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Development of a Microwave - Remote Sensing Based Snow Depth Product

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Development of a microwave - remote sensing based snow depth
product
By
Carlos Luis Pérez Díaz
B.S. (University of Puerto Rico, Mayagüez Campus, 2010)
M.S. (University of Puerto Rico, Mayagüez Campus, 2012)
A dissertation submitted to the Graduate Faculty in Engineering
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
In
Civil Engineering (Water Resources)
The City College of New York
2018
ProQuest Number: 10745516
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Carlos Luis Pérez Díaz
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i
This Manuscript has been read and accepted for the Graduate Faculty in Engineering in
satisfaction of the dissertation requirement for the degree of Doctor of Philosophy
Prof. Reza Khanbilvardi, Chair of Examining Committee
Date
Dr. Ardie D. Walser, Associate Dean for Academic Affairs
Date
EXAMINING COMMITTEE
Prof. Nir Krakauer, Department of Civil Engineering, The City College of New York
Prof. Naresh Devineni, Department of Civil Engineering, The City College of New York
Dr. Tarendra Lakhankar, Department of Civil Engineering, The City College of New York
Dr. Quanhua Liu, National Oceanic and Atmospheric Administration/National Environmental
Satellite, Data, and Information Service/Center for Satellite Applications and Research
ii
THE CITY COLLEGE OF THE CITY UNIVERSITY OF NEW YORK
Abstract
Development of a microwave - remote sensing based snow depth product
By
Carlos Luis Pérez Díaz
Advisor: Prof. Reza Khanbilvardi
Snow is a key component of the Earth’s energy balance, climate, environment, and a major source
of freshwater in many regions. Seasonal and perennial snow cover affect up to 50% of the Northern
Hemisphere landmass, which accounts for vast regions of the Earth that influence climate, culture,
and commerce significantly. Information on snow properties such as snow cover, depth, and
wetness is important for making hydrological forecasts, monitoring climate change, weather
prediction, and issuing snowmelt runoff, flash flood, and avalanche warnings. Hence, adequate
knowledge of the areal extent of snow and its properties is essential for hydrologists, water
resources managers, and decision-makers.
The use of infrared (IR) and microwave (MW) remote sensing (RS) has demonstrated the
capability of estimating the presence of snow cover and snowpack properties with accuracy.
However, there are few publicly accessible, operational RS-based snow depth products, and these
only provide the depth of recently accumulated dry snow because retrievals lose accuracy
drastically for wet snow (late winter - early spring). Furthermore, it is common practice to assume
snow grain size and wetness to be constant to retrieve certain snow properties (e.g. snow depth).
This approach is incorrect because these properties are space- and time- dependent, and largely
impact the MW signal scattering. Moreover, the remaining operational snow depth products have
not been validated against in-situ observations; which is detrimental to their performance and
future calibrations.
This study is focused on the discovery of patterns in geospatial data sets using data mining
techniques for mapping snow depth globally at 10 km spatial resolution. A methodology to develop
a RS MW-based snow depth and water equivalent (SWE) product using regression tree algorithms
is developed. The work divided into four main segments includes: (1) validation of RS-based IR
and MW-retrieved Land Surface Temperature (LST) products, (2) studying snow wetness by
iii
developing, validating, and calibrating a Snow Wetness Profiler, (3) development of a regression
tree algorithm capable of estimating snow depth based on radiative (MW observations) and
physical snowpack properties, and (4) development of a global MW-RS-based snow depth product
built on the regression tree algorithm.
A predictive model based on Regression Tree (RT) is developed in order to model snow depth and
water equivalent at the Cooperative Remote Sensing Science and Technology Center – Snow
Analysis and Field Experiment (CREST-SAFE). The RT performance analyzed based on
contrasting training error, true prediction error, and variable importance estimates. The RT
algorithm is then taken to a broader scale, and Japan Aerospace Exploration Agency (JAXA)
Global Change Observation Mission – Water 1 (GCOM-W1) MW brightness temperature
measurements were used to provide snow depth and SWE estimates. These SD and SWE estimates
were evaluated against twelve (12) Snow Telemetry (SNOTEL) sites owned by the National
Resources Conservation Service (NRCS) and JAXA’s own snow depth product. Results
demonstrated that a RS MW-based RT algorithm is capable of providing snow depth and SWE
estimates with acceptable accuracy for the continental United States, with some limitations. The
major setback to the RT algorithm is that it will only provide estimates based on the data with
which it was trained. Therefore, it is recommended that the work be expanded, and data from
additional in-situ stations be used to re-train the RT algorithm. The CREST snow depth and water
equivalent product, as it was named, is currently operational and publicly accessible at
https://www.noaacrest.org//snow/products/.
iv
Preface
This dissertation is original and independent work by the author, Carlos Luis Pérez Díaz.
Chapters 3, 5, and 6 are partially published (see references below):
Pérez Díaz, C., T. Lakhankar, P. Romanov, R. Khanbilvardi, and Y. Yu. 2015. “Evaluation
of VIIRS Land Surface Temperature Using CREST-SAFE Air, Snow Surface, and Soil
Temperature Data.” Geosciences 5(4): 334–360. doi:10.3390/geosciences5040334.
Pérez Díaz, C., J. Muñoz, T. Lakhankar, R. Khanbilvardi, and P. Romanov. 2017. “Proof
of Concept: Development of Snow Liquid Water Content Profiler Using CS650
Reflectometers at Caribou, ME, USA.” Sensors 17(3): 647. doi:10.3390/s17030647.
Pérez-Díaz, C., T. Lakhankar, P. Romanov, J. Muñoz, R. Khanbilvardi & Y. Yu. 2017.
“Evaluation of MODIS land surface temperature with in-situ snow surface temperature
from CREST-SAFE.” International Journal of Remote Sensing 38(16): 4722-4740. doi:
10.1080/01431161.2017.1331055.
Pérez-Díaz, C., C. Grassotti, Q. Liu, S. Liu, J. Chen, T. Lakhankar, and R. Khanbilvardi.
MiRS-retrieved LST validation with in-situ SURFRAD measurements. 2017. Earth and
Space Science. Submitted (under review).
Pérez-Díaz, C., T. Lakhankar, and R. Khanbilvardi. Snow depth and SWE prediction using
data mining techniques (regression tree algorithm) and snow physical and radiative
properties. 2017. Under preparation.
Sánchez, H., T. Lakhankar, C. Pérez Díaz, J. Nuñez, and R. Khanbilvardi. 2017. Impact of
Snowpack Temperature on Albedo and Radiation using CREST-SAFE Field Experiment
Observation. Geosciences. Submitted (under review).
v
Acknowledgments
The authors gratefully acknowledge support from NOAA under grants NA11SEC4810004 and
NA060AR4810162. All statements made are the views of the authors and not the opinions of the
funding agency or the U.S. government.
I dedicate this work to my family and Ana. Thank you for your unlimited love, support, and
motivation. I would like to thank my advisors, Professors Tarendra Lakhankar and Reza
Khanbilvardi. Their guidance has been invaluable. I would also like to acknowledge committee
members Profs. Nir Krakauer and Naresh Devineni, and Dr. Quanhua Liu for contributing to the
improvement of this work. Lastly, I want to thank Peter Romanov, Christopher Grassotti, and
Yunyue Yu for the hours spent providing insight and helpful suggestions.
vi
Table of Contents
Abstract .......................................................................................................................................... iii
Preface............................................................................................................................................. v
Acknowledgments.......................................................................................................................... vi
1
2
Introduction ............................................................................................................................. 1
1.1
Background ...................................................................................................................... 1
1.2
Statement of the Problem ................................................................................................. 2
1.3
Motivation and Research Objectives................................................................................ 5
1.4
Intellectual Merit .............................................................................................................. 6
1.5
Document Structure.......................................................................................................... 6
Literature Review.................................................................................................................... 8
2.1
Optical Properties of Snow .............................................................................................. 8
2.2
Microwave Properties of Snow ........................................................................................ 9
2.3
Snow Cover Mapping..................................................................................................... 12
2.4
Mapping of Snow Properties Using Microwave Bands ................................................. 13
2.5
The Effect of Snow Wetness in Microwave Retrievals ................................................. 15
2.6
Snow Wetness Model (SWM) ....................................................................................... 16
2.7
Complementary snow physical and microwave emission models ................................. 17
2.7.1
HUT Single Layer Model ....................................................................................... 17
2.7.2
SNTHERM (SNow THERmal Model) ................................................................... 20
vii
2.8
3
In-situ observations and satellite products ............................................................................ 25
3.1
4
Regression tree models................................................................................................... 22
In-situ observations ........................................................................................................ 25
3.1.1
Instrumentation at CREST-SAFE ........................................................................... 28
3.1.2
Supplementary instrumentation at NWS ................................................................ 33
3.2
Data Acquisition ............................................................................................................. 36
3.3
Satellite Products ............................................................................................................ 37
3.3.1
VIIRS onboard S-NPP satellite and its LST product .............................................. 37
3.3.2
MODIS onboard Terra and Aqua satellites and its LST product............................ 37
3.3.3
ASMR2 onboard GCOM-W1 satellite.................................................................... 40
3.3.4
ATMS onboard S-NPP and MiRS-retrieved LST .................................................. 40
Methodology ......................................................................................................................... 42
4.1
Compare and cross validate satellite land surface temperature products ....................... 42
4.2
Study temporal evolution of snow wetness and develop SWP ...................................... 43
4.3
Develop a regression tree algorithm that ingests snow physical and radiative properties
to estimate snow depth and SWE.............................................................................................. 44
4.4
Improve on global snow cover mapping by developing the prototype of a product capable
of estimating snow depth and SWE using MW RS .................................................................. 46
5
Validation of satellite LST products ..................................................................................... 47
5.1
VIIRS LST study............................................................................................................ 49
5.1.1
VIIRS LST pre-processing ..................................................................................... 50
viii
5.1.2
5.2
VIIRS LST validation ............................................................................................. 51
MODIS LST study ......................................................................................................... 65
5.2.1
Previous MODIS LST validation efforts ................................................................ 66
5.2.2
MODIS LST data .................................................................................................... 68
5.2.3
MODIS Terra (MOD11A1) and Aqua (MYD11A1) clear-sky LST ...................... 69
5.2.4
MODIS data pre-processing ................................................................................... 69
5.2.5
MODIS and CREST-SAFE temporal intersection ................................................. 70
5.2.6
MODIS LST validation........................................................................................... 70
5.2.7
Effect of increasing MODIS LST window size ...................................................... 76
5.2.8
MODIS LST validation summary ........................................................................... 79
5.2.9
MODIS LST validation conclusion ........................................................................ 80
5.3
MiRS LST study ............................................................................................................ 82
5.3.1
Previous IR and MW LST validation efforts .......................................................... 82
5.3.2
SURFRAD dataset .................................................................................................. 84
5.3.3
SURFRAD LST estimation .................................................................................... 85
5.3.4
MiRS algorithm and LST retrieval ......................................................................... 86
5.3.5
MiRS vs SURFRAD LST collocation and temporal matching .............................. 87
5.3.6
MiRS vs. SURFRAD station-by-station validation ................................................ 87
5.3.7
Impact of emissivity on retrieved LST ................................................................... 91
5.3.8
MiRS LST validation summary .............................................................................. 94
ix
5.4
6
Cross-comparison between satellite IR and MW LST products .................................... 95
Studying the effects of snow wetness in the snowpack ........................................................ 97
6.1
Snow wetness and previous studies ............................................................................... 98
6.2
Time-domain reflectometry.......................................................................................... 101
6.3
CS650 time-domain reflectometer ............................................................................... 103
6.4
Snow Wetness Profiler setup........................................................................................ 104
6.5
Obtaining LWC from dielectric constant measurements via empirical formulas ........ 105
6.6
Liquid water content simulations using SNTHERM ................................................... 106
6.7
Evaluation Criteria ....................................................................................................... 112
6.8
Results .......................................................................................................................... 113
6.8.1
Evaluating the SWP’s capability of estimating LWC and developing new statistical
relationships for different snow conditions......................................................................... 113
6.8.2
6.9
Validating SWP and new Statistical Relationships .............................................. 121
Discussion .................................................................................................................... 126
6.9.1
Advantages and limitations ................................................................................... 126
6.9.2
Uncertainties when estimating LWC using TDR ................................................. 127
6.9.3
Possible sources of uncertainty in SNTHERM simulations ................................. 129
6.9.4
Comparing the CS650 (and its precision) to other non-destructive LWC-measuring
instruments .......................................................................................................................... 132
6.9.5
6.10
Comparing results with other studies .................................................................... 133
Conclusion ................................................................................................................ 134
x
7
8
Prediction of snow depth using data mining techniques (regression tree algorithm) ......... 136
7.1
Response and predictor variables ................................................................................. 137
7.2
Data exploration ........................................................................................................... 138
7.3
Regression tree ............................................................................................................. 141
7.3.1
Details of the tree construction ............................................................................. 143
7.3.2
Residual plots ........................................................................................................ 146
7.3.3
Variable importance .............................................................................................. 147
7.4
Model performance evaluation..................................................................................... 149
7.5
Model validation .......................................................................................................... 151
Global model implementation............................................................................................. 153
8.1
Materials and methods ................................................................................................. 153
8.2
Snow depth and SWE global maps .............................................................................. 159
8.3
Validation of developed SD and SWE algorithms against existing RS products ........ 161
8.3.1
JAXA AMSR2 SD and SWE products ................................................................. 161
8.3.2
JAXA AMSR2 SD and SWE algorithm theoretical description .......................... 161
8.3.3
JAXA AMSR2 SD and SWE algorithm implementation ..................................... 164
8.3.4
Results ................................................................................................................... 167
8.4
Validation of SD and SWE products against field-based data ..................................... 186
8.4.1
SNOTEL ............................................................................................................... 186
8.4.2
SNOTEL stations .................................................................................................. 187
xi
9
8.4.3
SNOTEL SD and SWE measurements ................................................................. 188
8.4.4
Results ................................................................................................................... 192
8.5
Limitations ................................................................................................................... 194
8.6
CREST Snow Depth and SWE product ....................................................................... 197
Conclusions and future work .............................................................................................. 198
9.1
Conclusions .................................................................................................................. 198
9.2
Future work .................................................................................................................. 205
Appendix A – Research publications and conference presentations .......................................... 207
Appendix B – Software and tools used for product development .............................................. 209
Appendix C – SNOTEL stations................................................................................................. 212
References ................................................................................................................................... 219
xii
List of Figures
Figure 1. Capability to retrieve snow properties using optical and microwave bands. .................................................9
Figure 2. Microwave emissivity for common surface types. The differences in emissivity serve to differentiate
different types of snow and to distinguish snow from other features. (Source: Grody, 2008) .................................... 16
Figure 3. Changes in snow wetness as a function of snowpack temperature. ............................................................17
Figure 4. HUT simulation approach. ............................................................................................................................19
Figure 5. SNTHERM simulation approach....................................................................................................................20
Figure 6. Recursive partitioning algorithm. .................................................................................................................22
Figure 7. (a) State of Maine in the USA. (b) County of Caribou in the state of Maine, the USA. (c) CREST-SAFE
location within the premises of the Caribou Municipal Airport, Caribou, ME, USA. ....................................................25
Figure 8. Apogee Broadband Infrared Radiometer Model S-111. (Source:
http://www.apogeeinstruments.com/standard-field-of-view-infrared-radiometer-sensor-si-111/) ..........................28
Figure 9. Microwave Radiometers (10, 19, 37 and 89 GHz) at CREST-SAFE. The bigger the dome dome of the
radiometer, the smaller the MW frequency. ...............................................................................................................30
Figure 10. Air/snowpack temperature profilers at CREST-SAFE. (Source: Muñoz et al., 2014) ...................................31
Figure 11. (a) Judd Communications Ultrasonic Depth Sensor (b) RM Young Heavy Duty Wind Monitor for wind
speed and direction (c) Vaisala HMT330 Temperature/Relative Humidity probe .......................................................32
Figure 12. Snow wetness profiler during winter season (Source: Muñoz et al., 2014). ...............................................33
Figure 13. Distinctive ASOS station used by NWS. (Source: https://www.ncdc.noaa.gov/data-access/land-basedstation-data/land-based-datasets/automated-surface-observing-system-asos) .......................................................36
Figure 14. Flow chart of comparison and cross validation of satellite LST products. ..................................................42
Figure 15. Snow wetness analysis framework. ............................................................................................................43
Figure 16. Snow depth regression tree algorithm development and validation framework. ......................................44
Figure 17. Flow chart of snow depth Regression Tree model based on snow physical (snowpack temperature,
wetness, grain size) and radiative (IR/MW) properties. ..............................................................................................45
Figure 18. Snow depth and SWE satellite product development framework. .............................................................46
Figure 19. CREST-SAFE in-situ T-skin and T-air correlation with satellite VIIRS LST daytime and nighttime data for
winters 2013 and 2014. ...............................................................................................................................................52
Figure 20. CREST-SAFE land cover 750-m block ...........................................................................................................55
Figure 21. 750 m block of bare land 1km away from CREST-SAFE. .............................................................................56
Figure 22. CREST-SAFE in-situ T-skin and T-air vs. satellite VIIRS LST daytime and nighttime data for the bare land
pixel scatterplots for winters 2013 and 2014. .............................................................................................................57
Figure 23. 750 m block of land covered by forest and vegetation 2 km away from CREST-SAFE. ...............................58
xiii
Figure 24. CREST-SAFE in-situ T-skin and T-air vs. satellite VIIRS LST daytime and nighttime data for the
forest/vegetation covered pixel scatterplots for winters 2013 and 2014. ...................................................................59
Figure 25. T-skin derived empirical formula based on linear regression model between clear-sky VIIRS LST daytime
(wet snow) views with respective in-situ temperatures at CREST-SAFE. .....................................................................61
Figure 26. T-skin derived empirical formula based on linear regression model between clear-sky VIIRS LST nighttime
(dry snow) views with respective in-situ temperatures at CREST-SAFE. ......................................................................62
Figure 27. VIIRS LST daytime and nighttime views and inversely retrieved LSTs (wet and dry snow conditions) using
the empirical formulas derived from the linear regression models. Sky cover in the background. .............................63
Figure 28. Three-dimensional scatterplot of in-situ LST, VIIRS LST, and cloudiness with linear regression model in
mesh-grid form to estimate in-situ LST with RS LST and cloudiness as predictor variables. ........................................65
Figure 29. Terra and Aqua MODIS LST versus CREST-SAFE in-situ LST scatterplots with r linear correlation coefficient
values and biases for winters 2013 (a and b, respectively) and 2014 (c and d, respectively) at CREST-SAFE for MODIS
daytime and night-time overpasses. ...........................................................................................................................72
Figure 30. CREST-SAFE MODIS pixel (light purple rhombus) and CREST-SAFE site (red circle) overlaid on top of the
Caribou Municipal Airport premises. ...........................................................................................................................75
Figure 31. Bare land MODIS pixel approximately 2.50 km away from CREST-SAFE, partially forested pixel
approximately 1 km away from the site, CREST-SAFE pixel (all represented by light purple rhombi), and the CRESTSAFE site (red circle) overlaid on top of the Caribou Municipal Airport premises........................................................78
Figure 32. Scatter plots of the MiRS-retrieved LSTs vs SURFRAD-derived LSTs for each of the 6 SURFRAD stations for
the S-NPP ATMS ascending overpass for the period from May 1st, 2016 to May 31st, 2017. ....................................88
Figure 33. Scatter plots of the MiRS-retrieved LSTs vs SURFRAD-derived LSTs for each of the 6 SURFRAD stations for
the S-NPP ATMS descending overpass for the period from May 1st, 2016 to May 31st, 2017. ..................................89
Figure 34. Scatter plots of the difference of retrieved nighttime (descending) minus daytime (ascending) emissivity
on the x-axis versus the nighttime-daytime differences of MiRS-SURFRAD LSTs (i.e. difference of LST biases) on the
y-axis for all 6 SURFRAD stations. ................................................................................................................................93
Figure 35. Histograms of nighttime-daytime emissivity for two of the six stations (Mississippi and South Dakota),
showing the difference in distributions can be linked to the night vs. day LST biases. ................................................94
Figure 36. Snow Wetness Profiler snowpack dielectric permittivity (a) and temperature (b) measurements at
different depths (15, 30, 45, 60 and 75 cm) above the soil surface at CREST-SAFE for winter (6 February–22 April)
2014; The third panel (c) illustrates snow depth (ultrasonic depth sensor) and near-surface air temperature
(temperature and relative humidity probe) observations also collected at CREST-SAFE for the same period of time;
The bottom panel (d) shows SNTHERM snowpack melt rate and cold content simulations obtained by weatherforcing the model with CREST-SAFE in-situ meteorological data for the same time interval. All data are hourly. ...114
xiv
Figure 37. Snow Wetness Profiler (y axis) (estimated using Topp, Denoth, and Tiuri empirical formulas and
developed statistical relationships) vs. SNTHERM (x axis) LWC scatter plots for different depths ((a) 15, (b) 30, (c)
45, and (d) 60 cm) above the soil surface at CREST-SAFE for winter (6 February–22 April) 2014. ............................117
Figure 38. SNTHERM simulated LWC (y axis) vs. SWP dielectric permittivity (x axis) scatter plot for all depths (15, 30,
45, and 60 cm) above the soil surface combined at CREST-SAFE for winter (6 February–22 April) 2014. Third-degree
polynomial regressions were found to be the best fit for dry (LWC < 2%) and wet (LWC ≥ 2%) snow conditions. ....119
Figure 39. Frequency distribution for dry, moist, and wet snow conditions at CREST-SAFE for winters (a) 2014 and
(b) 2015......................................................................................................................................................................125
Figure 40. Confusion matrix (actual-SNTHERM vs. predicted-new statistical relationships) using three snow
conditions (dry, moist, wet) as classes for CREST-SAFE 2015 validation data. ..........................................................126
Figure 41. Scatter plot matrix for the response variable snow depth and twelve selected predictor variables at
CREST-SAFE. ...............................................................................................................................................................140
Figure 42. Scatter plot matrix for the response variable SWE and twelve selected predictor variables at CREST-SAFE.
...................................................................................................................................................................................141
Figure 43. Unpruned snow depth regression tree at CREST-SAFE. ............................................................................144
Figure 44. Snow depth regression tree cross-validated error as a function of pruning level and minimum leaf size.
...................................................................................................................................................................................144
Figure 45. Pruned snow depth regression tree at CREST-SAFE. .................................................................................145
Figure 46. Pruned SWE regression tree at CREST-SAFE. ............................................................................................146
Figure 47. Residuals plot depicting the predicted SD values on the x-axis and the residuals on the y-axis. .............147
Figure 48. Residuals plot depicting the predicted SWE values on the x-axis and the residuals on the y-axis. ..........147
Figure 49. Variable importance analysis for SD regression tree. ...............................................................................148
Figure 50. Variable importance analysis for SWE regression tree. ............................................................................148
Figure 51. Holdout set. 70% is used for training and 30 percent of the data is used for testing. ..............................149
Figure 52. CREST-SAFE SD and SWE observations and RT SD and SWE predictions for the year 2016. ....................152
Figure 53. Relationship between snow surface temperature and the V-H polarization gradient at the 89 GHz MW
frequency. ..................................................................................................................................................................156
Figure 54. Relationship between snowpack temperature and the vertical polarization gradient between the 10 GHz
and 19 GHz MW frequencies. ....................................................................................................................................157
Figure 55. Relationship between snowpack temperature and the vertical polarization gradient between the 19 GHz
and 37 GHz MW frequencies. ....................................................................................................................................158
Figure 56. RT developed SD global map using the JAXA GCOM-W1 AMSR2 MW brightness temperature (10, 19, 37,
and 89 GHz) products. ...............................................................................................................................................160
Figure 57. RT developed SWE global map using the JAXA GCOM-W1 AMSR2 MW brightness temperature (10, 19,
37, and 89 GHz) products. .........................................................................................................................................160
xv
Figure 58. JAXA snow depth global map vs RT developed snow depth global map daytime comparison for the
month of January. There are three cases - top: World, middle: World minus Antarctica and Greenland, bottom:
Americas only. ...........................................................................................................................................................168
Figure 59. JAXA snow depth global map vs RT developed snow depth global map nighttime comparison for the
month of January. ......................................................................................................................................................169
Figure 60. JAXA SWE global map vs RT developed SWE global map daytime comparison for the month of January.
...................................................................................................................................................................................170
Figure 61. JAXA SWE global map vs RT developed SWE global map nighttime comparison for the month of January.
...................................................................................................................................................................................171
Figure 62. JAXA snow depth global map vs RT developed snow depth global map daytime comparison for the
month of February. ....................................................................................................................................................172
Figure 63. JAXA snow depth global map vs RT developed snow depth global map nighttime comparison for the
month of February. ....................................................................................................................................................173
Figure 64. JAXA SWE global map vs RT developed SWE global map daytime comparison for the month of February.
...................................................................................................................................................................................174
Figure 65. JAXA SWE global map vs RT developed SWE global map nighttime comparison for the month of
February. ....................................................................................................................................................................175
Figure 66. JAXA snow depth global map vs RT developed snow depth global map daytime comparison for the
month of March. ........................................................................................................................................................176
Figure 67. JAXA snow depth global map vs RT developed snow depth global map nighttime comparison for the
month of March. ........................................................................................................................................................177
Figure 68. JAXA SWE global map vs RT developed SWE global map daytime comparison for the month of March. 178
Figure 69. JAXA SWE global map vs RT developed SWE global map nighttime comparison for the month of March.
...................................................................................................................................................................................179
Figure 70. JAXA snow depth global map vs RT developed snow depth global map daytime comparison for the
month of April. ...........................................................................................................................................................180
Figure 71. JAXA snow depth global map vs RT developed snow depth global map nighttime comparison for the
month of April. ...........................................................................................................................................................181
Figure 72. JAXA SWE global map vs RT developed SWE global map daytime comparison for the month of April. ..182
Figure 73. JAXA SWE global map vs RT developed SWE global map nighttime comparison for the month of April. 183
Figure 74. CREST Snow Depth and SWE product website home page. ......................................................................197
Figure 75. Analysis workflow for the CREST SD and SWE product development and current process. The blue ovals
represent the inputs to the analysis. The yellow boxes correspond to the tasks carried out using the MATLAB
Statistics and Machine Learning and Mapping Toolboxes. Black boxes correspond to miscellaneous tasks performed
by additional software (i.e. Linux, Windows Task Scheduler, and WinSCP). Green ovals correspond to model outputs.
xvi
Cloud defines the product server and the box with green outline is used to represent the software (Adobe
Dreamweaver) used to create the user-friendly interface for the product. ...............................................................210
Figure 76. MATLAB regression tree creation example. .............................................................................................211
Figure 77. SNOTEL station in Fairbanks, AK...............................................................................................................212
Figure 78. SNOTEL station in Hawley Lake, AZ. .........................................................................................................212
Figure 79. SNOTEL station in Blue Lakes, CA. ............................................................................................................213
Figure 80. SNOTEL station in Copeland Lake, CO. .....................................................................................................213
Figure 81. SNOTEL station in Moscow Mountain, ID. ................................................................................................214
Figure 82. SNOTEL station in Rocky Boy, MT. ............................................................................................................214
Figure 83. SNOTEL station in Summit Lake, NV. ........................................................................................................215
Figure 84. SNOTEL station in Signal Peak, NM. .........................................................................................................216
Figure 85. SNOTEL station in Miller Woods, OR. .......................................................................................................216
Figure 86. SNOTEL station in Little Bear, UT. .............................................................................................................217
Figure 87. SNOTEL station in Huckleberry Creek, WA................................................................................................217
Figure 88. SNOTEL station in Cole Canyon, WY. ........................................................................................................218
xvii
List of Tables
Table 1. HUT Model Input Parameters. .......................................................................................................................19
Table 2. Instruments and environmental parameters observed at the CREST Snow Research station in Caribou, ME.
