t o S p . [y i, otherwise y ! = { y‘!’ ^ Ixj, otherwise (8 b) ii) mutation that flips each bit in every individual in the population with mutation probability p m (in this study equal to 0.035) according to equation 9. r .- x „ if u (o , i x p . [ Xj, otherwise It is necessary to define the real limit of each parameter for the GA process. These values can vary within the range restricted by their physical nature, i.e. s e [0,5] and e e [5,30]. Theoretically, few backscattering models such as IEM have a wide range of applicability. In this case, generally, for a given cr0, there are two sets of solutions: one with lower s and quite higher s, and the other with quite higher s and lower s. Therefore, there is a possibility of obtaining a wrong solution by the inversion approach. This problem was not observed in this study. However, due to the fact that in the real world, an agricultural zone presenting a very large variation of soil surface parameters can rarely be found, this problem can be avoided by the introduction of a limit as outlined above (s e [0, 5] and s e [5,30]). To evaluate the accuracy of the results, the estimated values (j and e) were then compared with the measured in-situ parameters. The results are assorted based on two different presentations: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 136 1) Assorted by study area: this assortment presents the results based on a geographical target class. Figures 1 to 6 present the relationship between the measured and estimated soil parameter values from radar data for different study areas. Also Table 3 presents two indicators, the mean absolute error (M.A. error) and the root mean square error (R.M.S. error). These indicators show the accuracy of the estimated values for each site. The M.A errors were less that 0.57 cm (0.42 to 0.57 cm) and less than 3.5 (2.73 to 3.49) for s and e respectively. Table 3. Statistical results o f comparison between measured and calculated rms height and dielectric constantfor study areas M.A. error RMS error s (cm) e s (cm) e Data 1 0.55 3.31 0.69 3.88 Data 2 0.52 3.44 0.69 3.93 Data 3 0.43 2.73 0.48 3.27 Data 4 0.49 3.22 0.55 3.84 Data 5 0.57 3.29 0.62 3.26 Data 6 0.54 3.13 0.65 3.70 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 137 t. | 25- 8 0 ■C 3- 20- 1 ® 15- *5 « 10' 3 I o-r o 2 1 3 4 5‘ 0 5 10 5 20 15 25 30 M easured dielectric co n sta n t M easured rm s height (cm) (b) (a) Figure 1. Relationship between measured and estimated soil surface parameters for (a) rms height roughness and (b) dielectric constant. Data 1. £ 30- 8 JE o 25- 0 *5 ■■ ■a 2 0 - 1 . 1.' I 15- U) 10-1 0 1 2 3 4 M easured rm s height (cm) 5 10 15 20 25 30 35 M easured dielectric co n sta n t (a) (b) Figure 2. Relationship between measured and estimated soil surface parameters for (a) rms height roughness and (b) dielectric constant. Data 2. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 138 Measured dielectric con stant Measured rms height (cm) Figure 3. Relationship between measured and estimated soil surface parameters for (a) rms height roughness and (b) dielectric constant. Data 3. 3 1 I 8 o 2520- l U la 's ire m " 8 I 10- 1 3 3 E in ■i 55 W o 0 2 1 M easured rm s h eight (cm ) 3 0 5 10 20 15 25 30 M easured dielectric co n sta n t (a) (b) Figure 4. Relationship between measured and estimated soil surface parameters for (a) rms height roughness and (b) dielectric constant. Data 4. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 139 20 - 8 o .= ' 4 - 0> JC ■ ■■ 15- 103 E v> 0 1 2 3 4 5 6 0 M easured rm s height (cm) 5 10 15 20 25 Measured dielectric co n sta n t (b) (a) Figure 5. Relationship between measured and estimated soil surface parameters for (a) rms height roughness and (b) dielectric constant. Data 5. 6 5 t 20 £ - 8 o —4 15- a> ■a TJ 13 . 1 0 - 1 E 55 i 1 (0 5- o 0 1 2 3 4 5 M easured rms height (cm ) 6 0 5 10 15 20 25 Measured dielectric co n sta n t (a) (b) Figure 6 . Relationship between measured and estimated soil surface parameters for (a) rms height roughness and (b) dielectric constant. Data 6 . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 140 2) Assorted by radar configuration: this assortment classifies the data based on the configuration of radar sensors in band C (polarization and incidence angle) to verify the influence of sensor parameters on the results. Table 4 and Figures 7 to ll show these results. The M.A. error for s was minimum (0.44 cm) for 0 = 35-40° with polarization hh however the minimum M.A. error for s was observed with 0 = 20-21°. This result showed that the incidence angle near to nadir is more sensitive to soil humidity, which has been already shown by Ulaby et al. (1978) and Wang et al. (1986). These results indicate that the approach gives a good estimation of the soil surface parameters based on SAR satellite data. However, there are still errors. Sahebi et al. (2003a) have discussed the source of errors introduced in soil surface parameter estimations using SAR satellite data. For a more detailed investigation concerning the miscalculations, the following sections present the sensitivity analysis of the GA inversion and the IEM. Table 4. Statistical results of the comparison between measured and calculated rms height and dielectric constant for different radar configurations. Configuration Incidence M.A. error RMS error Polarization s (cm) e s (cm) e 2 0 -2 1 ° hh 0.65 2.78 0.75 3.35 23-24° w 0.49 2.93 0.57 3.46 25-27° hh 0.52 3.54 0.70 4.01 35-40° hh 0.44 3.51 0.58 3.03 45-47° hh 0.69 3.04 0.87 3.61 angle Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 141 £ 10 _ 20- 8 0 1 15V 1 1 1° - 3 E w 3 2 4 5 6 5- 0 10 5 15 20 25 M easured dielectric con stan t M easured rm s height (cm) (b) Figure 7. Relationship between measured and estimated soil surface parameters for (a) rms height roughness and (b) dielectric constant. R adar configuration: C-hh 20-21°. 4 £ 3 o> ® j= 8 25- 2 ® 20 - ■o £ JO m ■■ i 1 3 15- (0 ■■ 0 1 2 3 Measured rm s height (cm) (a) 10 15 25 20 30 Measured dielectric con stan t (b) Figure 8 . Relationship between measured and estimated soil surface parameters for (a) rms height roughness and (b) dielectric constant. R adar configuration: C -w 23-24°. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 142 25- M 0 20- 1 ■E 3- a> 15- *5 ^ 1°□ E B M l ^ CO 0 1 2 3 4 5 6 Measured rms height (cm) 10 5 0 20 15 25 30 Measured dielectric co n sta n t (b) (a) Figure 9. Relationship between measured and estimated soil surface parameters for (a) rms height roughness and (b) dielectric constant. Radar configuration: C-hh 25-27°. «2 30o 25- 20 - \V 0 1 2 3 4 5 M easured rms height (cm ) (a) 6 0 5 10 15 20 25 30 35 Measured dielectric co n sta n t (b) Figure 10. Relationship between measured and estimated soil surface parameters for (a) rms height roughness and (b) dielectric constant. Radar configuration: C-hh 35-40°. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 143 30 E 25- 3 £ & O 20- 1 ■S 15- ■■ I ■1 ■ .mm i CO 0 1 2 3 4 5 M easured rms height (cm) (a) 6 0 5 10 20 15 25 30 Measured dielectric con stan t (b) Figure 11. Relationship between measured and estimated soil surface parameters for (a) rms height roughness and (b) dielectric constant. R adar configuration: C-hh 45-47°. GA evaluation In order to test the robustness of the GA approach for inversing bare soil surface parameters, a simulated study was realized. To eliminate the possibility of other errors, a simulated data set was generated from the IEM. In this case, the different ranges of input parameters (rms height, dielectric constant, incidence angle and polarization) were chosen. Then, the simulated a 0 were introduced into the GA as input data and s and s, as output data, and were compared with the same initial parameters used for the calculation of simulated ct°. Figure 12 presents the relationship between initial (desired) and retrieval parameters. For this evaluation, M.A. errors of 0.14 cm and 0.98 were obtained for s and e respectively. First, results show very good agreement between die two sets of data and second, they give an idea concerning the accuracy of the GA approach in this study since its errors might influence the results of the parameter inversion. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 144 Another important source of error can be explained by the behaviour of the optimization algorithms applied to multi-parameter equations like the IEM. The solution of the IEM inversion is not usually unique and it is quite possible that there are more than one solution for this equation. For example, there are at least two sets of solutions (5 = 1.56, e = 10.00 and s = 2.46, s = 7.35) for inversion of the IEM when c° = -6.59 dB, 0 = 23.00° with hh-polarization. Mathematically, all the roots are correct but of course only one of them is capable of presenting the reality of the terrain. Unfortunately, this error is inevitable; however by presenting a good as well as restricted range of parameters in the GA, it is possible to limit the variation of the solution, therefore the possibility of finding real answers is increased. 35 30- O) JZ 25- k. 20 0 1 2 3 Simulated rm s height (cm ) (a) 4 - 15 20 25 30 35 Sim ulated dielectric co n sta n t (b) Figure 12. Relationship between desired and estimated soil surface parameters based on a theoretic simulation for (a) rms height roughness and (b) dielectric constant. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 145 Model evaluation To test the accuracy of the IEM, its backscatter coefficients were compared with the backscattering coefficients obtained with SAR images. To conduct this evaluation, the backscatter coefficients were simulated using the measured insitu parameters. The coefficients were then compared with the backscatter coefficients obtained from the SAR satellite images. Figure 13 presents the relationship between the measured and simulated backscattering coefficient values. The M.A. errors obtained were 1.66, 0.97, 1.34, 2.41, 1.98 and 2.00 dB for datal to data6 respectively. These errors are not considerable and show that the model provides good agreement with the satellite data measurements; however, they are sufficient to introduce miscalculations in the proposed approach. These miscalculations increase for rough and very rough surfaces. -5 - cET 2 , ■■ °b -IQ 'S ■■ 1S ■■ I (0 - 20 - -25 -25 -20 -15 -10 ■5 0 M ea su red a ° (d B ) Figure 13. Relationship between measured o° and estimated o° by calibrated IEM for all data. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 146 Conclusion Genetic algorithms (GAs) were designed to find near optimal solutions to complicated problems using the principles of Darwinian selection. GAs are classified among the most powerful optimization algorithms. In this study, a genetic algorithm was developed to estimate soil surface roughness and soil moisture simultaneously using only one SAR satellite image. It is to be noted that the effectiveness of the parameters used in GAs can be different for different problems. In order to adapt the GA to the objective of this study, the cost function was constructed by comparing measured and simulated backscattering coefficients obtained from SAR satellite images and calibrated IEM respectively. The calibrated IEM with an exponential correlation function can simulate the behaviour of the radar signal properties and target parameters notably better than traditional IEM. M.A. errors between 0.42 to 0.57 cm for rms height roughness and between 2.73 to 3.49 for the dielectric constant were obtained, which correspond to good estimations. The proposed method was tested over different sites (in Canada and France) with different incidence angles (23° to 47°) and polarizations (hh and w ), which increased the values of the results. In spite of some miscalculations, the estimation derived from satellite radar data is a useful and accurate enough tool for estimating soil surface parameters over extended areas. However, in this paper two important sources of errors were verified and it was demonstrated that major miscalculations could be introduced by using the IEM backscattering model. Acknowledgements On the Canadian side, funding was provided by the Natural Sciences and Engineering Research Council (NSERC) and the Fonds quebecois de recherche sur la nature et les technologies (FQRNT) On the French side, die work was supported by the BRGM and France’s Ministdre de la Recherche as part of the Actions Concertees Incitatives (ACI) project. Some RADARSAT images were provided by the Canadian Space Agency under the RADARSAT User Development Program (RUDP) and the Application Development and Research Opportunity Program (ADRO). Databases were produced from work carried out by the BRGM, the Centre d’etude des Environnements Terrestres et Planetaires (CEPT), and the Centre d’applications et de recherches en tel6 detection (CARTEL) of the Universite de Sherbrooke, Canada. The authors want to thank all the colleagues of CARTEL, BRGM and CEPT, especially P. Gagnon and A. Lavoie. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 147 References Angles, J., 2001. Separation de I ’humidite et de la rugosite dans le signal retrodiffuse des images RSO selon une approche multi-angle. M.Sc. thesis, University de Sherbrooke, QC, Canada, 82 p. Baghdadi, N., C. King, A. Bourguignon, and A. Remond, 2002a. Potential of ERS and RADARSAT data for surface roughness monitoring over bare agricultural fields. International Journal o f Remote Sensing, 23 (17): 3427-3442. Baghdadi, N., P. Paillou, M. Davidson, G. Grandjean, and P. Dubois, 2000c. Relationship between profile length and roughness parameters for natural surfaces. International Journal o f Remote Sensing, 21(17): 3375-3381. Baghdadi, N., Gaultier, S., and King, C. (2002b). Retrieving surface roughness and soil moisture from synthetic aperture radar (SAR) data using neural networks. Canadian Journal o f Remote Sensing, Vol. 28, No. 5, pp. 701-711. Baghdadi, N., I. Gherboudj, M. Zribi, M. R. Sahebi, C. King and F. Bonn, 2003. Semiempirical calibration of the IEM backscattering model using radar images and moisture and roughness field measurements, International Journal o f Remote Sensing, (submitted). Baret, F., 2000. RESEDA final report, CEE project no. ENV4-CT96-0326, 57 p. Bindlish, R. and A. P. Barros, 2000. Multifrequency soil moisture inversion from SAR measurements with the use of IEM. Remote Sensing o f Environment, 71: 67-88. Boisvert, J. B., Q. H. J. Gwyn, A. Chanzy, D. J. Major, B. Brisco and R. J. Brown, 1997. Effect of surface soil moisture gradients on modelling radar backscattering from bare fields. International Journal o f Remote Sensing, 18(1): 153-170. Coley, D., 1999. An introduction to genetic algorithms fo r scientists and engineers. World Scientific Publishing Ltd., London, UK, 227 p. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 148 Deb, K., 2001. Multi-objective optimization using evolutionary algorithms. John Wiley & Sons Ltd., New York, NY, 497 p. Delta Devices Ltd., 1996. Thetaprobe soil moisture sensor. User manual, Mll-UM-2, Delta Devices Ltd., Cambridge, U.K. 18 p. Dubois, P. C., J. Van Zyl, and T. Engman, 1995. Measuring soil moisture with imaging radars. IEEE Transactions on Geoscience and Remote Sensing, 33(4): 915-926. Fung, A. K. and K. S. Chen, 1992. Dependence of the surface backscattering coefficients on roughness, frequency and polarization states. International Journal o f Remote Sensing, 13(9): 1663-1680. Fung, A. K., 1994. Microwave scattering and emission models and their applications, Norwood: Artech House, 573 p. Goldburg, D. E., 1989. Genetic algorithms in search, optimization and machine learning, Addison-Wesley Longman, 412 p. Hallikainen, M., F. Ulaby, F. Dobson, M. El Rayes, and L. Wu, 1985. Microwave dielectric behavior of wet soil. Part I: Empirical models and experimental observations, IEEE Transactions on Geoscience and Remote Sensing, 23:25-34. Holland, J. H., 1975. Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor. King, C., 2001. Floodgen: un programme de recherche pour lutter contre le ruissellement excessif, rapport final CEE ENV 4 CT 96 0368, 65 p. Oh, Y., K. Sarabandi and F. T. Ulaby, 1992. An empirical model and inversion technique for radar scattering from bare soil surfaces. IEEE Transactions on Geoscience and Remote Sensing, 30(2): 370-381. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 149 Rakotoarivony, L., O. Taconet, D. Vidal-Madjar, P. Bellemain and M. Benall&gue, 1996. Radar backscattering over agricultural bare soils. Journal o f Electromagnetic Waves and Applications, 10(2): 187-209. Sahebi, M. R., J. Angles and F. Bonn, 2002. A comparison of multi-polarization and multiangular approaches for estimating bare soil surface roughness from spacebome radar data. Canadian Journal o f Remote Sensing, 28(5): 641-652. Sahebi, M. R., J. Angles and F. Bonn, 2003a. An inversion method based on multi-angular approaches for estimating bare soil surface parameters from RADARSAT data. Journal o f Hydrology (under revision). Sahebi, M. R., F. Bonn, and G. B. Bdnie, 2003b. Neural networks for the inversion of soil surface parameters from SAR satellite data. Canadian Journal o f Civil Engineering, (under revision). Ulaby, F. T., R. K. Moore and A. K. Fung, 1982. Microwave remote sensing active and passive. Vol. II: Radar Remote sensing and surface scattering and emission theory, Artech House, Ann Arbor, 457-1064. Ulaby, F. T., P. C. Dubois and J. van Zyl, 1996. Radar mapping of surface soil moisture. Journal o f Hydrology, 184: 57-84. Zribi, M., 1998. Developpement de nouvelles methodes de modelisation de la rugosite pour la retrodiffusion hyperfrequence de la surface du sol. Doctoral thesis, University de Toulouse. Zribi, M., O. Taconet, S. Le Hegarat-Mascle, D. Vidal-Madjar, C. Emblanch, C. Loumagne and M. Normand, 1997. Backscattering behavior and simulation: Comparison over bare soils using SIR-C/X-SAR and ERASME 1994 data over Orgeval. Remote Sensing o f Environment, 59: 256-266. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 150 Chapter 7 CONCLUSIONS AND FUTURE RESEARCH DIRECTIONS 7.1. Summary and conclusions This study has focused on the inversion of bare soil surface parameters from SAR data (specially using RADARSAT images). In previous studies, some approaches were presented with the same problematics as this study; but they had problems in applying the models over a selected study area to obtain accurate results. Therefore, different methods have been proposed in this study. This strategy not only allowed us to develop and validate different new approaches, but also provided a framework for comparing results. A multi-techniques approach was presented to discriminate the moisture and surface roughness components of the radar signal backscatter over the bare soils. In this case, to find the best radar configuration for estimating soil surface parameters, a simulation study using theoretical and empirical backscattering models was carried out. In chapter 2, two configurations (multi-angular and multi-polarization) and in appendix B three configurations (multi-angular, multi-polarization and multi-frequency) are compared using two rational and differential indicators. The simulation results point to the fact that the multi-angular approach is more sensitive to surface parameter conditions than the multi-frequency and multi polarization approaches. Among the present operational radar satellites, only RADARSAT-1 is capable of offering data at different incidence angles. Therefore, the images of this satellite acquired according to different modes can be used for estimating surface parameters. However, in practice, weather instability can be an important problem. There are often precipitations or frozen soil conditions between data acquisitions during the periods of bare soil in some regions like Quebec. Soil moisture and sometimes soil surface roughness can vary between two image pairs which is contrary to the basic hypothesis of the multi-angular approach. It must be noted that this problem can exist also when using the multi-polarization and multi-frequency approaches. For example, we could not use the data acquired on October 2001 and May 2002 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 151 because rainfall occurred between data acquisitions. Fortunately, since this problem did not occur with the 1999 data acquisition, we used these data for this study. The advantage of the multi-angular approach was the basis for continuing this work. As a sequel to this work, we continued our investigation following these axes: i) Based on die multi-angular approach, a new index, the NBRI (Normalized radar Backscatter soil Roughness Index), was presented to estimate and classify surface roughness in agricultural fields using two radar images with different incidence angles. The NBRI is a simple and fast approach; however, it is very sensitive to soil moisture changes. This supposes that the soil moisture conditions for the images must be the same. Therefore, this index is more practical for regions with stable climatic conditions. ii) To estimate soil moisture content, linear backscattering models were investigated. Three linear empirical models (Ji model, Champion model and the new proposed model) based on the Cloud model were evaluated. For the first two models (Ji and Champion models), results were unacceptable because of their large errors. These models were altered empirically for the study areas and the results improved significantly. The new linear model presented in this work is capable of integrating the influence of rms height and incidence angle simultaneously within the relationship between backscatter coefficient and soil moisture content. The results are very accurate. However, the constant coefficients were calculated for the study areas and this suggests that this model should be used with caution for other regions and if necessary, they have to be recalculated. iii) Chapter 4 demonstrated the possibility of using the multi-angular approach to derive soil moisture and surface roughness simultaneously from RADARSAT-1 data. In this case