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

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Departement 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
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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
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To the great loves o f my life:
to my parents Mehri and Manouchehr
to my wife Sudabeh
and to my daughter Saghar
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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
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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
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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,
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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.
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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.
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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.
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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.
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viii
Table of content
Resume
Summary
Table of content
Figures
Tables
Preface
Acknowledgement
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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
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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
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29
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30
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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
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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
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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
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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
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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
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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
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xii
Introduction
Methodology
Study site
Data
Ground data
Satellite data
Discussion and Results analysis
Conclusion
References
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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
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APPENDIX E: Optimization using non-linear Least square method
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APPENDIX F: Newton-Raphson method for nonlinear systems of equations
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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
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xiii
Validation of the IEM calibration
Effect of radar frequency on calibration
Conclusions
References
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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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
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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.
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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.
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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
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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
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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.
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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)
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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.
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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.
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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)
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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
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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.”
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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.
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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
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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
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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
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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)
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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).
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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)
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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).
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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).
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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.
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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
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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.
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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:
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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.
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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.
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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.
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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.
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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.
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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.
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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
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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
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(3)
© 2002 CASI
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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
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643
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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
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© 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
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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
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. 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
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© 2002 CASI
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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
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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
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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
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Henderson, F.M., and Lewis, A.J. 1998. Principles and applications o f
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652
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© 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.
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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
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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.
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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
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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
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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
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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.
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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
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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.
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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.
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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
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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-
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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
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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
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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
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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.
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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)
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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
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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
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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
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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
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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
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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 =
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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
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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.
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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
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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.
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74
Figure 11. rms height map in pixel scale
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75
45*14 31" N / 73r'42l41" W
Figure 12. Volumetric humidity map in pixel scale
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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
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Figure 14. Volumetric humidity map in homogeneous zone scale
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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
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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.
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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.
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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.
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ofBio-&Geo-physical Parameters from SAR Data, ESTEC, The Netherlands, pp. 471-477.
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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”.
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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,
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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
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Henderson F. M. and Lewis, A. J. (1998) “Principles and applications of imaging radar”.
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Oh, Y., Sarabandi, K. and Ulaby, F. T. (1992) “An empirical model and inversion
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several variables”, New York: Academic Press Inc, 572 p.
Pr6vot, L., Champion, I. and Guyot, G. (1993) “Estimating surface soil moisture and leaf
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No. 13, pp. 2613-2625.
Sahebi, M. R., Angles, J. and Bonn F. (2001) “A multi-angular Radarsat based C-band
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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
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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
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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
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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.
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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.
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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.
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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.
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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)
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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).
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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
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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
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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
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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
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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).
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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:
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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.
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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)
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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
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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.
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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
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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
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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
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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.
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109
Fig. 8. rms height map at pixel scale.
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110
Fig. 9. Dielectric constant map at pixel scale.
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Ill
14
12
10
8
6
*
%
4
2
A
0
1000m
Fig. 10. rms height map at homogeneous zone scale.
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112
Fig. 11. Dielectric constant map at homogeneous zone scale.
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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
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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:
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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
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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 )
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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.
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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.
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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.
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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
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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).
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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.
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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).
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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).
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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)
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(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)
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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.
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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.
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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
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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°
................... ...................
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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:
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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:
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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
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137
t.
|
25-
8
0
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20-
1
® 15-
*5
« 10'
3
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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.
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8
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M easured rm s height (cm)
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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.
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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
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M easured rm s h eight (cm )
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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.
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139
20
-
8
o
.= ' 4 -
0>
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15-
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0
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3
4
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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
£
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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 .
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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
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8
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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.
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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
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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.
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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
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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
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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
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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.
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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.
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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.
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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.
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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.
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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).
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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
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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.
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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.
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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.
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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
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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.
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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
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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.
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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;
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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
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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.
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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.
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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.
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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.
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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 )
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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
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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).
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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).
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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
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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
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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.
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183
APPENDIX D
IN-SITU MEASUREMENTS
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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.
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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
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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.
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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
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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
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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
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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).
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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.
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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
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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.
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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
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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.
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197
APPENDIXE
OPTIMIZATION USING NON-LINEAR LEAST SQUARE METHOD
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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)
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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
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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.
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201
APPENDIX F
NEWTON-RAPHSON METHOD FOR NONLINEAR SYSTEMS OF EQUATIONS
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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.
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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.
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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
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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
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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.
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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
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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.
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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.
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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.
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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
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(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
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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
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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
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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°
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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
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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
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-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
“
/
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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
«
£
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2
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/
-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
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♦
xfHx
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yx
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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> /
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O
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r
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**
/
-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
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oo
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& -20
a
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s -2b
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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
£
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1
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-15 -
-15 -
-20
-20
-
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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$*
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3.5
rms surface height [cm]
(a)
Fractal correlation function, X-band
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(b)
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(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
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3.5
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rms surface height [cm]
(a)
Fractal correlation function, L and C bands
50
1,40
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4094. HH44*.C
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♦ 004.
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HHSr.C
30
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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
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4094*
4.094*
□004*
■004*
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HH44* - C
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I 15
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&
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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).
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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
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Le H6garat-Mascle S., Zribi M., Alem F., and Weisse A., 2002, Soil moisture estimation from
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entre simulations et mesures radar hiliporte sur des surfaces agricoles de sol nu. Ph.D. Thesis,
University of Caen, 175 pages.
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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
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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,
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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.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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