(Source: Muñoz et al., 2014) ........................................................................................................................................27
Table 3. R2 correlation coefficient values between VIIRS LST, T-skin, and T-air at CREST-SAFE for winters 2013 and
2014 daytime and nighttime views. ............................................................................................................................51
Table 4. R and R2 correlation coefficient values, MAD, and biases between VIIRS LST daytime and nighttime views
for the bare land pixel, T-skin, and T-air at CREST-SAFE for winters 2013 and 2014. ..................................................56
Table 5. R and R2 correlation coefficient values, MAD, and biases between VIIRS LST daytime and nighttime views
for the forest/vegetation covered pixel and T-skin and T-air at CREST-SAFE for winters 2013 and 2014. ..................59
Table 6. Multiple linear regression model results for in-situ LST estimation using RS LST and cloudiness as predictor
variables. .....................................................................................................................................................................64
Table 7. Terra and Aqua MODIS LST versus CREST-SAFE in-situ LST r linear correlation coefficient values and biases
for winters 2013 and 2014 at CREST-SAFE for MODIS daytime and night-time overpasses........................................76
Table 8. r Correlation coefficient values and biases comparison between MODIS LST and CREST-SAFE in-situ LST by
increasing MODIS window size. ...................................................................................................................................77
Table 9. SURFRAD station information (location and surface type). ...........................................................................85
Table 10. Results for MiRS vs SURFRAD station-by-station (DRA, BON, FPK, GWN, PSU, and SXF) comparison from
May 1st, 2016 to May 31st, 2017. Four validation statistics (R or correlation coefficient, bias, standard deviation,
and RMSE) were used to evaluate the MiRS algorithm retrieval accuracy for LST. .....................................................90
Table 11. Cross-comparison between validation (against in-situ data) results for the VIIRS, MODIS, and MiRS LST
products. Two validation statistics (R or correlation coefficient and bias) were used to evaluate accuracy for LST. ..95
Table 12. CS650 operational specifications for soil temperature, dielectric permittivity, and LWC. .........................104
Table 13. Results from Snow Wetness Profiler LWC (estimated using Topp, Denoth, and Tiuri empirical formulas) vs.
SNTHERM LWC comparison at different depths (15, 30, 45, and 60 cm) above the soil surface at CREST-SAFE for
winter (6 February–22 April) 2014. ............................................................................................................................118
Table 14. Results from Snow Wetness Profiler LWC (estimated using Topp, Denoth, and Tiuri empirical formulas) vs.
SNTHERM LWC comparison for different snowpack conditions (dry, moist, and wet) at CREST-SAFE for winter (6
February–22 April) 2014. ...........................................................................................................................................119
Table 15. Results from Snow Wetness Profiler LWC (estimated using Topp, Denoth, and Tiuri empirical formulas and
new statistical relationships) vs. SNTHERM LWC comparison at different depths (15, 30, and 45 cm) above the soil
surface at CREST-SAFE for winter (30 November 2014–29 January 2015) 2015. ......................................................121
xviii
Table 16. Results from Snow Wetness Profiler LWC (estimated using Topp, Denoth, and Tiuri empirical formulas and
new statistical relationships) vs. SNTHERM LWC comparison for different snowpack conditions (dry, moist, and wet)
at CREST-SAFE for winter (30 November 2014–29 January 2015) 2015. ...................................................................123
Table 17. TDR dielectric permittivity comparison (MAE and RE) between Snow Wetness Profiler rods at different
depths (15, 30, 45, and 60 cm) above the soil surface at CREST-SAFE for winters 2014 and 2015. ..........................124
Table 18. Operational specifications for snow and soil LWC measurements for different LWC-measuring
instruments. ...............................................................................................................................................................133
Table 19. Predictor variables used to build the RT algorithm for snow depth prediction. ........................................137
Table 20. Training and true prediction errors for SD regression tree model developed using CREST-SAFE data. .....150
Table 21. Training and true prediction errors for SWE regression tree model developed using CREST-SAFE data. ..150
Table 22. Validation results for the developed SD and SWE regression tree models using CREST-SAFE 2016 data..151
Table 23. Predictor variables used to create SD and SWE global maps using RTs developed in Chapter 7. .............154
Table 24. Performance evaluation for the three empirical formulas developed to estimate GS, snow surface and
pack temperatures as a function of MW TBs. ............................................................................................................159
Table 25. Results for the JAXA snow depth global map vs RT developed snow depth global map daytime comparison
for the month of January for each case: World, World minus Antarctica and Greenland, and Americas only. ........168
Table 26. Results for the JAXA snow depth global map vs RT developed snow depth global map nighttime
comparison for the month of January for each case: World, World minus Antarctica and Greenland, and Americas
only. ...........................................................................................................................................................................169
Table 27. Results for the JAXA SWE global map vs RT developed SWE global map daytime comparison for the month
of January for each case: World, World minus Antarctica and Greenland, and Americas only. ...............................170
Table 28. Results for the JAXA SWE global map vs RT developed SWE global map nighttime comparison for the
month of January for each case: World, World minus Antarctica and Greenland, and Americas only. ....................171
Table 29. Results for the JAXA snow depth global map vs RT developed snow depth global map daytime comparison
for the month of February for each case: World, World minus Antarctica and Greenland, and Americas only. ......172
Table 30. Results for the JAXA snow depth global map vs RT developed snow depth global map nighttime
comparison for the month of February for each case: World, World minus Antarctica and Greenland, and Americas
only. ...........................................................................................................................................................................173
Table 31. Results for the JAXA SWE global map vs RT developed SWE global map daytime comparison for the month
of February for each case: World, World minus Antarctica and Greenland, and Americas only. ..............................174
Table 32. Results for the JAXA SWE global map vs RT developed SWE global map nighttime comparison for the
month of February for each case: World, World minus Antarctica and Greenland, and Americas only. ..................175
Table 33. Results for the JAXA snow depth global map vs RT developed snow depth global map daytime comparison
for the month of March for each case: World, World minus Antarctica and Greenland, and Americas only. ..........176
xix
Table 34. Results for the JAXA snow depth global map vs RT developed snow depth global map nighttime
comparison for the month of March for each case: World, World minus Antarctica and Greenland, and Americas
only. ...........................................................................................................................................................................177
Table 35. Results for the JAXA SWE global map vs RT developed SWE global map daytime comparison for the month
of March for each case: World, World minus Antarctica and Greenland, and Americas only. .................................178
Table 36. Results for the JAXA SWE global map vs RT developed SWE global map nighttime comparison for the
month of March for each case: World, World minus Antarctica and Greenland, and Americas only. ......................179
Table 37. Results for the JAXA snow depth global map vs RT developed snow depth global map daytime comparison
for the month of April for each case: World, World minus Antarctica and Greenland, and Americas only. .............180
Table 38. Results for the JAXA snow depth global map vs RT developed snow depth global map nighttime
comparison for the month of April for each case: World, World minus Antarctica and Greenland, and Americas only.
...................................................................................................................................................................................181
Table 39. Results for the JAXA SWE global map vs RT developed SWE global map daytime comparison for the month
of April for each case: World, World minus Antarctica and Greenland, and Americas only. ....................................182
Table 40. Results for the JAXA SWE global map vs RT developed SWE global map nighttime comparison for the
month of April for each case: World, World minus Antarctica and Greenland, and Americas only. .........................183
Table 41. Summary of the results for the JAXA SD global map vs RT developed SD global map comparison for all
overpasses and months combined for each case: World, World minus Antarctica and Greenland, and Americas only.
...................................................................................................................................................................................184
Table 42. Summary of the results for the JAXA SWE global map vs RT developed SWE global map comparison for all
overpasses and months combined for each case: World, World minus Antarctica and Greenland, and Americas only.
...................................................................................................................................................................................185
Table 43. Summary of the twelve SNOTEL stations used in this study based on elevation, latitude, longitude, ID, and
Hydrologic Unit Codes (HUCs). ...................................................................................................................................187
Table 44. SNOTEL criteria for SWE measurements. ...................................................................................................189
Table 45. SNOTEL criteria for SD manual measurements. .........................................................................................190
Table 46. SNOTEL criteria for SD automated measurements. ...................................................................................191
Table 47. JAXA vs SNOTEL SD comparison for twelve SNOTEL stations from January 1st to April 30th, 2017. .........192
Table 48. JAXA vs SNOTEL SWE comparison for twelve SNOTEL stations from January 1st to April 30th, 2017. ......193
Table 49. SD RT vs SNOTEL SD comparison for twelve SNOTEL stations from January 1st to April 30th, 2017. .......193
Table 50. SWE RT vs SNOTEL SD comparison for twelve SNOTEL stations from January 1st to April 30th, 2017. ....194
xx
List of Equations
Equation 1
3
Equation 2
17
Equation 3
18
Equation 4
18
Equation 5
19
Equation 6
20
Equation 7
21
Equation 8
21
Equation 9
21
Equation 10
21
Equation 11
23
Equation 12
23
Equation 13
23
Equation 14 ________________________________________________________________________________ 24
Equation 15
24
Equation 16
24
Equation 17
29
Equation 18
37
Equation 19
38
Equation 20 ________________________________________________________________________________ 41
Equation 21
41
Equation 22
62
Equation 23 ________________________________________________________________________________ 63
Equation 24 ________________________________________________________________________________ 64
Equation 25
85
Equation 26
86
Equation 27
86
Equation 28 _______________________________________________________________________________ 101
Equation 29 _______________________________________________________________________________ 102
Equation 30 _______________________________________________________________________________ 102
Equation 31 _______________________________________________________________________________ 102
Equation 32 _______________________________________________________________________________ 105
Equation 33 _______________________________________________________________________________ 106
Equation 34 _______________________________________________________________________________ 106
Equation 35 _______________________________________________________________________________ 106
xxi
Equation 36 _______________________________________________________________________________ 106
Equation 37 _______________________________________________________________________________ 111
Equation 38 _______________________________________________________________________________ 111
Equation 39 _______________________________________________________________________________ 112
Equation 40 _______________________________________________________________________________ 112
Equation 41 _______________________________________________________________________________ 112
Equation 42 _______________________________________________________________________________ 120
Equation 43 _______________________________________________________________________________ 120
Equation 44
143
Equation 45
143
Equation 46
156
Equation 47 _______________________________________________________________________________ 156
Equation 48
156
Equation 49
161
Equation 50
162
Equation 51
163
Equation 52
163
Equation 53
163
Equation 54
163
Equation 55
164
Equation 56
164
Equation 57
164
xxii
1
1.1
Introduction
Background
Snow is a key component of the Earth’s energy balance, climate, and environment, and a major
source of freshwater in many regions (Brown and Robinson, 2011; Frei et al., 2012). Seasonal and
perennial snow cover affect up to 50% of the Northern Hemisphere landmass, which accounts for
vast regions of the Earth that influence climate, culture, and commerce in significant ways (Tang
et al., 2009; Dominé and Shepson, 2002). Furthermore, on average, 60% of the Northern
Hemisphere has snow cover in midwinter and about 10% of the Earth’s surface is covered
permanently by snow (Bales, 2014). Knowledge of the snow cover’s extent is essential in water
resources management because it affects the hydrologic cycle, since water is stored over the winter
and released in a pulse during the spring melt. More importantly, snow cover plays a critical role
in the regional to global scale because rain-on-snow with warm air temperatures accelerates rapid
snow melt, which is responsible for the majority of the spring floods that damage property and
affect human lives (Chen et al., 2012). Spring floods present difficulties for water managers and
is partially the reason for the existence of man-made reservoirs. Additionally, avalanches impact
backcountry and mountain residents: an average estimated to be around 100,000 annually, with
10,000 reported to be related to property damage, injury, or death. The damage caused by
avalanches to buildings and structures is estimated to be $500,000 per year in the US, and it is
believed to be much higher in Europe because of densely-populated cities (Bales, 2014). Hence,
adequate knowledge of the snow conditions can lead to better management of our water resources,
resulting in more efficient energy production and the mitigation of human impacts on river
ecosystems (Barnett et al., 2005; DeWalle and Rango, 2008; Hogan, 2002).
Snow cover, wetness, average grain size, surface and snowpack temperatures are extremely useful
snow hydrology and climate variables for a number of reasons. In hydrology, these snow variables
(along with location) provide insight and knowledge of where snowmelt can possibly occur in a
basin. For hydrological models, they provide much needed inputs for snowmelt algorithms (Garen
and Marks, 2005). Knowledge of the areal extent of the snowpack defines where in the basin large
amounts of incoming solar radiation are reflected and where large amounts are absorbed (Rango,
1996). This difference in albedo is important for regional and global climate studies. Energy and
1
moisture exchanges are vastly different in snow-covered and snow free areas, which lead to
differences in local climate. These large differences in surface characteristics lead to large scale
effects that need to be considered in general circulation modeling (Rango, 1996). For this reason,
monitoring the spatial and temporal variability of snow conditions at high resolution provides
valuable information for hydrological and climatological applications.
While the canonical way of acquiring information on snow characteristics is via observation
techniques (e.g. snow pits, probing, and ultrasonic snow depth sensors) from a network of in-situ
meteorological stations with either manual or automated daily records, most of the Earth’s snow
is located in remote and inaccessible areas where populations are scarce - or nonexistent - and
extreme conditions limit the ability to monitor the snow conditions continuously (Hachem et al.,
2012). Remote monitoring techniques offer the possibility to retrieve important snow cover
parameters such as snow depth and water equivalent (SWE) from a safe distance (Schaffhauser et
al., 2008; Dozier and Painter, 2004; Nolin, 2010; Rango, 1993). Hence, the use of satellite remote
sensing (RS) in snow hydrology has received increasing emphasis as the means to monitor snow
cover and estimate snow properties for several decades. However, some of the most commonly
known satellite derived snow products are either not operational or only provide information on
areal snow extent, while a few other known products provide the SWE. In order to monitor spring
floods and the possibility of avalanches, the development of a product capable of estimating snow
depth as a function of snow wetness would be significant for snow RS and snow RS literature.
1.2
Statement of the Problem
Snow surface energy-balance models are dependent on spatially-distributed parameters such as:
snow cover, albedo, grain size, SWE, temperature profile, depth, wetness, and meteorological
conditions (including long and shortwave radiation) to produce accurate predictions. Moreover,
with information on the snowpack layers, energy-balance models can be integrated to meltwater
flux or snow metamorphism calculations (Lefebre et al., 2003). Hence, because of its spatial
heterogeneity and significant changes over time, the large-scale (continental-to-global) modeling
of snow processes for both validation, data assimilation techniques, and spring flood and avalanche
predictions is crucial for hydrologists, environmentalists, water resources engineers, and water
managers to make educated decisions that can protect and save human lives.
2
Using the visible and near-infrared (NIR) portions of the electromagnetic spectrum, we can
directly estimate snow-covered areas, from which we can calculate albedo. In the infrared (IR),
we can measure snow surface temperature. To the extent possible, the RS of snow properties stems
from first principles about the optical properties of snow. Radiative transfer models of snow
reflectance and transmittance treat the snow grains as independent variables because the grain
sizes, and their center-to-center separations, are much larger than the wavelength of the light
(Warren, 1982). Because of multiple scattering as light enters the snowpack, penetration depths
are restricted to no more than 0.5 m in the blue wavelengths and are only a few millimeters in the
NIR and IR bands (Dozier and Painter, 2004). Therefore, the possibility of remotely sensing snow
depth and snow wetness is severely limited, and one must use microwave (MW) RS to measure
snow variables dependent on the snowpack and not just the snow surface.
Previous satellite products use MW frequencies at 19GHz and 37GHz to derive snow depth with
the empirical equation developed by Chang et al. (1987) presented below:
ܵ‫ܦ‬ሺܿ݉ሻ ൌ ͳǤͷͻ ‫ כ‬ሾሺܶ‫ܤ‬ଵଽு െ ܶ‫ܤ‬ଷ଻ு ሻሿ
Equation 1
where SD is snow depth in centimeters, TB19H and TB37H are the microwave brightness
temperatures (TBs) at the 19 GHz and 37 GHz frequencies, both at the horizontal polarization
channels. However, while this empirical formula reduces the effects of ground temperature and
atmospheric perturbations on changes in TBs, it does not provide insight as to how wet the snow
is for more practical (from a water resources management standpoint) purposes. Additionally,
experimental data and the existing (more current) literature show that the 89 GHz frequency is also
sensitive to variations in snowpack properties (Weng et al., 2012; Foster et al., 2005).
Snow wetness detection at the surface can be done with a variety of sensors. The NIR experiences
a reflectivity reduction when liquid water is in the snow. Shi and Dozier (1995) have shown that a
spectral band centered at 1.0 μm can be used to separate liquid water from ice in the snowpack.
Furthermore, when the thermal IR band records 0°C for both night and day observations, it is likely
that there is liquid water in the snowpack. As the MW emission is greatly affected by liquid water,
MW techniques can be used to identify the initiation of melt metamorphism in the snowpack. As
a result, the presence of liquid water, wet snow causes a higher dielectric loss in the MW
frequencies resulting in a high MW emissivity in excess of dry snow. A passive MW radiometer
3
measures a pronounced jump in the TB when even a small amount of liquid water is produced in
a dry snowpack. For small percentages of liquid water in the snowpack, there is a quantitative
relationship between liquid water content and TB (Stiles et al, 1981).
Well-known over the past decades, the Northern latitudes have experienced noticeable changes in
its climate. Since 1970, the average annual temperature raised by 2°F and the average winter
temperature increased by 4°F (Hansen et al., 2010). Furthermore, a projected rising trend in global
warming will reduce snow cover areas and shorten the snow-covered winter season. Shorter
winters with multiple warm periods accelerate snow melting and increase snow wetness. As such,
snow wetness variability needs to be considered when using RS techniques to accurately estimate
snow depth and, more importantly, the two variables should be integrated to make engineering
decisions pertaining to water resources management. The satellite based monitoring of snow depth
during the melting and refreezing periods is crucial for snowmelt flood forecasting and avalanche
risk prevention (Macelloni et al., 2005; Mätzler, 1986).
The publicly available snow products currently available are:
NIMBUS-7 SMMR Derived global monthly snow cover and snow depth (SMMR) – Snow
cover and depth (not operational since 1987)
SSM/I derived global snow cover (SMMI) – Snow cover (operational)
Global monthly ease-grid snow water equivalent climatology – SWE (not operational
since 2003)
MODIS snow products – Snow cover (operational)
Advanced Microwave Scanning Radiometer (AMSR-E/2) – SWE (operational)
None of these products provide snow depth retrievals nor incorporate a snow wetness function in
the algorithm. These issues raised the following research questions:
x
How will incorporating snow physical properties and a snow wetness function - dependent
on average snowpack temperature and grain size - on a MW-based snow depth and SWE
algorithm improve its accuracy?
x
Could this algorithm be developed into a global product capable of assimilating RS MW
TBs to improve global snow cover and depth mapping?
4
1.3
Motivation and Research Objectives
Generally, passive MW data are not able to effectively map wet snow cover - nor wet snow depth
- since the penetration of the microwave signal upward through the snowpack is extremely low
when the snow is wet. Hence, the incorporation of a snow wetness function in a snow depth
estimation model might yield more accurate results and will also provide decision makers with
more tangible and meaningful feedback for the risk prevention of spring floods and avalanches.
Furthermore, accurate remotely-sensed snow depth and wetness estimations will lead to better
model simulations of the hydrological processes in snow-covered watersheds. The four main
objectives of this work include:
1. To compare and cross validate satellite land surface temperature (LST) products with
observed snow surface temperature readings. For this purpose, automated and continuous
snow surface temperature observations are conducted and recorded at the study area.
Additionally, recorded data accessible online from three satellite LST products will be
downloaded. The observations from the study area are considered to be in-situ LST, while
the satellite observations are the remotely-sensed LST. Since the three satellite LST
products will be used in future segments of this research, the accuracy with which the
satellite products can retrieve LST needs to be validated with in-situ observations.
2. To study the temporal evolution of snow wetness. Snow wetness plays a significant role in
wet-snow avalanche prediction, meltwater release, and water availability estimations and
assessments within a river basin. However, it remains a difficult task and a demanding
issue to measure the snowpack’s liquid water content (LWC) and its temporal evolution
with conventional in-situ techniques. We propose an approach based on the use of timedomain reflectometry (TDR) and CS650 soil water content reflectometers to measure the
snowpack’s LWC and temperature profiles. For this purpose, we created an easilyapplicable, low-cost, automated, and continuous LWC profiling instrument using
reflectometers at the Cooperative Remote Sensing Science and Technology Center-Snow
Analysis and Field Experiment (CREST-SAFE) in Caribou, ME, USA, and tested it
immediately after installation. Lastly, the Snow Wetness Model (SWM), developed by
Muñoz et al. (2014) based on Solberg et al. (2004) findings, will be integrated into the
5
regression tree algorithm. Microwave retrievals typically exhibit low accuracy and larger
errors at the end of the winter season (due to wet snow).
3. To develop a regression tree algorithm that ingests snow physical (snow surface and pack
temperatures, grain size, and wetness) and radiative (MW TBs at 10, 19, 37, and 89 GHz)
properties to estimate snow depth and SWE.
4. To improve on global snow cover mapping by developing a free, publicly accessible
product capable of estimating snow depth using MW RS. Accurate retrievals about the
spatial/temporal distribution of snow depth are important for predicting meltwater runoff
and forecasting wet snow avalanches. For this purpose, GCOM-W1 AMSR2 MW TB
retrievals will be used.
1.4
Intellectual Merit
The individual approaches used in this research are not novel. Data mining techniques such as
regression trees have been well used and criticized in different fields, and at least two studies have
tried to estimate snow depth and SWE at local scales. The actual novelty is indeed the spatial
(global) scale and integration of varying snowpack properties normally considered constant in
previous models. In spring flood and avalanche prone regions, there is an incredible need to
provide water management organizations and stakeholders with new tools that support their
decision-making process. This research will be able to advance knowledge of global snow depth
and SWE mapping by exploring a potentially transformative approach for the conjunctive
integration of snow physical and radiative properties. The developed products under this research
have the potential to improve water management systems by providing the thorough mapping of
snow and SWE globally by incorporating snow wetness.
1.5
Document Structure
This research presentation is broken into nine chapters. In Chapter 1, a review is presented on the
optical and MW properties of snow, snow cover mapping, snow MW retrievals, the effects of snow
wetness on MW retrievals, the Snow Wetness Model and other snow physical and radiative
models, and regression tree models. Furthermore, methods currently applied to map snow
properties are introduced. This chapter answers the question: what approaches, measurements, or
6
technologies would be able to successfully map snow depth and SWE at broader extents
considering limited time and economic resources?
Chapter 3 discusses the main climatic and land cover conditions of the study area, and the
instrumentation used at CREST-SAFE to observe various snowpack properties.
Chapter 4 presents the methodology used to complete this work.
Chapter 5 focuses on the validation of three different operational satellite LST products. This
chapter answers the questions: are current LST products accurate when compared to in-situ
observations? Why is snow surface temperature important for snow depth mapping?
Chapter 6 introduces the development, validation, and calibration of a Snow Wetness Profiler at
CREST-SAFE. This chapter intends to answer the question: what are the impacts of snow wetness
on MW snow depth retrievals?
Chapter 7 introduces the use of machine learning algorithms for the prediction of snow depth and
SWE using snow physical and radiative observations at CREST-SAFE. This methodology is
formulated, tested, and applied to CREST-SAFE data.
Chapter 8 integrates the developed regression tree algorithm with RS MW observations from the
Japan Aerospace Exploration Agency (JAXA) Global Change Observation Mission – Water 1
(GCOM-W1) Advanced Microwave Scanning Radiometer 2 (AMSR2) instrument. Later, these
snow depth and SWE estimates are validated against twelve (12) Snow Telemetry (SNOTEL) sites
owned by the National Resources Conservation Service (NRCS) and JAXA’s own snow depth
product. This chapter answers the following questions: can regression trees be used to estimate
snow depth using snow physical and radiative properties? Does the incorporation of varying
snowpack properties and snow wetness provides improvement over previous algorithms?
Finally, Chapter 9 ends with the closing remarks and possibilities for future work based on the
results found in this study.
7
2
2.1
Literature Review
Optical Properties of Snow
The spectral albedo of any surface is the upflux divided by the downflux at that particular
wavelength (Warren, 1982). The spectral albedo of fresh snow is high in the visible region of the
spectrum and decreases slowly as with snow age. In the NIR, the spectral albedo of aging snow
decreases significantly when compared to fresh snow (O’Brien and Munis, 1975; Warren and
Wiscombe, 1980; Wiscombe and Warren, 1980). The broadband albedo is the reflectance across
the reflective part of the solar spectrum. Broadband albedo decreases as grain size increases with
snow age (Choudhury and Chang, 1979), and melting causes snow grains to grow and bond into
clusters (Dozier et al., 1981; Grenfell et al., 1981; Warren, 1982). Snow albedo can decrease by
more than 25% within just a few days as grain growth continues (Nolin and Liang, 2000). Gerland
et al. (1999) measured a maximum albedo higher than 90% on Svalbard, Norway, before melt
onset, and approximately 60% after melt had progressed in the spring. Snow cover albedo is
influenced by the albedo of the land cover below it, especially when the snowpack is thin.
Grain size may be estimated using remotely-sensed data (Dozier, 1984; Nolin and Dozier, 1993).
When the snow surface is melting, grain size increases, and the NIR reflectance decreases
dramatically (Warren, 1982). NIR snow albedo is quite sensitive to snow grain size, while the
visible albedo is less sensitive to grain size, but affected by snow impurities. Warren and
Wiscombe (1980) performed modeling that demonstrated that small, yet highly absorbing,
particles can lower snow albedo in the visible part of the spectrum by 5 to 15%, compared to pure
snow. Hansen and Nazarenko (2004) reported that anthropogenic soot emissions have reduced
snow and ice albedos by 3% in Northern Hemisphere land areas, thus contributing to global
warming. While Dirmhirn and Eaton (1975) proved that the reflectance of freshly fallen snow is
nearly isotropic, Salomonson and Marlatt (1968) established that, as snow ages, the specular
reflection component increases, especially in the forward direction and with the solar zenith angle.
Furthermore, the anisotropic nature of snow reflectance increases with increasing grain size
(Steffen, 1987). Effective snow-grain radii typically range in size from approximately 50 μm for
new snow, to 1 mm for wet snow consisting of clusters of ice grains (Warren, 1982). Snow albedo
increases at all wavelengths with the solar zenith angle. Moreover, cloud cover normally causes
8
an increase in snow albedo due to multiple reflections caused by clouds (Grenfell and Maykutt,
1977; Warren, 1982). Figure 1 illustrates the capability to retrieve snow properties using optical
and microwave bands.
Figure 1. Capability to retrieve snow properties using optical and microwave bands.
2.2
Microwave Properties of Snow
In the microwave part of the spectrum (300 to 1 GHz, or 1 mm to 30 cm wavelength), RS can be
performed either by measuring emitted radiation with a radiometer or by measuring the intensity
of the return (in decibels) of a signal sent by a radar. Microwave emission from a layer of snow
over a ground surface consists of contributions from the snow itself and from the underlying
ground. Both contributions are dependent on the transmission and reflection properties of the airsnow and snow-ground interfaces, and the absorption/emission and scattering properties of the
snow layer.