some backscattering modes were inverted numerically using the Newton-Raphson method. The input data for this inversion were the sensor parameters (wavelength, incidence angle and polarization) and backscatter coefficients from the images and the output data were the rms height roughnesses and dielectric constants. The results provided a good estimation of the soil surface parameters over extended areas, in spite of some errors that can be reduced in some Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 152 cases. Using the right model, precise ground data and accurate image corrections can decrease these errors. In this study, one of the proposed solutions for obtaining more accurate results is to adapt the models locally. In chapter 3, it was shown that the adapted linear modes (for three models) significantly improve the performance of the models for estimating soil surface moisture. This fact is proven by the use of nonlinear models in chapter 4. The best results were obtained by inverting the Modified Dubois Model that was presented for the Quebec region. This conclusion can be expressed by the reality that actually there is no universal model which represents exactly the relationship between the radar signals received and the bare soil surface parameters. Therefore, they need to be evaluated and calibrated to be more powerful. Some models such as linear empirical models (presented in chapter 3) and the MDM (presented in chapter 4 and appendix C) are adapted based on the study area data. These adaptations have improved significantly the performance of the models to estimate soil surface parameters. iv) The neural network technique was applied to invert the soil surface parameters from radar data. The results were obtained through the performance testing on two different input schemes, single and dual (based on multi-angular configuration) sets, and two different databases (simulated and measured databases). A multi-layer perceptron (MLP) neural network with two hidden layers, trained by the Kalman filter method, was found to be the best for modeling the relationship between the soil surface parameters and the backscattering coefficients. The advantage of the multi-angular set with measured data was apparent. In this study, this approach presented the most accurate results for estimating soil moisture and soil surface roughness simultaneously. The final results of the methods proposed in chapters 4 and 5 were presented in the form of moisture and soil surface roughness maps over the same area. The maps, which present the same parameters, are not exactly the same and this is normal, because they were obtained through different methods. However, the differences are not very significant. The maps were drawn some time after that images were acquired and we could not verify the maps with Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 153 ground truth. According to field measurements and results presented in these chapters, the maps obtained by the neural network technique are slightly more accurate. v) As explained, the principal problem of the multi-technique approach presented by changing the soil surface parameters in the meantime of data acquisitions. This fact guides us to verify the possibility of using only one image for this estimation. According to classical mathematics, it is not possible to solve this problem. Therefore, in chapter 6 an optimization method was proposed. Generally, optimization methods find the nearest possible solutions for multi-parameter equations and if the chosen optimization method is robust enough, it can find solutions near enough to the exact solutions. For this study, a genetic algorithm (GA) was developed to solve this problem because GAs are a powerful method adapted to both simple and complicated equations. Chapter 6 presents the inversion of the backscattering model results. These results show that the proposed GA inversion derived from satellite radar data can estimate soil surface parameters over extended areas with very good accuracy. In this chapter the proposed model was applied on 6 different databases over different study areas (in Canada and France) with different incidence angles (23° to 47°) and polarizations (hh from RADARSAT images and w from ERS images). The calibrated Integral Equation Model (IEM) was employed for computation of the cost function. This version of the IEM simulates the behavior of the radar signal properties and target parameters is more realistic than the traditional IEM. The description of the calibrated IEM is presented in Appendix G. This study tried to present and validate different approaches for estimating soil surface parameters from SAR satellite images. This objective is one of the most complex problems in remote sensing. Many parameters, their behavior and their influence on SAR images are not yet completely clear. Until now, there is no perfect method for solving the problem and of course many research groups are working on this objective. Therefore, we are not capable of presenting one single approach as being the best. This research work presented different ways for clarifying different hypothesis. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 154 The results showed that the proposed approaches could significantly increase the accuracy of the estimated parameters and this accuracy is sufficient for many applications (i.e. use in hydrological models, management of agricultural area, estimation of sediments, ...) if the radar sets are adequate,which is not always the case, for the approaches requiring two images. 7.2. Prospects and recommendations for future research This study presents different methods in order to retrieve bar soil surface parameters. The results are satisfactory; however, there are several points that should be considered for future research work to improve the outcome. Future investigations may be oriented towards the following remarks: - All backscattering models, initially, were developed and/or tested from the scatterometer or the airborne data. Although, when they are applied on satellite data, the results are not often cheering. For improving the robustness of the models, investigations may be directed through two orientations: universally); 2) 1) enhancing the models by re-evaluating and revising them (locally or clarifying the precisions between the data from acquired scatterometer, airborne and satellite and determining their differences. - With the launching of the new generation o f SAR satellites, such as ENVISAT and RADARSAT-2, it will be possible to acquire the images with different polarization and incidence angles simultaneously (multi-angular-polarisation). This configuration may lead to interesting results. In addition, development of soil surface parameters monitoring system using polarimetry SAR data can be considered. - The presented approaches should be tested over other sites with different soil surface conditions, and the outcomes of these approaches should be made compatible with different hydrological and erosion models. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 155 APPENDIX A SPACEBORNE OBSERVATION OF CATCHMENT SURFACE CHANGING CONDITIONS GENERATING EXCESS RUNOFF, EROSION AND FLOOD RISK DOWNSTREAM Ferdinand BONN, Mahmod R. SAHEBI, Joel ANGLES, Laurie ST-ONGE, Eric ARSENAULT, Pham Van CU, Judith COULOMBE-SIMONEAU and Jill SMYTH Proceedings o f 12th International Soil Conservation Conference, ISC02002, M ai 26-31, 2002, Beijing, pp. 206-211. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 156 Spaceborne observation of catchment surface changing conditions generating excess runoff, erosion and flood risk downstream. Ferdinand Bonn, Mahmod Sahebi, Joel Angles, Laurie St-Onge, Eric Arsenault CARTEL, Universite de Sherbrooke, Sherbrooke, Quebec, Canada fbonn@courrier.usherb.ca Pham Van Cu VTGEO, NCNST, Hanoi, Vietnam, Judith Coulombe-Simoneau Viasat Geotechnologie Inc., Montreal, Quebec, Canada. Jill Smyth, Canadian Space Agency, St Hubert, Quebec, Canada Abstract The land use and land cover of catchment basins play an important role in the onset of runoff, erosion, sediment load and flood risk in many areas of the world. They control runoff coefficients, concentration time and resistance to erosion processes. Remote sensing and GIS tools have the capacity to provide information on the status of land use and soil protective cover in drainage basins, but this information is not always adaptable to hydrological modeling and forecasting. It has to be translated into parameters and coefficients that hydrological models can understand : Manning coefficients, SCS curve number, soil cover factors in soil loss equations, etc. Optical data such as those from LANDSAT Thematic Mapper are used to map land use classes (forest, crops, bare soils, etc) and soil protective cover by living and dry vegetation, while microwave data such as those from RADARSAT are used to evaluate soil surface roughness and soil moisture. Additionally, they can also be used to evaluate land use classes in areas which are not easily observed by optical data due to cloud cover or poor illumination conditions (wet tropics and northern latitudes). In order to be used reliably in hydrological and erosion modeling, remote sensing data must be calibrated and validated on the ground by appropriate measurements of the surface's spectral, dielectric and geometrical properties. These measurements are then linked to the satellite data which have to be previously geometrically and radiometrically corrected for the effects of topography (altitude, slope, aspect) and atmosphere. This paper presents tire team member's experience in applying earth observation data to this type of problems in Canada, Europe and Vietnam. 1. INTRODUCTION AND BACKGROUND Excess runoff has been a major disaster generating cause in recent years in many areas of the world, and especially in Northwest Europe. It occurs in regions having large fields of annual crops on loamy soils, leaving the soil unprotected by vegetation during 2 or 3 months per year. Excess runoff takes place on bare soils forming a sealing crust when exposed to strong rains. This crusting effect increases the runoff coefficient of the surface and therefore the amount and the speed of water sent downstream. This runoff water is also an important erosion and pollution agent, because phosphates move along the slopes with the suspended sediments and end up in rivers and lakes, contributing to silting and eutrophication. Figure la) shows the initiation of an erosion rill on one of the test sites in Normandy. Low vegetation cover and smooth, crusted surface create the initial conditions for this land degradation process. Land managers and some farmers in Normandy try to reduce these effects by planting grass on these waterways. This conservation practice seems to be relatively efficient to decrease runoff and increase infiltration, but it is sometimes perceived as a reduction of the cash crop producing area. Crusting can also be reduced by tillage or with a harrow in order to increase the surface roughness as shown on figure lb), taken on a test site in Ste-Angdle-de-Monnoir, Quebec, Canada. This action reduces the amount and the velocity of surface runoff, and therefore the erosive power of overland flow. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 157 Sealing crust Runoff coeff. = 0,7 0,8 Harrowed section Runoff coeff. = 0,3 a) Figure 1 : 0,4 b) a) Initiation o f an ero sio n rill ca u sed by e x c e s s runoff in Normandy. b) R em ains o f a sea lin g cru st on bare so il com pared to a recently harrowed sectio n with a greater rou gh n ess; Satellite imagery can help to map these different land surface conditions and to provide hydrologic and erosion models with input data that can refine their spatial distribution. Optical satellites can provide land use maps, especially for identifying crop types, bare soil areas and also anti-erosive measures such as the use of residues for soil protection. But their possible use is limited by the combination o f cloud cover and satellite overpasses. Radar satellites such as the Canadian RADARSAT system can see through clouds, and on bare soils, the signal backscattered to the satellite is a function of surface roughness and soil moisture. These considerations and the interest of end users in Normandy and Canada have given rise to a project called FLOODGEN (FLOOD risk reduction by spacebome mapping of excess runoff GENerating areas), funded by the European Union and by Canada (King et al., 1998). Two components of the runoff/erosion problem have been addressed by the Canadian partners of the project : the question of surface roughness and the question of soil protection by crops and residues. 2. C-BAND SAR MAPPING OF SURFACE ROUGHNESS OF BARE SOILS 2.1 In trod u ction One possible way to estimate surface roughness consists in using active microwave remote sensing. Previous work has shown that the backscattered radar signal is influenced by surface roughness and soil moisture (Ulaby et al., 1978). The potential retrieval of surface roughness status represents a crucial step before the assimilation o f remote sensing data into numerical models for predicting watershed runoff, especially in winter conditions when no other data could be operationally provided by optical sensors because of frequent cloud cover. 2.2 M ethodology and d a ta acquisition While ERS 1 and 2 acquire data on a fixed orbit with a 23° incidence angle and can observe the same site every 35 days, RADARSAT can be programmed with different resolutions and incidence angles ranging from 24 to 49°, according to user needs. This feature allows a more frequent coverage, up to 2 images per day on the same site if there is no competing site elsewhere. Images of the FLOODGEN test sites have been acquired during winter and early spring when many soils were without vegetation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 158 Simultaneous ground observations and measurements for position (GPS), roughness, moisture and soil cover have been made in order to be able to relate ground parameters with image data. Most RADARSAT images used in the project were provided by the Canadian Space Agency and have been precision geocoded and orthorectified by VIASAT inc. of Montreal, using precision GPS points and digital elevation models. The plots sampled in the field were then precisely located on the imagery and the backscattering coefficients (a°) for each of them were extracted from the imagery for statistical analysis. Results of this analysis were then used for image classification. Due to the fact that radar images cannot always separate bare soils from vegetated areas, a mask based on an optical image such as one from LANDSAT or SPOT has been applied on the radar images in order to concentrate the analysis on bare soils only. 2 .3 D ata a n a ly s is At every incidence angle (23°, 39° and 47°), an analysis of the 1998 and 1999 Normandy data shows that it is impossible to establish a relationship between radar data and soil moisture content over bare soils. This was explained by the low dynamics and high values of soil moisture content (30 to 40%), close to saturation. But the relationships between the backscattering coefficient and the rms of surface heights show that c° increases with the surface roughness. The mean difference between the roughest areas and smoothest areas is only of the order of ldB for ERS data at 23°, but of 3.5 dB for RADARSAT at 39°, and of 5 dB for RADARSAT at 47°. Figure 2 shows the relationship between ground measured roughness and satellite data (Coulombe-Simoneau et al., 2000). c -10 ♦♦ -12 -14 -16 -J -18 0,5 2 2,5 rms height (cm) Figure 2. Variation of th e satellite backscattering coefficien t o° a s a function of m ean su rface h eigh ts (rms) at 39° for the Normandy site. The results show that the best configuration for a surface roughness measurement requires the use of a SAR image at high incidence angle such as RADARSAT. The relatively good results obtained on the FLOODGEN sites are due to the fact that moisture was high and not very variable. But in order to increase the accuracy of the relation when moisture conditions are more variable, the radar signal related to roughness should be separated from the one related to moisture. This can be achieved with multiple image acquisitions in configurations such as 2 different angles or 2 different polarizations (Dubois et al, 1995, Sahebi et al., 2002, Angles et al., 2001). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 159 2.4 C lassification of ro u g h n e ss c la ss e s Soil surface roughness is one of the key parameters involved in the runoff process, whose measurement is of primary importance in the problem of modelling excessive runoff risk. By inversion of the relation obtained above, a pixel by pixel classifier separated the bare soils of the test area into three categories: (1) smooth areas (high runoff potential), (2) medium rough areas (moderate runoff potential) and (3) rough areas (low runoff potential). Figure 3 illustrates the result of this classification procedure with the 1999 RADARSAT image. Compared to observations, the classified RADARSAT images show good agreement with the test fields. The final product provides the localisation and quantity of various state of soil roughness inside a catchment basin. The overall classification accuracy is of 80%. The misclassification rates for individual categories are less than 20% except for the middle class (40%). Some sophisticated runoff models such as STREAM (Le Bissonais, 1991) may require more classes, but end users agreed that even these crude classes were better than roughness guesses from cropping calendars and helped them in runoff forecasting. 1999 RADARSAT 39° © CSA/ASC Figure 3: 2 .5 Smooth areas rms < 1 cm Medium rough areas 1 cm < rms < 2 cm S eg m en t o f RADARSAT im age and th e correspon d in g cla ssified im age. Image dim ension is 4.7km (horizontal) by 6.2km (vertical). C o n c lu s io n for r o u g h n e s s m a p p in g w ith RADARSAT The retrieval of physical parameters of the soil surface such as surface roughness is important for environmental management in hydrology and agriculture, as they appear to be among the major parameters for runoff forecasting on a watershed. In this study, the possible use of synthetic aperture radar (SAR) for mapping soil roughness classes over bare soils shows that RADARSAT at high incidence angles provides a better way than ERS to discriminate among the different roughness classes (smooth, medium rough and rough areas) of agricultural fields. However, when all the fields have a very high roughness, as is the case in the Solnan, another FLOODGEN site, tillage orientation has also Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 160 an important effect on backscattering, allowing the orientation to be extracted from RADARSAT imagery at high incidence angle (Smyth et al., 2000). This simple operational processing of radar images for retrieving soil surface roughness will allow applications to improve the characterisation of the roughness classes in a watershed so that it should be possible to assess the areas contributing to quickflow and to use them in spatial modelling of excessive runoff. However, the study sites of the different FLOODGEN teams vary significantly, and these results cannot be extrapolated on all sites. For example, on the Ruwer site (Germany), terrain slope effect is very strong due to the local topography and it masks the effect of roughness on radar imagery. On the Lombardia site (Italy), the very small agricultural field size and the proximity of buildings and roads generates much noise in the radar imagery, making extraction of radiometric values less reliable. Therefore, the extraction of roughness based on relations found in this work is applicable only in areas o f open fields with gentle topography. These conditions prevail in many agricultural areas of Northwest Europe. Similar approaches are presently tested on recently deforested lands in Vietnam. 3. OPTICAL OBSERVATION OF CROP RESIDUE COVER AS A WAY TO CONTROL EROSION AND RUNOFF 3.1 C rop re s id u e s a re a n efficient w ay to red u c e e ro sio n an d runoff Several agricultural practices have been developed to reduce runoff and erosion. Terraces, contour tillage, reduced till and no till are among the practices used. Application of crop residues to protect the soil from raindrop impact and to reduce the speed of runoff is one of the techniques under development. Field based experiments conducted in Ontario, Canada (Ketcheson and Stonehouse, 1989), and others in Switzerland, have shown that a residue cover of 30% can reduce the erosion rate by 80% and also reduce the runoff by a significant amount. In some areas, crop residue application is subsidised by the states, and therefore it is important to be able to assess the amount of land covered by residues. 3.2 M apping of cro p re s id u e s is p o ssib le with optical s e n s o rs o p eratin g in th e SWIR sp e ctra l ran g e Crop residues have a brownish colour relatively close to that of bare soil. Therefore, the usual remote sensing satellites such as SPOT, operating in the visible (VIS) and near infrared (NIR) range of the electromagnetic spectrum, have a tendency to confuse bare soils with crop residues. Classical vegetation indices such as NDVI do not make the difference either because they are based on the difference between chlorophyll absorption in the red band and cell structure reflection in the NIR band. Senescent vegetation does not absorb the red radiation anymore. Figure 4a) shows the colour similarity of the soil and the residues. New optical sensors looking at the short-wave infrared (SWIR) range can however make the difference between residues and bare soils. This is due to specific absorption features of cellulose and lignine, major components of crop residues, in the SWIR range. In order to investigate the capability of the new sensors to map crop residues, field spectra-radiometric campaigns have been conducted over several FLOODGEN sites. These campaigns have shown that the residues can be distinguished from bare soil by using either an approach based on spectral indices in the SWIR and NIR range or an approach based on spectral mixture analysis (SMA) (Biard and Baret, 1997; Arsenault and Bonn, 2001. Figure 4b) shows reflection spectra of bare soils and cereal residues on one of the test sites. Spectra of cereal residue and bare wet loamy soil are represented in green and red respectively. Even if both show the same water absorption bands, residues show also absorption by cellulose and lignine in the SWIR part of the spectrum. These features help to discriminate residues from bare soil and to map them from satellite data if SWIR bands are present. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 161 R e s id u e s lignine cellulose w ater 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Wavelength (microns) a) Figure 4 : b) a) Note th e difficulty to sep arate visually th e resid u e colour from th e bare soil; b) R eflectance sp ectra of bare so il and cereal residue. Lignine and c e llu lo se absorption bands help to discrim inate resid u es from bare soil. Combination of such maps with cadastral information can help authorities to enforce and verify soil conservation subsidy policies. Furthermore, these digital maps can then be imported into geographic information systems (GIS). This operation can improve the accuracy of runoff modelling or soil loss prediction in models such as ANSWERS, STREAM, LIS EM or the Universal Soil Loss Equation where the C factor accounts for the vegetative cover. 4. REFER ENC ES Arsenault E. and F. Bonn (2001) Evaluation o f Soil Erosion Protective Cover by Crop Residues Using Vegetation Indices and Spectral Mixture Analysis o f Hyperspectral Data. COST623 workshop, Strasbourg, France. Biard, F. and F. Baret (1997) Crop Residue Estimation Using Multiband Reflectance. Remote Sensing o f Environment, vol. 59, no 3, p. 530-536. Coulombe-Simoneau, J., Hardy, S., Bagndadi, N., King, C., Bonn, F. and Y. Le Bissonais (2000) : RADARSAT based monitoring o f soil roughness over an agricultural area affected by excessive runoff. Remote Sensing in Hydrology 2000, AIHS Red Book 267, p. 362-364. Dubois, P. C., Van Zyl, J., and Engman, T. (1995) “Measuring Soil Moisture with Imaging Radars”. IEEE Trans, in Geoscience and Remote Sensing, Vol. 33, No. 4, p. 915-926. Ketcheson, J.W. and Stonehouse, D.P. (1983) Conservation tillage in Ontario. Journal o f Soil and Water Conservation, vol. 38, no 3, p. 253-254. King C. and 15 co-authors (1998) FLOODGEN 2nd progress report to the European Commission, report # ENV4 CT96 0368 - BRGM report R40088 Le Bissonais, Y. (1990): Experimental study and modelling o f soil surface crusting processes. Catena Suppl. 17, 13-28. Sahebi, M.R., J. Angles, F. Bonn (2002) A comparison o f multi-polarization and multi-angular approaches for estimating bare soil surface roughness from spacebome radar data. Canadian Journal o f Remote Sensing. In press. Smyth, J., F. Bonn, S. Hardy, A. Remond and P. Clement (2000): Potential retrieval o f tillage direction as a runoff indicator using RADARSAT data. Remote Sensing in Hydrology 2000, AIHS Red Book 267, p. 368-370. Ulaby, F. T., P.P. Batlivala and M.C. Dobson (1978) “Microwave Dependence on Surface Roughness, Soil Moisture and Soil Texture : Part I - Bare Soil”. IEEE Transactions on Geoscience Electronics, Vol. 16, No. 4,p. 286-295. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 162 APPENDIX B A MULTI-ANGULAR RADARSAT BASED C-BAND BACKSCATTERING MODEL FOR ESTIMATION OF BARE SOIL SURFACE ROUGHNESS Mahmod Reza SAHEBI, Joel ANGLES and Ferdinand BONN Proceeding o f 23rd Canadian Symposium on Remote Sensing, August 21-24,2001, St-Foy (Quebec), Canada, pp. 865-871. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 163 A multi-angular RADARSAT based c-band backscattering model for estimation of bare soil surface roughness Mahmod Reza Sahebi Joel Angles and Ferdinand Bonn CARTEL, University de Sherbrooke, Sherbrooke, QC, Canada, J l k 2 R l Tel: (819) 821-8000 ext:3250 email: msahebi@hermes.usherb.ca CARTEL, University de Sherbrooke, Sherbrooke, QC, Canada, J lk 2R1 Tel: (819) 821-8000 ext:2964 email: joelangles@hotmail.com email: fbonn@courrier.usherb.ca ABSTRACT Roughness and moisture contents o f a soil surface both have a significant effect on microwave backscatter to the satellite. Specially, in agricultural regions, the estimation o f surface conditions using radar data could be very usefulfor the management andprevention o f risks related to excessive runoff The purpose o f this work is to evaluate the optimum operating configuration for the radar satellites that would allow choosing the best approach to extraction o f roughness for rough very rough surfaces. A simulation study using theoretical and empirical models has permitted the estimation o f the backscattering coefficient’s sensitivity to a relative variation in soil parameters in terms of radar characteristics. For roughness, the different configurations are verified and the results o f multi-angular configuration seem to give the best results for a rough surface. In this work, to estimate soil roughness from a multi-angular approach, a Normalized radar Backscatter soil Roughness Index (NBRI) is presented and was cross validated with ground data obtained in Chateauguay and Pike River watersheds, Quebec. This Index may allow the mapping o f soil roughness conditions over large area with C-band SAR data like that ofRADARSAT. 1. INTRODUCTION Estimates of the physical parameters of the soil surface, i.e. moisture content and surface roughness, are important for hydrological and agricultural studies, as they appear to be the two major parameters for runoff forecasting on an agricultural watershed (Bates et al., 1997). One possible way of estimating surface roughness consists in using active microwave remote sensing, based on scatterometers, airborne and spacebome data (Chanzy et al., 1990, Oh et al., 1992, Blyth, 1993, Ulaby et al., 1996). The important parameters significantly influencing the radar response of soils may be classified into two categories: 1) the target parameters and, 2 ) the sensor parameters such as frequency, polarization and incidence angle. In the first category, radar scattering by a bare soil surface is determined by two attributes: first, the geometry of the soil surface commonly known as surface roughness and second, the microwave dielectric properties of the soil medium, which depend on the soil characteristics such as moisture, particle size distribution and mineralogy. Roughness is one of the main factors for defining potential runoff from agricultural surfaces. At the scale of a field, roughness has a double role of trapping water, which helps infiltration, and slowing down runoff. At the scale of a catchment area, it is the macro-roughness of that will influence the concentration of runoff (Benallegue et al., 1995). This study examines the different configuration and the potential of mapping different roughness classes using C-band SAR data over a study site comprised of bare soils in St. Lawrence lowlands area, Qudbec, Canada. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 164 2. STUDY SITE AND DATA DESCRIPTION 2.1. S tu d y a re a The agricultural sites chosen for this study are the Chateauguay and Pike River watersheds located in the south shore of the Montreal region, Quebec, Canada (figure 1). Description of the plots was mostly performed in terms of surface roughness. These descriptions were generated according to the ploughing plots (very rough surface). Chateauguay and Pike River watersheds Figure 1. Localization o f study area 2.2. G round d a ta Many plots in the study area were chosen. The roughness and moisture of the surface were measured in-situ the same day as image acquisition. To calculate rms height, six 2 m long surface profiles (three parallel and three perpendicular to the furrows) were investigated for each plot. The method for extracting and modeling the roughness parameters has been described in detail by Beaulieu et al. (1995). To measure the humidity surface, a reflectometry instrument was used to measure soil moisture. About 5-8 samples were taken at each plot. Also, to control the results obtained by gravimetric, some soil specimens are transferred to laboratory for measuring soil moisture. 2.3. Satellite Data The satellite data used in this study correspond to a RADARSAT image pair. The first image was acquired on 12th November 1999 in the SI mode with incidence angles ranging from 20 to 25° and the second image was acquired on 18th November 1999 in the S7 mode with incidence angles ranging from 40 to 49°. The roughness and the moisture of the surface were measured in-situ the same dates as the satellite image were acquired. However, between the periods of data acquisition, the climate was almost stable and surface moisture had not changed significantly because of the low evaporation and temperature at that time of the year, but to satisfy completely the conditions of this study, the plots that have exactly the same moisture and the roughness for two dates are chosen. In order to describe the plots in the study area (homogeneous soil structure, bare soil, homogeneous ploughing) an average backscatter value ct° (in dB) was assigned to each plot area by converting the RADARSAT DN value to ct°. 3.METHODOLOGY In practice, estimation of surface roughness may be defined as a strong regression between the radar backscattering coefficient (or°) and roughness parameters, rms height (s) and correlation length (€), Thus, theoretically we have one equation with two unknowns (when humidity is known). To resolve this problem, two solutions are presented. First, using the assumption that defines surface roughness only by its horizontal distribution, it means that only rms height represents surface roughness and the influence of correlation length is negligible. In this case, correlation length that shows the horizontal distribution of surface roughness is not estimated. Secondly, it is possible to add a second equation with the same unknowns. This means using two images with two different conditions, for example using two images with different incidence angles or different polarizations, that can give two different backscattering coefficients for the same site, therefore there are two equations with two u n k n o w n s . In this study we use the second solution with three different methods, multi frequency, multi-polarization and multi-angular, to obtain the best configuration for estimating surface roughness. In this case, according to profile of study site concerning very rough surfaces, this comparison is carried out using Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission. 165 simulations by GOM (Geometric Optics Model; Ulaby et al., 1982 ) and Oh Model (Oh et al., 1992). These models are used to simulate surface roughness from bare soils. To perform these numerical calculations the parameters of three radar satellite sensors, RADARSAT-1, ERS1/2 and JERS-1 are chosen. Thus simulation was carried out using two frequencies in band C and L (frequency equal to 5.3 and 1.2 GHz respectively), two polarizations (HH and W ) and two incidence angles (20° and 40°). In this study, in order to obtain the best comparison possible, the following points are taken into consideration: 1) According to experimental results obtained by McNaim et al. (1996) in C-band polarization, HH is more sensitive than W or HV to surface roughness. Also Beaudoin et al. (1990) and Coppo et al. (1995) concluded that with incidence angles superior to 30° the sensibility of the backscattering coefficient to humidity decreases strongly, and on the opposite, its sensibility to roughness increases. Therefore, in this study, when the multi-polarization and multi-frequency approaches are verified, the incidence angle is constant (0=40°) and when the multi-angular and multi-frequency approaches are verified, polarization is constant (HH polarized). 2) The ratio indicator is chosen to show the differences and the rate of differences between the approaches. This indicator presents the ratio a°i/ a °2 that, in the multi-polarization approach can be defined as a°hh/cr0w, in the multi-frequency approach as <T°c/or0L and as ct°40o/ct°20 for the multi-angular approach. If this ratio becomes close to 1 (ct°i = a° 2), we can conclude that the proposed approach is not efficient enough to extract the necessary information for estimating surface roughness (Autret et al., 1989). 3) To estimate surface roughness by using the multi-angular approach, a new roughness index (NBRI) is proposed. 4) To validate the theoretical approach, field data from the St. Lawrence lowlands area and actual RADARSAT data are used. 4. RESULTS AND DISCUSSION 4.1. Sim ulation re su lts This section evaluates the applicability of the three approaches presented for the estimation of surface roughness. To be able to cover a large domain of possible surface conditions, two different soil moistures (mv =18 and 28%) were chosen that could be used in calculations. Figure 2 and 3 show the simulated results by Oh model. These figures clearly show the advantage of the multi-angular approach to estimate the roughness of rough and very rough surfaces. For this model the values of <s°\/g° 2 are almost equal to 1 (between 1 and 1.04) for multi-polarization and decrease rapidly for multi-frequency, however they are between 1.45 and 1.68 (for mv = 18 and 28% respectively) for the multi-angular approach. According to the Geometric Optics Model (GOM) a°hh= <7°w and ct°l= cr°c. This means that the indicator a°i/a °2 is always equal to 1 for rough and very rough surfaces and therefore the multi polarization and multi-frequency approaches are not efficient for estimation of surface roughness. As shown in figure 4, the o°i/a °2 indicator is greater than 1, however for extrem rough surfaces this value becomes equal to 1 and this phenomena may be explained by the behavior of microwave scattering, because when the surface is very rough it behaves like a Lambertian surface, the incidence signals being scattered in all directions almost uniformly, independently of the incidence angle. 4.2. C om parison of sa tellite configurations As explained above, in this study the simulation parameters were chosen close to the parameters of the RADARSAT-1, ERS1/2 and JERS-1 radar satellite sensors. This configuration may be used for comparing the capability of these satellites for estimating the surface roughness, and it can also be used for simulations of RADARSAT-2 and ENVISAT. The results obtained in the previous section show that for rough and very rough surfaces, the multi-angular approach gives satisfactory results whereas the results of the multi-polarization and multi-frequency approaches are questionable towards providing a good estimation of surface roughness. Therefore, following to the capability of RADARSAT-1 to acquire data in different incidence angles, we can conclude that using this satellite alone, we are capable of to obtaining the necessary images to estimate surface roughness. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 166 - 0- M«ltl*polarteation Multi-angular — MaltKfreqaency s m - 2 3 4 4,5 6 5 6,5 rm s h eig h t (cm ) Figure 2 Comparison between multi-polarization, multi-frequency and multi-angular approachesfor mv=18%; simulation by Oh model 1,6 - M altl-polarizatloa —4 —M ■hl-angalar to m *o N b 1,4 M altl-freqaency 1,2 b -©— ©— 0 — e— ©— o 1 r m s h e ig h t (cm ) Figure 3 Comparison between multi-polarization, multi-frequency and multi-angular approachesfor mv=28%; simulation by Oh model Maltl-angular, mv -18% 6 - f - M ultl-angulir, mv -28% 5 m T3 00 TJ_ 4 N B 3 B 2 1 2 3 4 5 6 rm s h e ig h t(c m ) Figure 4 Multi-angular approaches; simulation by GOM with a correlation length o f 10 cm Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 167 4.3. D efinition o f a m ulti-angular b a c k s c a tte r index using RADARSAT d a ta Assessment of the simulated results suggests a relationship between the backscatter coefficient and soil roughness (rms height roughness) for the same target conditions (soil roughness and soil moisture are constant for two pairs of data). The simple relation between multi-angular backscatter and soil roughness can be presented by: s=ax.p(<7^,<j%)+b ( 1) where s is the surface roughness, pfcPt.cP^ is the relation between two different backscatter coefficients obtained by two different incidence angles, and a and b are linear coefficients. p(cPi, can have the form presented as: arf,a$)=ln(NBRI) (2) where: NBR1=^ ~ f crf-cr§ (3) NBRI (Normalized radar Backscatter soil Roughness Index) can be used to generate soil roughness maps over large areas with C-band SAR data. 4.4. NBRI an d soil ro u g h n e s s relatio n sh ip fo r very rough s u rfa c e s Based on the knowledge of field conditions (very rough surface), the proposed approach was tested by simulated and actual backscatter values. To simulate backscatter coefficients, the Geometric Optics Model (GOM) was chosen with the following parameters: 3 < s < 6 cm, e = 8 , t = 4 cm. Figure 5 shows the results obtained by simulated backscatter values and a correlation coefficient higher than 99% was derived. This approach was tested with the backscatter coefficients obtained by RADARSAT images (figure 6 ) and a correlation coefficient higher than 83% was obtained, which is a strong relationship for actual satellite data. 5. CONCLUSION In this paper three configuration approaches (multi-polarization, multi-frequency and multiangular) are proposed to estimate the surface roughness in C-band for rough and very rough surfaces. In this case, the value of the backscattering coefficients was calculated by using two existing theoretical and empirical models for different conditions (2.5 < rms < 6 cm and mv = 18 and 28%). The simulation showed that, according to the models used for rough and very rough surfaces, a multi-angular approach was more sensitive to roughness than a multi polarization and multi-frequency approaches and based on these results it can be concluded that the RADARSAT-1 satellite with its large capability in terms of acquisition modes improves the identification of surface roughness. However, these results must be tested for another surface conditions. The strong relationship between rms and NBRI allows us to estimate the surface roughness from agricultural fields. This work is continuing towards extending the multi-angular approach to provide an estimation of surface roughness and separate roughness from soil moisture by using RADARSAT images. ACKNOWLEDGEMENTS This study was partly supported by FCAR (Action Concertde Radarsat), the FLOODGEN project (CSA-RUDP) and NSERC. The authors want to thank all the colleagues of CARTEL specially P. Gagnon, J. Deslandes, J. Cattai and J. Smyth as well as J.P. Fortin from INRS-Eau and the MCHE of Iran for granting a scholarship and financial support to M. Sahebi. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 168 y = 0,0762x + 1,3802 R2 = 0,9935 ,85 ■ cc CQ z c ,65- 1,55 2,5 3 3,5 4 4,5 5 5,5 6 6,5 rms hight (cm) Figure 5 Relationship between theoretical roughness index (NBRI) and Soil roughness; simulation by the GOM y = 0.5528X + 1,1004 R2 = 0,831 4,5- 0£ m z c 2,5- 2 2,5 3 3,5 4 4,5 5 5,5 6 rms height (cm) Figure 6 Relationship between measured roughness index (NBRI) and soil roughness on 10 field plot; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 169 REFERENCES Autret, M., Bernard, R., and Vidal-Madjar, D. (1989) Theoretical study of the sensitivity of the microwave backscattering to the soil surface parameters. International Journal of Remote Sensing, Vol. 10, No. 5,p. 171-179. Bates, P. D., Horritt, M. S., Smith, C. N., and Mason, D. (1997) Integrating Remote Sensing Observations of Flood Hydrology and Hydrolic Modelling. Hydrological Processes, Vol. 11, p. 1777-1795. Beaudoin, A., Le Toan, T., and Gwyn, Q. H. J. (1990) SAR Observations and Modeling of the C Band Backscatter Variability due to Multiscale Geometry and Soil Moisture. IEEE Transactions on Geoscience and Remote Sensing, Vol. 28, No. 5,p. 886-895. from C-Band Radar Backscatter. Canadian Journal of Remote Sensing, Vol. 22, No. 2,p. 154162. Oh, Y. Sarabandi K. Ulaby F. T. (1992) An Empirical Model and Inversion Technique for Radar Scattering From Bare Soil Surfaces. IEEE Transactions on Geoscience and Remote Sensing, Vol. 30, No. 2,p. 370-381. Ulaby, F. T. and Moore, R. K. and Fung A. K. (1982) Microwave Remote Sensing Active and Passive. Vol. II :Radar Remote Sensing and Surface Scattering and Emission Theory, Artech House, Ann Arbor. Ulaby, F. T., Dubois, P. C., and van Zyl, J. (1996) Radar mapping of surface soil moisture. Journal of Hydrology, Vol. 184, p. 57-84. Beaulieu, N. Leclerc G. and Moisan Y. (1995) Determination de la rougosit6 de surface par des m6thodes accessibles. Canadian Journal of Remote Sensing, Vol. 21, No. 2,p. 198-203. Benallegue, M., Normand, M., Galle, S., and Dechambre, O. (1994) Soil Moisture Assessment at a Basin Scale Using Active Microwave Remote Sensing. International Journal of Remote Sensing, Vol. 15, No. 3,p. 645-656. Blyth, K. (1993) The use of microwave remote sensing to improve spatial parameterization of hydrological models. Journal of Hydrology, Vol. 152, p. 103-129. Chanzy, A., Bruckler, L., Bertuzzi, P. (1990) Modelling evaporation on bare soil using microwave data. Proc. Remote Sensing and Water Resources, Enschede. Netherlands. Coppo, P., Luzi, G., and Schiavon, G. (1995) Understanding Microwave Backscatring of Bare soil by Comparing Models and Experimental Data Collected During Two Different Airborne Campaigns. IGARSS 95, p. 1346-1348. McNaim, H., Boisvert, J. B., Major, D. J., Gwyn, Q. H. J., Brown, R. J. and Smith A. M. (1996) Identification of Agricultural Tillage Practices Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 170 APPENDIX C A RADARSAT-1 BASED MULTI-ANGULAR APPROACH TO SEPARATE AND MAP MOISTURE AND SURFACE ROUGHNESS COMPONENTS OF THE RADAR SIGNAL BACKSCATTERED BY BARE SOILS Joel ANGLES, Mahmod Reza SAHEBI and Ferdinand BONN Proceedings o f 15th International workshop, applications o f remote sensing in hydrology, October 2-5,2001, M ontpellier, France. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 171 A RADARSAT-1 BASED MULTI-ANGULAR APPROACH TO SEPARATE AND MAP MOISTURE AND SURFACE ROUGHNESS COMPONENTS OF THE RADAR SIGNAL BACKSCATTERED BY BARE SOILS Abstract Soil surface roughness and moisture content are both positively correlated with microwave backscatter intensity. However, their influence on surface runoff works in opposite directions, rough and dry surfaces having less runoff and more infiltration than wet and smooth soils. Therefore, it is important to be able to separate moisture from roughness over bare soils, if information useful for hydrological and erosion modelling is to be derived from satellite imagery. This work evaluates the potential of a multi angular approach to derive moisture and roughness from SAR data. It is based on a modification of the semi-empirical model initially developed for multi-polarization imagery in order to adapt it for multi-angular single polarization data such as those of RADARSAT-1. The modified model and its limits of validity are presented for an agricultural area. Soil moisture and soil surface roughness maps of a sub-catchment close to Montreal (Canada) have been produced by using the new model and RADARSAT-1 imagery taken in the SI, S3 and S7 modes acquired at short intervals in November 1999. Validation of the model is based on a field campaign where roughness and moisture have were been measured in 27 fields in the basin. The S3 and S7 combination gives the best results for the separation of moisture and roughness components in the area and is also in agreement with the physical limits o f the model. The pointability and flexibility of RADARSAT-1 makes it possible to acquire these combinations from the same side on the same sites within a two day interval, allowing only small changes in moisture and roughness between the data acquisitions if it does not rain in the meantime. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 172 Introduction Microwave remote sensing techniques are of primary interest for monitoring land surfaces because of their all weather capabilities, their penetration depth through natural media and their sensitivity to surface variables (such as water content) difficult to estimate using optical remote sensing sensors. Several studies were conducted over the last 20 years to study the relation between the backscattering coefficient and soil parameters (Ulaby et a l, 1978, 1982, 1996; Dobson and Ulaby, 1986a, 1986b; Engman and Wang, 1987; Oh et al., 1992; Fung, 1994; Dubois et al., 1995). Most of the research work was oriented towards the estimation of soil moisture and the development of algorithms for mapping soil moisture distribution. Estimation of surface soil moisture was usually obtained by using an empirical relationship to convert the measured backscatter coefficient (ct°) into volumetric soil moisture (mv) (Dobson and Ulaby, 1986a; Pr6vot et al., 1993; Ulaby et al., 1996). Results showed that the radar specifications for optimum soil-moisture detection with minimum soil roughness influence were determined to be the C-band with HH polarization and an incidence angle around 10-12° (Benallege et al., 1998). The synthetic aperture radar (SAR) angle of present and future missions starts around 20° (23° for ERS1/2, 38° for JERS-1, 15-55° for SIR-C and 20-50° for RADARSAT-1/2). This means that the incidence angles of operational SAR systems are quite different from the 101 2 °optimum angle and that radar results are expected to depend on both soil water content and roughness. Based on simulation results, Sahebi et al. (2001, 2002) indicated that the multi-angular approach would be more sensitive to surface parameter conditions than multi-polarization and multi-frequency approaches. They concluded that the RADARSAT-1 satellite with its capability of acquiring data at different incidence angles could be used for estimating soil moisture and surface roughness. However, it is necessary to develop a method adapted to RADARSAT-1 data for estimating these parameters. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 173 The objective of this paper is to formulate and define a transformation approach to solve the inverse problem for the operational retrieval of soil surface roughness and moisture. The strategy consists in formulating the inverse problem in the context of multi-angular RADARSAT-1 data. We studied the relation between the C- band radar response and soil parameters, specially soil dielectric constant (e) and rms height (s), which are used as constraining target parameters in the Original Dubois Model (ODM) (Dubois et al, 1995) and the Modified Dubois Model (MDM) (Angles, 2001). Methodology The important parameters that significantly influence bare soil radar response may be classified into two categories: 1) the target parameters such as moisture and roughness and, 2 ) the sensor parameters such as frequency, polarization and incidence angle. Usually in remote sensing applications, the sensor parameters are known; however, the relationship between the target and measured signals are subjective. Estimation of surface soil parameters was usually obtained by using a theoretical or empirical relationship to convert the measured backscatter coefficient (a0) into soil surface roughness and moisture (Dobson and Ulaby, 1986a; Prdvot et a l, 1993; Ulaby et a l, 1996). Then for each target, we had one equation with two unknowns, or three if the model incorporates correlation length. As a consequence, the use of radar data acquired with single configuration does not generally permit the estimation of these variables. However, to estimate the surface parameters simultaneously over complex areas, multi technique concepts (multi-polarization, multi-angular, multi-sensor, multi-frequency, and multi-temporal) are the main solution. From a ground based experiment (Chanzy et a l, 1998) and a theoretical study (Sahebi et al, 2 0 0 1 , 2 0 0 2 ), it has been demonstrated that the multi-angular configuration gives the best configuration to estimate bare soil surface parameters. In this study, the multi-angular configuration is used for the inversion of backscattering models to account for roughness and soil moisture estimation using RADARSAT-1 data acquired within two different angular ranges. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 174 This process was carried out using two empirical backscatter models that introduce the relationship between backscatter coefficient and surface parameters (roughness and dielectric constant). Then, to validate the proposed approach, the results are compared with measured ground data. The following models were used in this work: Original Dubois Model (ODM) The Dubois model (Dubois et al., 1995) was developed using scatterometer data. The model is based on an empirical model for smooth and medium rough surfaces. The model is optimized for bare surfaces and requires radar channels at a frequency between 1.5 and 11 GHz. It gives best results for ks < 2.5, 0 > 30° and moisture contents (mv) <, 35% with NDVI (Normalized Difference Vegetation Index) less than 0.4; where k is the wave number (k=2n/X), X is the wavelength, s is the rms height and 0 is the incidence angle. The HH-polarized backscattering cross sections were found to follow this equation: 0 - 2 . 7 5 ___ „ 1,5 n cm = 10 0.028 tan &v c o s 5- - 10 1.4 0.7 (fe.sin<9) A ( 1) sin 0 where sr is the real part of the dielectric constant. Modified Dubois Model (MDM) As explained, the model developed by Dubois et al. is limited to surface conditions and incidence angle. It can cover neither rough (and/or very humid) surfaces nor incidence angles less than 30°. In the case of the RADARSAT-1 sensor configuration (band-C, HH-polarized and incidence angles programmable from 20° to 50°) an attempt was made by the University de Sherbrooke to modify this model for Quebec agricultural areas (Angles, 2000). This modification presented in equation 2 can be applied to all bare agricultural surfaces. cm=10 "3-76x c o s ^ xio 0112 t“ fl £x(kssin0)°m xA01 sin 0 (2 ) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 175 When used with RADARSAT data at two different incidence angles of the same target with short intervals, this approach generates a two equation system with two unknowns, which can be resolved to obtain s and e. STUDY SITE The agricultural site chosen for this study is part of the Chateauguay watershed (73°46' W, 45° 19' N), located on the south shore of the St. Lawrence River, southeast of Montreal, Canada (Figure 1). The area consists mainly of agricultural fields on a rather flat relief plateau. During the ground surveys the parcel surfaces were rough to very rough. Pouyr.-NoranOi OF -- ' 100mi J100kfll Chateauguay watershed Quebec " j ■ unaw a»\Montr4®1 x ------------ ^0ttaw r, Toranto New York ^Buffalo , p s ^ r * - us* # 1 * ; ^C oncord Albany ? P o r« mouth .......~ ‘ .Boston Springfield^ ® Figure 1. Location of study area. Data Ground data Roughness and moisture measurements were carried out over 27 fields, simultaneously with the image acquisitions. To calculate rms height, six 2 m long (1.5 cm sampling interval) surface profiles (three parallel and three perpendicular to the furrows) were investigated for Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 176 each parcel. These profiles were photographed and then digitized. The method for extracting and modeling the roughness parameters has been described in detail by Beaulieu et al. (1995). To measure surface moisture a reflectometry instrument was used. Fifteen samples were taken in each parcel. These measurements were carried out for soil depths of 0-5 cm with a Thetaprobe soil moisture sensor. Using the equation presented in the Thetaprobe soil moisture user manual (1996), the direct outputs (DC voltage in mV) were converted to soil water content (m3.m'3) and dielectric constant. Also, to evaluate the results obtained by this method, five 0-5 cm soil samples for each parcel were transferred to our laboratory. Wet and dry weights were used to determine gravimetric soil water content. The soil water contents (m3.m'3) obtained by these two methods were compared and a mean relative difference of 12 % (equivalent to 1 .8 % volumetric soil moisture) between the two methods was observed. Surface roughness and moisture were measured in-situ on November 15 and 18, 1999 (the same dates as the satellite image acquisitions). Between the periods of data acquisition, the weather was stable and surface moisture had not changed significantly because of the low evaporation and temperature at that time of the year. Average temperatures were 2.3 °C and there was no recorded rainfall between the two acquisition dates. However, to completely satisfy the conditions of this study, 2 0 parcels that had nearly the same moisture and roughness for the two dates were chosen. Satellite data The satellite data used in this study correspond to a RADARSAT-1 image pair. The first image was acquired on November 15, 1999 in S3 (Standard-3 Ascending) mode with incidence angles ranging from 30 to 35° and, the second image was acquired on November 18, 1999 in S7 (Standard-7 Ascending) mode with incidence angles ranging from 40 to 49°. The RADARSAT DN values were converted to c° using Shepard (1998). In order to include the spatial variability and to avoid problems related to georeferencing of individual pixels of the parcels in the study area (homogeneous soil structure, bare soil, homogeneous ploughing), an average o° (dB) was assigned to each parcel (20 to 30 pixels). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 177 DISCUSSION AND RESULTS ANALYSIS Figures 2 to 5 present a comparison between the values of the surface parameters estimated by the radar data inversion technique and those measured in-situ. For the surface parameters, MDM definitely has the best estimation with errors equal to 1.30 cm and 2.81 for rms height and dielectric constant respectively; however, for ODM, these errors increase to 2.89 cm for rms height and 28.74 for dielectric constant that are unacceptable. This fact can be explained by the models behavior. The ODM cannot be used for rough and very rough surfaces while for MDM, the estimation of the dielectric constant is more exact than the estimation o f rms height. This sensitivity to humidity may be explained by the behavior of the Dubois Model. According to this model, the statistical variation of surface roughness is characterized only by rms height and it does not take into account the correlation length that can introduce an error to present the real behaviors of the backscattered radar signal. However, the results are largely acceptable for satellite data. Conclusion This work has demonstrated the possibility of using the multi-angular approach to derive soil moisture and surface roughness from satellite remote sensing data. In spite of some errors, this estimation derived from satellite radar data is a useful tool for estimating soil surface parameters over extended areas. To minimize the influence of the errors associated with backscatter models, we propose the Modified Dubois Model (MDM) developed for agricultural sites in Quebec and presenting a good estimation of soil surface parameters. This result is obtained by comparing the same results calculated using the original and modified Dubois models. From an application point of view, the final products of this work are soil surface parameter maps (roughness and moisture). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 178 ■a 13 Measured dielectric constant Figure 2. Correlation between the dielectric constant measured and estimated by MDM £® U 30 o 15 45 Measured dielectric constant Figure 3. Correlation between the dielectric constant measured and estimated by ODM Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 179 Figure 4. Correlation between rms height measured and estimated by MDM Measured heught(cm ) Figure 5. Correlation between rms height measured and estimated by ODM Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 180 ACKNOWLEDGEMENTS This study was partly supported by FCAR (Action Concertee RADARSAT), NSERC and the Ministry of Science, Research and Technology of Iran provided a scholarship and financial support to M. Sahebi. The authors want to thank all the colleagues at CARTEL especially P. Gagnon, Q.H.J. Gwyn, P. Cliche and M. Lambert. REFERENCES Angles, J. (2001) Separation de l’humiditd et de la rugosite dans le signal retrodiffuse des images RSO selon une approche multi-angle. Memoire de Maitrise, Dep. de geographie et teledetection, Universite de Sherbrooke, QC, CANADA, 82 p. Beaulieu, N., Leclerc G. and Moisan Y. (1995) Determination de la rugosite de surface par des methodes accessibles. Canadian Journal o f Remote Sensing, Vol. 21, No. 2, pp. 198-203. Benallegue, M., Taconet, O., Vidal-Madjar, D. and Normand, A. (1998) The use of radar backscattering signals for measuring soil moisture and surface roughness. Remote Sensing o f Environment, Vol. 53, pp. 61-68. Chanzy, A., King, C. Prdvot, L. and Remond, A. (1998) Comparison of ERS and RADARSAT measurements on bare soils: first results. Second Int. Workshop on Retrieval o f Bio-&Geo-physical Parameters from SAR Data, ESTEC, Netherlands, pp. 471-477. Dobson, M. C. and Ulaby, F. T. (1986a) Active microwave soil moisture research. IEEE Transactions on Geoscience and Remote Sensing, Vol. 24, No. 1, pp. 23-36. Dobson, M. C. and Ulaby, F. T. (1986b) Preliminary evaluation of the SIR-B response to soil moisture, surface roughness, and crop canopy cover. IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-24, No. 4, pp. 517-526. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 181 Dubois, P. C., van Zyl, J., and Engman, T. (1995) Measuring soil moisture with imaging radars. IEEE Transactions on Geoscience and Remote Sensing, Vol. 33, No. 4, pp. 915-926. Engman, E. T. and Wang, J. R. (1987) Evaluating roughness models of radar backscatter. IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-25, No. 6 , pp. 709-713. Fung, A. K. (1994) Microwave scattering and emission models and their applications. Norwood: Artech House, 573 p. Oh, Y., Sarabandi K. and Ulaby, F. T. (1992) An empirical model and inversion technique for radar scattering from bare soil surfaces. IEEE Transactions on Geoscience and Remote Sensing, Vol. 30, No. 2, pp. 370-381. Prevot, L., Champion, I. and Guyot, G. (1993) Estimating surface soil moisture and leaf area index o f a wheat canopy using a dual-frequency (C and X bands) scatterometer. Remote Sensing o f Environment, Vol. 46, pp. 331-339. Sahebi, M. R., Angles, J. and Bonn, F. (2001) A multi-angular RADARSAT based C-band backscattering model for estimation of bare soil surface roughness. Proceedings o f the 23rd Canadian Symposium on Remote Sensing, August 21-24, 2001, Ste-Foy (Quebec), Canada, p 865-871. Sahebi, M. R., Angles, J. and Bonn, F. (2002) A comparison of multi-polarization and multiangular approaches for estimating bare soil surface roughness from spacebome radar data. Canadian Journal o f Remote Sensing, Vol. 28, No. 5, pp. 641-652. Shepard, N. (1998) Extraction of beta nought and sigma nought from RADARSAT CDPF products”. Report No:AS97-5001, ALTRIXSystems, Ontario, Canada, 12 p. Thetaprobe Soil Moisture Sensor (1996) User manual, Mll-UM-2, Delta Devices Ltd, U.K. 18 P- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 182 Ulaby, F. T., Batlivala, P. P. and Dobson, M. C. (1978) Microwave dependence on surface roughness, soil moisture and soil texture : Part I - bare soil. IEEE Transactions on Geoscience Electronics, Vol. 16, No. 4, pp. 286-295. Ulaby, F. T., Moore, R. K. and Fung A. K. (1982) Microwave remote sensing active and passive. Vol. II: Radar Remote Sensing and Surface Scattering and Emission Theory, Artech House, Ann Arbor, pp. 457-1064. Ulaby, F. T., Dubois, P. C., and van Zyl, J. (1996) Radar mapping of surface soil moisture. Journal o f Hydrology, Vol. 184, pp. 57-84. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 183 APPENDIX D IN-SITU MEASUREMENTS Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 184 As explained in the previous chapters, data were collected on the surface for soil moisture content, surface roughness and soil texture at the chosen sites. This appendix outlines some procedures for data collection and describes the preliminary analysis conducted on the parameters measured for the Chateauguay and Pike River watersheds. 1. Soil moisture 1.1. Instrument Data were collected on the surface soil moisture content using a Thetaprobe soil moisture (TDR) sensor designed by Delta-T devices and the Macaulay Land Use Research Institute (Delta Devices Ltd., 1996). The instrument converts the signal into a direct current (DC) voltage shown to be almost proportional to the soil moisture content. The direct output voltage readings (V) were recorded on a digital voltmeter; however, it can be converted into the volumetric soil moisture (mv) and soil dielectric constant (e). The probe (Figure 1) comprises •> four sharpened prongs of 6 cm in length. A moisture estimate is obtained for a 30 cm column of soil within these prongs (Delta Devices Ltd., 1996). The absolute accuracy of the probe is reported as between ± 0.02 and ± 0.05 cm3.cm'3 of soil water (2 to 5% in volumetric moisture) depending on calibration method. (Delta Devices Ltd., 1996). Figure 1. The dielectric Thetaprobe for measuring volumetric soil moisture. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 185 According to Gaskin and Miller (1996), the impedance of the emitted 100 MHz signal is influenced by two properties; the apparent dielectric constant and the ionic conductivity. The effect o f these factors depend on the signal frequency This means that the signal frequency maximizes the sensitivity of the signal to changes in the dielectric constant to minimize the effect o f changes in the ionic conductivity. 1.2. Sampling methods The first task was to check that the probe was operating normally (check the battery, wires and other components) and that the probe was clean, any small offset in voltage was noted before the sampling began. The probe was then inserted into the soil, perpendicular to the soil surface, covering soil depths o f 0-5 cm. The voltage reading was allowed to stabilize and then the value was noted. Fifteen samples were taken at three different random locations within approximately a 5 m by 5 m area in each field to account for the spatial heterogeneity of soil moisture within the parcel of land. The average of the recordings was then calculated and considered representative of the soil moisture content at that particular field. 1.3. Calibration The stated relationship between the output voltage of the probe and the volumetric soil moisture content is non-linear and dependent on the type of soil analyzed. According to the soil texture of the studies area, the calibration relationship chosen in this study was for mineral soils. The relationship between the output voltage (V) and the square root of the dielectric constant (Ve) can be expressed very accurately (R2 = 1.0) by the 5th order polynomial presented by Whalley (1993): 4e = / + 6.19V- 9.72V2 + 24.35V3 - 30.84V4 + 14.73V5 (1) The simple relationship between Vs and mv can be expressed in the form: The coefficients chosen for ao and aj are given as 1.60 and 8.40 respectively for a mineral soil (Delta Devices Ltd., 1996). These are derived from a large number of tests carried out on Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 186 mineral soils. The company gives other coefficients for organic soils, but we had no such soils in our test area. The value of e and mv were used as input to the backscattering models when these parameters were specified. However these parameters may be converted into each other using the relationship given by Hallikainen et al. (1985). 