The dielectric properties of snow at any given MW frequency are dependent on the proportion of
liquid and solid water in the snow by volume. At temperatures below 0 ºC, water exists in thin
films surrounding ice crystals (Hobbs, 1974), but is considered to be dry because it contains no
“free” liquid water (Leconte et al., 1990). However, snow that contains a large amount of liquid
water (> 5% by volume) has a high dielectric constant (> 35 below 20 GHz) when compared to
dry snow. In theory, the dielectric constant of snow comprises the sum of a real and imaginary
9
part. Snow is a mix of air and ice, the dielectric constants of air and ice for frequencies from 1
MHz to well above the MW region are 1.0 and 3.17 ± 0.07, respectively (Evans, 1965). Snow has
a dielectric constant between 1.2 and 2.0 when the snow density varies from 0.1 to 0.5 gcm−3
(Hallikainen and Ulaby, 1986).
If a dry snowpack contains ice and snow layers, reflection at the interfaces between layers may
occur resulting in enhanced backscatter in the case of MW RS (Mätzler and Schanda, 1984). Also,
if the grain sizes of a dry snowpack are large enough relative to the MW wavelength, volume
scattering will occur. Otherwise, the signal is returned mainly from the ground/snow interface.
Longer wavelengths travel almost unaffected through dry snow. The X-band (2.4–3.75 cm, 8.0–
12.5 GHz) or lower frequencies (longer wavelengths) are not generally useful for detecting and
mapping thin, dry snow because the size of snow particles is much smaller than the size of the
wavelength. Therefore, at these longer wavelengths, there is little chance for a MW signal to be
scattered by the relatively small ice crystals comprising a snowpack (Watte and MacDonald, 1970;
Ulaby and Stiles, 1980, 1981). Wavelengths longer than approximately 10–15 cm are not
obstructed as they move through most dry snowpacks (Bernier, 1987). For snow crystals of a radius
larger than 0.1 mm, scattering dominates emission at higher (> 15 GHz) MW frequencies (Ulaby
et al., 1986). Absorption is determined by the imaginary part of the refractive index. In dry snow,
the imaginary part is several orders of magnitude smaller than for water (Ulaby and Stiles, 1980).
The backscatter received by a synthetic-aperture radar (SAR) antenna is the sum of surface
scattering at the air/snow interface, volume scattering within the snowpack, scattering at the
snow/soil interface, and volumetric scattering from the surface below (if applicable). Most
techniques developed for mapping snow cover using SAR data show potential for mapping wet
snow (Rott and Nagler, 1993; Shi et al., 1994). This is because it is challenging to distinguish dry
snow from bare ground using SAR data at the X-band and lower frequencies in space.
Volume scattering from a shallow, dry snow cover (SWE below 20 cm) is undetectable at the Cband (5.3 GHz, 5.6 cm) because the backscatter is dominated by soil/snow scattering. Volume
scattering in dry snow results from scattering at dielectric disconnection created by the differences
in electrical properties of ice crystals and air. Atmospheric scattering is usually very small and can
be neglected in the MW bands (Ulaby and Stiles, 1980; Leconte et al., 1990; Leconte, 1995). In
the case of wet snow (Stiles and Ulaby, 1980; Ulaby and Stiles, 1980; Rott, 1984; Ulaby et al.,
10
1986), when at least one layer of the snowpack (within the penetration depth of the radar signal)
becomes wet (4–5% liquid water content), the penetration depth of the radar signal is reduced to
about 3–4 cm (or one wavelength at the X-band) (Matzler and Schanda, 1984). As a result, there
may be high contrast between snow-free ground and ground covered with wet snow, making it
possible to differentiate wet and dry land or snow using the SAR C-band from space. Furthermore,
volume scattering increases with snow grain size, internal layering, and amount of snow. Radiation
at wavelengths comparable in size to the snow crystal size (about 0.05–3.0 mm) is scattered in a
dry snowpack according to Mie scattering theory - Mie scattering predominates when the particles
causing the scattering are larger than the wavelengths of radiation in contact with them. Currently,
only MW sensors operate at these wavelengths from satellites.
Microwave radiation emitted from a perfect emitter is proportional to its physical temperature.
However, most real objects emit only a fraction of the radiation that a perfect emitter would emit
at its physical temperature. The equivalent temperature of the MW radiation thermally emitted by
an object is called its brightness temperature, expressed in Kelvins. This fraction defines the
emissivity of an object (Chang et al., 1976). Microwave emission from a layer of snow over a
ground medium consists of two contributions: (i) emission by the snow volume and (ii) emission
from the ground below. Both contributions are governed by the transmission and reflection
properties of the air-snow and snow-ground interfaces, and by the absorption/emission and
scattering properties of the snow layer (Stiles et al., 1981), and numerous physical parameters that
affect the emission (Derksen et al., 2002). As an electromagnetic wave emitted from the underlying
surface propagates through a snowpack, it is scattered by the randomly spaced snow particles in
all directions. As the snowpack grows deeper, there is more loss of radiation due to scattering, and
the emission of the snowpack is reduced, thus lowering the TB. The deeper the snow, the more
crystals are available to scatter the upwelling MW energy, and, thus, it is possible to estimate the
depth and water equivalent of the snow using MW RS. Snow grains scatter the electromagnetic
radiation incoherently and are commonly assumed to be spherical and randomly spaced within the
snowpack. Although most snow particles are generally not spherical in shape, using Mie theory,
their optical properties can be simulated as spheres (Chang et al., 1976). A wet snowpack radiates
like a blackbody at the physical temperature of the snow layer, and is therefore indistinguishable
from snow-free soil using MW RS (Kunzi et al., 1982). The dielectric constants of water, ice, and
snow are different enough so that even a little surface melting causes a strong MW response
11
(Schanda et al., 1983; Foster et al., 1987). The scattering loss decreases drastically with increasing
liquid water content (free water) and becomes negligible for values above 1% (Hallikainen, 1984).
2.3
Snow Cover Mapping
Original attempts to forecast runoff using the areal extent of snow cover used terrestrial
photographs (Potts, 1937). Along with volume, the areal extent of snow cover has been used to
predict snowmelt runoff and to forecast floods. Because of its high albedo, snow was first observed
by the Television Infrared Operational Satellite-1 (TIROS-1) weather satellite in 1960. Data from
meteorological satellites were suitable for observing changes in snow conditions due to rising
temperatures and rain-on-snow events (Singer and Popham, 1963). Later, seasonal streamflow
could also be estimated (Rango and Salomonson, 1977). Data from Environmental Science
Services Administration (ESSA) operational satellites were used as early as the mid-to-late 1960s
to determine the areal extent of snow cover.
A step forward in snow mapping came along with the Landsat sensor series in 1972. Landsat-1
carried a Multispectral Scanner (MSS) sensor with 80-m spatial resolution. With Landsat data
came the ability to create detailed basin-scale snow cover maps on a regular basis, when cloud
cover permitted. Initially, the overpass interval for the Landsat satellite was 18 days. It was later
decreased to 16 days with the launch of Landsat-4 in 1982. Landsats-4 and -5 carried a Thematic
Mapper (TM) sensor with 30-m resolution, while Landsat-7 carries an Enhanced Thematic Mapper
Plus (ETM+) with spatial resolution of 30 meters, except in the panchromatic band where the
resolution is 15 m. Landsat-8 carries two sensors - the Operational Land Imager (OLI) and the
Thermal InfraRed Sensor (TIRS). Though the Landsat series has provided high-quality snow
maps, the 16- or 18- day repeat-pass interval of the Landsat satellites is not adequate for most
snow-mapping requirements, especially during spring snowmelt.
The National Oceanic and Environmental Administration (NOAA) National Environmental
Satellite, Data, and Information Service (NESDIS) began to generate Northern Hemisphere
Weekly Snow and Ice Cover analysis charts derived from NOAA’s Geostationary Operational
Environmental Satellite (GOES) and Polar Orbiting Environmental Satellite (POES) visible
satellite imagers in November 1966. These maps were manually constructed, and the spatial
resolution was 190 km. Since 1997, the Interactive Multi-sensor Snow and Ice Mapping System
12
(IMS) has been used by analysts to produce daily products at a spatial resolution of about 25 km,
and utilizes a variety of satellite data to generate the maps (Ramsay, 1998). This snow cover record
has been studied carefully by Robinson et al. (1993) and Robinson (1997, 1999) and has been
renovated following adjustments for inconsistencies that were discovered in earlier sections of the
dataset by Robinson and Frei (2000) and Frei et al. (1999). Results show that the Northern
Hemisphere annual snow-covered areas have decreased (Robinson et al., 1993; Brown and
Goodison, 1996; Hughes and Robinson, 1996; Hughes et al., 1996; Armstrong and Brodzik, 1998,
2001; Frei et al., 1999; Brown, 2000), as demonstrated by Armstrong and Brodzik (2001) with a
decrease of about 0.2% per year from 1979–1999. The National Operational Hydrologic Remote
Sensing Center (NOHRSC) snow cover maps, are distributed electronically in near real-time to
users during the snow season (Carroll, 1987 and 1995; Cline et al., 1998; Carroll et al., 2001). The
NOHRSC 1-km maps are generated from the NOAA polar-orbiting satellites and GOES satellites
to develop daily digital snow cover maps for the United States and parts of southern Canada. More
recently, the Moderate Resolution Imaging Spectroradiometer (MODIS) is being used to produce
daily and eight-day composite snow cover products from automated algorithms (Hall et al., 2002a).
The MODIS maps provide global, daily coverage at 500-m resolution, and the climate-modeling
grid (CMG) maps are available at 0.05º resolution, which is approximately 5.6 km at the Equator.
2.4
Mapping of Snow Properties Using Microwave Bands
Satellite observations in the MW provide a better assessment of global snow because it allows for
the retrieval of other properties other than snow cover. However, snowpack MW emission is
dependent on the snowpack’s density, grain size, wetness, and depth (Grody, 2008). Deeper snow
increases the scatter of the MW signal and hence causes lower scene MW TB (Ulaby and Stiles,
1981). Larger snow grain sizes corresponding to aged or melted and refrozen snowpack also
increase scattering and reduce TB (Grody, 2008). Since the MW emission of wet snow depends
on the liquid water content in the snowpack, the average snowpack temperature and grain size are
critical to interpreting MW signals during the spring melting and refreezing period.
To derive the SWE using MW data, a radiative transfer approach is used in which, for example,
an average crystal size of 0.3 mm (radius), a density of 300 kgm −1, and a spherical shape are
assumed. It is also assumed that the crystals scatter radiation incoherently and independently of
13
the path length between scattering centers. These quantities are used in radiative transfer equations
to solve the energy transfer through the snowpack (Chang et al., 1976, 1987). However, if the
crystal radii and snow density vary significantly from the assumptions, poor SWE values may be
obtained. Current efforts are aimed at improving the methods to estimate SWE by incorporating
more dynamic parameterizations of these variables. While Mätzler (1997) discovered that crystal
size is strongly related to MW TB, modeling results from other studies demonstrated that the shape
of the snow crystal is negligible in the transfer of MW radiation from the ground through the
snowpack (Foster et al., 1999, 2000; Tsang et al., 2000). Currently, the SWE of a dry snowpack
can be estimated with MW sensors such as the SSM/I and AMSR-E/2. In Canada, SSM/I data are
used to provide operational SWE map products.
Snow grain size is another important parameter that influences MW TB. A model was developed
to study the growth of the depth-hoar layer at the base of the snowpack on the Arctic Coastal Plain
of Alaska during winter and compared to TB as derived from the SMMR by Hall et al. (1986).
Using SSM/I data, Mognard and Josberger (2002) modeled seasonal changes in snow grain size
using a temperature gradient approach. This information was used to parameterize the retrieval of
snow depth in the northern Great Plains during the 1996–1997 winter season. Taking this approach
further, Kelly et al. (2003) have recently developed a methodology to estimate snow-grain size
and density as the snowpack evolves through the season using SSM/I and statistical growth
models.
Snow wetness has been studied using C-, L- (1.25 GHz), and P-band (440 MHz) polarimetric SAR
of a mountainous area in Austria, Rott et al. (1992) showed the importance of surface roughness
at C- and L-band frequencies, and the increasing importance of the snow volume contribution with
the longer wavelength P-band sensor. Furthermore, using European Remote Sensing Satellite
(ERS)-1 images acquired before, during, and after the melt period, Koskinen et al. (1997)
successfully mapped snow wetness with C-band SAR in sparsely forested regions in northern
Finland.
Numerous studies have shown that the 19, 37, and 85/89 GHz bands from the Special Microwave
Imager (SSM/I) and Advanced Microwave Scanning Radiometer (AMSR-E) have been used to
estimate snow depth (Grody and Basist, 1996; Kelly et al., 2003; Romanov et al., 2000; Simic et
al., 2004). While in earlier studies, the snow depth estimates from MW instruments have been
14
retrieved from the algorithm derived by Chang et al. (through experiments and applications) in
1982 using the gradient in MW TB values between the 19 GHz and 37GHz bands (Chang et al.,
1976, 1982; Kunzi et al., 1976, 1982; Goodison and Walker, 1994; Goodison et al., 1986; Grody
and Basist, 1996; Foster et al., 1997; Kelly and Chang, 2003). The reason for the use of these
channels is that the 37 GHz data are more affected by scattering within the snow than the 19 GHz
data; therefore the difference between these two channels is a measure of the amount of scattering
within the snow, which can be used to retrieve snow information. Nonetheless, snow depth
retrieval algorithms still show significant error in accuracy. These errors can be attributed to
variations in snow physical and radiometric properties due to snowpack metamorphism.
2.5
The Effect of Snow Wetness in Microwave Retrievals
Limitations in the MW retrieval of snow properties are related to the uncertainties in estimating
snow wetness. Snow wetness is a key component in snow hydrological processes and avalanche
research (Lu et al., 2012). While dry snow can be defined as the mixture of snow crystals and air,
wet snow is a combination of snow crystals, air, and liquid water. Liquid water may come from
rainfall or snowmelt. The latter being generated by near-surface air temperature and incoming solar
radiation. The radiative properties of dry, wet, and refrozen snow are inherently different, as
illustrated in Figure 2. Wet snow yields higher emissivity than dry and refrozen snow. While dry
snow presents higher emissivity than refrozen snow.
15
Figure 2. Microwave emissivity for common surface types. The differences in emissivity serve to
differentiate different types of snow and to distinguish snow from other features. (Source: Grody, 2008)
Muñoz et al. (2014) determined that there is a direct relationship between snow wetness, snowpack
temperature, and snowpack grain size and developed a snow wetness model that will be discussed
in the next section and used as part of this work. Additionally, it was demonstrated that microwave
emission at 37 and 89 GHz is highly correlated to daily melting-refreezing periods - with higher
brightness temperature values related to wet snow and the lower values to refrozen snow (as
demonstrated previously by Grody, 2008) – and that during the melting phase, the generation of
liquid water in the snowpack caused an increase in the absorption, due to an increase in the
imaginary part of snow permittivity. Consequently, the emission increased. While all through the
refreezing period, the reduction in the MW emission was due to both the decrease in temperature
as well as the refreezing of the snowpack.
2.6
Snow Wetness Model (SWM)
The snow wetness model developed by Muñoz et al. (2014) can be described as an exponential
function of snowpack temperature constrained by snow grain size (Equation 2). The model was
16
developed based on the findings by Solberg et al. (2004) establishing that increases in snowpack
temperature can be combined with rapid increases in grain size, while the snow surface
temperature remains approximately 0°C, to produce high wetness values (Figure 3). The developed
SWM, in conjunction with a MW emission model, is expected to reduce modeling errors during
the melting and refreezing periods characterized by wet snow.
భ
ܵ݊‫ݏݏ݁݊ݐܹ݁ݓ݋‬ሺΨሻ ൌ ͳǤͺͶ͵͵݁ ௌ௉் ‫כ‬
ሺ ሻ
ீௌ ఱ
ଵ଴
Equation 2
Where SPT is snowpack temperature in ºC and GS is grain size in mm.
Figure 3. Changes in snow wetness as a function of snowpack temperature.
The model was calibrated using four years of data (winters 2011, 2012, 2013 & 2014) and the
results showed high agreement with the expected behavior of snow wetness in the snowpack.
2.7
Complementary snow physical and microwave emission models
For this study, the SNow THERmal Model (SNTHERM) and Helsinki University of Technology
(HUT) Snow Emission Model will be used as the snow physical and MW emission models to
simulate snowpack properties and MW TBs, respectively.
2.7.1 HUT Single Layer Model
The original Helsinki University of Technology (HUT) Model is a semi-empirical model which
describes the emission behavior of a homogeneous snowpack to estimate the brightness
17
temperature of snow-covered ground with the assumption that snow cover is a single homogeneous
layer, scattered MW radiation is mostly in the forward direction (Hallikainen et al., 1997;
Lemmetyinen et al., 2010) (Figure 4). The emission from the snow cover is a function of snow
depth, snow density, snow grain size, and snow temperature for dry snow and also surface
roughness of the air/snow boundary and snow wetness. The HUT Model establishes that the
brightness temperature inside a snowpack of depth d may be expressed as follows:
TB (d ,T )
1
TB (0 ,T )e ( ke qks) d cos
T
1
k aTs
1 e ( keqks) d cos T
k e qk s
Equation 3
Where:
Θ
incident angle
TB (0+,θ)
brightness temperature at the ground-snow interface
Ts
snowpack physical temperature
q (q=0.96)
empirical parameter - the fraction of intensity scattered in the direction θ
κe
extinction coefficients
κs
scattering coefficients
κa
absorption coefficients
The absorption coefficient (κa) is calculated from the complex dielectric constant of dry snow. The
effect of snow grain size is described through the extinction coefficient, modeled empirically as a
function of snow grain size as follow (Hallikainen, 1987):
κe = 0.0018 f 2.8(φ)2
Equation 4
where κe is in decibels, f is the frequency in GHz, and φ is the snow grain diameter in millimeters.
The reflection of radiation from snow surface is controlled by the angle in which the radiation
strikes the surface, and the dielectric constant of the snow. The real part of the dielectric constant
18
of dry snow depends on the snow density as numerically expressed (Hallikainen, 1986), where the
snow density ρs is expressed in Mgm-3.
έ = 1 + 1.9ρs
Equation 5
The absorption coefficient is determined by the imaginary part of the dielectric constant and has
some dependence on temperature. The absorption coefficient is very small for dry snow; therefore
propagation of MW radiation through dry snow is generally dominated by scattering. Wiscombe
and Warren (1980) noted that increased ice grain size affect to lower values of spectrally integrated
scattering. The HUT model input parameters are shown in Table 1 and its simulation approach in
Figure 4.
Table 1. HUT Model Input Parameters.
Snow parameters
Tsnow,n Physical temperature of the snow layer n
rsnow,n Snow density of the snow layer n
mv,snow,n Snow wetness of the snow layer n
Dn Snow grain size of the snow layer n
dn Thickness of the snow layer n
Soil parameters
Tsoil Physical temperature of soil
mv,soil Soil water content
rsoil Soil bulk density
Rms Rms height of the soil surface
Cl Correlation length of the soil surface
Figure 4. HUT simulation approach.
19
2.7.2 SNTHERM (SNow THERmal Model)
SNTHERM (Jordan, 1991) is a physically based snow and soil model that is forced by
meteorologically determined surface fluxes. The model is primarily used to predict snowpack
properties. Operational snow products like the NOAA National Weather Service's National
Operational Hydrologic Remote Sensing Center (NOHRSC) Snow Data Assimilation System
(SNODAS) (Carroll, 2001) integrate SNTHERM into their framework.
SNTHERM uses meteorological input data to simulate physical snowpack properties (Figure 5).
The model simulates most in-snow properties and processes, using conservation of energy,
momentum and mass equations such as Darcy's law for water flow, Fourier's law for conductivity
of heat flow (i.e. energy), and interpolation methods. As output, the model provides snow depth,
snow temperature profiles, water content, density, grain size, and surface fluxes of sensible heat
and evaporation. The model also includes empirical and numerical approximations in order to
predict changes in the snowpack physical properties based on metrological variations. For
example, specific enthalpy equations are used to estimate the thermodynamic energy of the
snowpack while radiation entering the snowpack is estimated from an empirical fit. Detailed model
and technical documentation for the model was presented by Jordan (1991).
Figure 5. SNTHERM simulation approach.
The model calculates the thermal properties of the snowpack and fluid flow through the snow
using energy conservation. Using conservation of energy allows the model to physically represent
the heat movement through the snow strata instead of interpolating the flux. The snow and soil
layers are defined in the model by the finite difference method. The conservation equation is
expressed as:
∂/∂t∫vγbΩdV = avg(-∑b∫sJdS)+ ∫v avg(SdV)
Equation 6
20
Where V is the volume of the snow, soil layer or control volume, Ω is the heat or amount of water
being conserved, J is the flux, S is the source density. γb is the bulk density of the snowpack,
where b is i,l,v or a, which stands for ice, liquid water, water vapor, or air components of the
snowpack.
The bulk density of the snowpack is defined as:
γb = θbρb
Equation 7
where θb is the volume fraction of the air, ice, liquid water, or water vapor, and ρb is the intrinsic
density of the component. The intrinsic density is defined as the mass of b per unit volume of b.
In case energy is conserved, bulk density, and source density remain uniform throughout the snow
or soil layer, the conservation equation reduces to:
∂/∂tγbΩ∆z = - Σavg[Jj+1/2 - Jj-1/2] + S∆z
Equation 8
where z is the layer thickness of the snow or soil, j is the nodal index of the control volume, j+1/2
is the upper boundary of the layer j, and j-1/2 is the lower boundary of the layer j and J refers to
convective flux, diffusive flux or a combination of the two mechanisms.
The conductive - diffusive flux component is represented by:
avg[Jj+1/2 - Jj-1/2] = -avg[(D∂Ω/∂z)j+1/2 - (D∂Ω/∂z)j-1/2]
Equation 9
where D is the diffusion coefficient. The net convective flux component is represented by:
avg[Jj+1/2 - Jj] = avg[(qΩ)j+1 - (qΩ)j]
Equation 10
where q is the mass flux.
21
2.8
Regression tree models
Tree-based regression models trace back to Morgan and Sonquist (1963). Breiman et al. created
Classification and Regression Trees (CART) in 1984 and provided a thorough description on both
models. Most research efforts concentrate on classification trees in Machine Learning (Hunt et al.,
1966; Quinlan, 1979; Kononenko et al., 1984). However, efforts on regression trees started later
with RETIS (Karalic & Cestnik, 1991) and M5 (Quinlan, 1992). When compared to CART, RETIS
uses a different pruning methodology based on the Niblet and Bratko (1986) algorithm and mestimates (Cestnik, 1990). M5 was developed by Quinlan (1992) with a more novel approach
because it uses linear regression models in the tree leaves. A further extension of M5 was described
by Quinlan in 1993. This extension entailed combining the predictions of the trees with k nearest
neighbor models.
Regression trees use a recursive partitioning algorithm. The algorithm builds a tree by dividing the
training sample into smaller subsets. Figure 6 presents a description of the algorithm. The
௡೟
, and generates a test node t if
algorithm receives a set of n data points as input, ‫ܦ‬௧ ൌ ሼ‫ݔۃ‬௜ ǡ ‫ݕ‬௜ ‫ۄ‬ሽ ௜ୀଵ
a termination criteria is not achieved. These subsets consist of cases that logically require the split
test s* in the node t, ‫ܦ‬௧ಽ ൌ ሼ‫ݔۃ‬௜ ǡ ‫ݕ‬௜ ‫ܦ א ۄ‬௧ ‫ݔ ׷‬௜ ՜ ‫ כ ݏ‬ሽ, and the remaining cases, ‫ܦ‬௧ೃ ൌ
ሼ‫ݔۃ‬௜ ǡ ‫ݕ‬௜ ‫ܦ א ۄ‬௧ ‫ݔ ׷‬௜ ե ‫ כ ݏ‬ሽ . Then, the best split test is chosen at each node according to the local
criterion.
Figure 6. Recursive partitioning algorithm.
22
The algorithm has three components:
1. Selecting a split test (the splitting rule).
2. Determining when a tree node is terminal (termination criterion).
3. Assigning a value to each terminal node.
The usual method for building a regression model based on a sample of an unknown regression
surface involves trying to obtain the model parameters that minimize the following least squares
error criterion:
ଵ
௡
ଶ
σ௡௜൫‫ݕ‬௜ െ ‫ݎ‬ሾߚǡ ‫ݔ‬௜ ሻ൯
Equation 11
where n is the sample size; ‫ݔۃ‬௜ ǡ ‫ݕ‬௜ ‫ ۄ‬is a data point ; and ‫ݎ‬ሾߚǡ ‫ݔ‬௜ ሻ is the prediction of the regression
model ‫ݎ‬ሾߚǡ ‫ݔ‬ሻ for the case ‫ݔۃ‬௜ ǡ ‫ݕ‬௜ ‫ۄ‬.
LS minimization states that the constant k that minimizes the expected value of the squared error
is the mean value of the target variable. Based on this theorem, the constant that should be assigned
to the leaves of a regression tree obtained using LS error criterion is the average of the target values
of the cases within each leaf l:
݇௟ ൌ ଵ
௡೗ σ஽೗ ‫ݕ‬௜
Equation 12
where, nl is the cardinality of the set Dl containing the cases in leaf l (i.e. nl = #Dl). Some systems
use non-constant models in the tree leaves like linear polynomials instead of averages.
The splitting rule for each node states that the inner node of the trees has two descendent nodes.
These inner nodes split the training into two subsets depending on the result of a test on one of the
input variables. Cases that satisfy the test follow to the left branch, the others go to the right branch.
The split test is selected with the purpose of refining the fitting error of the resulting tree. Any path
from the root node to a node t corresponds to a partition Dt of the input cases. If we assume the
constant obtained with Equation 12, we define the fitting error of a node t as the average of the
squared differences between the Y values in the node and the node constant kt,
‫ݎݎܧ‬ሺ‫ݐ‬ሻ ൌ ଵ
௡೟
σ஽೟ሺ‫ݕ‬௜ െ ݇௜ ሻଶ
Equation 13
23
Also, we define the error of a tree T as a weighted average of the error in its leaves by:
‫ݎݎܧ‬ሺܶሻ ൌ σ௟‫א‬j ܲሺ݈ሻ ൈ ‫ݎݎܧ‬ሺ݈ሻ ൌ σ௟‫א‬j
௡೗
௡
ൈ
ଵ
௡೗
ଵ
σ஽೗ሺ‫ݕ‬௜ െ ݇௟ ሻଶ ൌ σ௟‫א‬j σ஽೗ሺ‫ݕ‬௜ െ ݇௟ ሻଶ ௡
Equation 14
where, P(l) is the probability of a case falling into leaf l; n is the total number of training cases; n l
is the number of cases in leaf l; and Ŧ is the set of leaves of the tree T.
A binary split divides a set of cases in two. The goal of the splitting rule is to choose the split that
maximizes the decrease in the error of the tree resulting from this division. The error of a split s is
the weighted average of the errors of the resulting sub-nodes:
‫ݎݎܧ‬ሺ‫ݏ‬ǡ ‫ݐ‬ሻ ൌ ௡೟೗
௡೟
ൈ ‫ݎݎܧ‬ሺ‫ݐ‬௟ ሻ ൅ ௡೟ೝ
௡೟
ൈ ‫ݎݎܧ‬ሺ‫ݐ‬௥ ሻ
Equation 15
where, tL is the left child node of t defining a partition Dtl that contains the set of cases {< xi , yi >
‫ א‬Dt : xi → s } and ntL the cardinal of this set; and tR is the right child node of t defining a partition
DtR that contains the set of cases {< xi , yi > ‫ א‬Dt : xi →/ s } and ntR the cardinal of this set. Then
comes the best split for a node t given a set S of candidate splits. The best split s* is the split
belonging to S that maximizes:
∆Err (s,t) = Err (t) – Err (s,t)
Equation 16
This greedy criterion guides the choice of a split for all inner nodes of an LS regression tree. On
each iteration of the recursive partitioning algorithm, all possible splits of each of the predictor
variables are evaluated. The one with best ∆Err is chosen.
24
3
3.1
In-situ observations and satellite products
In-situ observations
In-situ observations were performed in the county of Caribou in the state of Maine located in the
Northeast of the United States of America. The coordinates for the study area are 46º55’ N, 68º01’
W (Figure 7). The site is apt and suitable for snow research, given how it is covered in snow from
late November to early April. Average seasonal snowfall is 2.8 m, with a record high of 5 m.
Seasonal snow accumulation typically reaches its maximum (around 50-60 cm) by late February
or the beginning of March.
Figure 7. (a) State of Maine in the USA. (b) County of Caribou in the state of Maine, the USA. (c)
CREST-SAFE location within the premises of the Caribou Municipal Airport, Caribou, ME, USA.
The region is categorized as gentle rolling terrain with low-rounded mountains that elevate from
120 – 300 m, and approximately half of the land adjacent to the study area is agricultural. The rest
is considered to be spruce fir forests and maple beech birch. Forest fraction increases from
southeast to northwest in the region. Four active United States Geological Survey (USGS) gauges
25
record streamflow information of the Aroostook River as well as other smaller rivers and streams.
Naturally, snowmelt water presents the majority of the yearly runoff to local rivers. Hence, the
area offers fitting hydrology and agriculture applications. The county of Aroostook, where Caribou
is located, is known for its winter recreational activities and tourism, making the snow a profitable
natural resource that generates jobs and revenue for the local economy.
The Field Snow Research Station (also referred to as Snow Analysis and Field Experiment, SAFE)
is operated by the NOAA Cooperative Remote Sensing and Technology Center (CREST) in the
City University of New York (CUNY). The field station is located in Caribou, ME within the
premises of the municipal airport (46˚52’59”N, 68˚01’07”W) and close proximity to the National
Weather Service (NWS) Regional Forecast Office. The station was established in 2010 to support
studies in snow physics and snow remote sensing.
Since its establishment, the station tallies a total of twenty two instruments that provide continuous
and automated all-year round measurements of the physical characteristics of snow, soil
temperature down to 20 cm into the ground, and all basic meteorological parameters (Table 2).
The list of measured snowpack physical properties include snow depth, SWE, snowfall, and
snowpack temperature profile. Two station web cameras provide real time images of the site
(http://crest.ccny.cuny.edu/snowcam1/ and http://crest.ccny.cuny.edu/snowcam2/ ).
The observation of snowpack physical properties is complemented with snowpack radiative
measurements in the IR and the MW spectral bands. The snowpack IR TB is measured with an IR
camera at the 11μm wavelength. While four microwave radiometers (10GHz, 19 GHz, 37 GHz,
and 89 GHz) provide snowpack MW emission observations at both vertical and horizontal
polarizations. Observations with all radiometers are conducted continuously at less than 1 min time
intervals. Calibration is performed twice a year prior to the beginning and at the end of the winter
season.
Additional instruments include: a SWE gamma sensor and a snow wetness profiler.
The
microwave radiometers were selected because these reproduce MW observations from the DMSP
SSM/I and SSMIS, Aqua ASMR-E, and the Global Change Observation Mission-Water First
satellite (GCOM-W1) AMSR2.
26
The datasets accumulated during the first three winter seasons (2010, 2011, and 2012) were used
to quantify seasonal variations of the snowpack physical properties and snow microwave emission
to assess the performance of snowpack physical models (Lakhankar et al., 2013). Access to all
ground-based observation data includes: snowpack physical properties, snow stratigraphy, and
microwave
radiometer
data
can
be
obtained
through
http://www.star.nesdis.noaa.gov/smcd/emb/snow/caribou/microwave.html.
Table 2. Instruments and environmental parameters observed at the CREST Snow Research station in
Caribou, ME. (Source: Muñoz et al., 2014)
Parameter
Air Temperature
Air Humidity
Wind Speed
Wind Direction
Snow/Rain Precipitation
Shortwave Radiation (U/D/N)
Longwave Radiation (U/D/N)
Snow depth
Snow water equivalent
Snowpack temperature profile
Snow density vertical profile
Snow grain size vertical profile
Snow liquid water content
Tb at 10 GHz (V/H)
Tb at 18 GHz (V/H)
Tb at 37 GHz (V/H)
Tb at 89 GHz (V/H)
Snow Skin Temperature
Snow directional reflectance, (~ 50
observations within lower hemisphere)
Soil moisture& temperature,
3 levels (2.5, 5, 10 cm)
Aerosol optical depth and size
distribution (derived)
Live images
1
2
Instrument used
Automated (A) or
manual (M)
Meteorology
A
A
A
A
Accuracy1
Vaisala Temperature/RH
Probe
RM Young Wind
Monitor (Alpine
version)
Stand Pipe Station
A
Hukseflux 4-Component
A
A
Net Radiation Sensor
Snowpack Physical Properties
Ultrasonic depth sensor
A
Ruler
M
Snow pillow
A
Gamma Sensor
A
Tube
M
Temperature probes
A
every 5 cm
FLIR Infrared Thermal
M
Imaging Camera
Wedge cutter, every 10
M
cm
Microscope, every 10
M
cm
Set of “snow forks”
A
Snow Radiative/Reflective Properties
Microwave radiometer
A
Microwave radiometer
A
Microwave radiometer
A
Microwave radiometer
A
Apogee Infrared
A
Radiometers
CIMEL sunphotometer,
A
8 spectral bands within
0.4 -1.2 μm range
Other
Stevens Hydra probe
A
CIMEL sunphotometer,
8 spectral bands within
0.4 -1.2 μm range
Two web cameras
Sampling
time interval2
Current status, Operational (O)
or Planned Addition (P)3
3 min
3 min
3 min
3 min
O
O
O
1%
1%
3 min
3 min
3 min
O
O
O
1 cm
1 cm
N/A
N/A
1 mm
3 min
2-3 days
3 min
3 min
2-3 days
O
O
O
O
O
0.1K
3 min
O
0.2K
2-3 days
O
N/A
2-3 days
O
N/A
2-3 days
O
3 min
O
1 min
1 min
1 min
1 min
O
O
O
O
0.2°C
3 min
O
0.01
Hourly,
during
daytime
O
3 min
O
0.2 °C
.7%
0.3m/s
3°
0.2 K
0.2 K
0.2 K
0.2 K
A
0.01
A
N/A
Hourly,
during
daytime
30 sec
O
O
O
Accuracy of manual observations is an estimated value and corresponds to the typical accuracy of this type of measurements
The true sampling interval of automated observations is different and varies mostly from 30 sec to 1 min. For convenience of the analysis observations and to reduce the volume of data the results
are averaged within 5 min “effective” sampling interval
3
Instruments marked as “Planned Addition” are currently being acquired and will be installed at the CREST station prior to or during the 2013-2014 winter season.
27
3.1.1 Instrumentation at CREST-SAFE
This section offers an overview of the instruments used for the execution of observations and
measurements used in this study. Instrument descriptions (i.e. accuracy, calibration) are described
as specified in their respective manuals.
3.1.1.1 Soil surface/Snow surface IR temperature sensor
An
Apogee
Broadband
Infrared
Radiometer
Model
SI-111
(Figure
8)
(http://www.apogeeinstruments.com/content/SI-100-manual.pdf/) is used at CREST-SAFE to
measure T-skin and soil surface temperature (during the snowless season). The half-angle for the
SI-111 model is 22.0º, meaning that the diameter of the target circle is approximately 1.7 meters.
The target is a circle from which 98 percent of the radiation viewed by the IR radiometer detector
is emitted.
Figure 8. Apogee Broadband Infrared Radiometer Model S-111. (Source:
http://www.apogeeinstruments.com/standard-field-of-view-infrared-radiometer-sensor-si-111/)
The SI-111 calibration provides a measurement uncertainty of ±0.2 ºC from -30 to +65 ºC when
the sensor body temperature is within 20 ºC of the target. The target temperature is derived using
the resistance of an internal thermistor inside the instrument. The resistance of the internal
thermistor is computed using excitation voltage input and output voltage readings. As the
Steinhart-Hart equation states, the resistance of a semiconductor is temperature dependent
(Steinhart and Hart, 1968). Hence, we can obtain the detector temperature using the resistance of
the internal thermistor. Then, following the fundamental physics of the Stefan-Boltzmann Law,
where radiation transfer is proportional to the fourth power of absolute temperature, the instrument
28
calculates target temperature by using the linear proportionality in the energy balance between
target and detector, analogous to energy emission being linearly proportional to the fourth power
of temperature in the Stefan-Boltzmann Law (Bohren and Huffman, 1998). An appropriate
correction for surface emissivity is usually required for accurate surface temperature
measurements because the radiation (observed brightness temperature) detected by the infrared
radiometer is constituted by two components: 1) radiation directly emitted by the target surface,
and 2) reflected radiation from the background (generally the sky when the target temperature is
outdoors). Errors for emissivity correction in environmental applications are typically negligible
when using the Apogee Broadband Infrared Radiometer because a large proportion of the radiation
emitted by terrestrial objects is in the 8-14μm waveband that corresponds to it, and the surface
emissivity for most terrestrial objects does not vary significantly in that waveband. However, the
emissivity correction was conducted using Equation 17, which is directly derived from StefanBoltzmann’s Law.
ర
ܶ୘ୟ୰୥ୣ୲ ൌ ට
்౏౛౤౩౥౨ ర ିሺଵିఌሻൈ்ా౗ౙౡౝ౨౥౫౤ౚ ర
ఌ
Equation 17
Where ܶୗୣ୬ୱ୭୰ is the brightness temperature measured by the infrared radiometer, ܶ୘ୟ୰୥ୣ୲ is the
actual temperature of the target surface, ܶ୆ୟୡ୩୥୰୭୳୬ୢ is the brightness temperature of the
background (usually the sky), and ߝ is the emissivity of the target surface. The emissivity value is
constant and dependent on the target surface observed by the infrared radiometer. When calibrating
the Apogee Broadband Infrared Radiometer, the surface that will be observed by the instrument
has to be provided in the software installation process. Then, based on a lookup table, the
emissivity value is assigned. The emissivity of snow assigned by the software is 0.97. Since this
emissivity value is congruent with previous studies that have found the emissivity of snow to be
within the range of 0.97 - 0.99, the emissivity value was not modified (Hori et al., 2006).
3.1.1.2 Microwave Radiometers
Instruments at the site include four dual-polarization microwave radiometers manufactured by
Radiometrics Corporation in Boulder, CO, USA. The radiometers operate at 10, 19, 37, and 89
GHz and are mounted on top of a trailer at a height 4 m (Figure 9) aiming at the surface at a 55
degrees incidence angle.
29
Figure 9. Microwave Radiometers (10, 19, 37 and 89 GHz) at CREST-SAFE. The bigger the dome dome
of the radiometer, the smaller the MW frequency.
The observation incidence angle was selected to match the observation geometry of Special Sensor
Microwave Imager (SSM/I) onboard DMSP satellites and the Advanced Microwave Scanning
Radiometer (AMSR-E) onboard the Aqua satellite. The radiometer footprint has an elliptical shape
with a 2.6-m major axis and a 1.2-m minor axis. The half antenna beam width of the antenna is 3
dB and the radiometer stability is > 2 K. The radiometers were calibrated using ambient
temperature microwave absorber (warm reference) and liquid nitrogen (cold reference) targets of
known temperatures. The calibration target measurement error is < 1 K. Microwave TB
measurements are recorded at one minute intervals.
3.1.1.3 Snowpack Temperature Profiler
The vertical snowpack temperature distribution is measured a temperature profiler. The instrument
(Figure 10) is comprised of 16 Watlow rigid sheath thermocouples placed at a 5 to 10 cm interval.
30
Figure 10. Air/snowpack temperature profilers at CREST-SAFE. (Source: Muñoz et al., 2014)
The Watlow rigid sheath thermocouples have a 3/16 inch diameter sheath, 24 gauge stranded
fiberglass lead with stainless steel over braid, grounded junction, and split lead termination. The
thermocouples are connected to a CR3000 datalogger, where data is recorded every 3 minutes.
The temperature profiler is placed near the microwave radiometer footprint.
3.1.1.4 Ultrasonic Depth Sensor
The Judd Communications ultrasonic depth sensor (Figure 11a) measures the time required for an
ultrasonic pulse to travel to and from a target surface. An integrated temperature probe with solar
radiation shield provides an air temperature measurement for properly compensating the distance
measured. The instrument is installed 2.5 m above the soil surface and has an accuracy of 1 cm or
.4 % distance to the target.
3.1.1.5 Wind speed and direction monitor
Wind speed and direction is measured at approximately 2 meters from the soil surface using an
RM Young Heavy Duty Wind Monitor-HD-Alpine-Model 05108-45 (Figure 11b) with a wind
speed range from 0-100 ms-1 and an azimuth of 360°. Wind speed accuracy is ± 0.3 ms-1 or 1% of
reading and wind direction ± 3 degrees. The process is automated at a 3-minute sampling interval.
31
3.1.1.6 Near-surface air temperature probe
The near-surface air temperature is measured directly at a 2-meter height from the ground by a
Vaisala HMT330 Temperature/Relative Humidity probe (Figure 11c) through an automated
process; at a 3 minute sampling interval to an accuracy of 0.2 °C.
(b)
(c)
(a)
Figure 11. (a) Judd Communications Ultrasonic Depth Sensor (b) RM Young Heavy Duty Wind Monitor
for wind speed and direction (c) Vaisala HMT330 Temperature/Relative Humidity probe
3.1.1.7 Snow Wetness Profiler
Snow permittivity vertical distribution observations in the snowpack are done with a snow wetness
profiler. The instrument (Figure 12) consists of 14 CS650 soil reflectometers at 10 to 15 cm
intervals. CS650 reflectometers measure volumetric water content, electrical conductivity,
dielectric permittivity, and temperature of the porous medium. The measurements are reported
through SDI-12 communication. Volumetric water content information is derived from the
probe’s sensitivity to the dielectric permittivity of the medium surrounding its stainless-steel rods.
The reflectometer is arranged as a water content reflectometer with the two parallel rods forming
an open-ended transmission line. A differential oscillator circuit is connected to the rods and a
state change activated by the return of a reflected signal from one of the rods. The travel time of
the electromagnetic waves that are induced by the oscillator on the rod varies with changing
32
dielectric permittivity. Water is the main contributor to the bulk dielectric permittivity of the
porous medium. Hence, the travel time of the reflected wave increases with increasing water
content. The CS650 has the capability of measuring snow temperature as well. The reflectometer
measures the dielectric permittivity of the media and applies Topp equation (Topp et al., 1980) to
estimate volumetric water content.
Figure 12. Snow wetness profiler during winter season (Source: Muñoz et al., 2014).
3.1.2 Supplementary instrumentation at NWS
Sky cover hourly data were obtained from the NWS website. These measurements were observed
and collected by the Automated Surface Observing System (ASOS) (Figure 13) station in the
Caribou local airport close (90 meters) to the NWS Caribou offices and CREST-SAFE (130
meters). ASOS is an array of instruments for observing temperature, precipitation, wind, sky cover,
visibility, and pressure. It was developed as a joint effort between the NWS, Federal Aviation
Administration (FAA), and Department of Defense (DOD). ASOS serves as the USA’s primary
surface observing system and takes meteorological readings every minute, 24-hours a day at
almost 1000 locations.
33
The ASOS (http://www.nws.noaa.gov/asos/aum-toc.pdf/) uses a laser beam ceilometer with a
vertical measuring range of 12,600 feet and reporting range of 12,000 feet. The ASOS cloud
sensor, or CHI, is a vertically pointed laser transmitter and receiver. Its operation is similar to radar
in that the time interval between pulse transmission and reflected reception from a cloud base is
used to determine the cloud height. The CHI consists of a gallium arsenide laser beam ceilometer
operating in the NIR portion of the electro-magnetic spectrum at a wavelength of about a 0.9
microns. The instrument employs Light Detection and Ranging (LIDAR) principles and computer
algorithms to provide cloud coverage and height information. The CHI reports will contain only
opaque clouds. Moisture layers, or thin clouds detected by the CHI and considered too thin to be
a cloud, will be reported as a restriction to vertical visibility or simply not reported. The reporting
of vertical visibility is dependent on the thickness and density of the moisture layer. To correctly
classify these signals received by the ceilometer, sensor software processes the data into three
categories: “no hit,” “cloud hit,” and “unknown hit.” The signal signature of a cloud return or
“cloud hit” is characterized by a rapid increase in backscatter when the beam passes from the clear
air beneath the cloud into the moist conditions within the cloud. At the end of a 12-second
sampling, the CHI produces a detailed, high-resolution backscatter profile from which a unique
determination of the cloud base can be made. The cloud base “hits” (or returns) from each pulse
are assigned to one of the 252 50- foot vertical data bins within the 12,600 foot measurement range;
resulting in a vertical resolution of 50 feet.
The sky condition algorithm works so that every 30 seconds a sample is compiled from the CHI’s
backscatter returns taken from the most recent two or three 12-second processing intervals
completed within the 30-second period. Each 12-second interval processes more than 9,000 signals
for back scatter returns. These data are processed to determine the height of the returns and whether
the sample compiled from these returns is a “cloud hit” or an “unknown hit.” Every minute, ASOS
processes the most recent 30 minutes of 30-second sample data; the last 10 minutes of data are
processed twice (double weighted) to be more responsive to the latest changes in sky condition.
This technique provides a total of 80 samples; 40 in the first 20 minutes and 40 in the last 10
minutes. The cloud signal hits for the latest 30 minutes are then rounded or “binned” to the nearest
100 feet for cloud heights between the surface and 5,000 feet; to the nearest 200 feet for heights
between 5,000 and 10,000 feet; and to the nearest 500 feet for heights above 10,000 feet. Each
minute, if more than fives bin height values have been recorded (during the last 30 minutes), the
34
cloud heights are clustered into layers using a least-square statistical procedure until there are only
five bins remaining (each bin can have many “hits’ in it). These bins, or clusters, are then ordered
from lowest to highest height. Following this clustering, ASOS determines whether the clusters
can be combined into “meteorologically significant” height groups. This second clustering is done
so that very close layers are not reported. At the end of this combining process, all cluster heights
between the surface and 5,000 feet are rounded to the nearest 100 feet. Above 5,000 feet, the
algorithm rounds the cluster height values to the nearest reportable value (i.e., nearest 500 ft. up
to 10,000 ft. and nearest 1,000 ft. above 10,000 ft.). These bins now are called “layers” and the
algorithm will select up to three of these layers to be reported in accordance with cloud layer
reporting
priority
as
specified
in
Federal
Meteorological
Handbook
No.
1
(http://www.ofcm.gov/fmh-1/fmh1.htm/). The amount of sky cover is determined by adding the
total number of hits in each layer and computing the ratio of those hits to the total possible. If there
is more than one layer, the “hits” in the first layer are added to the second (and third) to obtain
overall coverage. For reporting purposes, the ASOS measured cloud amount for each layer is then
converted to a statistical functional equivalent of a human observation. All cloud layer heights are
reported Above Ground Level (AGL) with respect to field elevation. The cloud amounts below
12,000 feet reported by ASOS are in five categories: clear (CLR, means when the cloud coverage
is from zero up to 5 %), few (FEW, from 5 up to 25 % coverage), scattered (SCT, from 25 up to
50 % coverage), broken (BRK, from 50 up to 87 % coverage), and overcast (OVC, from 87 up 100
% coverage). The sky condition algorithm also tests for total obscurations. Necessary conditions
for reporting totally obscured sky include a surface visibility of one mile or less and a high
percentage of “unknown hits” at or below 2,000 feet AGL. When these conditions are met, ASOS
processes and formats cloud return values classified as “unknown hits” into the sky condition
report.
Doelling et al. (2005), Joro, Hyvärinen, and Kotro (2010), and Sharma et al. (2015) validated
satellite retrieved cloud amounts over the Continental United States with ASOS ceilometer data.
While it is known that ASOS cannot detect high thin clouds and the ASOS cloud categories are
coarse, daytime overcast agreement with satellite retrieved cloud amounts was better than 90%
and clear-sky agreement better than 80%. Some identified discrepancies were due to orographic
effects.
35
Ceilometer
Figure 13. Distinctive ASOS station used by NWS. (Source: https://www.ncdc.noaa.gov/data-access/landbased-station-data/land-based-datasets/automated-surface-observing-system-asos)
3.2
Data Acquisition
CREST-SAFE uses an integrated multi-source data collection system. Radiometric data is stored
on a computer laptop inside the site trailer. This data is then transmitted to CREST via FTP servers
for preprocessing. Meteorological and snow information is stored on a CR3000 datalogger. The
CR3000 can operate under harsh environments in remote locations. Real-time CREST-SAFE data
can be accessed through:
x
http://www.star.nesdis.noaa.gov/smcd/emb/snow/caribou/microwave.html
x
http://noaacrest.org/snow/
36
3.3
Satellite Products
3.3.1
VIIRS onboard S-NPP satellite and its LST product
The Visible Infrared Imaging Radiometer Suite (VIIRS) instrument onboard the Suomi National
Polar-orbiting Partnership (S-NPP) spacecraft was launched in October 2011. VIIRS is a crosstrack scanning radiometer sensor that measures reflected and emitted radiation from the Earthatmosphere system in 22 spectral bands, spanning from 412 nm to 12,050 nm. It has a wide swath
(~3000 km) that allows it to fully sample the Earth every day (Guillevic et al., 2012; Jackson et
al., 2013) VIIRS provides a majority of NOAA CLASS’s (Comprehensive Large Data Array
Stewardship System) EDRs (Environmental Data Records). The VIIRS Land Surface Temperature
(LST) EDR provides the skin temperature of the uppermost layer of the land surface (and larger
inland waters) in swath format (Schueler et al., 2003). The VIIRS LST product was acquired over
the evaluation site (CREST-SAFE) with its corresponding moderate-band terrain-corrected
geolocation Sensor Data Records (SDR) (GMTCO) at 750 m resolution. The VIIRS LST data for
this study was retrieved by the Split Window (SW) algorithm which applies data from the VIIRS
M15 and M16 bands centered at wavelengths of 10.8 μm and 12.0 μm, respectively (Sun and
Pinker, 2003). The algorithm is described as follows:
LSTi = c0(i) + c1(i)T11 + c2(i)(T11 − T12) + c3(i)(sec θ – 1) + c4(i)(T11 − T12)2
Equation 18
where i is the index of 17 International Geosphere-Biosphere Program (IGBP) surface types; cj(i)
are the algorithm regression coefficients in which j represents the term’s sequential position in the
equation; T11 and T12 are the brightness temperatures of M15 and M16 VIIRS bands,
respectively; θ is the satellite zenith angle.
3.3.2 MODIS onboard Terra and Aqua satellites and its LST product
The Moderate Resolution Imaging Spectroradiometer (MODIS) is a 36-channel (ranging in
wavelength from 0.4 μm to 14.4 μm) visible to thermal-infrared sensor onboard the Terra (1999)
and Aqua (2002) satellites launched by the flagship of the National Aeronautics and Space
Administration‘s (NASA) Earth Observing System (EOS) program. MODIS collects visible and
37
infrared imagery and radiometric measurements of the land, atmosphere, cryosphere, and oceans.
MODIS daily LST products provide radiometric LST values over land and larger inland waters in
swath and grid format.
The MODIS LST product is retrieved using the generalized split-window (SW) algorithm (Wan
1996, 1999):
ܶ௦ ൌ ‫ ܥ‬൅ ቀ‫ܣ‬ଵ ൅ ‫ܣ‬ଶ ൈ
ଵିఌ
ఌ
οఌ
൅ ‫ܣ‬ଷ ൈ ఌమ ቁ ൈ
்యభ ା்యమ
ଶ
൅ ቀ‫ܤ‬ଵ ൅ ‫ܤ‬ଶ ൈ
ଵିఌ
ఌ
οఌ
൅ ‫ܤ‬ଷ ൈ ఌమ ቁ ൈ
்యభ ି்యమ
ଶ
Equation 19
where Ts is LST; T31 and T32 are MODIS band 31 and 32 brightness temperature; ε31 and ε32 are
MODIS band 31 and 32 surface emissivity; C, A1, A2, A3, B1, B2, and B3 are regression coefficients.
MODIS surface emissivity in bands 31 and 32 are available in MOD11_L2 and MYD11_L2
products. They are assigned based on land cover types. Constant emissivity values are used in the
view angle range from 0 to 45°. A simple linear scheme is used to scale emissivity when sensor
view zenith angle is larger than 45°. It has a 1 km spatial resolution at nadir.
Daily MODIS Terra and Aqua land surface temperature and emissivity 5-min level-2 swath 1-km
dataset (MOD11_L2 and MYD11_L2, respectively) products are dependent on several parameters
related to the satellites’ platform and sensor and are generated using the product generation
executive (PGE16) code. The MOD11_L2 and MYD11_L2 are in swath format and collected
sequentially on a single overpass. The swath is composed of several products, including
geolocation, sensor radiance, atmospheric temperature and water profiles, cloud mask, quarterly
land cover, and snow cover. Several MODIS land surface temperature products are produced at
daily, 8-day, or monthly intervals at a gridded resolution of 1 km and 6 km and on a 0.058 grid.
The MOD11A1 and MYD11A1 products used in this work are produced by mapping daily single
clear-sky observation MOD11_L2 and MYD11_L2 swath data onto 1-km tiled grids in sinusoidal
projection.
The MODIS Terra and Aqua satellites are in sun-synchronous near-polar orbits, with Aqua in an
ascending orbit and Terra in a descending orbit. The orbital structures dictate equatorial crossings
at 1030 for Terra and 1330 for Aqua (local solar time). Because of the near-polar orbit, there is
progressively more swath overlap at locations greater than 308 latitude, thus producing multiple
daily observations in these regions (Williamson et al., 2013).
38
The MODIS LST datasets used in this study are the MOD11A1 and MYD11A1 h11 tile data
acquired daily under clear-sky conditions, using reprocessing Collection 5. Both datasets contain
single observations in each grid cell rather than averaged observations. MODIS data were
downloaded from the Land Processes Distributed Active Archive Center (LPDAAC;
https://lpdaac.usgs.gov/). The basic 1-km gridded MODIS land surface temperature is produced
with a split-window technique that uses MODIS bands 31 and 32 (10.78–11.28 mm and 11.77–
12.27 mm, respectively) (Wan et al., 2002). This technique uses a global land surface
classification-based emissivity lookup table to estimate emissivity values in these two bands
(Snyder et al. 1998). A split-window technique is used to produce the 1-km LST product, whereas
the 5-km LST product uses the day/night algorithm. The split-window class of techniques uses the
difference in water vapor absorption that exists between band 31 and band 32 to determine surface
temperature. The MOD11A1 and MYD11A1 quality control flags were used for cloud screening,
as done by Nishida et al. (2003) and Ackerman et al. (1998). The quality flag information relating
to Collection 5 of the MODIS land surface temperature products can be found in the product users’
guide
(http://www.icess.ucsb.edu/modis/LstUsrGuide/MODIS_LST_products_Users_guide_C5.pdf).