1.4. Data verification To validate the results obtained by the Thetaprobe for selected parcels of land, gravimetric samples were collected for comparing moisture measurements made by the Thetaprobe and the laboratory results. The standard procedure was at first to collect 5 samples in the regions where Thetaprobe measurements were carried out. Based on the manual of Agriculture Canada (Sheldrick, 1984), a representative sample was collected using sections of metallic gutter piping 5 cm in length and approximately 5 cm in diameter. The initial weight of the sample was taken, oven dried at 105°C for over 24 hours, and then re-weighted. The average gravimetric moisture content, normally expressed as g water g 1 soil (oven dried) or as a percentage, was then calculated using the following formula (Sheldrick, 1984): gravimetric moisture = (mass o f water lost / mass o f oven dried soil)xl 00 (3) It was then converted into volumetric soil moisture by dividing the mass of water lost by the volume of the sample (equivalent to its volume because density of water is 1 g.cm'3). The soil water content obtained by these two methods (Thetaprobe and laboratory) were compared and a mean relative difference of 12% (equivalent to 1 .8 % volumetric soil moisture) between the two methods was observed. This shows that the accuracy of the Thetaprobe is within the specifications gives by the manufacture, which claims errors from 2 to 5% in volumetric moisture. The results of this data verification exercise are shown in Tables 1 and 2. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 187 Table 1. Results of volumetric soil moisture (readings from the Thetaprobe and standard laboratory method) and rms height for the Pike River site. Parcel No. Volumetric soil moisture estimation with Thetaprobe (cm3.cm'3)xl00 Volumetric soil moisture estimation in lab. (cm3.cm‘3)xl00 Roughness rms height (cm) 2 20 22 5.0 4 28 26 3.1 5 30 27 2.4 6 25 23 5.5 7 20 22 4.5 8 24 21 3.8 10 17 19 4.6 11 14 10 4.8 14 24 22 4.5 15 26 24 4.0 17 25 23 3.3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 188 Table 2. Results of volumetric soil moisture (readings from the Thetaprobe and standard laboratory method) and rms height for the Chateauguay site. Parcel No. Volumetric soil moisture estimation with Thetaprobe (cm3.cm'3)x l 0 0 Volumetric soil moisture estimation in lab. (cm3.cm"3)x l 00 Roughness rms height (cm) 100 11 12 3.9 101 22 26 3.1 102 16 17 3.1 103 12 13 4.4 104 10 13 1.3 105 13 106 12 15 16 107 19 21 3.8 4.9 3.9 108 16 17 5.2 109 26 27 4.0 no 19 20 4.7 111 13 13 3.9 112 18 18 3.8 113 114 13 15 13 16 3.0 4.2 115 29 28 2 .2 116 16 4.4 117 15 18 18 2 .8 118 13 14 3.7 119 16 3.7 120 15 16 16 3.9 121 22 22 1.5 122 21 22 123 15 17 2.7 3.7 124 14 15 3.7 125 23 23 2.9 126 18 19 1.5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 189 2. Surface roughness 2.1. Definitions As outlined previously, it is essential to quantify the roughness properties of a bare soil surface as one of the most important target parameters can influence the backscatter signal. This insitu measurement allows to validate the roughness estimated using radar data. As explained in Chapter 1, in this study, the standard deviation of surface heights, also known as root mean square (rms) height and abbreviated as s presents the statistical parameters of soil surface roughness because correlation length has no real influence of runoff. This parameter is presented in units of centimeters. The method of measurement and derivation of this parameter is discussed below. This information is reflected in the specifications of the equipment used and the field methodology employed. Outlined below are the basic definitions of rms height, the procedures adopted in the field and the method for its determination. This method was already used by Smyth (1999) and Angles (2001). 2.2. rms height The rms height of a surface indicates to what degree discrete measurements of the height of a surface above an arbitrary plane varies. Obviously the greater the spread of height measurements, the greater the value of rms height. For the series zi, i=l,2,.... n the rms height in the case of the discrete one-dimensional values (sp) is given by (Beaulieu et al., 1995): (4) where, n (5) and n is the number of samples. In all cases the number of discrete height measurements exceeded 134. The actual number taken varied in two ways. First, with respect to deriving the correlation coefficient value that is used in some backscattering models, and secondly, in an attempt to derive an optimized Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 190 methodology of data collection with the aim of making the data collection process more accurate (Ulaby et al., 1982). For each parcel of land, six surface profiles were investigated. Three profiles were parallel and three profiles were perpendicular to the soil furrows. Then, the rms height for each parcel of land is presented as (Smyth, 1999): (6) where sp\\ represents the mean of parallel rms heights and sp± the mean of perpendicular rms heights. 2.3. The profilometer The equipment used to derive the rms height is a pin profilometer constructed at CARTEL (Universite de Sherbrooke) measuring 2 meters in length. The device initially was constructed with 134 pins with a separation of 1.50 cm. The aluminum pins were attached to a wooden frame with locking clips that could trap the pins against the frame. Also fixed to the frame was a spirit level to enable the frame to be on a horizontal plane. Behind the frame was attached a sheet of thin black plywood, providing a reference with which the pins would be shown against. The profilometer frilly set is shown in Figure 2 for the Pike River watershed. Figure 2 .2m (134 samples) profilometer used for measuring surface height values (Built by J. Angles and F. Bonn). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 191 The procedure was first to reset the pins, to place the profilometer vertically on the surface and adjust the metal rods at the side so that the spirit level indicated that the frame was horizontal. The pins were then released and would assume the shape of the surface below. When all of the pins were just touching the ground a photograph of the pins was taken against the background of graph paper. 2.4. Photograph analysis The photographs were developed to 7x5 inches (17.8x12.7 cm). The photos were then digitized using ARC INFO software by choosing a reference horizontal level and by digitizing the top of the pins with reference to this plane. This was carried out until all of the pins were digitized. The relative heights o f the pins were then converted to centimeters by transforming the edges of the graph paper to units of length (normalization). It should be noted that the absolute value of the heights are less important than the statistics of their heights. The measurements were entered into a spreadsheet for further analysis (Beaulieu et al., 1995). Figure 3 shows two example profiles collected for a Chateauguay and Pike river surface. 40 Pike River 35 Chateauguay 30 25 ■a 20 3 SG 15 10 5 0 0 30 60 90 120 150 180 Distance (cm) Figure 3. Examples of profiles recorded for the Chateauguay and the Pike River watersheds. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 192 The results of rms height for the Chateauguay and Pike River sites are shown in Tables 1 and 2. 2.5. Problems and alternative methods When using the pin profilometer method, errors can be introduced into the analysis. First, the profile has to be horizontal and checks need to be made to ensure that all the pins are touching the ground. The photograph should also be taken on the level. When digitizing, it is important that the very tip of the pin is registered for every profile. As this process is made manually, human errors are inevitable; however, this can be minimized with proper due care and attention. Other methods for obtaining surface roughness measurements were investigated. For example, the laser profilometer (Huang and Bradford, 1990) is one such method. This profilometer, originally developed to look at micro-relief in wind erosion studies, can measure surface elevation data by storing the elevation data recorded by a laser beam returning from the aimed soil surface. The resolution of the sampling can be controlled from a computer and typically would be 1.5 mm (Geneq Web site: http://www.geneq,com/frames.html), yielding over 40, 000 readings per plot. Obviously such a high resolution of readings would not be required for this study and the fixed sampling, as explained before, would be sufficient. However, the advantages for such a device are numerous; surface elevations and roughness statistics could be calculated directly using a simple computer program, human error would be practically eliminated. Another approach consists in using three-dimensional images obtained from stereovision photographies (Zribi et a l, 2000). For data acquisition, two digital cameras are kept next to each other at a constant distance. By taking pictures simultaneously, it is possible to create a model of the photographed surface in 3-D. This 3-D model of the soil surface topography with fine resolution offers a new way for describing soil surface roughness. Presently, a team at CARTEL (Universite de Sherbrooke) is working on this approach. However, the results obtained are not convincing in terms of results vs. processing time. 3. Soil texture Soil texture influences the dielectric properties of the soil medium, as mentioned in Chapter 1 and therefore it is important that these properties be measured. The methodology used data Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 193 consisting of original samples collected in the field and analyzed in the laboratory according to Sheldrick (1984). Data on the particle size distribution of the soil at the parcels of land were analyzed in the mineralogy laboratory of the University de Sherbrooke. At each parcel, 5 samples were collected from the upper 5 cm of the surface material. The mass of the sample was approximately 100 grams. The method for deriving the particle size distribution in terms of percentage sand, silt and clay uses a sedimentation technique followed by sieving. The particle size class distinction is one commonly used in Canada based on standard laboratory procedures as outlined in the Agriculture Canada manual (Sheldrick, 1984); sand-size particles are between 0.05 to 2 mm, silt-size particles are between 0.002 to 0.05 mm and clay-size particles are less than 0.002 mm. Hie sand fraction is separated using a 0.05 sieve for coarse sand, a 0.025 mm sieve for fine sand, whereas the clay fraction is determined by particle settling times in distilled water at a constant temperature. The methods used here to determine the particle size distribution are suitable for most soils and sediments. Dry sieving can only be conducted if high proportions of sand are present (Rowell, 1994). As most agricultural soils contain significant amounts of silt and clay, pipette and hydrometer methods (based on sedimentation techniques) were used. The technique of sedimentation is based on theoretically derived settling times, calculated using Stokes' Law, for particles of different sizes. The density of the settling liquid is kept constant using a water bath (set at a constant temperature of 20°C) and great care is taken not to disturb the samples after they have been thoroughly mixed (Rowell, 1994). The results of the particle size analysis for the samples collected at the Chateauguay watershed are shown in Table 3. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 194 Parcel N o. Clay (% ) sO 0s Fine san d (% ) Sand (% ) C oarse sand (% ) Total o f sand Total o f fines R eduction volum e CO (% ) MO (% ) Table 3. Soil analysis results of particle size for the Chateauguay watershed 100 13 19 37 31 <1 68 32 8.55 3.23 5.56 101 12.5 20 36.5 31 <1 67.5 32.5 12.9 2.10 3.62 102 12.5 19.5 9 59 <1 68 32 12.4 1.48 2.56 103 56 32 7 5 <1 12 88 16.1 1.02 1.75 104 15.5 17 2.5 65 <1 67.5 32.5 14.4 1.52 2.61 105 49 37 2 12 <1 14 86 11.4 2.03 3.50 106 45.5 38.5 3 13 <1 16 84 10.1 2.78 4.79 107 52 38.5 2 7.5 <1 9.5 90.5 14.4 1.46 2.52 108 47 40.5 0.5 12 <1 12.5 87.5 13.85 1.69 2.91 109 43 47 2 8 <1 10 90 16.1 1.03 1.78 110 28 41 14.5 16.5 <1 31 69 11.8 2.28 3.94 111 22 28 3 47 <1 50 50 5.95 2.37 4.08 112 29 43.5 3 24.5 <1 27.5 72.5 9.4 2.98 5.14 113 55.5 37 1.5 6 <1 7.5 92.5 16.1 0.99 1.71 114 42 46.5 2 9.5 <1 11.5 88.5 9 2.88 4.97 115 44 52 1 3 <1 4 96 12 4.96 8.56 116 39 52 3 6 <1 9 91 6.75 3.55 6.12 117 31 48.5 2 18.5 <1 20.5 79.5 14.9 1.38 2.38 118 30 49.5 2 18.5 <1 20.5 79.5 10.8 2.33 4.01 119 11 8 1 80 <1 81 19 18.5 0.33 0.58 120 36 21 1 42 <1 43 57 12.7 2.02 3.48 121 38 25 2.5 34 <1 36.5 63 11.15 1.83 3.16 122 43 37 2 18 <1 20 80 10.45 2.37 4.09 123 44 22.5 2 31.5 <1 33.5 66.5 12 2.26 3.89 124 44 33.5 2.5 20 <1 22.5 77.5 10.85 2.30 3.96 125 37 46.5 2.5 14 <1 16.5 83.5 8.2 3.24 5.58 126 7 36.5 6.5 50 <1 56.5 43.5 11.65 2.33 4.01 5 cc Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 195 References: Angles, J. (2001) Separation de l’humiditd et de la rugosity dans le signal retrodiffuse des images RSO selon une approche multi-angle. Mdmoire de Maitrise, Ddp. de gdographie et teledetection, University de Sherbrooke, Canada, 82 p. Beaulieu, N.; Leclerc, G. and Moisan, Y. (1995) Determination de la rugosity de surface par des methodes accessibles. Canadian Journal o f Remote Sensing, Vol. 21, No. 2, pp. 198-203. Delta Devices Ltd. (1996) Thetaprobe soil moisture sensor. User manual, Mll-UM-2. Delta Devices Ltd., Cambridge, U.K. Gaskin, G. J. and Miller, J. D. (1996) Measurment of soil water content using a simplified impedence measuring technique. Journal o f Agricultural Engineering Research. Vol. 63, pp. 153-160. Halikainen, M. T.; Ulaby, F. T.; Dobson, M. C.; El-Rays, M. A. and Wu, L. (1985) Microwave dielectric behavior of wet soil - Part I - Empirical models and experimental observations. IEEE Transactions on Geoscience Electronics, Vol. GE-23, No. 1, pp. 25-34. Huang, C. and Bradford J. M. (1990) Portable laser scanner for measuring soil surface roughness. Soil Science Society o f America Journal. Vol. 54, pp. 1402-1406. Rowell, D. L. (1994) Soil science: methods and applications. Longman Scientific and Technical. 350 p. Sheldrick, B. H. (1984) Analytical methods manual 1984. Land Resource Research Institute, Agriculture Canada, Ottawa, Ontario. Smyth J. (1999) Utilisation des donnees RADARSAT pour l’observation des propriytes de surfaces agricoles sensible au ruissellement. Memoire de maitrise de gyographie. University de Sherbrooke, Sherbrooke, Canada, 80 p. Ulaby, F. T.; Moore, R. K. and Fung A. K. (1982) Microwave remote sensing active and passive. Vol. II: Radar remote sensing and surface scattering and emission theory, AddisonWesley, Reading, MA, pp. 457-1064. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 196 Whalley,W. R. (1993) Considerations on the use of time-domain reflectometiy (TDR) for measuring soil water content. Journal o f Soil Science. Vol. 44, pp. 1-9. Zribi, M.; Ciarletti, V.; Taconet, O.; Paille, J. and Biossard, P. (2000) Characterisation of the soil structure and microwave backscattering based on numerical three-dimentional surface representations: analysis with a Fractional Brownian model. Remote Sensing o f Environment, Vol. 72, pp. 256-266. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 197 APPENDIXE OPTIMIZATION USING NON-LINEAR LEAST SQUARE METHOD Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 198 In chapter 3, a nonlinear Least Square method was used for optimization. This appendix explains some details about this method. We shall first state the most general form of the problem that we are addressing, namely: Minimize F(x) reSR" (1) The basic mathematical optimization problem is to minimize a total errors E which is a function of the errors at the individual data points. An important special case for E is the nonlinear least squares problem that may be presented as: E = £ _ /?(* ) (2 ) /=1 Each subfunction f(x ) represent a component of the total error E and if a vector valued function F is defined by: F T = \ f i x ) f 2(x) ■••/„(*)], (3) E =f f (4) where T signifies the transpose of a matrix. Differentiation of equation 2 with respect to Xi in turn as: => VE(x) = 2 J rf (6 ) Where J is Jacobian matrix associated with F and is an m m matrix of the form: df <7) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 199 Hence, the p-th row is the derivative vector of the p-th subfunction with respect to each element of x. A second partial differential of equation 2, assuming that the f have continuous second partial derivatives, gives: dl£ dxfiXj => . V, dXj jzi dxk _ 2y % S\f, Jj 6xtdxk V 2E(x) = 2 {jTJ + B} (8 ) (9) Where V2E is , of course, the nxn symmetric Hessian matrix of E. The (mxn) matrix B, which is the sum of the Hessian matrices of the individual subfunctions, is defined as: 5 = Z /; 0 °) In other hand, Gradiant methods for optimization are based on the Taylor expression given by: f ( x + A x ) a f ( x ) + g rAx + jA x rHAx (11) Where g T isdefined as the transpose of the gradient vector Vf which is a row matrix o f first order partial derivatives ( g T=V/=[j£- ••• and Ax is the change in the parameter values. The Taylor expression of equation 11 can be used to approximate the minimum value o f the objective function from points x near to the minimum xmin as f(x+Ax) *f(xmin). Thus, using the equations 9 and 10, the equation 11 can be presented as: Ax = - [ j Tj ] ' j Tf = -H -'V E (12) In generalJTJ is positive, so that this applications of theNewton-Raphson method should converge. In this case a fraction k of the predicted change Ax is used and the process becomes Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 200 xk+i= xk +AAxk (13) Where X<1 can either be fixed in advance or found by a linear search. The algorithm can be summarized as follows: Step 1: Input data xo, and functions f Set k=0. Step 2: Evaluate f k and Ek. If Ek has not reduced over a number of iterations, terminate the minimization and output xmin = xk and Emin = Ek. Step 3: Evaluate the nxm matrix J. Step 4: Derive VE = 2Jrf abd the Hessian H = 2JrJ. Step 5: Compute IT1 and solve for Ax = -H 1VE. Step 6 : Generate a new point x*+/ = x^+Ajc. Set k = k+1, and return to step 2. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 201 APPENDIX F NEWTON-RAPHSON METHOD FOR NONLINEAR SYSTEMS OF EQUATIONS Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 202 In chapter 4, the Newton r method was used for inversing the backscattering models. This appendix explains some details about this method. More details about the method were presented in Ortega and Rheinboldt (1970) and Press et al. (1992). A typical problem gives N functional relations to the zeroed, involving v a r i a b le s / = 1 ,2 ,..., N: fi(Xl,X2,...JCN)=0 i = 1 ,2 ,..., N (1) If we let X denote the entire vector of values x t then, in the neighborhood of X, each o f the functions^ can be expanded in Taylor series: f i ( X + S 0 = f i Q 0 + f ^ j S v + H iS X 2) where SX and (2) are the unknown errors and HfdX2) is the second and higher order terms. By neglecting terms of order SX2 and higher, we obtain a set of linear equations for the corrections of SX that move each function closer to zero simultaneously, namely: 2jxijSxj=/3i (3) j =i where OCy and Pi can be defined by and -fi respectively. Equation 3 can be solved by the Lower and Upper triangular decomposition method (Westlake, 1968). The corrections are then added to the solution vector, new old „ Xi =Xi +OU . _ T 1 = 1 ,2 , ...,N (4) and the process is iterated to convergence. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 203 REFERENCES Ortega, J. M. and Rheinboldt W. C. (1970) Iterative solution of nonlinear equations in several variables. New York: Academic Press Inc, 572 p. Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T. (1992) Numerical recipes in C. Cambridge: Cambridge University Press, 735 p. Westlake, J. R. (1968) Handbook of numerical matrix inversion and solution of linear equations. New York: John Wiley & Son Inc., 171 p. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 204 APPENDIX G SEMI-EMPIRICAL CALIBRATION OF THE IEM BACKSCATTERING MODEL USING RADAR IMAGES AND MOISTURE AND ROUGHNESS FIELD MEASUREMENTS Nicolas BAGHDADI, Imen GHERBOUDJ, Mehrez ZRIBI, Mahmod SAHEBI, Christine KING and Ferdinand BONN International Journal o f Remote Sensing, submitted on July, 2003 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 205 SEMI-EMPIRICAL CALIBRATION OF THE IEM BACKSCATTERING MODEL USING RADAR IMAGES AND MOISTURE AND ROUGHNESS FIELD MEASUREMENTS Abstract Estimating surface parameters by radar-image inversion requires the use of well-calibrated backscattering models. None of the existing models is capable of correctly simulating scatterometer or satellite radar data. We propose a semi-empirical calibration of the Integral Equation Model (IEM) backscattering model in order to better reproduce the radar backscattering coefficient over bare agricultural soils. As correlation length is not only the least accurate but also the most difficult to measure of the parameters required in the models, we propose that it be replaced by a calibration parameter that would be estimated empirically from experimental databases o f radar images and field measurements. This calibration was carried out using a number o f radar configurations with different incidence angles, polarization configurations, and radar frequencies. Using several databases, the relationship between the calibration parameter and the surface roughness was determined for each radar configuration. In addition, the effect of the correlation fimction shape on IEM performance was studied using the three correlation functions (exponential, fractal, and Gaussian). The calibrated version of the IEM was then validated using another independent set of experimental data. The results show good agreement between the backscattering coefficient provided by the radar systems and that simulated by the calibrated version of the IEM. This calibrated version of the IEM can be used in inversion procedures to retrieve surface roughness and/or moisture values from radar images. Key words: Integral Equation M odel (IEM), calibration, radar images, soil roughness, soil moisture. 