The MODIS quality flag used in this study is the LST and emissivity quality control layer. The
first bit indicates whether the produced LST is of good quality and does not require further
inspection of the quality flags or if the LST was produced but the quality is unreliable or
unquantifiable and further quality flag inspection is required. Inspection of all the MODIS quality
flags produced for the unreliable or unquantifiable quality first bit provides differentiation of the
average temperature quality flags as ≤3, ≤2, and ≤1 K, which is the nominal (or minimum) level;
the > 3 K-average temperature quality flag was not assigned to any of the data considered in this
study. Grid cells with the MODIS quality flags raised related to emissivity and subpixel cirrus
cloud presence were eliminated from this study; these affected less than 3% of the total dataset.
MOD11A1 and MYD11A1 LST and their coincident local solar view time for the same years of
in-situ data were reprojected from sinusoidal projection to 1-km gridded GeoTiff Albers equal area
projection, North American Datum 83 (NAD83), using nearest neighbour resampling. This
processing step was batch run using the MODIS Reprojection Tool (MRT) (Dwyer and Schmidt
2006) available from the LPDAAC. These LST product layers were converted to local solar time
39
and
temperature
using
the
conversion
factors
provided
at
https://lpdaac.usgs.gov/products/modis_products_table/. The view times in the MOD11A1 and
MYD11A1 products are in local solar time, which is defined as the MODIS observation time in
UTC plus longitude in degrees at the 1-km grid cell divided by 15. MODIS view times were
converted from local solar time to local time to enable comparison with CREST-SAFE
observations.
3.3.3 ASMR2 onboard GCOM-W1 satellite
The Advanced Microwave Scanning Radiometer 2 (AMSR2) is a twelve-channel, six-frequency,
passive-microwave radiometer system. It measures horizontally and vertically polarized brightness
temperatures at 6.9 GHz, 10.7 GHz, 18.7 GHz, 23.8 GHz, 36.5 GHz, and 89.0 GHz. Spatial
resolution of the individual measurements varies from 5.4 km at 89 GHz to 56 km at 6.9 GHz.
AMSR2 overpass times are near 1:30 a.m. (ascending) and 1:30 p.m. (descending) local time at
the Equator.
3.3.4
ATMS onboard S-NPP and MiRS-retrieved LST
The Advanced Technology Microwave Sounder (ATMS) is a 22-channel passive microwave
radiometer with a swath width of 1,429 miles. It was launched by NASA on October 28th, 2011 on
the S-NPP satellite for NOAA. The ATMS sensor is an “integrate-while-scan” total-powerradiometer, with 96 FOVs per scan sweep covering the frequency range of 23.8 GHz to 190 GHz.
MiRS (Microwave Integrated Retrieval System) is a One-Dimensional Variational inversion
scheme (1DVAR) (Boukabara et al. 2011, 2013), currently operational at NOAA for SuomiNPP/ATMS,
POES
N18/N19,
Metop-A,
Metop-B,
DMSP-F17/F18,
and
Megha-
Tropiques/SAPHIR, that employs the Community Radiative Transfer Model (CRTM) as the
forward and adjoint operators. It simultaneously solves for surface (temperature, emissivity), and
atmospheric parameters (temperature, water vapor, non-precipitating cloud and hydrometeor
profiles). The 1DVAR algorithm uses an iterative approach in which a solution is sought that best
fits the observed satellite radiances, subject to other constraints.
The 1DVAR algorithm uses an iterative approach in which a solution is sought which “best fits”
the observed satellite radiances, subject to other constraints. To reach the iterative solution, the
algorithm seeks to minimize the cost function:
40
ଵ
ଵ
ଶ
ଶ
‫ܬ‬ሺܺሻ ൌ ቂ ൈ ሺܺ െ ܺ଴ ሻ் ൈ ‫ି ܤ‬ଵ ൈ ሺܺ െ ܺ଴ ሻቃ ൅ ቂ ൈ ሺܻ ௠ െ ܻሺܺሻሻ் ൈ ‫ି ܧ‬ଵ ൈ ሺܻ ௠ െ ܻሺܺሻሻቃEquation
20
where X in the 1st term on the right is the retrieved state vector, and the term itself represents the
penalty for departing from the background X0, weighted by the error covariance matrix B. The 2nd
term represents the penalty for the simulated radiances Y departing from the observed radiances
Ym , weighted by instrument and modeling errors E. This leads to the iterative solution:
݉
οܺ௡ାଵ ൌ ሼ‫ܭܤ‬௡் ሺ‫ܭ‬௡ ‫ܭܤ‬௡் ൅ ‫ܧ‬ሻିଵ ሽൣ൫ܻ െ ܻሺܺ݊ ሻ൯ ൅ ‫ ݊ܭ‬οܺ݊ ൧
Equation 21
where ∆X is the updated state vector at iteration n+1, and K is the matrix of Jacobians which
contain the sensitivity of the radiances to changes in X (parameters to retrieve). This is then
followed by the post-processing step which uses as inputs the elements of the state vector X.
MiRS retrieval parameters include: temperature and water vapor profiles, rain rate, land surface
emissivity, SWE, and snow grain size, sea ice concentration and sea ice age, and 3-dimensional
depiction of severe weather and tropical cyclone structure.
More details about each satellite instrument and its respective products will be discussed in
following chapters.
41
4
Methodology
This chapter describes in detail the methodology implemented to complete this study.
4.1
Compare and cross validate satellite land surface temperature products
This section will compare and validate satellite land surface temperature (LST) products with insitu (CREST-SAFE) near-surface air temperature (Vaisala Temperature/RH probe) and snow
surface temperature (Apogee IR radiometer) readings. Figure 14 illustrates - in detail - the
secondary and primary steps taken to perform this validation. These steps include: statistical
analyses for both datasets (satellite retrievals and in-situ observations) to remove null values and
outliers, and the collocation and temporal matching between datasets. Additional steps were taken
to only use clear-sky satellite LST retrievals in the validation.
Figure 14. Flow chart of comparison and cross validation of satellite LST products.
42
4.2
Study temporal evolution of snow wetness and develop SWP
The second objective is to study the temporal evolution of snow wetness. Snow wetness plays a
significant role in wet-snow avalanche prediction, meltwater release, and water availability
estimations and assessments within a river basin. However, it remains a difficult task and a
demanding issue to measure the snowpack’s liquid water content (LWC) and its temporal
evolution with conventional in-situ techniques. We propose an approach based on the use of timedomain reflectometry (TDR) and CS650 soil water content reflectometers to measure the
snowpack’s LWC and temperature profiles. For this purpose, we created an easily-applicable, lowcost, automated, and continuous LWC profiling instrument using reflectometers at the Cooperative
Remote Sensing Science and Technology Center-Snow Analysis and Field Experiment (CRESTSAFE) in Caribou, ME, USA, and tested it immediately after installation. Lastly, the Snow
Wetness Model (SWM), developed by Muñoz et al. (2014) based on Solberg et al. (2004) findings,
will be integrated into the regression tree algorithm. Microwave retrievals typically exhibit low
accuracy and larger errors at the end of the winter season (due to wet snow).
Figure 15. Snow wetness analysis framework.
43
4.3
Develop a regression tree algorithm that ingests snow physical and radiative properties
to estimate snow depth and SWE
The third objective of this study is to develop a regression tree algorithm that ingests snow physical
(snow surface and pack temperatures, grain size, wetness) and radiative (MW TBs in bands 10,
19, 37 GHz, and 89 GHz) properties to estimate snow depth and SWE. Figure 16 illustrates the
procedure that will be undertaken to perform this task. The regression tree algorithm will ingest 4
years (2012 – 2015) of in-situ and simulated data at CREST-SAFE. The in-situ data that will be
ingested by the snow depth regression tree algorithm will be hourly MW TBs at 37GH and 89
GHz, and snow surface and snowpack temperatures. Since the microwave radiometers at 10GHz
and 19GHz were installed at the station in 2014 and 2015, respectively, the HUT model will be
used to simulate the MW TBs at those two frequencies for the 4 years. This can be done because
Muñoz et al. (2014) demonstrated that the HUT model provides acceptable MW retrievals (when
using in-situ CREST-SAFE snow physical and meteorological observations) with in-situ MW
readings at CREST-SAFE.
Figure 16. Snow depth regression tree algorithm development and validation framework.
44
The SWM will be used to produce snow wetness values using in-situ SPT and simulated GS via
SNTHERM. Corona et al. (2015) validated simulated snowpack properties using SNTHERM, by
forcing the snow evolution model with meteorological data at CREST-SAFE, with actual
observations of in-situ CREST-SAFE snow physical properties and demonstrated that the outputs
of the SNTHERM model show good agreement with observed data. Lastly, while the snow depth
regression tree algorithm will be trained using the 4 years of data, the model will be validated using
in-situ and simulated data at CREST-SAFE from winter 2016.
Figure 17. Flow chart of snow depth Regression Tree model based on snow physical (snowpack
temperature, wetness, grain size) and radiative (IR/MW) properties.
45
4.4
Improve on global snow cover mapping by developing the prototype of a product
capable of estimating snow depth and SWE using MW RS
The last objective of this study is to improve on global snow cover mapping by developing the
prototype of a product capable of estimating snow depth and SWE using MW RS and the snow
depth regression tree algorithm proposed in Section 4.3. Figure 18 illustrates the procedure that
will be undertaken to perform this task. The MW TB products from JAXA’s GCOM-W1 AMSR2
and the snow depth regression tree algorithm will be used to produce global snow depth and SWE
maps. Snow surface and pack temperatures and grain size will be retrieved using semi-empirical
equations developed at CREST-SAFE and the MW TBs from AMSR2. These equations will be
discussed in following chapters.
Figure 18. Snow depth and SWE satellite product development framework.
46
5
Validation of satellite LST products
This chapter focuses on the validation of three (VIIRS1, MODIS2, and MiRS3 LST) different
operational satellite LST products. This chapter answers the questions: are current LST products
accurate when compared to in-situ observations? Why is snow surface temperature important for
snow depth mapping?
Land surface temperature is an important parameter for hydrological, meteorological,
climatological, and environmental studies because it integrates the products of all surface–
atmosphere interactions and energy fluxes (Li et al. 2014). Knowledge of the LST and its
fluctuations provide information on the temporal and spatial variations of the surface equilibrium
state (Li et al. 2013). Generally, in-situ LST is implicitly observed at ground stations through IR
emission. However, due to the limitation that ground stations (i.e. lack of stations in some regions
of the World, point-based observations, physical inaccessibility to sites, and digital inaccessibility
to the data) present to provide global LST readings, satellite remote sensing (RS) has been the
adopted method for LST retrievals over large areas, with the aid of in-situ stations (Xia et al. 2014;
Robeson 1995; Jin and Dickinson 2010).
It is necessary to assess the accuracy and precision of the retrievals to provide potential LST users
with reliable information on the quality of the data. Hence, satellite LST validation is required to
identify possible deficiencies and subsequently introduce improvements in the algorithms. Two
methods are commonly applied to validate the LST products generated from RS data: the
temperature-based method (T-based) and the radiance-based method (R-based). The T-based
method involves direct comparison with ground measurements performed at the thermally
homogenous sites concurrent with the satellite overpass. The R-based method does not require
ground measured LST values but does require atmospheric temperature and water vapor profiles,
and the surface emissivity over the validation site at the time of satellite overpass (Li et al. 2014).
1
Pérez Díaz, C.L.; Lakhankar, T.; Romanov, P.; Khanbilvardi, R.; Y. Yu (2015) Evaluation of VIIRS Land Surface
Temperature Using CREST-SAFE Air, Snow Surface, and Soil Temperature Data. Geosciences, 2015, 5, 334-360.
2
Pérez-Díaz C.L., Lakhankar T., Romanov R., Muñoz J., Khanbilvardi J. & Yunyue Yu (2017) Evaluation of MODIS
land surface temperature with in-situ snow surface temperature from CREST-SAFE, International Journal of Remote
Sensing, Vol. 38 , Iss. 16,2017.
3
Pérez-Díaz, C., C. Grassotti, Q. Liu, S. Liu, J. Chen, T. Lakhankar, and R. Khanbilvardi. MiRS-retrieved LST
validation with in-situ SURFRAD measurements. 2017. Earth and Space Science. Under review.
47
This study focuses on using the T-based method for satellite LST validation. Therefore, it is
compulsory that the LST observed by the ground instrument be truly representative of the average
LST over the instantaneous field of view (FOV) of the satellite sensor - in other words, the site
must be thermally homogeneous from the point scale to several kilometers. However, most of the
Earth's surface is heterogeneous at spatial scales. For this reason, high-quality ground validation
data are usually limited to few surface types such as: lakes, silt playas, grasslands and agricultural
fields (Wan et al. 2002, 2004; Wang et al. 2004; Coll et al. 2005). With the exception of Lake
Tahoe with its automated validation site (Hook et al. 2007), where lake surface temperatures have
been continuously measured since 1999. Nevertheless, few stations provide automated LST
readings around the World. Recently, automated LST validation sites have been established in
Europe and Africa (Trigo et al. 2008). Furthermore, the National Oceanic and Atmospheric
Administration’s (NOAA) Office of Global Programs also established seven Surface Radiation
Budget Network (SURFRAD) stations in 1993 in an ambitious effort to provide ground-based LST
(along with other meteorological variables) measurements in differing climatic regions around the
United States of America to validate satellite-based estimates.
An important aspect of the RS LST retrievals is to validate and improve global hydrological
modeling, and a key component of the Earth’s hydrologic cycle is snow - and its surface
temperature (Brown and Robinson 2011; Frei et al. 2012). Hence, accurate LST readings for snowcovered landscapes represent a critical role in hydrological modeling because the snowpack can
be considered a seasonal reservoir. This investigation was driven by the few existing studies using
the T-based method to validate the relationship between in-situ LST, NOAA’s VIIRS, and
NASA‘s MODIS LST products in regions that remain covered in snow for the majority of the year
(Hall et al. 2008; Westermann, Langer, and Boike 2011). Numerous studies have validated RS
LST accuracy over snow free barren or vegetated surfaces (Li et al. 2014; Vancutsem et al. 2010;
Coll et al. 2005; Wan et al. 2002, 2004; Wang et al. 2004; Zhu, Lű, and Jia 2013; Shuman et al.
2013).
In the next sub-sections, results for the T-based validation of the VIIRS LST EDRs and MODIS
MOD11A1 (Terra) and MYD11A1 (Aqua) LST products will be discussed. The T-based method
was applied using automated and continuous LST and near-surface air temperature (T-air) in-situ
data from CREST-SAFE during the years of 2013 (January-April) and 2014 (February-April). The
48
results will aid the existing VIIRS and MODIS LST literature by providing another T-based
validation for a snow-covered site. Furthermore, a T-based validation of the MiRS LST product
was performed against SURFRAD LST from 6 different stations across the United States from
May 2016 to May 2017.
In addition, the results of supplementary analyses using other meteorological variables (i.e. wind
speed, percentage of cloud cover) recorded at the site to study their effects on in-situ snow surface
temperature (T-skin) and T-air are included.
5.1
VIIRS LST study
In this study, the Visible Infrared Imager Radiometer Suite (VIIRS) Land Surface Temperature
(LST) Environmental Data Record (EDR) was evaluated against snow surface (T-skin) and nearsurface air temperature (T-air) ground observations recorded at the Cooperative Remote Sensing
Science and Technology Center—Snow Analysis and Field Experiment (CREST-SAFE), located
in Caribou, ME, USA during the winters of 2013 and 2014. The satellite LST corroboration of
snow-covered areas is imperative because high-latitude regions are often physically inaccessible
and there is a need to complement the data from the existing meteorological station networks. Tskin is not a standard meteorological parameter commonly observed at synoptic stations. Common
practice is to measure surface infrared emission from the land surface at research stations across
the world that allow for estimating ground-observed LST. Accurate T-skin observations are critical
for estimating latent and sensible heat fluxes over snow-covered areas because the incoming and
outgoing radiation fluxes from the snow mass and T-air make the snow surface temperature
different from the average snowpack temperature. Precise characterization of the LST using
satellite observations is an important issue because several climate and hydrological models use
T-skin as input. Results indicate that T-air correlates better than T-skin with VIIRS LST data and
that the accuracy of nighttime LST retrievals is considerably better than that of daytime. Based on
these results, empirical relationships to estimate T-air and T-skin for clear-sky conditions from
remotely-sensed (RS) LST were derived. Additionally, an empirical formula to correct cloudcontaminated RS LST was developed.
49
5.1.1 VIIRS LST pre-processing
The VIIRS LST daytime and nighttime pixels with the closest proximity to CREST-SAFE’s
location at Caribou, Maine (46°52'59"N, 68°01'07"W) were extracted from these files.
Additionally, the satellite overpass time, sensor view zenith angle, and VIIRS Quality Flag (QF)
were also extracted. According to the QF information, only high/good quality data of the VIIRS
LST product were used for evaluation. Then, the VIIRS LSTs were matched with the groundmeasured temperatures according to the satellite observation time. The satellite observation time
was derived by linearly interpolating the start and end times of the VIIRS product swath. Suomi
NPP ascends (descends) over Caribou around 1:00–3:00 a.m. (1:00–3:00 p.m.) LT. The LST data
are recorded twice (daytime and nighttime views) daily and downloadable as HDF5 files. VIIRS
LST data were compared with the ground-observed (CREST-SAFE) near-surface air temperature
and snow surface temperature. The specific (five in 2013 and four in 2014) cases when the RS
minus in-situ absolute differences were larger than 10 °C were treated as outliers and excluded
from the analysis. These nine cases happened in the month of April for both years, when T-air
rises considerably and the depth of the snowpack is commonly between 2–5 cm; leading to possible
errors in T-skin readings because the snow surface is quite close to the soil surface and further
from the 2 m height at which T-air is observed. These nine cases happened in the month of April
for both years, when T-air rose considerably (up to 20 ºC), and the depth of the snowpack was
commonly between 2–5 cm. However, the CREST-SAFE time series for both years show that
April temperatures never rose to 20 ºC on a regular basis. This lead to considering the nine
observations as possible erroneous measurements by the instrument. Furthermore, chances are that
the target circle observed by the instrument measuring T-skin was a combination of snowless soil
and snow-covered soil due to snow melting after mid-April. Uncharacteristically high T-air will
make the RS minus in-situ absolute difference unreasonably high, whilst a combination of snowcovered and snowless soil will yield erroneous T-skin measurements that can impact the RS minus
in-situ absolute difference. Nonetheless, it should also be mentioned that these large absolute
differences can be attributed to emissivity biases due to the impacts on VIIRS LST by the changes
in the radiative transfer properties of the surface when the snow is melting, since in April the
snowpack can have a wet snow layer at the surface during daytime that changes the emissivity of
the snow surface, thus, affecting the thermal IR TB which is used to retrieve VIIRS LST, although
the VIIRS M15 and M16 bands centered at 10.8 μm and 12.0 μm should minimize the effects of
50
water bands (Jensen, 2007; Schultz, 2000). Additionally, all valid points were also examined
manually to exclude cloud contaminated pixels with unreasonably low LST values. The lengths of
the time series used for the VIIRS LST and CREST-SAFE temperature matches were from 1
January to 30 April for the year 2013 and from 22 February to 30 April for 2014.
5.1.2 VIIRS LST validation
Pérez Díaz, C.L.; Lakhankar, T.; Romanov, P.; Khanbilvardi, R.; Yu, Y. Evaluation of VIIRS Land
Surface Temperature Using CREST-SAFE Air, Snow Surface, and Soil Temperature
Data. Geosciences 2015, 5, 334-360.
CREST-SAFE in-situ T-skin and T-air (abscissas) vs. VIIRS LST (ordinates) daytime and
nighttime scatterplots (Figure 19) were created to obtain the R and R2 linear correlation coefficient
values (Table 3) as well as the Mean Absolute Difference (MAD) and biases for both years.
Table 3. R2 correlation coefficient values between VIIRS LST, T-skin, and T-air at CREST-SAFE for
winters 2013 and 2014 daytime and nighttime views.
2013 Daytime
T.
2013 Nighttime
MAD
Bias
(°C)
(°C)
R
R2
Air
0.71
0.51
6.6
Skin
0.82
0.67
5.0
2014 Daytime
MAD
Bias
(°C)
(°C)
R
R2
−5.76
0.87
0.76
6.6
−4.35
0.81
0.66
4.0
2014 Nighttime
MAD
Bias
(°C)
(°C)
R
R2
−6.66
0.80
0.64
6.4
−2.70
0.62
0.38
4.6
R
R2
−6.11
0.95
−2.68
0.93
MAD
Bias
(°C)
(°C)
0.90
7.1
−7.07
0.86
2.6
−1.31
T.: Temperature
R and R2 linear correlation coefficient values between VIIRS LST and in-situ T-air daytime data
vary from 0.71–0.80 and 0.51–0.64, respectively. R and R2 correlation values for daytime VIIRS
LST and in-situ T-skin range from 0.62–0.82 and 0.38–0.67. These correlation values drop
drastically for T-soil and vary from 0.26–0.57 and 0.07–0.32. Nighttime R and R2 linear correlation
coefficient values are generally higher for all temperatures (T-skin and T-air) with few exceptions.
This is mostly because the atmospheric water vapor is less and LST behaves almost
homogeneously at night. Therefore, the ground temperature measurements during nighttime are
more representative of the LST at the satellite pixel scale than those during daytime (Li et al.,
2014). For T-air, the correlation values fluctuate between 0.87–0.95 and 0.76–0.90, respectively.
The correlations values range from 0.81–0.93 and 0.66–0.86 for T-skin. Results indicate that a
higher correlation exists between T-air and the RS LST. VIIRS LST readings have a lower
51
correlation with the T-skin values observed at CREST-SAFE. However, it should be noted that
these values improved from one winter (2013) to the next (2014) for T-air and T-skin. This might
be indicative of the continuous and ongoing improvements done to the VIIRS LST product. T-soil
does not change much over time (remains around 0ºC), making it almost constant and naturally
very different from RS LST, T-air, and T-skin. MAD daytime T-air values vary barely, ranging
from 6.4–6.6 °C. Daytime MAD values for T-skin range from 4.6–5.0 °C. Nighttime MAD values
for T-air and T-skin vary from 6.6–7.1 °C and 2.6–4.0 °C, respectively. VIIRS daytime biases vary
from −6.11 °C to −5.76 °C and −4.35 °C to −2.68 °C for T-air and T-skin, respectively. Nighttime
biases vary from −7.07 °C to −6.66 °C and −2.70 °C to −1.31 °C for T-air and T-skin, respectively.
We can say that the evaluation results for nighttime are better than those during daytime, especially
in terms of R and R2 values and, to some extent, MAD, and biases. The cold biases for all
temperatures and satellite overpasses indicate that the VIIRS LST algorithm underestimates the
LST for snow-covered surfaces.
Figure 19. CREST-SAFE in-situ T-skin and T-air correlation with satellite VIIRS LST daytime and
nighttime data for winters 2013 and 2014.
52
While simpler to explain why the RS vs. in-situ correlations are higher during nighttime, the reason
for discrepancies between T-air and T-skin are less trivial. Foremost, cloud cover and wind speed
play an important role in the behavioral patterns of T-air and T-skin. Generally, if there is no (or
weak) advection and no clouds, T-diff is mostly driven by the radiative cooling of the land surface
because the radiative heating by the sun is quite small compared to it. On the other hand, the
presence of clouds provides a substantial downward thermal flux that heats the surface and, to a
lesser extent, the air; therefore reducing T-diff (Walsh, Jasperson, and Ross, 1985; Holtslag and
De Bruin, 1988). This accounts partially for in-situ T-skin having lower correlation values with
VIIRS LST, because changes in T-skin happen at a slower pace (unlike bare soil) than they do for
T-air.
Another remark is that the low correlation values between VIIRS LST and in-situ T-skin can be
attributed to the fact that VIIRS characterizes the brightness temperature of the vegetation (whose
temperature is closer to T-air) that is abundant in the vicinity of the field experiment, as seen by a
750 m block around the site—not to be confused with the satellite swath—in Figure 20
(approximately 45% grassland, 35% residential homes, 15% paved roads, 5% forest cover).
Satellite radiometry is applied to large areas (750 m in this study) which often consist of various
land and vegetation types. A low spatial resolution will undoubtedly include some vegetation
(forest cover) in the region and divert the RS LST from its true point value. Moreover,
meteorological conditions for snow accumulation and melt on forest floors differ from those in
clearings because of the influence of the canopy (Platt and Prata, 1993). Additionally, snow
becomes patchy while melting, giving a heterogeneous surface with large contrasts in
characteristics such as albedo (i.e., reflectance, TB) (Gelfan, Pomeroy, and Kuchment, 2004).
Hence, the combination of above freezing temperatures during daytime with below freezing
temperatures at night cause multiple freezing and melting events within the snowpack during the
melting period (late winter). Daytime solar radiation causes snowmelt in the uppermost layer that
produces higher water content in the superior layers of the snowpack. These events cause a large
diurnal variation in the RS TB that is difficult to reproduce using satellite retrievals (Pomeroy,
Essery, and Toth, 2004). When comparing satellite RS and in-situ point-wise data, the primary
issue is whether the surface properties at the site are representative for land surface properties
within the instrument Field Of View (FOV). The temperature of vegetation canopy is usually
closer to the T-air than to the land surface temperature. Therefore, for forested areas covered with
53
snow in winter, the VIIRS LST is better correlated with T-air (Rosenfeld and Grody, 2000; Yang
et al., 2006).
Furthermore, when discussing the radiative properties of the snow surface, while not uniform, the
IR emissivity of snow is understood enough to compensate for its effects in the remote sensing of
T-skin. At near-normal viewing angles, the RS TB can be as much as 1.5 ºC lower than the
thermodynamic temperature at wavelengths around 13 μm (Dozier and Painter, 2004). At the
shorter IR wavelength window (3.5–4 μm), uncertainty in emissivity does not translate into
uncertainty in temperature because of the nonlinear nature of Planck’s function, but at longer
wavelengths it does. Fortunately, the highest and unreliable uncertainties in emissivity are beyond
the 10.5–12.5 μm atmospheric window that the VIIRS LST SW algorithm uses for retrievals.
However, studies indicate that snow grains are independent scatterers, and that emissivity decreases
with grain size and the presence of liquid water in the snow (Dozier and Warren, 1982; Salisbury,
D’Aria, and Wald, 1994). Nonetheless, T-skin measurements have been used in few climate or
hydrologic studies. Results have shown that the differences between RS LST and T-skin have not been
due to emissivity as much as: orographic effects, topography, topographic shadowing, and snow
deposition (Stroeve and Steffen, 1998; King et al., 2004; Fily, Dedieu, and Durand, 1999; Marks,
Winstral, and Seyfried, 2002).
54
Figure 20. CREST-SAFE land cover 750-m block
For this particular reason, two additional pixels (one bare land, one forest cover/vegetation) were
considered in this study to check whether the T-air and T-skin data observed at CREST-SAFE is
representative of other areas that surround the site in Caribou with different land cover. Figure 21
illustrates a 750-m block of bare land 1 km away from CREST-SAFE, Figure 22 displays the
CREST-SAFE in-situ T-skin and T-air vs. VIIRS LST daytime and nighttime for the bare land
pixel scatterplots, and Table 4 contains the R and R2 linear correlation coefficient values, MADs,
and biases for the scatterplots for both years.