1. Introduction Many studies have been carried out on the possible use of radar remote sensing for retrieving soil moisture and roughness values. Inverting the radar signal in terms of roughness and moisture Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 206 requires either a backscattering model capable of reproducing the radar signal regardless of soil roughness or moisture, or a large set of experimental data linking the backscattering coefficient to the various soil parameters (roughness, moisture) and to the instrumental parameters of the radar sensors (incidence angle, polarization, wavelength). However, to produce a database that is representative of all possible physical conditions of the soil surface using different radar configurations would require a huge investment in time and manpower, making the use of this inversion procedure difficult. Soil parameters can be retrieved from imaging radar data using radar surface diffusion models, which can be either statistical or physical. The first approach requires a large number of experimental measurements in order to derive empirical models (e.g. Oh et a l, 1992; Dubois et a l, 1995; Shi et a l, 1995). These models are dependent on the site and surface type on which they were developed and tested; furthermore, they are obtained for limited ranges of incidence angle, wavelength, and soil parameters. The second approach involves using theoretical models based on electromagnetic scattering theories; it provides relationships that are valid for different radar parameters (polarization, incidence angle, wavelength) and surface conditions (surface roughness and soil moisture). The physical approach is therefore preferable because it provides site-independent relationships. The Integral Equation Model (IEM) (Fung, 1994) is the most commonly used physical model. Unlike other models (SPM, GOM, POM, etc.) that are usually adapted to smooth or rough surfaces, the validity domain of the IEM covers the range of surface roughness values encountered with agricultural soils. To be capable of inverting this model would be particularly useful, as the physical parameters of the soil surface could be retrieved from radar images. However, none of the existing models provide consistently good agreement with the measured data from satellite radar (Rakotoarivony et a l, 1996; Remond, 1997; Zribi et a l, 1997; Baghdadi et a l, 2002b). The discrepancy between simulations and measurements can reach several decibels, which renders the inversion results inaccurate. According to numerous studies, the discrepancy between models and measured data increases with incidence angle (Oh et a l, 1992; Rakotoarivony, 1995; Boisvert et a l, 1997). It is therefore essential that these models be calibrated so as to correct or compensate for any possible defects. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 207 The description of surface roughness on bare agricultural soils is currently based on three parameters, namely the standard deviation of heights, the correlation length, and the correlation function. This is not sufficient to correctly characterize the true geometric structure of the soil. Normally, the correlation function is adjusted using an exponential or Gaussian function. However, a number of studies have shown that the backscattering coefficient varies considerably depending on the shape of the correlation function (Altese et al., 1996). Furthermore, measuring the correlation length (L) is a problem because of the substantial instability of agricultural soils. Recent studies have shown that roughness parameters estimated from field measurements are very sensitive to die length of the roughness profile (Baghdadi et al., 2000c). They have also shown that the surface height (rms) and the correlation length (L) increase with profile length. Using simulations, Oh and Kay (1998) showed that correlation length measurements are unreliable when conventional profilometers of 1 or 2 m long are used (error over 50%), whereas the accuracy associated with the rms is of the order of 15%. New approaches based on the fractal analysis o f the surface have been introduced to improve simulation of the radar signal by incorporating a new roughness parameter, namely the fractal dimension (Zribi et al., 2000). The backscattering model that we decided to test and calibrate empirically is the IEM. It takes the state of the soil into account through input parameters such as moisture (mv), standard deviation o f heights (rms), correlation length (L), and correlation function shape. Baghdadi et al. (2002a, b) undertook a study to understand the behaviour of the IEM and to develop a robust empirical calibration that would allow a good fit between the model-simulated data and the radar data. The discrepancy between the IEM and the satellite radar data should be directly related to either the shape of the correlation function or the accuracy of the correlation length measurements, as the other IEM input parameters (standard deviation of heights, soil moisture, incidence angle, and radar wavelength) are relatively accurate. The approach consisted in replacing the measured correlation length by a calibration parameter (Lopt) so that model simulations would closely agree with radar measurements. The calibration parameter (Lopt) integrates the true correlation length as well as the imperfections of the IEM. In this first study, Baghdadi et al. (2002a, b) used an exponential shape for the correlation function. Initial results from only three databases (CW 23°, C-HH39°, and C-HH-47°) showed that the calibration parameter is dependent on roughness and incidence angle. This led to the preliminary conclusion that the IEM does not correctly describe angular dependence. The dependence between the calibration parameter and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 208 the incidence angle actually artificially corrects this weakness of the model. Exponential expressions were produced for the calibration parameter (Lopt) as a function of the rms and the incidence angle (0 ). In this study, we intend to investigate this semi-empirical approach further by analyzing the effect o f the correlation function shape: in addition to the exponential correlation function, we looked at a fractal correlation function and a Gaussian function. In order to improve calibration robustness, we used a number of databases (eight experimental databases) acquired from different sites in France and Canada. The effect of radar frequency and polarization on IEM behaviour was also examined using available L-, C-, and X-band data. This paper describes the databases and the IEM. As a first step, the IEM was tested by comparing the backscattering coefficient from the radar data and the backscattering coefficient from the model. Then, an empirical calibration of the IEM was carried out in order to correct the model’s errors. Finally, the calibrated version o f the IEM was validated using another database. 2. Databases 2.1. Study areas Six measurement campaigns were carried out in France (Orgeval 94-95, Alpilles 97, and Pays de Caux 94-98-99) and two in Canada (Brochet 99 and Chateauguay 99, in the Province of Quebec). The study sites consisted of agricultural fields on low-relief plateaus. Fieldwork was carried out at the same time as airborne and satellite radar overpasses and provided descriptions of the soils and their dielectric and structural properties (roughness, moisture). > The first study area was in the Pays de Caux, in Normandy, France (long. 0°50rW, lat. 49°47'N). It was selected as a study area for the European FLOODGEN project (FLOOD risk reduction by spacebome recognition of indicators of excess runoff GENerating areas) (King, 2001). Soil composition at this site is about 67% silt, 13% clay, and 17% sand. Fieldwork was carried out in 1994, 1998, and 1999 to describe the roughness and moisture parameters in a few reference plots. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 209 > The second study area was in the Rhdne valley in southern France (the Alpilles; long. 4°45'E, lat. 43°47'N). It was chosen as part of the European RESEDA project (Baret, 2000). Soil composition is 54% silt, 40% clay, and 6 % sand. Fieldwork was carried out in 1997. > The third study area was the Orgeval site, 70 km east of Paris (long. 3°07'E, lat. 48°51'N). Soil composition is about 78% silt, 17% clay, and 5% sand. Several radar measurement campaigns were carried out over this basin, particularly as part of the international SIR-C/X SAR’94 project and the European AIMWATER project (Le Hegarat et a l, 2002). In addition, fieldwork was carried out to measure soil moisture and roughness (Zribi et al., 1997; Quesney et a l, 2 0 0 0 ). > Two study areas in Canada were also used, the first in the Chateauguay River basin south of Montreal (long. 73°46'W, lat. 45°19'N) and the second in the 650 km2 basin of the Riviere aux Brochets (long. 72°54'W, lat. 45°08'N), a tributary of Lake Champlain on the borders of Quebec, Vermont, and New York State. Soil composition at both sites is about 42% silt, 36% clay, and 2 2 % sand. 2.2. Satellite data Satellite data were obtained from the various study areas using ERS, RADARSAT, SIR-C, XSAR, and ERASME sensors. Image characteristics are described in Table 1. The radar data are available in HH and W polarizations, with incidence angles between 23° and 57°, and for three frequencies (L, C, and X). The radar images underwent various types of pre-processing in order to retrieve calibrated and georeferenced radiometric information. The average backscattering coefficient was calculated for each reference plot. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 210 Table 1. Description of the database. Database Field data Orgeval 94 CETP «094» 06 parcelles Orgeval 95 CETP «095» Pays de Caux 94 CETP «C94» Pays de Caux 98 BRGM «F98» Pays de Caux 99 BRGM «F99» Alpilles 96-97 BRGM «RES» Brochet 99 CARTEL «BRO» CMteauguay99 CARTEL «CHA» 11 parcelles Radar configuration Radar data (frequency, polarization, incidence) (roughness, moisture) SIR-C, SAR-X ERS-2 08 parcelles ERASME 45 parcelles ERS-2 RADARSAT 18 parcelles ERS-2 RADARSAT 16 parcelles ERS-2 RADARSAT C -W -440 ; L -W -44 0 C-HH-440, 45°, 52°, 55°, 57° L-HH-440, 45°, 52°, 55°, 57° X -W -450, 48°, 52°, 55°, 57° C-W -23° parcelles RADARSAT C-HH-250 C -W -250 C-W -230 C-HH-390, 47° C-W -23 ° C-HH-230, 39° C-W -23 ° C-HH-230, 40° C-HH-21°, 45° 27 parcelles RADARSAT C-HH-250, 35°, 47.5°, 47.7° 11 2 3 . Field data During the measurement campaigns, reference plots were visited and physical parameters (moisture and surface roughness) were measured at the same time as radar data were acquired. The main characteristics of the data sets used are shown in Table 1. Roughness measurements were made using laser and needle profilometers (1 and 2 m long and with 0.5, 1, and 2 cm sampling intervals). Four to twelve roughness profiles were established for each training field. From these measurements, the standard deviation of surface height (rms) and the correlation length (L) were calculated using the mean of the autocorrelation function. The surface was assumed to be isotropic and the autocorrelation function was fitted to an exponential function. The rms values depend on the agricultural practices used and the aggressive effects of rain on bare soil surfaces; lower values correspond mainly to sowed fields and higher values to recently ploughed fields. Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission. 211 The volumetric water content at field scale was assumed to be equal to the mean value estimated from several samples (4 to 15 per field) collected from the top 5 cm of soil using the gravimetric method and a TDR (Time Domain Reflectometry) probe. The soil moisture measurements used in this study were acquired either on the same day as the radar data or on different days, but in similar meteorological conditions. The standard deviation of the measured volumetric water content is about 5%. The empirical model developed by Hallikatnen et a l (1985) was used to link the volumetric water content to the corresponding complex dielectric constant. This model uses the sand and clay composition of the soil. 3. Modelling the radar signal 3.1. Integral Equation Model (IEM) backscattering model The Integral Equation Model (IEM) backscattering model (Fung, 1994) has a validity domain that covers the range of roughness values that are commonly encountered for agricultural surfaces (k.rms<3, where k is the wave number = 1.11 cm'1 in C band). It provides a value for the backscattering coefficient (cr°) using the characteristics of the sensor (incidence angle, polarization, and radar wavelength) and the target (dielectric constant, standard deviation o f heights, correlation length, and correlation function). Over bare soils in agricultural areas, the backscattering coefficient of the surface contribution is expressed as: a pp = — I/ J V n"H*,0" ,g£ (4rms2k2cos20y w (n)(2ksin 0 ,0 ) 2 n~\ n\ Re(f*pFpp) e-3™3*'™'8£ (4rms2k2cos20y w (n)(2k sin 0,0) + 2 + — \F f „=j h! (rms2k 2cos20) -W (n)(2ksm0,O) where: fhh ~ - 2 Rh cos 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (1) 212 2 *v /v vv cos 0 sin 20 4R> Fm ~ 2 CO S0 j_ sin 20 \ V 2/) N er cos20 (i jursr - s i n 20 r,r+ c o s # - J s . ( l - s m 20) _ , „ . , . , , . . R. = y : =4-: Fresnel coefficient at honzontal polarization h cos 0 + ^ s r(l - sin 20) c o s # -^ — ( l - s i n 2#) Sr K = COS0 + : Fresnel coefficient at vertical polarization — ( l - s i n 20 ) VS r Ww (a,b) = — j j p '( x , y)e -liax+by)dxdy 2n W {n) is the Fourier transform of the nth power of the surface correlation coefficient. sr : dielectric constant, which is obtained on the basis of volumetric water content using the empirical model of Hallikainen et al. (1985). Hr : relative permitivity 6 : incidence angle rms: standard deviation of surface height L: correlation length pp: co-polarization (pp = HH or W ) Re: real part of the complex number Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 213 f pp: conjugate of the complex number f pp p(x, y) : surface correlation function. Its distribution is exponential for low surface roughness values and Gaussian for high surface roughness values. Zribi (1998) proposed a fractal correlation function for bare soils in agricultural areas. For one-dimensional roughness profiles, the correlation functions are defined as follows: -f£] p (x) - e yLJ : : exponential Gaussian (2) fractal with x= -1.67 D +3.67. D is the fractal dimension calculated from the empirical correlation function that best adjusts the experimental function so that it is between the Gaussian function and the exponential function. It is approximately 1.4 for agricultural plots (Zribi, 1998). Thus, the coefficient x is approximately 1.33. This difficulty in characterizing soil roughness also applies to correlation length. The correlation length is calculated from the correlation function and is always highly variable, even on plots with homogenous soil (Rakotoarivony, 1995). This variability can introduce significant errors in the modelled radar signal. We used the IEM for this study because it is theoretically valid for a wide range of roughness values. However, many studies have shown that a discrepancy exists between simulations based on the IEM and experimental data extracted from various radar sensors (ERS, RADARSAT, SIRC, X-SAR, etc.) (Rakotoarivony, 1995; Baghdadi et al., 2002b; Zribi et al., 1997). If this discrepancy is confirmed, we would expect to correct its behaviour through a semi-empirical calibration of the model. 3.2. IE M resu lts The IEM backscattering model allows us to simulate, for a given radar configuration, the backscattering coefficient of a surface from its physical characteristics. Simulations of a 0 were Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 214 done using different databases. In order to study the effect of the shape of the correlation function, simulations were done using each of the three correlation functions: exponential, fractal, and Gaussian (Eq. 2). Values of o° simulated using the IEM and a 0 measured from radar images were compared (Figs. 1 and 2). In each case, the IEM-simulated backscattering coefficient differed from the radar-measured backscattering coefficient, regardless of the radar configuration used. Table 2 presents the results obtained (mean and standard deviation of the difference between IEM a 0 and radar cr°). In Figures 1 and 2, the mean and the standard deviation of the error were calculated on the one hand for each database and on the other hand for all the databases with similar radar configurations (slightly different incidence angles). Table 2. Comparison of uncalibrated IE M simulations and radar data for the available ERS and RADARSAT (IEM-radar) configurations. Exponential, fractal, and Gaussian correlation functions were used. ERS W 237240 RADARSAT RADARSAT RADARSAT HH217247257260 HH357397400 HH45747747.5747.70 mean standard deviation mean standard deviation mean standard deviation mean standard deviation Exponential -0.78 5.39 -1.31 3.84 1.61 3.06 3.43 2.64 Fractal 1.41 3.64 2.77 2.78 3.80 2.70 5.02 3.36 Gaussian 3.71 2.47 5.39 3.95 1.73 8.06 -5.29 17.25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 215 Backscattering coefficient from the IEM [dB] 10 5 Fractal correlation function Exponential correlation function F99: (IEM-radar) [dB] • +3.10*236 F98: (IEM-radar) [dB] - +0.12*3.98 095: (IEM-radar) [dB] • +0.63*3.16 RES: (IEM-radar) [<IB] - +2.98*2.67 Total: (IEM-radar) [dBt ■ +1.41*3.64 FSS: (IEM-radar) [dB]» +0.33*4.31 Fee: (IEM-radar) [dB] * -324*6.65 096: (IEM-radar) [dB] * +3.26*1.91 RES: (IEM-radar) [dB] » +1.19*3.89 Total: (IEM-radar) [dB]»-0.78*5.39 0 -5 -10 -10cs -15 -15 ■20 -25 -25 -20 -15 -10 -5 0 5 Backscattering coefficient from ERS [dB] -25 -25 10 -20 5 -15 -10 -5 0 Backscattering coefficient from ERS [dB] 10 Gaussian correlation function F9e: (IEM-radar) [dB]* +442*2.95 F98: (IEM-radar) [dB] • +3.13*229 095: (IEM-radar) [dB]« +3.39*1.54 RES: (lEMradar) [dB] • +4.46*236 Total: (IEM-radar) fdBl ■ +3.71*2.47 ♦ F99W23* XF98W23* A095W23’ ARESW24' (C) Figure 1. IEM-simulated backscattering coefficient (with L measured) as a function of the backscattering coefficient measured from radar images. Exponential, fractal, and Gaussian correlation functions were used: (a), (b) and (c) ERS W 23°/24° Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 216 Fractal correlation functfon Exponential correlation function BRO: (IEM-radar) [dB] - +3.08*2.74 RES: (IEM-radar) (dB) - +0.83*2.77 CHA: (IEM-md8r)(dB] • +3.02*1.77 FB0: (IEM-radar) pB) - +3.31*2,41 Total: (IEM-radar) fdBl • +2.77*2.78 from the IEM [dB] BR O ; (IEM-radar) (dB) > -3.56*4.28 R E S : (IEM-radar) [dB] • -1.68*3.44 CHA: (IEM-radar) [dB] - -1.76*3.81 FB9: (IEM-radar) [dB) - +0.01*3.17 Total: (IEM-radar) IdBI • -1.31*3.84 1 € i +V -10 ■10 0+ •15 OBROHH21' ARES HH24* + CHAHH25' ♦F90HH26* -20 •25 •25 -15 •20 5 ■10 -5 0 •15 Backscattering coefficient from Radarsat [dB] -20 •25 -25 10 •20 -15 •10 •5 0 5 Backscattering coefficient from Radarsat [dB] 10 OBRO HH2V ARESHH24' + CHAHH26* ♦ F09HH26* BRO: (IEM-radar) [dB]« +10.1*2.62 R E S: (IEM-radar) [dB] - +2.70*2.41 CHA: (IEM-radar) [dB] • +6.71*3.35 F09: (tEM-radar) |dB] - +4.09*3.47 Total: (IEM-radar) fdBl ■ +6.38*3.05 Backscattering coefficient from Radarsat [dB] (f) Figure 1 (continued). IEM-simulated backscattering coefficient (with L measured) as a function of the backscattering coefficient measured from radar images. Exponential, fractal, and Gaussian correlation functions were used: (d), (e) and (f) RADARSAT HH21724725726 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 217 Exponential correlation function Fractal correlation function 10 CHA: (IEM-radar) [dB] - +3.62*2.12 F88: (IEM-radar) [dB] * +4.09*3.33 RES: (IEM-radar) [dB] - +2.62*1.77 F99: (IEM-radar) [dB] - +4.68*2.68 Total: (IEM-radar) [dB] <++3.80*2.70 CHA; (IEM-radar) (dB) = -025*2.82 F98:(IEM-radar) (dB) ■ +1.98*3.13 RES: (IEM-radar) (dB) - +1.61*1.70 F99: (IEM-radar) [dB]« +3.73*2.49 Total: (IEM-radar) [dB] •+1.61*3.06 +M4| -10 -20 - -20- . X -40 -40 -50 I -50' -60 / -30 - -30 - -60 s W / y -60 -W -50 -30 0 -20 -10 Backscattering coefficient from Radarsat [dB] -60 10 -50 -40 -30 -20 -10 OCHA HH35’ XF98 HH39* ORESHH39* ♦ F99 HH40* 111 1 " 0 10 Backscattering coefficient from Radarsat [dB] (b) (a) 10 0*o Ul Gaussian correlation function CHA: (IEM-radar) [dB]» +0.32*11.4 FOB: (IEM-radar) [dB] ■ +428*5.82 RES: (EM-radar) [dB] - +1.68*4.89 F99: (IEM-radar) [dB] * -0.94*7.05 Total: (IEM-radar) [dB] -+1.73*8.06 j& k JS » ■20■ / / 8 -30- X X C. ♦ / ° / -40 -50 -60 -60 0 / -50 -40 -30 -20 -10 OCHAHH35* XF98HH39* ARES HH39* ♦ F99HH40" 0 10 Backscattering coefficient from Radarsat [dB] (C) Figure 2. IEM-simulated backscattering coefficient (with L measured) as a function of the backscattering coefficient measured from radar images. Exponential, fractal, and Gaussian correlation functions were used: (a), (b) and (c) RADARSAT HH35°/39740° Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 218 10 Exponential correlation function Fractal correlation function 10 BRO: (IEM-radar) [dB] * +2.16*2.22 F98: (IEM-radar) [dB) • +2.81*3,41 CHA47.6: (IEM-radar) [dB] • +3.36*1.85 CHA47.7: (IEM-radar) [dB] ■ +4.92*1.76 Total: (tEM-radar) [dB] “+3.43*2,64 H BRO: (IEM-radar) [dB)• +5.76*2.13 F99:(IEM-radar) [dB] » +4.28*3.87 CHA47.5: (iEM-radar) [dB] - +4.63*3.06 CHA47.7; (iEM-radar) [dB] * +6.14*3.08 Total: (iEM-radar) [dB] •+5.02*3.36 0 E i • H -10 r o y /X / X / k / X X / to .25 •30 •30 / >4 /^ ° + X CBROHH45* XF98 HH47° + CHA HH47.5" OCHAHH47.7* x -25 -20 -15 -10 -6 0 5 Backscattering coefficient from R adarsat [d B] OBROHH45* XF98HH47" + CHA HH47.5” OCHA HH47.7* <0 -25 •30 -30 10 -25 -20 -15 -10 -5 0 6 Backscattering coefficient from Radarsat [dB] 10 (e) (d) Gaussian correlation function 0 -10 BRO: (lEM+adar) rdB]--2.06*13.1 F98: (lEM+adar) [dB] * +226*7.47 CHM7.S: (lEM+adar) [dB] « -11.9*20.8 CHA47.7: (lEM+adar) [dB]■-10.7*20.8 Total: (lEM+adar) [dB] -5.29*17.3 -20 -30 -40 ** -50 0+ O) •60 q- I -80 IGO -90 OBROHH45* xF98HH4r + CHAHH47.5" OCHAHH47.7° -100 0- -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 Backscattering coefficient from Radarsat [dB] (f) Figure 2 (continued). IEM-simulated backscattering coefficient (with L measured) as a function of the backscattering coefficient measured from radar images. Exponential, fractal, and Gaussian correlation functions were used: (d), (e) and (f) RADARSAT HH45°/47747.5747.7° Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 219 For both the exponential and the fractal correlation functions, the bias increases as the incidence angle increases. For an exponential function, the bias varies from -0.78 dB for W 2372 4 ° to 3.43 dB for HH45°/47747.5747.7°. The IEM underestimates the radar c° for W 23724° and HH21724725726° and overestimates it for HH357397400 and HH45747°/47.5°/47.7°. Bias is greater for the fractal function than for the exponential function, varying from 1.41 dB for W 2 3 7 2 4 0 to 5.02 dB for HH45747747.5747.7°. For the fractal function, the IEM overestimates the radar ct° regardless of the radar configuration used. Unlike the results provided by the exponential and fractal functions, the bias associated with the Gaussian function is high at low incidence angles (3.71 dB for W 23724° and 5.39 dB for HH21724725726°). It is 1.73 dB for HH35739740° and -5.29 dB for HH45°/47747.5747.7°. It should be noted that for all correlation functions, the bias is less for configuration W 23°/24° than for configuration HH21724/25726°. With both the exponential and the fractal correlation functions, the standard deviation of the error is very high for W 23°/24° (5.39 dB for the exponential correlation function and 3.64 dB for the fractal correlation function). With the exponential function, it decreases with increasing incidence angle (from 5.39 dB for W 237240 to 2.64 dB for HH45°/47747.5747.7°). With the fractal function, it shows little variation with the incidence angle (maximum variations of about 1 dB). With the Gaussian function, it increases with increasing incidence angle (2.47 dB for W 23°/24° and 17.2 dB for HH45°/47747.5747.7°). These results led to the conclusion that the IEM results are far from accurate, regardless o f the correlation function used. They show that defects in the IEM introduce a clear inadequacy to the measurements. All the reference plots were used in this study, regardless of the surface roughness. The poor correlation noted between the IEM and the experimental data has nothing to do with the IEM’s validity domain (poor result regardless of k.rms). However, the exponential correlation function appears to be the best adapted to agricultural plots. A number of hypotheses have been developed to explain this discrepancy between the IEM and the radar data. The inadequacy noted could be related to the uncertainty of the correlation length measurements and/or to the model itself. According to recent studies, roughness parameters calculated from field measurements (rms and L) are very sensitive to the length of the roughness Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 220 profile (Baghdadi et a l, 2000c). These studies have shown that L increases with profile length. In addition, Oh and Kay (1998) used simulations to demonstrate that correlation length measurements are unreliable when conventional profilometers of 1 or 2 m long are used (error over 50%), whereas the accuracy associated with the rms is of the order of 15%. However, measurements are more robust and reliable for the other IEM input parameters, such as rms, soil moisture, and incidence angle. This discrepancy between the model and the data is presented herein as an introduction to the problem. In the following paragraph, we propose a semi-empirical calibration of the IEM by estimating a calibration parameter that integrates the measured correlation length and the imperfections of the model so as to ensure better agreement between the model and the data. 4. Semi-empirical calibration of the IEM Our objective is to develop a robust calibration that would ensure good agreement between IEMsimulated data and radar-sensor data. The approach involves adjusting the correlation length so as to force the model to better reproduce the data. It should be possible to extrapolate this calibration to other databases that are not used in the calibration process. In concrete terms, this would involve replacing the measured correlation length by an optimal calibration parameter (Lopt) for each radar configuration. The optimal calibration parameter Lopt is a forcing parameter that compensates for both the very approximate correlation length (L) measurement and any defects of the model. It is a semi-empirical calibration and, consequently, no modification of the model formulation should be required. Figure 3 shows the behaviour of the IEM as a function of the correlation length for a given plot. It shows that for a radar-measured backscattering coefficient, parameter L has two possible solutions, Loptl and Lopt2, which ensure good agreement between the IEM and the radar a 0. The calibration parameters Loptl and Lopt2 were calculated for all reference plots. For a small number of plots, it proved impossible to determine the values of Loptl and Lopt2 because o f a lack of agreement between the IEM and the radar cr°. In previous work, Baghdadi et al. (2002a, b) used the solution corresponding to Loptl (the lowest value), which they considered to be the optimal calibration parameter. In addition, only the exponential correlation function was used. Initial results showed that the calibration parameter Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 221 depends on the roughness and the incidence angle. In our study, we used the three correlation functions (exponential, Gaussian, and fractal) to examine the behaviour of the two solutions Loptl and Lopt2. Similarly, the calibration was improved through the use of new databases. Most of the data are from C-band radar sensors. Only the Orgeval 94 database contains data from L-, C-, and X-band radar. This database also made it possible to examine the behaviour of Lopt as a function of radar frequency. am sUJ 1 <y° r a d a r E £ 0 0 -10 1o Q -12 O ) c •c l-« ! <0 ffl Lopt2 L o p tl -10 -18 rm s -1 .7 cm ; mv=30% ; C-HH24° ; ex p o n e n tia l co rrela tio n fu n ctio n -20 0 20 40 60 80 100 C o rrelatio n le n g th [cm ] Figure 3. IEM behaviour as a function of correlation length for an exponential correlation function. Surface characteristics are defined as mv=30% and rms=1.7 cm. The radar configuration used is C-HH24°. Figures 4, 5 , 6 , and 7 show the relationship between calibration parameters and surface roughness for each C-band radar configuration and each correlation function. Two trends are noted for Loptl. The first is seen at low rms values and is characterized by a constant Loptl. The second is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 222 defined for higher rms values and for a Loptl that increases with the rms; it can be described using a power-type behaviour for the three correlation functions: Loptl (rms,0,pp)= a rmsp (3) In the case o f Lopt2, a single trend was noted for the rms, regardless of the radar configuration or the correlation function shape. This trend is described using a power-type behaviour (Eq. 3) for both the exponential and fractal correlation functions and a linear behaviour for the Gaussian correlation function (Lopt2= a.nns+P). Figure 8 shows the relationship between the calibration parameters and the measured correlation length. Baghdadi et al. (2002a, b) used exponential behaviour to describe the trend between Loptl and the rms. Only those plots having k.rms <; 3 were used. In our study, all reference plots were used, regardless o f their rms. The exponential behaviour, which is no longer valid for high rms values, was replaced by a power-type behaviour better adapted to the wide range of rms values (from 0.25 to 5.5 cm). The optimal calibration parameter must ensure better agreement between the IEM a 0 and the radar a 0 as well as correct physical behaviour between the IEM a 0 and the rms (increasing c° with increasing rms for a given moisture value). When exponential behaviour was used to describe the trend between Loptl and the rms, it proved difficult to find a function that ensured the correct physical behaviour for some configurations, especially those with low incidence angles. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 223 Exponential correlation function Exponential correlation function 250 L o p tl «24.78 rms1,684® £200 150xx 100 - 3 10 ■at 0.5 0.78 1 2 2.5 1.5I rma surface height [cm] 4.5 3.5 0.5 2.5 rma surface height [cm] (a) (d) Fractal correlation function 20 Fractal correlation fiaictlon 120 18 Calibration parameter "Loptl" [cm] 4.5 3.5 Lop£2=16.79 rms1-2628 §100 Loptl=1.3978 rms1 16 80 12 60 10 8 40 6 • F90W23* X FOB W23* A 005 W23* a RE3W24* -— Loptl 4 Loptl - 0.01 2 20 0 0 0 0.5 0.70 1 1.5 3 2.5 rms surface height [cm] 2 3.5 0 4 0.5 3 2 2.5 rms surface height [cm] 1 (b) 3.5 4 4.5 (e) Gaussian correlation function Gaussian correlation function Calibration parameter -Loptl" [cm] Lopt2=8.34 rms+ 1.10 I Loptl=1.0604 rms1 8 ) 6 4 15♦ F00W23* X F08W23* A 005 W23* a RESW24* — Loptl Loptl - 0.02 2 0 25 0 0.5 0.S 1 1.5 2 2.5 3 rms surface height [cm] (C) 3.5 4 4.5 ♦ F00W23* X FOB W23® A 006 W23* a RESW24* — Lopt2 10- % o 0 0.5 1 1.5 2 2.5 3 rms surface height [cm] 3.5 (f) Figure 4. Calibration parameters Loptl and Lopt2 for W 2 3°/W 24° (ERS) as a function of surface height, for exponential, fractal, and Gaussian correlation functions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 4.5 224 Exponential correlation function Exponential comlaHan function o BROHH214 a RE8HH24* -i- CHAHH25* • F09HH20* - - Upt2HH21* Lopt2 HH24*^5*^6C f 500 o 40- 400 Lopfl *2.0737 300200 20- 10- o BROHH2V A RES HH24* + CHAHH25* • FMI*420* toptl -2,05 100 —H*1 0.5 2.5 3.5 rms surface height [cm] 1 4.5 2 0 5.5 0.5 1 2.5 3 3.5 rms surface height [cm] 1.5 4 2 (d) (a) Fractal correlation function Fractal correlation function 350 c * BRO HH21* RE8HH24* 4- CHAHH26* « F09HH26* - - Lopt2 HH21* LoPt2 HH24*.2S* 300 .14 • 200 - ++ o BROHH21* A RE8HH24* Loptl -1.57 +CHA1W 25* >, • F09HH26* -— Loptl 0.5 1.6 3.5 2 2.5 rms surface height [cm] 4.5 5 0 5.5 0.5 1 1.5 2 2.5 3 3.5 rms surface height [cm] (b) 4.5 4 4.5 5 (e) Gaussian correlation function 10 4 correlation function o 8ROHH21* a RES HH24* + CHAHH26* • F09HH20* - - Lopt2HH21* L0Pt2 HH24*.2S*.26< e +1.60 6 4 +ofH | O2 0 o BROHH2V a RESHH24' + CHAHH26' * F00 HH26S 10- —-L o p tl 0 0.5 1 2.5 3 3.5 rms surface height [cm] 2 (c) 4 4.5 5 5.5 0 0.5 1 1.5 2.5 3 3.5 rms surface height [cm] 2 (f) Figure 5. Calibration parameters Loptl and Lopt2 for HH21°/24725°/26° (RADARSAT) as a function of surface height, for exponential, fractal, and Gaussian correlation functions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 5.5 225 Calibration parameter "Loptl” [cm] Fractal correlation function 14 - Exponential correlation function 300 + CHAHH85* X F08HH38* * RESHH40* * FM-HH40* §250 - ■ Loptl HH35° Lootl HH38*.40* 200 10- Lop/2=17.5 rms145 150 4*X 100 • + CHA HH36* X FO0HH30* a RESHH40* ♦ F00HH40* —Lopa 2 2.5 3.5 rme surface height [cm] 0.5 4 5 0 5.5 0.5 1 1.5 2 2.5 3 rme surface height [cm] (a) Calibration parameter "Loptl" [cm] to 30 5 5.5 Fractal correlation function 160 CHAHH35* F98HH3Q* RES HH40* F00HH40* Loptl HH36* Loptl HH39M0* 140 I 120 100 Lop/2=10.62 rms1 i 20 8 10 40 • Loptl *0.7399 im r Loptl -1,20 O 1.5 0.5 2 2.5 3.5 rms surface height [cm] 4.5 + X A • — ♦£! 0 o 5.5 0.5 1 2.5 3 3.5 rms surface height [cm] 2 (b) 5 4.5 Calibration parameter "Loptl" [cm] 4.5 (d) Exponential correlation function + X A ♦ - — 4 4 3.5 5 5.6 Gaussian correlation function 35 CHAHH36* F08 HH39* RESHH40* FM HH40* Loptl HH3S* •Loptl HH3©e,400 4.5 (e) Gaussian correlation function + X A « ----- 4 CHAHH36* F08HH38* RE8HH40* F09HH40* Lopt2 I 10 Lop/2 *5.34 rms +0.60 25 Lop/1=0.7665 rms10142 3- 20 2.515 2 1.5 1 Loptl "0,82 * + 10 x* ' '& £ ■ 5 0.5 0 0 0.5 -t- CHAHH36* X F98HH38* a RESHH40* ♦ F0OHH4O* — Lopt2 Lop/1*0.5469 rms10®44 *xl 1 1.5 2 2.5 3 3.5 rms surface height [cm] (c) 4 4.5 5 5.5 0 0.5 1 1.5 2.5 3 3.5 rms surface height [cm] 2 4 4.5 (f> Figure 6 . Calibration parameters Loptl and Lopt2 for HH35739°/40° (RADARSAT) as a function of surface height, for exponential, fractal, and Gaussian correlation functions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 5.5 226 Exponential correlation function o BRQHH45* X FB8HH47* + CHAHH47.5* o CHA HH47.r — - Loptl HH450 -------Lopt HH47*&4745*:47.7* 18 Calibration parameter "Loptl" [cm] Exponential correlation function 180 20 16 14 0 ^ 160 a O Lopf1=0.5931 rms1* 47 / 120- V / * /« s 12 10 8 6 100 - Lop(2=11.63 rms1'5836 80OX 4 ^ Loptl -0.70 2 0 o BROHH45* I\ *4 v S ^ sfx X FS8HH47* + CHAHH47.5* Lppfl -0.4258 rms?0573 o CHA HH47.7* — LopC 4 0 0.5 1 1.5 2 Z5 3 3.5 4 rms surface height [cm] 4£ 5 5.5 0 6 0.5 1 1.5 2 Calibration parameter "Loptl" [cm] 8- 0 X + 0 — • 4.5 5.5 6 Fractal correlation function 100 BROHH45* FB8HH47" CHAHH47.5* CHAHH47.7* Loptl HH45* Lopt tfrt47";47.6*;47.7* Oo I Lqp/1=0.5397 rms148“ 70- 6 Lopf2»7.98 ims1*416 50- &40o BROHH46* X F98HH4r + CHA HH47.6* Lopfl=0.4106 rms Loptl “ 0.70 x off "T 0 0.5 o I" 1 1.5 2 2.5 3 3.5 4 rme surface height [cm] 4.5 5 5.5 6 0 0.5 1 1.5 2 (b) 3.5 3 2.5 CHAHH47.7* —lope o X + 0 BRO HH45" FOB HH47* CHA HH47.5* CHA HH47.7* — . Loptl HH4S0 • Lopt HH47*;47,5*;47.7* 3 3.5 4 2.5 rms surface height [cm] 4.5 5 5.5 6 (e) Gaussian correlation function Calibration parameter "Loptl* [cm] 5 (d) (a) Fractal correlation function 10 2.5 3 3.5 4 rms surface height [cm] Gaussian correlation function 25 20 Loptl - 0.4983 rma ! Lop(2=3.86 rms+0.588 15 2 10 1.5 1 Loptl .0.4377 rma10574 X £ -,0 66 + s * * f e x* 0.5 o BROHH45* X FS8HH47* + CHAHH47.6* 5 o CHAHH47.7* ~-Lapt2______ 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 mm surface height [cm] (c) 4.5 5 5.5 6 0.5 1 1.5 2 2.5 3 3.5 4 mis surface height [cm] 4.5 5 (f) Figure 7. Calibration parameters Loptl and Lopt2 for HH45747°/47.50/47.7° (RADARSAT) as a function of surface height, for exponential, fractal, and Gaussian correlation functions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.5 6 227 200 70 180 60 e, H 50 160 1 140 3 120 ' S 40 100 30 A 20 10 0 0 10 20 30 40 50 60 70 20 Mesured correlation length [cm] 40 80 100 120 140 160 180 200 Mesured correlation length [cm] (e) (a) Calibration parameter "L optl” [cm 600 60 - 500 - 50 400 40 300 30 - 20 | 200 3 100 - - ♦ HH26-F99 ♦ HH26-F99 10 + HH25-CHA HH24-RES + HH25-CHA 0 HH21-BR0 OHH21-BRO A 20 30 40 HH24-RES 50 Mesured correlation length [cm] (b) 60 70 A 0 200 300 400 500 100 Mesured correlation length [cm] (f) Figure 8 . Comparison between calibration parameters and measured correlation length, for an exponential correlation function: (a) and (e) C -W 230/24° (b) and (f) C-HH21 °/24725°/26° Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 600 228 300 250 ■ q 200 40 1 15030 - o 100 OHH35-CHA OHH35-CHA X HH39-F98 X HH39-F98 A HH39-RES ♦ HH40-F99 0 10 20 30 40 50 60 ♦ HH40-F99 0 70 100 50 150 200 250 300 Mesured correlation length [cm] Mesured correlation length [cm] (C) (g) 200 60 150 - S 50 is 40 - E 1 00 - 30 - 20 - 50 OHH45-BRO 10 - 0 o<p 10 20 30 40 + HH47.5-CHA + HH47.5-CHA OHH47.7-CHA O HH47.7-CHA 50 Mesured correlation length [cm] (d) Figure O HH45-BRO X HH47-F98 XHH47-F98 60 70 0 50 100 150 Mesured correlation length [cm] (h) (continued). Comparison between calibration parameters and measured correlation length, for an exponential correlation function: (c) and (g) C-HH35°/39°/40° (d) and (h) C- HH45747747.5°/47.7° 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 200 229 Figures 9 and 10 illustrate the behaviour of a 0 as a function o f rms by using the analytical expressions of Loptl and Lopt2 in the IEM. Only Lopt2 comes close to providing a correct physical behaviour of a 0 as a function of rms, regardless of the correlation function used. The use o f fractal and Gaussian correlation functions leads to an extension of the IEM’s theoretical validity domain from k.rms=3 to k.rmsw5.3. With the exponential correlation function, the IEM ensures correct physical behaviour to approximately k.rms=3. The results show that the optimal calibration parameter Lopt2 is highly dependent on the incidence angle (Fig. 11). It decreases as the incidence angle increases. For this reason, it proved impossible to identify a single trend between RADARSAT configuration HH21° and RADARSAT configurations HH24°/25°/26°. As for polarization, the Lopt2 value was slightly less for W 23724° than for HH247257260. The difference between the two polarizations is slight with the Gaussian correlation function and very high with the fractal correlation function. In order to evaluate the efficiency of the calibration, simulations were carried out using the calibrated IEM for each radar configuration and each correlation function. The correlation length measured for each plot was replaced by the relevant calibration parameter Lopt2 extracted from the previously established relationship between Lopt2 and the parameters rms, 0, and pp. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 230 L Is given by the relationship between Lopt2 and m e for G-W23724* L is given by the relationship between Loptl andntBf6rC-W23<724° -4 3 i I -10 -10 -12 -12- -14 -14- -16- -16- -e-Biponentlel -18 -18- — xt—Fractal -20 -20 -B-Gaussian 0 1 as 15 2 3 3.5 4 4.5 0 1 0.5 2 25 3 rms surface height [crrj m s sufeoe height [cm] (a) 25 4 4.5 (d) L is given by the relafiORshlp between Loptl and rms for C4W21724V25726* Lis given by the relationship between Lopt2 and rms for C-M24*/25*/26* mv=40%, e=23* ID E. 3 i« ■" £ i -io E ODDOD O BOB -5 £ i 4» -10 1-15 -15 -20- -20 -25 -•-Exponential -s-Gaussian -25 0 0.5 1 1.5 2.5 3 2 3.5 m a surface height [cm] (b) 4 4.5 5 5.5 0 0.5 1 1.5 2 25 3 3.5 rms surface height [cm] 4 4.5 5 (e) Figure 9. IEM behaviour as a function of rms surface height, using the analytical expressions of Loptl and Lopt2: (a) C -W 23°, mv=40%, Loptl extracted from C -W 237240 (b) C-HH23°, mv=40%, Loptl extracted from C-HH21724725726° (c) C-W 23°, mv=40%, Lopt2 extracted from C-W 23724° (d) C-HH23°, mv=40%, Lopt2 extracted from C-HH247257260. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.5 231 L Is given by the relationship between Lopt2 and mis lor C-HH35°/39740° L Is given by the relationship between Loptl and rms for C-HH39°/40“ ie « i -10- a -15 -15 -20- -20- 1 -25 -25 0 0.5 1 1.5 2 2.5 3 3.5 4 rms auface height [cm] 4.5 5 5.5 6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 m s surface height [cm] (a) (d) L Is given by the relationship between Loptl and rms lor C-HH47747J F m .V L Is given by the relationship botwuon Loptt and rms for C-HH45*M7*/47.S747.7* IEM [dB] S T 2, ie -5£ I -10i ## -10 9C-15- -15 -20 a! -20-25 -25 0 0.5 1 1.5 2 2.5 3 3.5 4 m s surface height [cm] (b) 4.5 5 5.5 6 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 rms surface height [cm] (e) Figure 10. IEM behaviour as a function of rms surface height, using the analytical expressions of Loptl and Lopt2: (a) C-HH38°, mv=40%, Loptl extracted from C-HH39°/40° (b) C-HH470, mv=40%, Loptl extracted from C-HH47747.5°/47.7° (c) C-HH38°, mv=40%, Lopt2 extracted from C-HH35739°/40° (d) C-HH470, mv=40%, Lopt2 extracted from C- HH45747747.5747.7 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 232 Exponential correlation function 400 — Lopt2W23724* — Lopt2HH24725726* 350 - ■ Lopt2 HH35/39740’ 300 - —Lopt2 HH45T47747.5747.7" T 1 250 ■ 150 - 100 • 50 - 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 rms surface height [cm] (a) Fractal correlation function 250 Lopt2W23724° Lopt2 HH24725V26" § 200 - Lopt2 HH35739740° Lopt2 HH45747747.5747.7* 150 • 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 rms surface height [cm] (b) Gaussian correlation function 45o. 40 ■ 35 - Lopt2 HH24725726* — Lopt2 HH35739740* Lopt2 HH45747747.5747.7" 30 - 25 20 S 15 JB 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 rms surface height [cm] (C) F igure 11. Effect of incidence angle and polarization on calibration parameter Lopt2. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 233 Figures 12 and 13 present a comparison of a 0 simulated by the calibrated IEM and a 0 measured from radar data. Table 3 presents statistics relating to the difference between o° simulated by the calibrated IEM and radar ct°. After calibration, the bias between the IEM and the radar data decreased markedly to less than 1 dB, regardless o f the radar configuration or the correlation function used. For example, for HH45747°/47.5747.7°, the bias decreased from 3.46 dB to -0.07 dB for the exponential function, from 5.18 dB to -0.28 dB for the fractal function, and from 4.76 dB to -0.91 dB for the Gaussian function. Furthermore, the standard deviation of the error noted before calibration decreased substantially with the calibrated IEM (cf. Table 3). After calibration, it was about 1.3 dB for W 2 3 7 2 4 0, 1.7 dB for HH21724725726°, 1.4 dB for HH35739740°, and 1.8 dB for HH45747°/47.5747.7°. In conclusion, the calibration was efficient for every radar configuration used. The best results were provided by the fractal correlation function. Table 3. Comparison of calibrated IE M simulations and radar data for the available ERS and RADARSAT (IEM-radar) configurations. Exponential, fractal, and Gaussian correlation functions were used. ERS W 23724° mean standard deviation RADARSAT RADARSAT RADARSAT HH21724725726° HH357397400 HH45747747.5747.70 mean standard deviation mean standard deviation mean standard deviation Exponential 0.15 1.31 -0.40 1.73 0.35 1.49 -0.07 1.80 Fractal 0.05 1.32 -0.63 1.76 0.11 1.36 -0.28 1.60 Gaussian -0.01 1.31 +0.26 1.54 0.08 1.48 -0.91 2.05 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 234 Exponential correlation function 10 I E o Fractal correlation function 10 F 9 9 : (lEM-radar) [OBJ = +0.49*1.39 F 9 8 : (IEM-radar) [dB] ■ -024*1.05 0 9 5 : (lEM-radar) [dB] « +0.98*1.89 ‘ RES: (IEM-radar) [dB] = +0.20*1.19 T otal: (lEM-radar) [dB]» +0.15*1.31 * F99: (EM -radar) {dB] = +0.37*1.40 F98: (IEM-radar) {dB] = -0.19*1.11 095 : (iEM-radar) [dB] * +0.78*1.94 RES: (IEM-radar) [dB]« -0.11*1.18 Total: (IEM-radar) IdB) * +0.05*1.32 -5 «r -10 - -10 - -15 - -15 ♦ F 99W 23* X F98W 230 A 0 9 5 W23® -20 2 A RES W 24* —IK.