55
Table 4. R and R2 correlation coefficient values, MAD, and biases between VIIRS LST daytime and
nighttime views for the bare land pixel, T-skin, and T-air at CREST-SAFE for winters 2013 and 2014.
2013 Daytime
T.
2013 Nighttime
MAD
Bias
(°C)
(°C)
0.38
7.31
0.50
5.73
R
R2
Air
0.62
Skin
0.70
2014 Daytime
MAD
Bias
(°C)
(°C)
0.70
7.16
0.60
4.50
R
R2
−6.45
0.84
−4.98
0.77
2014 Nighttime
MAD
Bias
(°C)
(°C)
0.74
6.00
0.75
4.37
R
R2
−7.16
0.86
−3.15
0.87
R
R2
−5.70
0.96
−2.16
0.95
MAD
Bias
(°C)
(°C)
0.91
6.75
−6.75
0.90
2.17
−0.58
T.: Temperature.
Figure 21. 750 m block of bare land 1km away from CREST-SAFE.
R and R2 linear correlation coefficient values between VIIRS LST for the bare land pixel and insitu T-air daytime data vary from 0.62–0.86 and 0.38–0.74, respectively. R and R2 correlation
values for daytime VIIRS LST and in-situ T-skin range from 0.70–0.87 and 0.50–0.75.R and R2
nighttime correlation values for T-air fluctuate between 0.84–0.96 and 0.70–0.91, respectively.
These correlations values range from 0.77–0.95 and 0.60–0.90 for T-skin. MAD daytime T-air values
vary from 6.0–7.31 °C. Daytime MAD values for T-skin range from 4.37–5.73 °C. Nighttime MAD
values for T-air and T-skin vary from 6.75–7.16 °C and 2.17–4.50 °C, respectively. VIIRS daytime
biases vary from −6.45 °C to −5.70 °C and −4.98 °C to −2.16 °C for T-air and T-skin, respectively.
Nighttime biases vary from −7.16 °C to −6.75 °C and −3.15 °C to −0.58 °C for T-air and T-skin,
56
respectively. When comparing these values with those obtained by matching CREST-SAFE insitu vs. VIIRS LST from the CREST-SAFE pixel, it can be seen that the two pixels display very
similar results, regardless of the differences in land cover.
Figure 22. CREST-SAFE in-situ T-skin and T-air vs. satellite VIIRS LST daytime and nighttime data for
the bare land pixel scatterplots for winters 2013 and 2014.
R and R2 linear correlation coefficient values between VIIRS LST for the bare land pixel and insitu T-air daytime data vary from 0.62–0.86 and 0.38–0.74, respectively. R and R2 correlation
values for daytime VIIRS LST and in-situ T-skin range from 0.70–0.87 and 0.50–0.75.R and R2
nighttime correlation values for T-air fluctuate between 0.84–0.96 and 0.70–0.91, respectively.
These correlations values range from 0.77–0.95 and 0.60–0.90 for T-skin. MAD daytime T-air values
vary from 6.0–7.31 °C. Daytime MAD values for T-skin range from 4.37–5.73 °C. Nighttime MAD
values for T-air and T-skin vary from 6.75–7.16 °C and 2.17–4.50 °C, respectively. VIIRS daytime
biases vary from −6.45 °C to −5.70 °C and −4.98 °C to −2.16 °C for T-air and T-skin, respectively.
Nighttime biases vary from −7.16 °C to −6.75 °C and −3.15 °C to −0.58 °C for T-air and T-skin,
respectively. When comparing these values with those obtained by matching CREST-SAFE in-
57
situ vs. VIIRS LST from the CREST-SAFE pixel, it can be seen that the two pixels display very
similar results, regardless of the differences in land cover.
In Figure 23, a 750 m block of land covered by forest and vegetation 2 km away from CRESTSAFE is illustrated. There are VIIRS LST satellite pixels in Caribou that have 100% forest cover
but these are more than 10km away from the site, which would render the CREST-SAFE in-situ
temperatures useless for a comparison. Figure 24 displays the CREST-SAFE in-situ T-skin and Tair vs. VIIRS LST daytime and nighttime for forest/vegetation covered pixel scatterplots, and
Table 5 shows the R and R2 linear correlation coefficient values, MADs, and biases for the
scatterplots for both years.
Figure 23. 750 m block of land covered by forest and vegetation 2 km away from CREST-SAFE.
R and R2 linear correlation coefficient values between VIIRS LST for forest/vegetation covered
pixel and in-situ T-air daytime data vary from 0.67–0.89 and 0.45–0.80, respectively. R and R2
correlation values for daytime VIIRS LST and in-situ T-skin range from 0.74–0.91 and 0.55–0.82.
R and R2 nighttime correlation values for T-air fluctuate between 0.86–0.96 and 0.74–0.91,
respectively. These correlations values range from 0.80–0.93 and 0.64–0.87 for T-skin. MAD
daytime T-air values vary from 5.00–7.22 °C. Daytime MAD values for T-skin range from 3.36–5.30
58
°C. Nighttime MAD values for T-air and T-skin vary from 6.46–6.99 °C and 2.34–4.50 °C,
respectively. VIIRS daytime biases vary from −6.53 °C to −4.62°C and −4.74 °C to −0.91 °C for Tair and T-skin, respectively. Nighttime biases vary from −6.99 °C to −6.46 °C and −3.13 °C to −0.57
°C for T-air and T-skin, respectively.
Table 5. R and R2 correlation coefficient values, MAD, and biases between VIIRS LST daytime and
nighttime views for the forest/vegetation covered pixel and T-skin and T-air at CREST-SAFE for winters
2013 and 2014.
2013 Daytime
T.
2013 Nighttime
MAD
Bias
(°C)
(°C)
R
R2
Air
0.67
0.45
7.22
Skin
0.74
0.55
5.30
2014 Daytime
MAD
Bias
(°C)
(°C)
R
R2
−6.53
0.86
0.74
6.99
−4.74
0.80
0.64
4.50
2014 Nighttime
MAD
Bias
(°C)
(°C)
R
R2
−6.99
0.89
0.80
5.00
−3.13
0.91
0.82
3.36
MAD
Bias
(°C)
(°C)
0.91
6.46
−6.46
0.87
2.34
−0.57
R
R2
−4.62
0.96
−0.91
0.93
T.: Temperature.
Figure 24. CREST-SAFE in-situ T-skin and T-air vs. satellite VIIRS LST daytime and nighttime data for
the forest/vegetation covered pixel scatterplots for winters 2013 and 2014.
59
The similar linear correlation coefficients, MADs, and biases displayed by three pixels with
evident different land covers lead to the notion that the CREST-SAFE T-air and T-skin might be
representative of the county of Caribou, ME. However, when compared to the CREST-SAFE
pixel, the bare land pixel showed small improvement in VIIRS LST’s estimation of T-skin and Tair. There was also some improvement in VIIRS LST’s estimation of the in-situ observations when
comparing the forest/vegetation covered pixel with the CREST-SAFE pixel, although it was not
as effective as the RS LST estimations for the bare land pixel. The small improvement shown by
the bare land and forest/vegetation covered pixels was expected due to the surface homogeneity in
the bare land and forest/vegetation covered pixels, when compared to the CREST-SAFE pixel.
However, it is not significant enough to establish that VIIRS LST is affected by land cover in the
region under study. Instead, it can be established that the differences between RS LST and in-situ
observations are due to the unpredictability in both the physical and radiative properties of the
snow and its surface, as stated previously, sky cover, and wind speed. These findings lead to the
proposition of empirical formulas to derive T-skin and T-air from RS LST to improve the
understanding of VIIRS LSTs.
In order to derive these empirical formulas, CREST-SAFE in-situ T-skin observations were subdivided into two different groups. The recorded in-situ temperatures that happened during daytime
are to be considered wet snow observations due to possible snow melting at the top layer of the
snowpack with the incoming solar radiation, changing the dielectric properties of the snow, and
affecting its emissivity and the VIIRS radiative transfer signal. Inversely, T-skin measurements
logged during nighttime were regarded as dry snow due to snow refreezing in the evening creating
a more homogeneous snow surface. All the observations used to develop the formulas were under
clear-sky conditions. Figure 25 illustrates the validation data used to derive T-skin using RS LST
under wet snow conditions (daytime) based on the linear regression model (Equation 22) that was
created, and the 95% upper and lower Confidence Intervals (CIs) for said model. The Sum of
Square Errors (SSE) and degrees of freedom are 1455.3 °C2 and 87, respectively. All but two
observations are within the 95% confidence intervals. More importantly, the R2, Adjusted R2, and
Root Mean Square Error are 0.783, 0.781, and 4.09 °C, respectively. All metrics indicating that the
numerical predictions by the model are satisfactory.
60
Figure 25. T-skin derived empirical formula based on linear regression model between clear-sky VIIRS
LST daytime (wet snow) views with respective in-situ temperatures at CREST-SAFE.
61
.
Figure 26. T-skin derived empirical formula based on linear regression model between clear-sky VIIRS
LST nighttime (dry snow) views with respective in-situ temperatures at CREST-SAFE.
Figure 26 displays the validation data used to derive T-skin using RS LST under dry snow
conditions (nighttime) based on the linear regression model (Equation 23) that was created, and
the 95% upper and lower confidence intervals (CIs) for the model. The Sum of Square Errors
(SSE) and degrees of freedom are 674.62 °C2 and 126, respectively. All but four observations are
within the 95% confidence intervals. Furthermore, R2, Adjusted R2, and RMSE are 0.919, 0.918, and
2.31 °C, respectively. As expected, all metrics indicate that the numerical predictions by the model
are highly satisfactory. Additionally, when compared to the wet snow model, it is confirmed that
VIIRS makes better LST estimates during nighttime.
Tskin-dry = 0.873 × LST + 3.908 (Dry snow)
Equation 22
62
Tskin-wet = 0.928 × LST + 1.232 (Wet snow)
Equation 23
In light of the good accuracy provided by the linear regression models, the idea of producing an
additional formula to correct RS LST with sky cover was developed. The developmental details
are presented next.
The good accuracy for numerical predictions provided by the linear regression models led to the
idea of using the developed empirical formulas inversely by utilizing the in-situ T-skin from
CREST-SAFE to obtain what were named in-situ wet and dry snow LSTs, and compare them with
the actual VIIRS LSTs via a relation with cloudiness. These wet and dry snow LSTs would ideally
be the RS LST (daytime and nighttime, respectively) under clear-sky conditions, since the
empirical formulas were created using clear-sky observations only. Figure 27 illustrates the VIIRS
LST daytime and nighttime retrievals, the derived wet and dry snow LSTs, and the cloud cover in
the background. The wet and dry snow LSTs were created using T-skin observations that matched
temporally with all VIIRS LST (cloud-contaminated and clear-sky).
Figure 27. VIIRS LST daytime and nighttime views and inversely retrieved LSTs (wet and dry snow
conditions) using the empirical formulas derived from the linear regression models. Sky cover in the
background.
63
A multiple linear regression analysis with linear correlation coefficients was used to correlate
derived in-situ LSTs (output) with RS LST and cloudiness as predictor variables. It should
be mentioned that other correlation coefficient combinations were used, but few showed
improvements in the model and these were minimal. Figure 28 illustrates a three-dimensional
scatterplot with its representative multiple linear regression model (Equation 24) in meshgrid form. Degrees of Freedom (DFE), R2, Adjusted R2, and RMSE are 163, 0.547, 0.538,
and 7.128 °C, respectively. Metrics indicate that the linear regression model can estimate insitu LST with reasonable accuracy. However, it is clear that cloudiness variability affects the
predictions considerably. Table 6 shows the multiple linear regression results.
Equation 24
LSTIn-situ = 0.54 × (LSTSatellite) + 7.13 × (Cloudiness) − 9.40
Table 6. Multiple linear regression model results for in-situ LST estimation using RS LST and cloudiness
as predictor variables.
Multiple Linear Regression Analysis Results
--
Coefficient
SE
tStat
pValue
Intercept
RS LST
Cloudiness
−9.3982
0.5376
7.1266
1.2799
1.5978
0.0665
−7.3427
4.4601
8.0737
9.4521 × 10−12
1.5197 × 10−5
1.4251 × 10−13
The coefficient estimates for RS LST (0.5376) and cloudiness (7.1266) highlight again how RS
LST underestimates in-situ LST for the region under study. The coefficient estimate results
indicate that a 30% change in sky cover will result in a 2 °C change between in-situ LST and RS
LST. Low SE values are indicative of the regression’s capability of estimating both input variables
with reasonable accuracy. Lower p-values for cloudiness indicate that there is a 95% probability that
it has significant effect on estimating in-situ LST using RS LST. The RMSE value of 7.13 °C shows
that there is error in the model’s in-situ estimation due to cloud variability. Lastly, it should be noted
that these proposed equations might not apply elsewhere, but are a step in the right direction for the
improvement of VIIRS LST retrievals. If anything, these equations still provide user-friendly,
preliminary means to estimate T-skin using RS LST retrievals, as well as an empirical formula to
correct the RS LST for cloud contamination.
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Figure 28. Three-dimensional scatterplot of in-situ LST, VIIRS LST, and cloudiness with linear
regression model in mesh-grid form to estimate in-situ LST with RS LST and cloudiness as predictor
variables.
5.2
MODIS LST study
This section presents the procedure and results of a temperature-based validation approach for the
Moderate Resolution Imaging Spectroradiometer (MODIS) Land Surface Temperature (LST)
product provided by the National Aeronautics and Space Administration Terra and Aqua Earth
Observing System satellites using in-situ LST observations recorded at the Cooperative Remote
Sensing Science and Technology Center – Snow Analysis and Field Experiment (CREST-SAFE)
during the years of 2013 (January–April) and 2014 (February–April). A total of 314 day-and-night
clear-sky thermal images, acquired by the Terra and Aqua satellites, were processed and compared
to ground-truth data from CREST-SAFE with a frequency of one measurement every 3 min.
65
CREST-SAFE is a synoptic ground station, located in the cold county of Caribou in Maine, USA,
with a distinct advantage over most meteorological stations because it provides automated and
continuous LST observations via an Apogee Model SI-111 Infrared Radiometer. This section also
attempts to answer the question of whether a single pixel (1 km2) or several spatially averaged
pixels should be used for satellite LST validation by increasing the MODIS window size to 5 × 5,
9 × 9, and 25 × 25 windows.
Several trends in the MODIS LST data were observed, including the underestimation of daytime
values and night-time values. Results indicate that although all the data sets (Terra and Aqua,
diurnal and nocturnal) showed high correlation with ground measurements, day values yielded
slightly higher accuracy (about 1°C), both suggesting that MODIS LST retrievals are reliable for
similar land-cover classes and atmospheric conditions. Increasing the MODIS window size
showed an overestimation of in-situ LST and some improvement in the daytime Terra and nighttime Aqua biases, with the highest accuracy achieved with the 5 × 5 window. A comparison
between MODIS emissivity from bands 31, 32, and in-situ emissivity showed that emissivity errors
(relative error = −0.30%) were insignificant.
5.2.1 Previous MODIS LST validation efforts
The Moderate Resolution Imaging Spectroradiometer (MODIS) is a 36-channel (ranging in
wavelength from 0.40 to 14.40 μm) visible to Thermal Infrared Sensor on board the Terra (1999)
and Aqua (2002) satellites launched by the flagship of the National Aeronautics and Space
Administration’s (NASA) Earth Observing System programme. MODIS collects visible and IR
imagery and radiometric measurements of the land, atmosphere, cryosphere, and oceans. MODIS
daily LST products provide radiometric LST values over land and larger inland waters in swath
and grid format. However, it is necessary to assess the accuracy and precision of the retrievals to
provide potential LST users with reliable information on the quality of the data. Hence, MODIS
LST validation is required to identify possible deficiencies and subsequently introduce
improvements in the algorithms. Two methods are commonly applied to validate the LST products
generated from RS data: the temperature-based method (T based) and the radiance-based method
(R based). The T-based method involves direct comparison with ground measurements performed
at the thermally homogenous sites concurrent with the satellite overpass. The R-based method does
not require ground-measured LST values but does require atmospheric temperature and water
66
vapour profiles, and the surface emissivity over the validation site at the time of satellite overpass
(Li et al. 2014).
This study focuses on using the T-based method for MODIS LST validation. As such, it is
necessary that the LST observed by the ground instrument at the test site be truly representative of
the average LST over the instantaneous field of view (FOV) of the satellite sensor, meaning that
the site must be thermally homogeneous from the point scale to several kilometres. Since most of
the Earth’s surface is heterogeneous at these spatial scales, high-quality ground validation data are
limited to few surface types such as lakes, silt playas, grasslands, and agricultural fields (Wan et
al. 2002; 2004; Wang et al. 2004; Coll et al. 2005). An exception is the Lake Tahoe-automated
validation site (Hook et al. 2007), where lake surface temperatures are continuously measured
since 1999. Nevertheless, few stations provide automated LST readings around the World.
Recently, automated LST validation sites have been established in Europe and Africa (Trigo et al.
2008). Furthermore, the National Oceanic and Atmospheric Administration’s Office of Global
Programs also established seven Surface Radiation Budget Network (SURFRAD) stations in 1993
in an ambitious effort to provide ground-based LST (along with other meteorological variables)
measurements in differing climatic regions around the USA to validate satellite-based estimates.
An important aspect of the RS LST retrievals is to validate and improve global hydrological
modelling, and a key component of the Earth’s hydrologic cycle is snow – and its surface
temperature (T skin) (Brown and Robinson 2011; Frei et al. 2012). Hence, accurate LST readings
for snow-covered landscapes represent a critical role in hydrological modelling because the
snowpack can be considered a seasonal reservoir. This investigation was driven by the few existing
studies using the T-based method to validate the relationship between in-situ LST and NASA’s
MODIS LST products in regions which remain covered in snow for the majority of the year (Hall
et al. 2008; Westermann, Langer, and Boike 2011; Hall et al. 2015; Wenny, Xiong, and Madhavan
2012; Shuman et al. 2014). Hall et al. (2008) and Shuman et al. (2014) validated ice, snow surface,
and near-surface air temperatures with MODIS ice and snow LST in Greenland. While
Westermann, Langer, and Boike (2011) validated MODIS LST with summer surface temperatures
in the Norwegian archipelago of Svalbard. Hall et al. (2015) validated MODIS ice and snow
surface temperatures with the Bromine, Ozone, and Mercury Experiment (BROMEX) in Barrow,
Alaska, and Wenny, Xiong, and Madhavan (2012) validated MODIS ice and snow surface
67
temperatures using in-situ observations from the Automated Weather Stations in the French-Italian
Corcordia Research Station at Dome C, Antartica. However, none of these studies have been
conducted in a sub-Arctic location and, in general, the majority of the RS LST validation studies
evaluate its accuracy over snow free barren or vegetated surfaces (Li et al. 2014; Vancutsem et al.
2010; Coll et al. 2005; Wan et al. 2002; 2004; Wang et al. 2004; Zhu, Lű, and Jia 2013).
This study shows results for the T-based validation of the MODIS MOD11A1 (Terra) and
MYD11A1 (Aqua) LST products. The T-based method was applied using automated and
continuous in-situ LST data from a snow-covered suburban site in the sub-Arctic Caribou, Maine,
USA. The results will aid the existing MODIS LST literature by providing another T-based
validation for a snow-covered site. In addition, it will include the results of studying the effects of
different MODIS window sizes on in-situ LST estimations.
5.2.2 MODIS LST data
The daily MODIS Terra and Aqua LST and emissivity 5 min level 2 swath 1 km dataset
(MOD11_L2 and MYD11_L2, respectively) products are dependent on several parameters related
to the satellites’ platform and sensor and are generated using the product generation executive
(PGE16) code. The MOD11_L2 and MYD11_L2 are in swath format and collected sequentially
on a single overpass. The swath is composed of several products, including geolocation, sensor
radiance, atmospheric temperature and water profiles, cloud mask, quarterly land cover, and snow
cover. Several MODIS LST products are produced at daily, every 8 days, or monthly intervals at
a gridded resolution of 1 and 6 km and on a 0.05° grid. The MOD11A1 and MYD11A1 products
used in this study are produced by mapping daily single clear-sky observation MOD11_L2 and
MYD11_L2 swath data onto 1 km tiled grids in sinusoidal projection. The MODIS Terra and Aqua
satellites are in Sun synchronous near-polar orbits, with Aqua in an ascending orbit and Terra in a
descending orbit. The orbital structures dictate equatorial crossings at 10:30 for Terra and 13:30
for Aqua (local solar time). Because of the near-polar orbit, there is progressively more swath
overlap at locations greater than 30° latitude, thus producing multiple daily observations in these
regions (Williamson et al. 2013).
68
5.2.3 MODIS Terra (MOD11A1) and Aqua (MYD11A1) clear-sky LST
The MODIS LST datasets used in this study are the MOD11A1 and MYD11A1 h11 tile data
acquired daily under clear-sky conditions, using reprocessing Collection 5 (C5). Both datasets
contain single observations in each grid cell rather than averaged observations. MODIS data were
downloaded from the Land Processes Distributed Active Archive Center (LPDAAC) (LPDAAC
2015). The basic 1 km gridded MODIS LST is produced with a split-window technique that uses
MODIS bands 31 and 32 (10.78–11.28 and 11.77–12.27 μm, respectively) (Wan et al. 2002). This
technique uses a global land surface classification-based emissivity lookup table to estimate
emissivity values in these two bands (Snyder et al. 1998). A split-window technique is used to
produce the 1 km LST product, whereas the 5 km LST product uses the day/night algorithm. The
split-window class of techniques uses the difference in water vapour absorption that exists between
band 31 and band 32 to determine surface temperature. The MOD11A1 and MYD11A1 qualitycontrol flags were used for cloud screening, as done by Nishida et al. (2003) and Ackerman et al.
(1998). The quality flag information relating to C5 of the MODIS LST products can be found in
the product users’ guide (Guide 2015a). The MODIS quality flag used in this study is the LST and
emissivity quality control layer. The first bit indicates whether the produced LST is of good quality
and does not require further inspection of the quality flags or whether the LST was produced but
the quality is unreliable or unquantifiable and further quality flag inspection is required. Inspection
of all the MODIS quality flags produced for the unreliable or unquantifiable quality first bit
provides differentiation of the average temperature quality flags as ≤3, ≤2, and ≤1 K, which is the
nominal (or minimum) level; the >3 K average temperature quality flag was not assigned to any
of the data considered in this study. Grid cells with the MODIS quality flags raised related to
emissivity and subpixel cirrus cloud presence were eliminated from this study; these affected less
than 3.00% of the total dataset.
5.2.4 MODIS data pre-processing
The MOD11A1 and MYD11A1 tile data were subset to the study area. MOD11A1 and MYD11A1
LST and their coincident local solar view time for the same years of in-situ data (2013 and 2014)
were reprojected from sinusoidal projection to 1 km gridded GeoTiff Albers equal area projection,
North American Datum 83, using nearest neighbor resampling. This processing step was batch run
69
using the MODIS Reprojection Tool (Dwyer and Schmidt 2006) available from the LPDAAC.
These LST product layers were converted to local solar time and temperature using the conversion
factors (Guide 2015b). The view times in the MOD11A1 and MYD11A1 products are in local
solar time, which is called the MODIS observation time in UTC plus longitude in degrees at the 1
km grid cell divided by 15. MODIS view times were converted from local solar time to local time
to enable comparison with CREST-SAFE observations.
5.2.5 MODIS and CREST-SAFE temporal intersection
Daily MODIS layers containing LST values and each grid cells’ associated view time (time of
LST capture) were matched with CREST-SAFE using nearest neighbour sampling. The MODIS
data used covers from January–April 2013 and February–April 2014. T skin is recorded every 3
min at CREST-SAFE. Hence, even though MODIS LST values are hardly ever recorded at the
hour, the temporal matching between MODIS LST and CREST-SAFE in-situ temperatures was
not off by more than 3 min. Terra MODIS usually overpasses Caribou between 14:00 (2:00) and
15:00 (3:00) LT, while Aqua MODIS’s overpass is between 17:00 (5:00) and 18:00 (6:00) LT.
MODIS LSTs are typically recorded twice daily. Whenever the MODIS view time was in the early
morning, it was considered a daytime observation. When the MODIS view time was in the
afternoon, it was treated as a night-time observation.
5.2.6 MODIS LST validation
CREST-SAFE in-situ T skin (abscissas) versus Terra and Aqua MODIS LST (ordinates) daytime
and night-time scatter plots and results (r linear correlation coefficient values and biases) for both
years of study are illustrated in Figure 29. The average r linear correlation coefficient values
between Terra and Aqua MODIS LST and in-situ T-skin daytime data obtained were 0.78 and
0.90, with average daytime biases of −1.49°C and −1.29°C, respectively. Night-time average r
linear correlation coefficient values yielded slightly less accuracy with Terra and Aqua MODIS
versus T-skin fluctuating between 0.70 and 0.84, with average night-time biases of −2.37°C and
−2.26°C, correspondingly. Better daytime validation results coincide with previous studies that
indicate higher confidence in the MODIS cloud mask during the day (Williamson et al. 2013,
2014; Ackerman et al. 1998). However, all biases indicate that the RS LST can estimate in-situ
LST/T-skin with reasonable accuracy (±2°C) when compared to previous studies (Wang, Liang,
70
and Meyers 2008; Li et al. 2014; Vancutsem et al. 2010; Coll et al. 2005; Wan et al. 2002; 2004;
Wang et al. 2004; Zhu, Lű, and Jia 2013; Shuman et al. 2014; Jin and Dickinson 1999).
Furthermore, MODIS has proved to be underestimated at cold temperatures (Wenny, Xiong, and
Madhavan 2012; Shuman et al. 2014; Hall et al. 2015) due to calibration issues because the MODIS
thermal emissive band on-orbit calibration is performed over the range of 270–315 K. Wenny,
Xiong, and Madhavan (2012) observed an obvious difference for the Terra and Aqua C5 data,
especially for the coldest scenes during the winter. This dynamic range differences are largest on
the shorter wavelength bands than the longer wavelengths, because these scene temperatures are
well below the typical TB for each band. Hence, some uncertainties can be expected at exceedingly
cold temperatures. It should also be noted that the difference between available MODIS instrument
observations for comparison with in-situ CREST-SAFE data varied with the satellite (Aqua or
Terra) and, consequently, the atmospheric conditions at the time of overpass. For this reason, as
seen in Figure 29, there were fewer in-situ temperature observations above 0°C to validate MODIS
Aqua, the opposite can be said for MODIS Terra and all night-time observations in general. This
traces back to the C5 calibration issues mentioned earlier that lead to dynamic differences between
the MODIS instruments on board both satellites.
71
Figure 29. Terra and Aqua MODIS LST versus CREST-SAFE in-situ LST scatterplots with r linear
correlation coefficient values and biases for winters 2013 (a and b, respectively) and 2014 (c and d,
respectively) at CREST-SAFE for MODIS daytime and night-time overpasses4.
Furthermore, it is possible and common for both satellites to orbit over the same location multiple
times in the same day, and for one of the MODIS instruments to record a ‘missing value’ during
its satellite’s overpass. This can be attributed to the sensor’s inability to make an observation at
the time of overpass due to cloud contamination or water. Hence, the difference in availability
between the number of observations per satellite for the period under study. The interannual
4
For all subplots, results in the upper left corner correspond to daytime observations, while results in the bottom right
corner correspond to night-time observations. Dotted line represents 45° line.
72
difference between biases and r correlation values is mainly due to the fact that the 2014 in-situ
LST data record was only available for the warmer months (snow metamorphism alters snow
surface emissivity) of March and April, whereas 2013 CREST-SAFE LST included the months of
January and February (when the snow is dry). It should be noted that intersatellite differences are
due to the fact that Terra and Aqua observations are not coincident. Hence, some variations due to
time of day and atmospheric profile differences are expected. Additionally, there is a known
bandpass difference between Terra and Aqua bands 24 and 25, and this shift has shown a radiative
transfer modelling of +4 and +2 K between Terra and Aqua for bands 24 and 25, respectively
(Wenny, Xiong, and Madhavan 2012). As such, even if to a smaller extent, this shift and temporal
differences will create discrepancies between both satellite LST observations.
It is known that remotely sensed LST records the radiative energy emitted from the ground surface,
including building roofs, paved surfaces, vegetation, bare ground, and water (John 2003; Voogt
and Oke 2003). Therefore, the pattern of land cover in urban landscapes may potentially influence
LST (John 2003; Forman 1995). In addition to influencing LST through direct modification of
surface characteristics, land-cover pattern may also influence LST through its effects on the
movements and flows of organisms, material, and energy in a landscape (Forman 1995; Turner
2005). Numerous studies have demonstrated that increasing vegetation cover or surface water
could significantly decrease LST and thus help to mitigate excess heat in urban areas, whereas the
increase of buildings and paved surfaces would significantly increase LST (Buyantuyev and
Jianguo 2010; Liang and Weng 2008; Weng 2003; Weng, Dengsheng, and Schubring 2004; Xiao
et al. 2008). LST has proved to be the highest for impervious surfaces among all land-cover types.
Impervious surfaces exhibit the highest mean temperatures, whereas the lowest mean temperatures
are observed in waterbodies. Amongst all common land-cover types, the influences of impervious
surfaces, vegetation, and water on LST are stronger, while that of croplands and bare land are
weaker (Song et al. 2014). The surrounding area of the CREST-SAFE site, while not exactly urban
in the city-like sense, comprises the heterogeneity of residential homes, paved roads, and some
grassland. For this particular reason, two additional (four total) MODIS Terra and Aqua pixels
(two bare land, two partially forest covered) within the proximity of CREST-SAFE were
considered in this study to check whether T-skin data observed at the station are representative of
other areas with different land cover that surround the site in Caribou. The idea was to select one
land-cover type that is considered to affect the MODIS LST significantly (vegetation) and another
73
whose effect on MODIS LST is minimal (bare land), in order to compare with the CREST-SAFE
MODIS pixel (Figure 30). All pixels appear to be either completely or mostly snow covered
throughout the study.
Lastly, while (manual and automated) station data indicate that the ground surface was snow
covered throughout the period of study, we recognize the possibility that there were periods of
time when there was no snow, or a very thin (<2 cm) snow layer covering the ground. This is due
to the fact that snow-depth measurements and observations at the station are performed in an area
adjacent to where the IR radiometer was installed. Therefore, there might have been no snow
present in the IR target area, at the same time there was some snow where depth observations were
performed for the warm month of April. This could explain the fact that some in-situ and RS
MODIS LST ‘snow-covered’ surface values are above 0°C. Additionally, if some areas of the 1
km MODIS pixels were undergoing the same phenomena (i.e. melting snow leading to thin
snowpack remnants or no snow), the presence of the underlying ground surface or vegetation will
have undeniably yielded LST values above 0°C. Nonetheless, all results indicate that the MODIS
LST was able to capture the in-situ LST changes throughout the winter.
74
Figure 30. CREST-SAFE MODIS pixel (light purple rhombus) and CREST-SAFE site (red circle)
overlaid on top of the Caribou Municipal Airport premises.
75
The validation results for the bare land MODIS pixel approximately 2.50 km away from CRESTSAFE and the partially forested pixel approximately 1 km away from the site are illustrated in
Table 7. Figure 31 shows all three pixels with the CREST-SAFE site as reference. Similar linear
correlation coefficients and biases were displayed by all pixels, regardless of their different landcover classes. This is indicative that CREST-SAFE LST could be a reliable source for analogous
surfaces under equivalent atmospheric conditions. The small improvement in MODIS LST
estimation when using the bare land and partially forest covered pixels is due to more surface
homogeneity, when compared to the CREST-SAFE pixel.
Table 7. Terra and Aqua MODIS LST versus CREST-SAFE in-situ LST r linear correlation coefficient
values and biases for winters 2013 and 2014 at CREST-SAFE for MODIS daytime and night-time
overpasses.
Terra 2013
Pixel
Aqua 2013
Terra 2014
Aqua 2014
Overpass
r
Bias (°C)
r
Bias (°C)
r
Bias (°C)
r
Bias (°C)
Day
0.60
- 0.43
0.81
- 0.37
0.85
- 1.73
0.92
- 2.72
Night
0.72
- 1.93
0.91
- 2.23
0.88
- 2.57
0.90
- 2.55
Day
0.62
- 0.67
0.81
- 0.17
0.86
- 1.62
0.91
- 2.36
Night
0.70
- 2.01
0.89
- 2.42
0.87
- 2.22
0.91
- 2.67
Bare land
Vegetated
5.2.7 Effect of increasing MODIS LST window size
This section investigates whether the sampling procedure used (nearest neighbour) to obtain the
MODIS LST pixel in the study influenced the final validation results by conducting a sensitivity
analysis increasing the MODIS window to different sizes (5 × 5, 9 × 9, and 25 × 25). A spatial
window with varying size can help to determine the size of the area over which in-situ LST
measurements relate best, if that is the case, with MODIS LST observations.
To understand the effects of LST window size on the MODIS LST-in-situ LST relationship, areally
averaged LST time series over multiple windows of the MODIS LST grid were generated. When
window size was larger than 1 × 1, the mean value from the pixels overlapped by each window
76
was calculated to produce the MODIS LST time series. The mean of each window was derived
only for those times when at least two-thirds of the window members were valid LST pixels (i.e.
no missing values due to cloud mask or water). Since the emissivity of water is considerably higher
than that of vegetation (Hughes, Hall, and Fovell 2007; Benali et al. 2012), pixels over water in
the larger windows were removed from the analysis. Generally, spectral mixing of heterogeneous
land-cover types should be minimal for smaller windows. Hence, the smallest window size should
provide the most homogeneous local land cover. Conversely, the in-situ LST receives convective
sensible heat from local features spread over a larger extent rather than accommodated by a single
pixel. Thus, it can be expected that the in-situ LST represents the integrated effects of an area
larger than the 1 km2 covered by a MODIS pixel. Varying the window size might help discover
the optimal spatial extent over which MODIS LST agrees with in-situ LST. Results are illustrated
in Table 8 by comparing the results from the 1 km2 Terra and Aqua MODIS pixel from the
previous section with the 5 × 5, 9 × 9 and 25 × 25 window sizes.
Correlations improved slightly for Terra MODIS LST when the window size was increased from
1 to 25 pixels. The opposite happened to Aqua MODIS LST correlations. All biases demonstrated
a MODIS LST overestimation when increasing the window size, this is compatible with the effects
of vegetated and urban land covers (kilometres away from the site) on RS LST discussed in the
previous section. However, changes in the magnitude of the biases were insignificant and only
improved slightly for night-time Aqua MODIS LST. Therefore, results indicate that increasing the
MODIS LST window size does not provide significant improvement over the study area and that
CREST-SAFE is representative of areas extending up to 25 km away.
Table 8. r Correlation coefficient values and biases comparison between MODIS LST and CREST-SAFE
in-situ LST by increasing MODIS window size.
Terra
1 km
Overpass
r
Bias
(°C)
Aqua
5 km
r
Bias
(°C)
9 km
r
Bias
(°C)
25 km
r
Bias
(°C)
1 km
r
Bias
(°C)
5 km
r
Bias
(°C)
9 km
r
Bias
(°C)
25 km
r
Bias
(°C)
Day
0.70
- 1.49
0.85
1.28
0.85
1.33
0.87
1.31
0.84
- 1.29
0.65
1.97
0.66
1.99
0.63
1.72
Night
0.78
- 2.37
0.81
2.07
0.80
2.18
0.80
2.23
0.90
- 2.26
0.83
0.52
0.83
0.55
0.85
0.58
77
Figure 31. Bare land MODIS pixel approximately 2.50 km away from CREST-SAFE, partially forested
pixel approximately 1 km away from the site, CREST-SAFE pixel (all represented by light purple rhombi),
and the CREST-SAFE site (red circle) overlaid on top of the Caribou Municipal Airport premises.
78
5.2.8 MODIS LST validation summary
Remotely sensed LST validation results for daytime observations were better than those during
night-time, indicating higher confidence in the MODIS cloud mask during the day. Furthermore,
all biases displayed a MODIS LST underestimation of in-situ LST. This is indicative of needed
improvements in the MODIS cloud mask for night-time observations to yield more reliable LST.
In general, all biases were low (about 1–2°C) and indicative of good agreement between the
MODIS LST product and in-situ LST. Therefore, MODIS LST readings are reliable for estimating
in-situ T skin in areas nearby the station, extending all the way to 25 km, as demonstrated by
increasing the window size. Additionally, the validation results of pixels with different land covers
from the one surrounding the site indicate that CREST-SAFE might be representative of similar
surfaces under similar atmospheric conditions.
It is important to mention that, while it did not seem to affect the results of this study, the difference
between MODIS LST and in-situ LST can be attributed to the fact that the MODIS pixel might be
characterizing different land cover that is abundant in the vicinity of the region of study. Although
results indicate that land cover did not affect significantly the MODIS LST estimation of in-situ
LST in the region of study, this is rarely the case. Satellite radiometry is applied to large areas (1
km2 in this study) which often consist of various land and vegetation types. Moreover,
meteorological conditions for snow accumulation and melt on forest floors differ from those in
clearings because of the influence of the canopy (Platt and Prata 1993). Also, snow becomes patchy
while melting, giving a heterogeneous, layered structure – each layer having different physical and
mechanical characteristics – with large contrasts in characteristics such as albedo (i.e. reflectance,
TB) (Gelfan, Pomeroy, and Kuchment 2004; Prihodko 1997; Datt et al. 2008; Lundquist and Lott
2008). Hence, the combination of above freezing temperatures during daytime with below freezing
temperatures at night causes multiple freezing and melting events within the snowpack during the
melting period (late winter). Daytime solar radiation causes snowmelt in the uppermost layer that
produces higher water content in the superior layers of the snowpack. These events cause a large
diurnal variation in the RS TB that is difficult to reproduce using satellite retrievals (Pomeroy,
Essery, and Toth 2004). When comparing satellite RS and in-situ point-wise data, the primary
issue is whether the surface properties at the site are representative for land surface properties
within the instrument FOV. The temperature of vegetation canopy is usually closer to the air
temperature than to the LST.
79
Lastly, when discussing the radiative properties of the snow surface, while not uniform, the IR
emissivity of snow is understood enough to compensate for its effects in the RS of T skin. At nearnormal viewing angles, the RS TB can be as much as 1.50°C lower than the thermodynamic
temperature at wavelengths around 13 μm (Dozier and Painter 2004). At the shorter IR wavelength
window (3.50–4.00 μm), uncertainty in emissivity does not translate into uncertainty in
temperature because of the nonlinear nature of Planck’s function, but at longer wavelengths it
does. Fortunately, the highest and unreliable uncertainties in emissivity are beyond the 10.50–
12.50 μm atmospheric window that the MODIS LST split-window algorithm uses for retrievals.
Several studies have confirmed this by finding that the differences between RS LST and T-skin
have not been due to emissivity as much as orographic effects, topography, topographic
shadowing, and snow deposition (Stroeve and Steffen 1998; King et al. 2004; Fily, Dedieu, and
Durand 1999; Marks, Winstral, and Seyfried 2002). However, it should be noted that Dozier and
Warren (1982) and Salisbury, D’Aria, and Wald (1994) found that snow grains are independent
scatterers, and that emissivity decreases with grain size and the presence of liquid water in the
snow. For this reason, the MODIS MOD11A1 and MYD11A1 emissivity products from this study
were analysed and found to vary from 0.97 to 0.99 for all retrievals (Terra and Aqua MODIS), and
when compared to the surface emissivity value (0.98) assigned to the Apogee Broadband Infrared
Radiometer, the average relative error was negligible (−0.30%).
5.2.9 MODIS LST validation conclusion
In this study, the efficacy of estimating LST for snow-covered regions using the MODIS LST and
emissivity MOD11A1 and MYD11A1 products from the MODIS instrument aboard NASA
satellites Terra and Aqua by comparing it with in-situ LST observations from the CREST-SAFE
ground station located in Caribou, ME for the winters of 2013 and 2014 was assessed. Quantifying
the accuracy of LST products for different land-cover conditions will both improve their
effectiveness and help improve the LST retrieval algorithms, particularly over snow-covered
regions due to synoptic station scarcity.
The results indicate that the current MODIS LST product yields acceptable accuracy (±1–2°C) for
daytime and night-time in-situ T-skin observations for the region studied with average biases of
−1.40°C and −2.31°C, respectively. These cold biases indicate that MODIS LST underestimates
in-situ LST. This is congruent with previous studies that have proved MODIS underestimates at
cold temperatures due to calibration issues. For this particular reason, the MODIS Characterization
80
Support Team (MCST) delivered a revised and updated TB calibration approach – named
Collection 6 (C6) – to mitigate the cold bias previously observed for TB retrievals below the
temperature range of 270–315 K. Hence, it is recommended to use C6 for MODIS LST validations.
Additionally, intersatellite differences are due to the fact that Terra and Aqua observations are not
coincident. These have variations due to time of day and atmospheric profile differences, and
different calibration coefficients in Collection 5. Fortunately, the C6 calibration removes the
dynamic range differences and allows Terra to retrieve colder temperatures more consistent with
Aqua. It is also recommended to use C6 for satellite cross validation.
Lastly, MODIS TBs are calibrated using a quadratic algorithm relating the detector response to
the Earth view radiance with three calibration coefficients: a linear term (b1), an offset (a0), and
nonlinear term (a2). The linear b1 term is derived from scan-by-scan observations of a blackbody.
The a0 and a2 terms were derived pre-launch and are monitored on-orbit through analysis of
blackbody warm-up/cool-down activities that vary the temperature from 270 to 315 K. Since, as
discussed by Wenny, Xiong, and Madhavan (2012), the MCST found that making the a0
coefficient 0 (C6 update) for all Terra bands and Aqua bands 31–36 yields better LST retrievals in
cold temperatures, another recommendation would be to calibrate and use a separate
(daytime/night-time) a2 coefficient to improve night-time observations, especially because this
coefficient is derived from the cool-down (from the warm-up/cool-down activities) that occurs at
night.
Additional insight might be drawn by conducting a similar study only for the spring months of
March and April when snow cover is still present, but the snowpack is undergoing metamorphic
changes that will alter the snow surface temperature’s physical and radiative properties.
Furthermore, another study can be done by examining the relationship between MODIS LST and
forest cover fraction within the sensor FOV. This way, changes in forest fraction can be related to
changes in MODIS LST. While there may be no fully forested or non-forested pixels, LST
estimates can be extrapolated to estimate LST to 0.00% and 100.00% forest fraction if there is an
ample range of different forest cover fractions with their respective LST estimates. Lastly, it would
be ideal to have analogous ground measurements over other regions with comparable snow
conditions and land cover to be able to contrast with this study.
81
5.3
MiRS LST study
Land Surface Temperature (LST) is a key parameter for hydrological, meteorological,
climatological, and environmental studies because it combines the results of all surfaceatmosphere interactions and energy fluxes. Satellite microwave-based retrievals provide the
capability to measure LST with near-global coverage and high temporal resolution for both clear
and cloudy (non-raining) conditions, as opposed to infrared-based retrievals. However, all satellite
retrievals have to be validated with reference datasets to assess their accuracy. This study presents
the procedure and results of a temperature-based validation approach between the Microwave
Integrated Retrieval System (MiRS) LST product - retrieved from Suomi National Partnership
Program/Advanced Technology Microwave Sounder (S-NPP/ATMS) measurements – and
Surface Radiation Budget Network (SURFRAD)-derived LST observations from six locations
(Nevada, Illinois, Montana, Mississippi, Pennsylvania and South Dakota) across the coterminous
United States over a 13-month period (May 2016 – May 2017). Results indicated high performance
between all stations, despite their considerably different climates and surface characteristics.
5.3.1 Previous IR and MW LST validation efforts
Land Surface Temperature (LST) is defined as the thermodynamic temperature of the uppermost
layer of the Earth's surface. LST is a key parameter in the surface-atmosphere interactions that
define the Earth’s energy and water fluxes (Li et al., 2014). Because of its spatial heterogeneity
and significant changes over time, it is common practice to use long-term satellite-based LST
retrievals for the large-scale (continental-to-global) modeling of land surface processes for both
validation and data assimilation techniques (Corbari & Mancini, 2014; Friedl, 2002; Sun et al.,
2016).
Commonly-used global LST products are derived from thermal infrared (TIR) sensors (e.g. Visible
Infrared Imaging Radiometer Suite (VIIRS), Moderate Resolution Imaging Spectroradiometer
(MODIS)) onboard numerous satellite systems (e.g., polar-orbiting Suomi National Partnership
Program (S-NPP), Terra, Aqua, as well as geostationary platforms). The satellite spatial resolution
for TIR retrievals normally ranges from 90 m (Advanced Spaceborne Thermal Emission and
Reflection Radiometer (ASTER)) to 1 km (MODIS) for polar-orbiting satellites to 2 km
(Geostationary Operational Environmental Satellite-R (GOES-R) - 3 km (Spinning Enhanced
Visible and IR Imager (SEVIRI)) for geostationary platforms (Sobrino et al., 2008; Yu et al.,
82
2009). TIR LST retrievals are performed under clear-sky conditions, assuming the TIR land
surface emissivity is known. However, these retrievals need to be corrected for atmospheric
constituents such as: water vapor, aerosols, and particulate matter (Sobrino et al., 2008).
Furthermore, TIR retrievals are impossible to execute under cloudy conditions. Hence, cloudcovered skies present a major obstacle when performing TIR LST retrievals over land. Especially
when it has been previously demonstrated that, on average, 50% of the land surface is commonly
cloud-covered at any given time (Rossow & Gardner, 1993; Rossow et al., 1993).
Passive microwave (MW) instruments represent an alternative (or complement) to TIR sensors for
LST retrievals. Microwave frequencies at the 18 GHz and 37 GHz are commonly used for these
applications (Holmes et al., 2009; Mao et al., 2007; McFarland et al., 1990). More importantly,
passive MW measurements at these bands present a reduced sensitivity to soil surface
characteristics and high atmospheric transmissivity (Colwell et al., 1983). However, MW LST
retrievals are limited by snow, frost, and frozen soil, as these conditions have a large effect on the
MW surface emissivity that cannot be easily characterized (Grody, 2008). Furthermore, rain clouds
or active precipitation with droplets scatter the MW emission, providing yet another limitation for
MW retrievals (Ulaby et al., 1986). MW measurements of surface temperature are also sensitive
to the so-called penetration or emission depth – the depth where the majority of the emitted
electromagnetic signal originates, and this is dependent on soil texture, vegetation, soil moisture
and frequency. This is typically on the order of 1 mm to about 3 cm for the frequencies considered
here (Njoku & Li, 1999; Zhou et al., 2016) which is considerably larger than that corresponding
to TIR-based measurements. Additionally, satellite MW measurements have a coarser spatial
resolution – dependent on the instrument, channels, and satellite - that ranges from approximately
5 km (Advanced Microwave Scanning Radiometer 2 (AMSR2)) to 75 km (Advanced Technology
Microwave Sounder (ATMS)) when compared to TIR observations (Grant & Miller, 2012; Kachi
et al., 2013).
Validation is an essential component of every satellite product accuracy assessment. Normally, all
satellite products (TIR and MW) are validated using either other global products, models, or,
preferably, in-situ ground stations for comparison. Extensive literature has proven the accuracy of
satellite TIR LST products through validation efforts (Guillevic et al., 2012; Wan et al., 2002,
2004, 2014; Wang et al., 2008). While few studies have focused on validating satellite MW LST
products (Chen et al., 2011; Karbou et al., 2003; Parinussa et al., 2008; Prigent et al., 2015; Zhang
83
et al., 2011). Moreover, currently operational satellite products need to be validated frequently, as
instruments may deteriorate, experience calibration changes, and/or lose channels/bands, resulting
in possibly erroneous retrievals. This study presents the procedure and results of a temperaturebased validation approach between the Microwave Integrated Retrieval System (MiRS) LST
product - retrieved from S-NPP/ATMS – and Surface Radiation Budget Network (SURFRAD)derived LST observations from six locations (Nevada, Illinois, Montana, Mississippi,
Pennsylvania and South Dakota) across the continental United States over a 13-month period (May
2016 – May 2017). Previous results of S-NPP ATMS MiRS-retrieved LST validation using in-situ
SURFRAD-derived LST were presented in Boukabara et al. (2013) based on an older version of
the MiRS algorithm.
5.3.2 SURFRAD dataset
SURFRAD consists of eight surface radiation and meteorological measurement sites spread across
climatologically diverse regions of the United States (SURFRAD, 2017). Six SURFRAD stations
were used in this study and their locations are shown in Table 9. For simplicity, three-letter
abbreviations will be used to reference each SURFRAD station. The SURFRAD site abbreviations
are as follows: DRA = Desert Rock, NV; BON = Bondville, Illinois; FPK = Fort Peck, Montana;
GWN = Goodwin Creek, Mississippi; PSU = Pennsylvania State University, Pennsylvania; and
SXF = Sioux Falls, South Dakota. Two sites were not used for this analysis. These are: Table
Mountain (TBL) in Boulder, Colorado and the Southern Great Plains (SGP) in Lamont, Oklahoma.
SURFRAD stations provide high-quality measurements of upwelling and downwelling shortwave
and longwave radiation. The upwelling and downwelling longwave radiative fluxes are measured
with the precision infrared radiometer, which is sensitive in the spectral range from 3000 to 50,000
nm (Pinker et al., 2009). These data have been available since 1995 for four sites (BON, FPK,
TBL, and GWN). Sites DRA, PSU, and SXF have been providing data since 1998. Data are
recorded every minute.
84
Table 9. SURFRAD station information (location and surface type).
Station name
Surface
Latitude (N)/longitude (W)
Elevation (m)
U.S. state
ID
Desert Rock
Open shrub land
36.63˚/116.02˚
1007
NV
DRA
Bondville
Cropland
40.06˚/88.37˚
230
IL
BON
Fort Peck
Grassland
48.31˚/105.10˚
634
MT
FPK
34.25˚/89.87˚
98
MS
GWN
Goodwin Creek Deciduous forest
Penn State
Mixed forest
40.72˚/77.93˚
376
PA
PSU
Sioux Falls
Grassland
43.73 ˚/96.62 ˚
473
SD
SXF
5.3.3 SURFRAD LST estimation
SURFRAD LST is derived from upwelling and downwelling longwave radiation flux
measurements using the following relationship:
భ
ൌ ൣ൫ ୳୵ െ ሺͳ െ ɂሻ ୢ୵ ൯Ȁሺɂɐሻ൧ర
Equation 25
where ‫ܴܫ‬௨௪ and ‫ܴܫ‬ௗ௪ are the infrared longwave upwelling and downwelling radiation fluxes,
respectively, ߝ is the broadband longwave surface emissivity, and ɐ is the Stefan-Boltzmann
constant (Heidinger et al., 2013). In this study, the broadband longwave emissivity was assumed
to be 0.97. This value is representative of the results shown in Wang et al. (2005), where the
broadband values were derived using a regression based on the SeeBor emissivity for the MODIS
bands with central wavelengths of 8.5, 11, and 12 ߤm. Heidinger et al. (2013) demonstrated that a
0.1 error in emissivity equates to a 0.25 K error in SURFRAD-derived LST. Therefore, while not
negligible, it does not present a dominant source of uncertainty.
85
5.3.4 MiRS algorithm and LST retrieval
The MiRS is an iterative physically-based one-dimensional variational (1-DVAR) retrieval
algorithm (Boukabara et al., 2011, 2013; Liu & Weng, 2005). The goal is to minimize a two-term
penalty function, which is composed of the departure of the simulated radiances from
measurements, and the departure of the retrieved parameters from their respective a priori
backgrounds.
The 1-DVAR algorithm finds the optimal solution that best fits the observed satellite radiance,
subject to other constraints (Liu et al., 2017).The cost function to be minimized is:
‫ܬ‬൫ܺ൯ ൌ ൣభమ൫ܺ െ ܺͲ൯ܶ ൈ ‫ି ܤ‬ଵ ൈ ൫ܺ െ ܺͲ൯൧ ൅ ൣభమሺܻ݉ െ ܻሺܺሻሻܶ ൈ ‫ି ܧ‬ଵ ൈ ሺܻ݉ െ ܻሺܺሻሻ൧
Equation 26
where X is the retrieved state vector. The first item on the right represents the penalty for departing
from background X0 weighted by the error covariance matrix B. The second term represents the
penalty for the simulated radiances Y departing from the observed radiances Ym , weighted by
instrument and modeling error E. Assuming local linearity (i.e. ‫ݕ‬ሺ‫ݔ‬ሻ ൌ ‫ ݕ‬ቀ‫ݔ‬଴ ቁ ൅ ‫ܭ‬ሾ‫ ݔ‬െ ‫Ͳݔ‬ሿ), we
can find the iterative solution:
οܺ௡ୀଵ ൌ ሼ‫ܭܤ‬௡் ሺ‫ܭ‬௡ ‫ܭܤ‬௡் ൅ ‫ܧ‬ሻିଵ ሽ ቂ ቀܻ݉ െ ܻሺܺ௡ ሻቁ ൅ ‫ܭ‬௡ οܺ௡ ቃ
Equation 27
where ΔX is the increment of the state vector iteration n + 1, and K is the matrix of Jacobians (i.e.
derivatives) which contains the sensitivity of the radiances to changes in X (parameters to retrieve).
This is then followed by the post-processing step which uses as inputs the elements of the state
vector X. One of the many outputs retrieved in the geophysical state vector is skin temperature or
LST.
In this study, the processing of ATMS data was done with version 11.1 of MiRS which was first
implemented in operations at NOAA in 2015.
86
5.3.5 MiRS vs SURFRAD LST collocation and temporal matching
Corresponding to the input ATMS measurement data, MiRS produces approximately 2700
granules daily that contain core retrieval and post-processing (VIPP) components. Core products
are retrieved simultaneously as part of the geophysical state vector (including LST). VIPP products
are derived through vertical integration (hydrometeors), catalogs (sea ice concentration, snow
water equivalent), or fast regressions (rain rate). For each day, 2-3 granules (ascending and
descending overpasses) collocate with each station. For those granules, the shortest distance from
the station to the nearest field of view (FOV) was calculated, and its corresponding MiRS LST
value and UTC time were extracted. In most cases, this distance fluctuated from 10-30 km. The
SURFRAD LST that matched the UTC time of the collocated FOV (to the nearest minute) was
obtained. Quality flags for MiRS retrievals and SURFRAD observations were verified and
possibly erroneous measurements were not included in the analysis. Additionally, possibly rainy
or snow-covered retrievals (according to MiRS) were filtered out as well.