■■MU -25 -25 -20 -15 -10 -5 0 5 ♦ F99 W23" XF88 W23* o -20 A095 W23* A RES W24° -25 10 -25 B a ck sca tte rin g coefficient from ERS [dB] -20 -15 -10 -5 0 5 10 B ackscattering coefficient from ERS [dB] (a) (*>) G a u ssia n correlation function 10 i--------------------------------------- -» e FB9; (lEM-mdar) [dB] - +0.48*1.38 [dB ]+0.48*1,30 F 09 8 :(IE : (lEM-radar) [dB] - -0.18*0.98 -0.19*0.88 M -m d ar)p B ]= c -redar)[dB)- +0.91*1.92 +0.91*1.32 0 09 56 :(IEM -radar)[dB]0 ' RES: (lEM-mdar) (IEM-radar) [{dB] d B ]- - -0.86*1.10 -0.58*1.18 T o tal: f IEM-radar) IdBl - -0.01*1.31 Totel:(KM -radar>ldB1--0.01*1.31 * S g • £ 0- | -5 - / / / / / / / M -1° - /* A 19 r ♦- F99 — Foe W 23* / S “ / " X F98W F 9 8 W23* 23A 0 9B5W 5 W 23* AO *A RES W 24+ 24* / „ / -25 Y~ -25 :-------- 1-------- 1-------- 1-------- r-J---- 1--------20 -15 -10 -5 0 5 10 B ackscattering coefficient from ERS [dB] (C) Figure 12. Comparison between the backscattering coefficient simulated by the calibrated IEM and the backscattering coefficient measured from radar images. Exponential, fractal, and Gaussian correlation functions were used: (a), (b) and (c) ERS W 23°/24° Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 235 10 m Si E xponential correlation function 5 z ui <D £ 0 C ® o + .JT nity a *a 0 * -dgr* ♦ O 'S fjjL A o> c ■c -15 OBRO HH21° A RES HH24" + CHA HH250 ♦ F09 HH26* 2 •20 8 m -25 -20 -15 -5 -10 /* & A -25 -----r - i♦e -5 O c) 1 s BRO: (lEM-radar) [dB] ■-0.08*1.07 RES: (IEM-radar) [dB] *-1.44*1.28 CHA: (lEM-radar) [dB] * +0.88*0.87 F99: (IEM-radar) [dB] = -1.61*2.14 Total: (lEM-radar) (dB) * -0.63*1.76 a2 , BRO: (lEM-radar) [dB]« +0.06*1.09 RES: (lEM-radar) [dB] ■ -1.31*1.37 CHA: (IEM-radar) [dB]» +1.08*0.94 ' F99: (IEM-radar) [dB] « -1.18*2.07 Total I (lEM-radar) [dB] =■-0.40*1.73 E ■s Fractal correlation function 10 -10 -5 0 5 OBRO HH210 a RES HH24* + CHAHH26" ♦ FB9 HH26“ 8 m -25 -25 10 -20 -15 -10 -5 0 5 10 Backscattering coefficient from Radarsat [dB] B a c k s c a tte rin g c o e ffic ie n t from R a d a rs a t [dB] (d) (e) 10 CD 2. S LLJ G a u s s ia n c o rre la tio n fun ctio n BRO: (lEM-radar) [dB] * +0.00*1.07 RES: (lEM-radar) [dB] * -0.56*1.21 CHA: (iEM-radar) [dB] * +0.69*0.89 ' F99: (lEM-radar) [dB]» +0.92*2.18 Total: (lEM-radar) [dB] * +0.26*1.54 « £ -5 A / O) /+ rc •15 !s 2 o8 / -25 - ' .......1..............f ...... ■"11 -25 -20 -15 -10 " 1"...........11 -5 0 OBRO HH21" ARES HH24+ CHA HH25* ♦ F99 HH26* 1 r 5 10 B a c k s c a tte rin g c o e ffic ie n t from R a d a rs a t [dB] (f) Figure 12 (continued). Comparison between the backscattering coefficient simulated by the calibrated IEM and the backscattering coefficient measured from radar images. Exponential, fractal, and Gaussian correlation functions were used: (d), (e) and (f) RADARSAT HH21°/24725726° Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 236 10 m g, s a 0 5 E 1 5 0 E x ponential c o rrelatio n function 10 CHA: (IEM-radar) [dB] • +0.51*1.48 FSB: (IEM-radar) (dB] « '*0.10*1.86 - RES: (lEM-radar) [dB] - -1.76*0.96 FSB: (lEM-radar) (dB] * -*0.11*1.88 Total: (lEM-radar) [dB] -0.07*1.80 F ra c ta l co rrela tio n fu n ctio n CHA: (IEM-radar) [dB]« +0.03*1.50 F98: (lEM-radar) (dB] * +0.11*1.38 - RES: (lEM-radar) [dB] * -1.73*1.08 F99: (iEM-radar) [dB]■-0.29*1.91 Total: (lEM-radar) [dB] --0.28*1.60 -5 I *3 -10 I S’ •c £u <s ♦ xfHx -15 a yx -20 -25 OCHAHH35" XF96HH390 ARES HH39" ♦ F99 HH40° / -30 -30 -25 -20 -15 -10 -5 0 5 OCHA HH35“ XF98 HH39* a RES HH36* ♦ F99 HH40* -30 -30 10 -25 -20 -15 -10 -5 0 5 10 B ackscattering coefficient from R ad arsat [dB] Backscattering coefficient from R adarsat [dB] (a) (b) G aussian correlation function 10 CD 5L s UJ CHA: (lEM-radar) [dB]« +0.82*1.54 F98: (lEM-radar) [dB] » -0.89*1.44 - RES: (IEM-radar) [dB] ■ -2.56*1.42 F99: (lEM-radar) [dB] = -2.16*2.22 Total: (lEM-radar) [dB] -0.91*2.05 E £ -5 SL J> / 8 . 15 O ) e r | n ** / -20 OCHA HH350 XF98 HH39* A RES HH39° ♦ F09HH4O0 -25 CD -30 -30 -25 -20 -15 -10 -5 0 5 10 Backscattering coefficient from R adarsat [dB] (c) Figure 13. Comparison between the backscattering coefficient simulated by the calibrated IEM and the backscattering coefficient measured from radar images. Exponential, fractal, and Gaussian correlation functions were used: (a), (b) and (c) RADARSAT HH35°/39740° Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 237 Exponential correlation function Fractal correlation function 10 BRO: (lEM-radar) (dB) - *0.12*1.40 FOB: (lEM-radar) [dB]» +0.58*1.56 CHA47.5: (lEM-radar) [dB] - -0.88*1.12 CHA47.7: (lEM-radar) [dB]» +0.88*1.36 Total: (IEM-radar) [dB] -+0.28*1.48 m a i BRO : (lEM-radar) [dB] - +0.03*1.38 F98: (lEM-radar) [dB] - +0.25*1.18 - CHA47.5: (IEM-radar) [dB]»-0.86*1.09 CHA47.7: (IEM-radar) [dB]» +0.58*1.31 Total: (IEM-radar) [dB] >+0.02*1.32 i 1 -5 E ® 0 -10 1S 0 -15 " -15 o SMRw f CO 1 -20 OBRO HH45 XF88HH47* + CHA HH47.5 OCHA HH47.7* -30 -30 -30 -25 -20 -15 -10 -5 0 5 OBROHH450 XF08 HH47“ + CHA HH47.5® OCHA HH47.7” -25 -30 10 -25 -20 -15 -10 10 Backscattering coefficient from Radarsat [dB] Backscattering coefficient from Radarsat [dB] (e) (d) Gaussian correlation function 10 BRO : (lEM-radar) [dB] = +1.15*1,38 F98: (lEM-radar) [dB] = +0.55*124 S' 2, 5 - CHA47.5: (lEM-radar) [dB] = -1.29*1.17 3? CHA47.7: (lEM-radar) [dB] = +0.06*1.35 UJ Total: (IEM-radar) [dB] «0.01*1.51 o n JZ f= £ -5 c *3 -10 t oo -15 e & -20 a s s -2b m OBRO HH45" XF98 HH47* + CHA HH47.5* OCHA HH47,7° -30 -30 -25 -20 -15 -10 -5 0 5 10 Backscattering coefficient from Radarsat [dB] (f) Figure 13 (continued). Comparison between the backscattering coefficient simulated by the calibrated IEM and the backscattering coefficient measured from radar images. Exponential, fractal, and Gaussian correlation functions were used: (d), (e) and (f) RADARSAT HH45747747.5°/47.7° Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 238 5. Validation of the IEM calibration In order to validate the IEM calibration, we used the Pays de Caux 94 database with its two Cband configurations (W 25° and HH25°). This database was not used in the calibration. The helibome ERASME radar sensor was used during this campaign. Figures 14 and 15 illustrate the results provided by the IEM before and after calibration. In the calibrated version of the IEM, we used the Lopt2 extracted from the analytical expressions established during the calibration of W 2 3 °/W 2 4 ° and HH24°/HH25°/HH26°. Table 4 presents validation results for the calibrated IEM. These results show that the proposed semi-empirical calibration of the IEM is robust, as it provides improved results. The biases and the standard deviations of the error have decreased for the two radar configurations and the three correlation functions. The results obtained using the Gaussian correlation function are not quite as good as those arrived at with the exponential and fractal correlation functions. Table 4. Calibration validation using ERASME VV-250 and ERASME HH-250 (Pays de Caux 94) data. The mean and the standard deviation of the difference between IEM a° and radar a 0 were calculated before and after calibration. ERASME W 2 5 ° Before calibration ERASME HH25° After calibration Before calibration After calibration Exponential 0.64 1.97 -0.09 1.54 0.40 2.33 -0.46 0.91 Fractal -0.61 3.37 -0.35 1.73 -0.92 3.24 0.03 1.20 Gaussian -2 1 .2 0 27.83 -0.96 2.21 -19.89 20.29 0.31 1.51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 239 F ractal co rrelatio n function E xponential correlation function CS4: (lEM-radar) (dB]« +0.40*2.03 CB4: (IEM-radar) [dB] • -0.92*3.24 aat s Ul 0 £ E 1 I <£ -10 • -15 - -15 - -20 -20 - re m -25 - -25 0 -20 -15 -10 -5 Backscattering coefficient from ERASME [dB] -25 -20 -25 -15 -10 ■5 0 Backscattering coefficient from ERASME [dB] (b) (a) G aussian correlation function C94 : (lEM-radar) [dB] • -19.89*20.29 -15 - S -25 - -35 - ■8 -55 - 1 | -65 - 8 ° -75 ■75 -65 -55 -45 -35 -25 -15 -5 5 Coefficient de rdtrodlffusion ERASME [dB] (C) Figure 14. Backscattering coefficient simulated by the uncalibrated IEM as a function of the backscattering coefficient measured by the ERASME sensor. Exponential, fractal, and Gaussian correlation functions were used: (a), (b) and (c) C-HH25° Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 240 Exponential correlation function Fractal correlation function CM: (IEM-radar) (dB]« +0.64*1.07 * -10 CM : (IEM-radar) [dB] = -0.61:l:3.37 -10 - -15- -20 - -15 - S -20 - - -25 -25 -25 -20 -10 -15 0 -5 -25 Backscattering coefficient from ERASME [dB] -20 -15 -10 -5 0 Backscattering coefficient from ERASME [dB] (e) (d) Gaussian correlation function CM :(IEMradar)]dB]*-21.20*27.B3 « -15 - i -25- £ § -35-45 a -55 -65 -75 ■75 -65 -55 -45 -35 -25 -15 -5 5 Backscattering coefficient from ERASME [dB] (f) Figure 14 (continued). Backscattering coefficient simulated by the uncalibrated IEM as a function of the backscattering coefficient measured by the ERASME sensor. Exponential, fractal, and Gaussian correlation functions were used: (d), (e) and (f) C -W 25° Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 241 Backscattering coefficient from the IEM [dB] Exponential correlation function Fractal correlation function C94: (IEM-radar) [dB]=-0.46*0.91 CB4: (lEM-radar) [dB) - +0.03*1.20 -5 - -10 - -10 -15- a -2 0 - f - -15 - -20 ♦ C94-HH25' -25 -25 -25 -20 -10 -15 -5 -25 0 -20 -15 -10 -5 0 Backscattering coefficient from ERASME [dB] Backscattering coefficient from ERASME [dB] (a) (b) G au ssian correlation function C94: (lEM-radar) [dB] = +0.31*1.61 t -10 - o -1 5 - -20 - -25 -20 -15 -10 -5 0 B ackscattering coefficient from ERASME [dB] (C) Figure 15. Backscattering coefficient simulated by the calibrated IEM as a function of the backscattering coefficient measured by the ERASME sensor. Exponential, fractal, and Gaussian correlation functions were used: (a), (b) and (c) C-HH25° Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 242 E xponential correlation function Fractal correlation function C94: (IEM-radar) [dB| —0.09*1.64 -10 C84: (EM-radar) [dB] = -0.35t 1.73 -10 - -15 - 8 - -15- o> 3 -20 -20 - -25 - -25 -25 -20 -15 -10 -5 0 -20 -25 Backscattering coefficient from ERASME [dB] -15 -10 ■5 0 Backscattering coefficient from ERASME [dB] (d) (e) Gaussian correlation function C94: (lEM-radar) [dB] - -0.96*2.21 -5 - -10 - 8 -15 - g -20 - -25 -25 -20 -15 -10 ■5 0 Backscattering coefficient from ERASME [dB] (f) Figure 15 (continued). Backscattering coefficient simulated by the calibrated IEM as a function of the backscattering coefficient measured by the ERASME sensor. Exponential, fractal, and Gaussian correlation functions were used: (d), (e), and (f) C-W 25° Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 243 6. Effect of radar frequency on calibration In order to study the effect of radar frequency on the IEM calibration, simulations were done using the Orgeval 94 database, or L-, G-, and X-band data from the SIR-C sensor were acquired using several different incidence angle and polarization configurations. Figure 16 shows the behaviour o f the calibration coefficient Lopt2 as a function of surface roughness for X-band data retrieved using W polarization and incidence angles from 45° to 57°. As was the case for Cband data, the calibration parameter Lopt from X-band data increased with increasing surface roughness. Figure 17 presents L-band and C-band calibration results for radar configurations with HH polarization and incidence angles from 44° to 57°. The parameter Lopt2 and the rms increase regardless of the correlation function or the radar frequency. With the exponential correlation function, the C-band Lopt2 was higher than the L-band Lopt2. The opposite behaviour was noted for the Gaussian correlation function (L-band Lopt2 higher than C-band Lopt2). For the fractal correlation function, the C-band Lopt2 appears to be slightly higher than the L-band Lopt2. From these results, we conclude that the IEM calibration is dependent on the radar frequency. Calibration parameter Lopt2 increases abruptly with the rms for both exponential and fractal (exponential or power type) correlation functions. This increase is less significant for the Gaussian (linear type) correlation function. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 244 100-n 90 an - Exponential correlation function, X-band ©004 W4$* XO04 W48* +O04W52* □O04WS5* X 094W Sr m"l 70■1 60O 1 50- Ic 40 - 1 30- S n 20- u 10 o --- T O 1 0.5 1.5 2 2.5 3.5 rms surface height [cm] (a) Fractal correlation function, X-band ©004 W45* X094W 4T +ow w a r 0004 WSS" x ow vvsr 30 - , 20 - 0.5 1 1.5 2 2.5 3.5 rms surface height [cm] (b) 30 •25 • a Gaussian correlation function, X-band ©004W 46* XO04W 48* +O04W 52* OO04W 56* XO04W6r 20 15 ■ + B 1 I a 0.5 (c) 9 ° * * 1.5 | ° 2 2.5 3.5 rms surface height [cm] Figure 16. Behaviour of the calibration parameter Lopt2 for X-band radar data (Orgeval 94 database) with configurations W 45748752755°/57° (SIR-C). Exponential, fractal, and Gaussian correlation functions were used. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 245 Exponential correlation function, L and C bands 90- •-1 AO04*HH44#*C OO04-HH8T-L ■094-HH6r.C 0 0 9 4 - HHB5* - L 70 • 10 ♦O04-HHB5*«C Ot»4-HH57#-L •004-HH57*-C • 0.5 1 1.5 2 2.5 3.5 3 4 rms surface height [cm] (a) Fractal correlation function, L and C bands 50 1,40 40 0 4 - HH44*-L 4094. HH44*.C □004■ 004. 0004* ♦ 004. 0004* •0 0 4 . HH82*-L HH62°«C HH 6T-1 HH56* - C HH5T-L HHSr.C 30 .20 10 0.5 (b) 1 1.5 2 2.5 rm s surface height [cm] 3 3.5 Gaussian correlation function, L and C bands 30 £ 25 g 4094* 4.094* □004* ■004* 0094♦004. 0004•004- HH44° - L HH44* - C HH52® - L HHB2* -C HH W -L HH65* - C HHBr-L H H Sr-C o 20 I 15 E & O 10 33 & JQ 0.5 1.5 2 2.5 3.5 rms surface height [cm] (c) Figure 17. Calibration parameter Lopt2 as a function of rms for L- and C-band radar data (Orgeval 94 database), HH polarization, and incidence angles between 44° and 57°. Exponential, fractal, and Gaussian correlation functions were used. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 246 7. Conclusions Modelling radar signals requires a good description of the soil surface and a suitable backscattering model that is capable of reproducing a backscattering coefficient similar to that measured by radar sensors. The IEM backscattering model was selected for analysis in this study because its validity domain is adapted to agricultural soil surfaces. However, the IEM does have defects that are not insignificant as it does not accurately reproduce the backscattering coefficient measured by radar sensors. To correct these defects, a semi-empirical calibration of the model was carried out and evaluated over a number of study sites in France and Canada in order to improve the correlation between simulated and measured data. The proposed calibration markedly improved the IEM’s performance for all radar configurations and study areas (reduced bias and standard deviation of the error). This calibration proved to be robust and widely applicable, as it is not dependent on either the database or the sensor used. The IEM was calibrated using radar configurations with different incidence angles (23° to 57°), polarizations (HH and W ) , and radar frequencies (L, C, and X bands). The results revealed that the calibration parameter and the instrumental parameters (incidence angle, polarization, and frequency) were interdependent. To identify the best correlation function shape, we tested exponential, fractal, and Gaussian correlation functions; the fractal function proved to be optimal for good performance of the IEM. The calibration function was found to be dependent on surface roughness. With this calibration method, by inverting radar signals, it would be possible to initially characterize bare agricultural soils using two surface parameters (rms surface height and soil moisture) instead of three (rms surface height, correlation length, and soil moisture). This result suggests a possible operational use for the calibrated version of the IEM: it could be used in radar data inversion (ERS, RADARSAT, ENVISAT, etc.) to retrieve surface moisture and roughness data on bare agricultural soils. The next step will be to study other radar configurations in order to fully calibrate the proposed method (incidence angle, polarization, and radar frequency). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 247 Acknowledgem ents On the French side, this work was supported by the BRGM and France’s Ministdre de la Recherche as part of the Actions Concertdes Incitatives (ACI) project. On the Canadian side, funding was provided by the Natural Sciences and Engineering Research Council (NSERC) and the Fonds qudbdcois de recherche sur la nature et les technologies (FQRNT). Some RADARSAT images were provided by the Canadian Space Agency under the RADARSAT User Development Program (RUPD) and the Application Development and Research Opportunity Program (ADRO). Databases were produced from work carried out by the BRGM, the Centre d’dtude des Environnements Terrestres et Planetaires (CEPT), and the Centre d’applications et de recherches en teldddtection (CARTEL) o f the University de Sherbrooke, Canada. 8. References Altese E., Bolognani O., and Mancini M., 1996. Retrieving soil moisture over bare soil from ERS1 synthetic aperture radar data: Sensitivity analysis based on a theoretical surface scattering model and field data. Water Resources Research, vol. 32, no 3, pp. 653-661. Baghdadi N., King C., Bourguignon A., and Remond A., 2002a. Potential of ERS and RADARSAT data for surface roughness monitoring over bare agricultural fields. International Journal o f Remote Sensing, vol. 23, no 17, pp. 3427-3442. Baghdadi N., King C., Chanzy A., and Wingneron J.P., 2002b. An empirical calibration of IEM model based on SAR data and measurements of soil moisture and surface roughness over bare soils. International Journal o f Remote Sensing, vol. 23, no 20, pp. 4325-4340. Baghdadi N., Paillou P., Davidson M., Grandjean G., and Dubois P., 2000c. Relationship between profile length and roughness parameters for natural surfaces. International Journal o f Remote Sensing, vol. 21, no 17, pp. 3375-3381. Baret F., 2000. RESEDA final report, CEE project no. ENV4-CT96-0326, 57 pages. Boisvert J., Gwyn Q., Chanzy A., Major A., Brisco B., and Brown R., 1997. Effect of surface soil moisture gradients on modelling radar backscattering from bare fields. International Journal o f Remote Sensing, vol. 18, pp. 153-170. Dubois P.C., Van Zyl J., and Engman T., 1995. Measuring soil moisture with imaging sadars, IEEE Transactions on Geoscience and Remote Sensing, vol. 33, no 4, pp. 915-926. Fung A.K., 1994. Microwave scattering and emission models and their applications. Artech House, Inc., Boston, London, 573 pages. Hallikamen M., Ulaby F., Dobson F., EL Rayes M., and Wu L., 1985. Microwave dielectric behavior of wet soil. Part I: Empirical models and experimental observations, IEEE Transactions on Geoscience and Remote Sensing, vol. 23, pp. 25-34. King C., 2001. Floodgen un programme de recherche pour lutter contre le ruissellement excessif, rapport final CEE ENV 4 CT 96 0368, 65 pages. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 248 Le H6garat-Mascle S., Zribi M., Alem F., and Weisse A., 2002, Soil moisture estimation from ERS/SAR data: Toward an operational methodology, IEEE Transactions on Geoscience and Remote Sensing, in press. Oh Y., and Kay Y., 1998. Condition for precise measurement of soil surface roughness. IEEE Transactions on Geoscience and Remote Sensing, vol. 36, no 2, pp. 691-695. Oh Y., Sarabandi K., and Ulaby F.T., 1992. An empirical model and an inversion technique for radar scattering from bare soil surfaces. IEEE Transactions on Geoscience and Remote Sensing, vol. 30, no 2, pp. 370-381. Quesney A., Le Hegarat-Mascale S., Taconet O., Vidal-Madjar D., Wigneron J.P, Loumagne C., and Normand M., 2000. Estimation of watershed soil moisture index from ERS/SAR data, Remote Sensing o f Environment, vol. 72, pp. 290-303. Rakotoarivony L., 1995. Validation de modules de diffusion 61ectromagn6tique: Comparaison entre simulations et mesures radar hiliporte sur des surfaces agricoles de sol nu. Ph.D. Thesis, University of Caen, 175 pages. Rakotoarivony L., Taconet O., Vidal-Madjar D., Bellemain P., and Benallegue M., 1996. Radar backscattering over agricultural bare soils. Journal o f Electromagnetic Waves and Applications, vol. 10, no. 2, pp. 187-209. Remod A., 1997. Image SAR: potentialitds d’extraction d’un parametre physique du ruissellement, la rugosit6 (modelisation et experimentation). PhD Thesis, Universite de Bourgogne, Pub. BRGM no 261, Orleans, France, 254 pages. Shi J., Wang A., Hsu Y., O’Heil P.E., and Engman E.T., 1995. Estimation of bare surface soil moisture and surface roughness parameter using L-band SAR measurements. IEEE Transactions on Geoscience and Remote Sensing, vol. 1, pp. 507-509. Zribi M., 1998. Developpement de nouvelles methodes de modelisation de la rugosite pour la retrodiffusion hyperfrequence de la surface du sol. Doctoral thesis, University of Toulouse, pp. 14-15. Zribi M., Taconet O., Le Hegarat-Mascle S., Vidal-Madjar D., Emblanch C., Loumagne C. and Normand M., 1997. Backscattering behavior and simulation: Comparison over bare soils using SIR-C/X-SAR and ERASME 1994 data over Orgeval. Remote Sensing o f Environment, vol. 59, pp. 256-266. Zribi M., Ciarletti V., Taconet O., Pailld J., Boissard P., and Chapron M., 2000. Characterisation of the soil structure and microwave backscattering based on numerical three dimensional surface representation: Analysis with a Brownian model, Remote Sensing o f Environment, vol. 72, pp. 159-169. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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