5.3.6 MiRS vs. SURFRAD station-by-station validation
Scatter plots of the MiRS-retrieved LSTs vs SURFRAD-derived LSTs for each of the six (6)
SURFRAD stations were generated for the ascending (Fig. 32) and descending (Fig. 33) S-NPP
ATMS overpasses. The results are summarized in Table 10 using four (4) validation parameters the linear correlation coefficient (R), bias, standard deviation, and Root Mean Square Error
(RMSE). The nomenclature ASC and DSC will be used for the ascending (daytime) and
descending (nighttime) satellite overpasses, respectively. The term COM will be used for the
combination of both satellite overpasses.
87
Figure 32. Scatter plots of the MiRS-retrieved LSTs vs SURFRAD-derived LSTs for each of the 6
SURFRAD stations for the S-NPP ATMS ascending overpass for the period from May 1st, 2016 to May
31st, 20175.
Overall, the MiRS LST retrievals exhibited a cold bias when compared to SURFRAD in-situ
observations. However, the MiRS LST underestimation appears to be greater for the ascending
overpass; possible explanations for this characteristic are given in the discussion below, and in
section 5.3.7. All MiRS LST retrievals lie close to the 1:1 line (R values displayed high correlation
between satellite and in-situ measurements), indicative of the MiRS algorithm’s sensitivity to LST.
Furthermore, the overall standard deviation and RMSE fluctuated from 4.0-6.0 K and 4.2-7.9 K,
respectively. For reference, these values meet requirements set by the Joint Polar Satellite System
5
Scatter plots are labeled at the top left corner by station ID, along with the number of observations (n). Results are
presented in Table 10.
88
Environmental Data Records (JPSS EDRs) for satellite passive microwave LST performance. The
JPSS EDRs requirements for bias, standard deviation, and RMSE for MW LST performance are:
4, 7, and 8 K, respectively.
Figure 33. Scatter plots of the MiRS-retrieved LSTs vs SURFRAD-derived LSTs for each of the 6
SURFRAD stations for the S-NPP ATMS descending overpass for the period from May 1st, 2016 to May
31st, 20176.
6
Scatter plots are labeled at the top left corner by station ID, along with the number of observations (n). Results are
presented in Table 10.
89
Table 10. Results for MiRS vs SURFRAD station-by-station (DRA, BON, FPK, GWN, PSU, and SXF)
comparison from May 1st, 2016 to May 31st, 2017. Four validation statistics (R or correlation coefficient,
bias, standard deviation, and RMSE) were used to evaluate the MiRS algorithm retrieval accuracy for LST.
MiRS vs SURFRAD station-by-station comparison
DRA
Validation
BON
FPK
GWN
PSU
SXF
ALL
Parameter
D
A
S
S
D
A
S
S
C
C
C
C
R
0.90
0.96
0.96
0.90
0.92
Bias (K)
-3.3
-6.6
-4.9
-1.5
Std. dev. (K)
4.7
4.2
4.8
RMSE (K)
5.7
7.8
6.8
COM
D
A
S
S
D
A
S
S
C
C
C
C
0.93
0.77
0.89
0.91
0.87
0.86
-1.6
-1.6
2.3
-1.7
0.2
0.2
4.1
4.1
4.1
4.8
6.0
5.8
4.4
4.4
4.4
5.3
6.2
5.8
COM
COM
D
A
S
S
C
C
0.88
0.84
0.93
-6.6
-3.3
1.1
4.2
4.3
5.4
4.2
7.9
6.3
COM
D
A
S
S
C
C
0.90
0.85
0.93
-3.1
-1.0
0.4
4.5
4.0
4.7
4.6
5.1
4.8
COM
D
A
S
S
C
C
0.92
0.85
0.92
0.92
-1.7
-0.6
-0.2
-3.5
-1.8
5.1
4.2
4.8
4.9
5.1
5.3
5.1
4.5
4.8
4.9
6.1
5.6
COM
COM
The station-by-station analysis indicates that MiRS LST retrievals have similar performance across
all regions, despite that fact that the stations span widely different climates with different surface
characteristics. Nevertheless, stations DRA and GWN exhibited slightly colder biases than the
other four stations for the ascending overpass. This might be due to the effect the diurnal cycle has
on LST for their respective surface types. SURFRAD station DRA is situated in an open shrub
land with desert characteristics, where LST changes drastically from day to night; making it
difficult for accurate satellite retrievals (Liu et al., 2001; Pinker et al., 2007). Station GWN is
located in a deciduous forest. Numerous studies have demonstrated that forest cover significantly
decreases LST (Buyantuyev & Wu, 2010; Liang & Weng, 2008; Weng et al., 2004; Xiao et al.,
2008). Amongst all common land-cover types, the influences of vegetation and water on LST are
stronger, while that of croplands and bare land are weaker (Song et al., 2014). Another factor that
is likely contributing to the systematically colder biases during the ascending (daytime) overpasses
for all stations relates to the surface emissivity retrievals. Analysis of the ascending vs. descending
emissivity retrieval differences (see section 5.3.7 below) indicates that some of the normal diurnal
signal in the LST is being interpreted as emissivity changes, which would lead to some
underestimation of the daytime LST.
90
Three main factors may explain many of the differences between MiRS-retrieved LST and
SURFRAD-derived LST. First, there are different spectral (MW vs IR) sampling characteristics
between MiRS satellite retrievals and SURFRAD in-situ observations. Microwave radiometer
observations have a penetration/emission depth slightly below the surface, with values ranging
from a few millimeters to up to 2-3 centimeters (Njoku & Li, 1999; Zhou et al., 2016), while IR
radiometer measurements are representative of the very top surface layer, representing on the order
of up to 50 microns depth (Parinussa et al., 2008). Second, there are inherent differences between
the horizontal spatial characteristics of the observations. The MiRS LST is the averaged surface
temperature integrated over the effective FOV of the satellite (which can vary from about 30 km
at nadir, to over 100 km at the edge of the satellite swath), while the SURFRAD in-situ
measurement is a point observation. Therefore, it is expected that both random and systematic
biases will exist between the two data sources. Random differences will likely be accentuated
when the area measured by the satellite is more heterogeneous. However, the high linear
correlation values may indicate that the SURFRAD observation is representative of the wider
region observed by S-NPP ATMS MiRS as a result of the land cover’s high homogeneity
(Guillevic et al., 2012; Parinussa et al., 2008; Wan et al., 2002). Lastly, during nighttime, the
thermal equilibrium conditions between the near-surface air, forest canopy, and soil surface are
quite stable (Holtslag & De Bruin, 1988; Platt & Prata, 1993). This results in small differences
between the satellite-retrieved LST and in-situ LST. Thus, the lower bias between datasets during
the satellite’s descending (nighttime) overpass.
5.3.7 Impact of emissivity on retrieved LST
In order to gain further insight on the role of retrieved emissivity biases in the apparently larger
negative daytime (ascending pass) biases seen for most stations, scatterplots of nighttime-daytime
emissivity differences were plotted against nighttime-daytime LST bias differences (i.e.
differences of the differences) (Fig. 34). The goal is to determine if any of the observed nighttimedaytime differences in LST biases can be explained by the corresponding differences in emissivity.
The surface emission term in the MW radiative transfer equation contains the product of LST and
emissivity, and for window channels this contributes to the majority of the signal in the observed
brightness temperatures. Therefore, since MiRS retrieves all elements of the geophysical state
simultaneously, it is possible that errors in either the LST or emissivity could project into the other
91
variable (sometimes referred to as “cross-talk”). The assumption being made is that in the absence
of precipitation or dew accumulation, there should be no significant changes in emissivity at a
location in the time between the two daily satellite overpasses. As seen in the scatterplots, there is
a relatively strong correlation for all 6 stations analyzed, with R values ranging between -0.49 and
-0.68. The negative slope indicates that points in which the day time emissivity was higher (lower)
than the nighttime emissivity, tend to occur with points where the daytime LST bias was less
(greater), or more (less) negative, than the nighttime bias – indicating that there may be a crosstalk effect.
This is further highlighted in Fig. 35 in which histograms for the night-day emissivity differences
corresponding to two of the six stations are shown. The histogram for Mississippi (GWN) shows
a systematic shift toward negative values as seen in the mean and median values (meaning daytime
emissivities tended to be higher than at nighttime), and this is associated with larger daytime biases
of -6.6 K, and a larger night minus day difference of biases (0.2 K and -6.6 K, respectively). On
the other hand, the histogram for South Dakota (SXF) shows a shift with positive mean and median
values, and the corresponding daytime LST bias is -1.7 K and a smaller night minus day difference
of biases (0.4 K and -1.7 K, respectively). There are limitations to this analysis (e.g. the true
emissivity is not known, and other local effects such as water vapor and clouds may modulate the
LST retrieval errors). Nevertheless, these results are consistent with the idea that a portion of the
natural diurnal signal of the LST is being projected into the retrieved emissivity, leading to a
relatively larger underestimation of LST with respect to SURFRAD during the day than at night,
and that this effect may vary with location. Further detailed analysis, beyond the scope of this
paper, might clarify the extent to which the biases in emissivity retrievals are impacting the LST
estimates. This would require more careful controlling for atmospheric and surface conditions.
Avenues for improving the MiRS LST retrievals might focus on better constraining the emissivity
LST via the a priori covariances, as well as on the use of temporally and spatially variable
emissivity climatologies.
92
Figure 34. Scatter plots of the difference of retrieved nighttime (descending) minus daytime (ascending)
emissivity on the x-axis versus the nighttime-daytime differences of MiRS-SURFRAD LSTs (i.e.
difference of LST biases) on the y-axis for all 6 SURFRAD stations.
93
Figure 35. Histograms of nighttime-daytime emissivity for two of the six stations (Mississippi and South
Dakota), showing the difference in distributions can be linked to the night vs. day LST biases.
5.3.8 MiRS LST validation summary
In this study, a validation between the MiRS LST product - retrieved from S-NPP/ATMS
measurements – and SURFRAD-derived LST observations from six locations (Nevada, Illinois,
Montana, Mississippi, Pennsylvania and South Dakota) across the continental United States over
a 13-month period (May 2016 – May 2017) was presented. Samples represented both clear and
cloudy (but non-precipitating) conditions. Results indicated relatively consistent performance
between all stations, despite their considerably different climates and surface characteristics.
Overall, for the six locations analyzed, the combined R, Bias, and Standard Deviation were 0.92,
-1.8 K, and 5.3 K, respectively. Generally, MiRS LST retrievals exhibited a cold bias when
compared to SURFRAD LST observations. Daytime overpasses displayed a slightly colder bias
than nighttime overpasses. This is possibly due to thermal equilibrium conditions at night.
However, an analysis of night vs. day retrieved emissivities indicated that a portion of this bias is
likely due to errors in the retrieved emissivity, which may be reflecting part of the natural diurnal
signal in LST, thus leading to higher underestimation relative to SURFRAD during the warmer
daytime conditions.
Given that the six stations span a large range of climate and surface characteristics, the results
indicate that the MiRS LST retrievals may be suitable for various applications that require
estimates in other regions not well-observed by conventional ground based observations, or those
94
characterized by frequent cloudiness which preclude satellite IR-based estimates. This may include
studies of local and regional climates, general applications such as large-scale (continental-toglobal) modeling of land surface processes for validation, data assimilation, and for decisions that
can possibly impact human lives.
5.4
Cross-comparison between satellite IR and MW LST products
The following section presents a cross-comparison between validations for the three satellite LST
products discussed in Sections 5.1, 5.2, and 5.3. The purpose of this comparison is to find out if
there is a significant difference in accuracy between IR and MW LST satellite products, given the
different instruments, and their respective limitations when it comes to LST retrievals. This
comparison was based on the biases and R linear correlation coefficients obtained when validating
each LST satellite product with in-situ data in the previous sections of this chapter. Results from
the cross-comparison between the VIIRS, MODIS, and MiRS LST products are shown in Table
11.
Table 11. Cross-comparison between validation (against in-situ data) results for the VIIRS, MODIS, and
MiRS LST products. Two validation statistics (R or correlation coefficient and bias) were used to evaluate
accuracy for LST.
Instrument
Parameter
MODIS (IR)
VIIRS (IR)
MiRS (MW)
Terra
Aqua
Bias (K)
-2.76
-1.93
-1.77
-1.84
R
0.80
0.74
0.87
0.92
Results demonstrate that all three satellite LST products provide similar accuracy when compared
to in-situ observations. Moreover, the cross-comparison shows that there is no apparent benefit to
using IR LST retrievals, as opposed to MW-based ones. While IR LST retrievals have the
advantage of a higher spatial resolution, there is significant limitation due to cloud contamination.
On the other hand, MW LST retrievals may have lower spatial resolution (than IR-based LST
retrievals) and MW penetration depth below the surface, but there is the appealing advantage of
95
not having to deal with cloud screening. Furthermore, as it was discussed in Section 5.2.7, LST is
hardly a point-based phenomenon. Hence, it reaches equilibrium over large spaces that might be
better embraced by lower pixel resolution or an average of high resolution pixels. Based on this
assessment, it is recommended to use MW-retrieved LST for regional-to-global studies, modeling,
and validations, as using IR LST retrievals provide no additional value.
96
6
Studying the effects of snow wetness in the snowpack
The quantity of liquid water in the snowpack defines its wetness. The temporal evolution of snow
wetness’s plays a significant role in wet-snow avalanche prediction, meltwater release, and water
availability estimations and assessments within a river basin. However, it remains a difficult task
and a demanding issue to measure the snowpack’s liquid water content (LWC) and its temporal
evolution with conventional in-situ techniques. We propose an approach based on the use of timedomain reflectometry (TDR) and CS650 soil water content reflectometers to measure the
snowpack’s LWC and temperature profiles. For this purpose, we created an easily-applicable, lowcost, automated, and continuous LWC profiling instrument using reflectometers at the Cooperative
Remote Sensing Science and Technology Center-Snow Analysis and Field Experiment (CRESTSAFE) in Caribou, ME, USA, and tested it during the snow melt period (February–April)
immediately after installation in 20147. Snow Thermal Model (SNTHERM) LWC simulations
forced with CREST-SAFE meteorological data were used to evaluate the accuracy of the
instrument. Results showed overall good agreement, but clearly indicated inaccuracy under wet
snow conditions. For this reason, we present two (for dry and wet snow) statistical relationships
between snow LWC and dielectric permittivity similar to Topp’s equation for the LWC of mineral
soils. These equations were validated using CREST-SAFE in-situ data from winter 2015. Results
displayed high agreement when compared to LWC estimates obtained using empirical formulas
developed in previous studies, and minor improvement over wet snow LWC estimates.
Additionally, the equations seemed to be able to capture the snowpack state (i.e., onset of melt,
medium, and maximum saturation). Lastly, field test results show advantages, such as: automated,
continuous measurements, the temperature profiling of the snowpack, and the possible
categorization of its state. However, future work should focus on improving the instrument’s
capability to measure the snowpack’s LWC profile by properly calibrating it with in-situ LWC
measurements. Acceptable validation agreement indicates that the developed snow LWC,
temperature, and wetness profiler offers a promising new tool for snow hydrology research.
7
Pérez Díaz, C., J. Muñoz, T. Lakhankar, R. Khanbilvardi, and P. Romanov. 2017. “Proof of Concept: Development
of Snow Liquid Water Content Profiler Using CS650 Reflectometers at Caribou, ME, USA.” Sensors 17(3): 647.
doi:10.3390/s17030647.
97
6.1
Snow wetness and previous studies
Seasonal snow is an influential reservoir constituent in the hydrological cycle that discharges
temporarily stored freshwater to the forelands (Brown and Robinson, 2011; Frei et al., 2012).
Downstream water suppliers (e.g., Western USA, the Rhine River in Europe, the Canadian prairies,
etc.) (Barnett et al., 2005) are greatly reliant on snow meltwater discharge from the alpine head
watersheds to supply potable and irrigation water. An important snow parameter, the snow water
equivalent (SWE) is commonly known as the amount of water contained within the snowpack, or
the depth of water that would theoretically result if the entire snowpack melted instantaneously
(DeWalle and Rango, 2008; U.S.A.C.E., 1956). However, this measurement does not deliver
information on the condition of melting snow. On the other hand, the liquid water content (LWC),
qw, of the snowpack describes its snow wetness. Snow wetness is used as an indicator of snow
melt and snow instability (Mitterer et al., 2011). An increase in the liquid water (wetness) of the
snowpack leads to an onset of meltwater runoff within a catchment. This type of information is
relevant for flood predictions during intense melting due to rain-on-snow events combined with
warm air temperatures (Chen et al., 2012; Kattelmann, 1997). Quantitative and temporal meltwater
delivery predictions are often required by water resources engineers and decision makers in the
water management field to deal with: reservoir management and hydropower generation (Barnett
et al., 2005; Koch et al., 2011), and catchment runoff and flood forecasts (Strasser and Mauser,
2011; Weber et al., 2010; Prasch et al., 2013). Additionally, information on the LWC and wetness
of the snowpack is essential for wet-snow avalanche forecasting, because the permeating water in
the snowpack dampens its mechanical strength and creates instability (Kattelmann, 1987; Baggi
and Schweizer, 2009; Mitterer et al., 2011).
Generally, snow wetness is quite difficult to measure in-situ. Furthermore, to account for the
spatiotemporal evolution of meltwater runoff and snow instability, non-destructive and continuous
snow LWC monitoring is necessary because changes in the LWC can rapidly alter various
snowpack properties and its meltwater outflow (Mitterer et al., 2011; Heilig et al., 2009).
Moreover, these processes are non-linear and, as such, difficult to detect or forecast, and the most
common type of measurement, manual snow wetness observations in snow pits, only provides a
rough estimate and is based on a wetness index (Fierz et al., 2009).
Techel and Pielmeier (2011) and Boyne and Fisk (1987) provide a review of numerous in-situ
snow wetness measurements. The majority of these in-situ snow wetness measurement techniques
98
are based on dilution, centrifugal, dielectric, and calorimetric measurement methods. Common
instruments used to measure the permittivity of wet snow are: the Finnish Snow Fork (Sihvola and
Tiuri, 1986) and the Denoth meter (Denoth et al., 1984; Denoth, 1989). However, these
measurement techniques are known to be destructive, time-consuming, and need to be executed at
accessible sites. Other less invasive and, consequently, non-destructive in-situ methods that have
been employed include: time-domain reflectometry (TDR) (Schneebeli and Johnson,1998; Stein
and Kane, 1983; Stein et al., 1997; Lundberg, 1997; Stacheder et al., 2009; Jones et al., 2002), the
Snowpack Analyser (SPA) (Heggli, 2013), and the upward-looking frequency modulated wave
(upFMCW) and ground-penetrating radar (upGPR) systems (Okorn, 2014; Kohler et al., 2013;
Heilig, 2008). The latter being unreasonably expensive (order of magnitude of 10, when compared
to TDR instrument setups), difficult to install (large antennas at the lower frequencies, heavier than
TDR reflectometers by an order of magnitude of 100), and requires specific, additional postprocessing.
The aim of this study is to: (1) test the capability of the CS650 soil water content reflectometer to
provide reliable snow LWC measurements and (2) provide a non-destructive, non-invasive, lowcost, automated, and continuous alternative to in-situ snow LWC measurements at different
snowpack heights above the soil surface by creating a snow wetness profiler (SWP) setup using
TDR and a series of CS650 water content reflectometers. The determination of LWC using TDR
is based on the relationship that exists between the relative complex dielectric constant of the
medium and its water content. The first use of TDR to determine LWC was executed in soils by
Topp et al. (Topp et al., 1980, 1982a, 1982b). Later, time-domain reflectometry was proven to be
a technique that can be used to indirectly measure the in-situ LWC of snow (and monitor snowmelt
percolation in the snowpack) by Stein and Kane (1983). They presented the first application of
TDR to the measurement of snow density and LWC. However, they only showed the signal, but
did not make any calibrations. Stein and Kane only explained how to use TDR to obtain the LWC
of snow by means of its relative complex dielectric constant and density. Later, Schneebeli and
Davis (1993) calibrated the dielectric constant and LWC of snow for a limited number of values.
Stein et al. (1997) and Schneebeli et al. (1998) expanded on the practice of the TDR technique in
snow, and developed relationships between its relative complex dielectric constant, density, and
LWC by conducting separate field campaigns and, in the case of Schneebeli et al. (1998),
laboratory experiments using time-domain reflectometers (model Tektronix 1502B (Melrose, MA,
99
USA)). Concurrently, Lundberg (1997) performed a laboratory comparison of the TDR technique
with the dilution method, and demonstrated that TDR has the potential to register variations in
snow liquid water content down to 1–2 vol. % by fitting an empirical model to seasonal snow of a
higher density (350 kg/m3). Moreover, Lundberg concluded that continuous registration of
snowpack wetness with acceptable spatial resolution (approximately 5 cm) was possible to achieve
with several sets of probes—mounted with 3 cm vertical and 5 cm horizontal spacing—combined
with a multiplexer and a storage unit to record the data. Additionally, a more recent study by
Waldner et al. (2001) makes use of literature on the dielectric properties of snow by Looyenga
(1965), Tiuri et al. (1984), and Frolov and Macharet (1999) to calibrate two newly developed TDR
sensors to estimate snow wetness and density. Consequently, Waldner et al. (2004) make use of
the TDR equipment described by Schneebeli et al. (1998) to derive the dielectric permittivity of
snow (and its LWC) using the algorithm described in his previous study (Waldner et al., 2001).
Ultimately, the efforts by Waldner et al. demonstrated new instrument setups that make use of
TDR to estimate snow density and LWC.
To our knowledge, there is no existing literature on the usage of the CS650 TDR sensor to provide
snow LWC measurements. Furthermore, most of the snow TDR studies mentioned previously
have been conducted manually, not in automated, continuous fashion, nor has an in-situ seasonlong, field-withstanding instrument that provides the LWC and temperature profiling (at different
depths above the soil surface) of the snowpack simultaneously been developed. Therefore, the
SWP will be a novel contribution as an alternative to execute year-round, automated, undisturbed
in-situ snow LWC measurements, and provide insight on the snowpack state (e.g., dry, moist, wet)
at different snowpack heights above the soil surface. The SWP was developed using two arrays of
low-cost (approximately $400 per array; will depend on quantity of reflectometers) and -power
consuming, easily-assembled (reflectometers come ready to be used, no need for prior setup) and
–installed (reflectometer instructions provide all the information needed for cable connection to
datalogger) moisture reflectometers. SWP observations are automated and continuous.
Snow Thermal Model (SNTHERM) LWC simulations forced with in-situ meteorological data
were used to evaluate the accuracy of the instrument due to the lack of LWC in-situ observations
at the study site. In order to cross-validate the accuracy of SNTHERM LWC simulations, these
were compared to LWC estimates obtained using empirical formulas developed in previous studies
by Topp et al. (1980), Denoth et al. (1984), and Tiuri et al. (1984). Additional contributions to
100
snow TDR and hydrology are presented in the form of the development of two (for dry and wet
snow) statistical relationships between snow LWC and dielectric permittivity of similar nature to
Topp’s equation for the LWC of mineral soils.
6.2
Time-domain reflectometry
Time domain reflectometry is a highly accurate and automatable method for the determination of
the LWC of porous media and its electrical conductivity (Jones et al., 2002). LWC is inferred from
the dielectric permittivity of the medium, whereas electrical conductivity is inferred from TDR
signal attenuation. In a fairly simple approach, empirical and dielectric mixing models are used to
relate a medium’s LWC, dielectric permittivity, and density. In some cases, the relationship
between LWC and dielectric permittivity requires individual calibration when dealing with nonmineral (e.g., clay and organic matter, etc.) soil media or snow. Numerous TDR probe
configurations provide users with site- and media- specific options. Hence, continuous
developments in TDR technology and in other dielectric methods offer the promise for less
expensive and more accurate tools for the electrical determination of LWC.
Time domain reflectometry is related to the measurement of the relative complex dielectric
constant, which is a component of the capacitance (Stein and Kane, 1983). The capacitance is a
constant of proportionality that relates the potential difference between conductors to the amount
of equal, but opposite electric charges in each of them. Capacitance is quite dependent on the
geometry of the two conductors and the relative complex dielectric constant (Markus, 1966).
However, the relative complex dielectric constant (Equation (28)) is variable for most materials;
it has a real and an imaginary part; both frequency dependent (Topp et al., 1980):
‫ ܭ‬ൌ ‫ ܭ‬ᇱ ൅ ݆ሼሺߪௗ௖ Ȁ߱ߝ଴ ሻ‫ܭ‬dzሽǡ
Equation 28
where ‫ ܭ‬complex dielectric constant; ‫ ܭ‬ᇱ real dielectric constant; ‫ܭ‬dz dielectric loss; ߪௗ௖
conductivity; ߱ angular frequency; ߝ଴ permittivity of free space; and ݆ = (−1)1/2.
Thus, the complex dielectric constant of a material can be determined from the propagation of a
pulse along a transmission line. The velocity of a pulse (‫ݒ‬௣ ) along a transmission line is given by:
101
‫ݒ‬௣ ൌ ‫ܮ‬௥ Ȁ‫ݐ‬ǡ
Equation 29
where ‫ܮ‬௥ , is the physical length of the transmission line (or length of the probe) and ‫ ݐ‬is the time
of propagation. Furthermore, distributed circuit analysis dictates that at high frequencies, and for
non-magnetic materials (Stacheder et al., 2009):
‫ݒ‬௣ ൌ ܿȀ‫ ܭ‬ଵȀଶ ǡ
Equation 30
The combination of both equations yields:
‫ ܭ‬ൌ ሺܿ‫ݐ‬Ȁ‫ܮ‬௥ ሻଶ ǡ
Equation 31
where ‫ܮ‬௥ is the length of the line set by the user, ܿ is the velocity of an electromagnetic wave in
free space, and ‫ ݐ‬is determined using the time domain reflectometer. Time domain reflectometry
measures both the real and imaginary parts of the complex dielectric constant (as shown in
Equation (28)). As such, the term “apparent dielectric constant” ሺ‫ܭ‬௔ ሻ is sometimes used. However,
for low loss materials (i.e., snow), ‫ ܭ‬ൌ ‫ ܭ‬ᇱ and henceǡ ‫ܭ‬௔ ൌ ‫ ܭ‬ᇱ (Stein and Kane, 1983; Stein et al.,
1997; Lundberg, 1997; Markus, 1966). Therefore, in this paper the dielectric constant refers only
to the real part.
In short, a TDR measurement unit consists of a pulse generator (generating a step pulse, which is
being transformed to a lower frequency), a registration unit (an oscilloscope for commercially
available TDR units) and one or several sets of rods (probes) mounted parallel in the studied
medium. The dielectric constant (electrical permittivity) can be determined from the velocity of
propagation of an electromagnetic wave through a medium. The generated pulse is reflected when
it reaches the end of the rods. The travel time of the reflected pulse is a function of the dielectric
constant of the surrounding medium. Because the difference in dielectric constant between water
(Kw~80) and ice (KI~3) is significant at the 1 MHz to 1 GHz range, the dielectric constant is
primarily a function of the liquid water content of the snow (Tiuri et al., 1984; Lundberg, 1997;
Waldner et al., 2001; Looyenga, 1965). Additionally, density variations in the snow have some
influence in dielectric constant measurements due to the difference between the dielectric
102
constants of air (KA = 1) and ice (KI~3) (Lundberg, 1997). This is particularly true for wet snow
because it is a mixture of ice crystals, liquid water, and air.
6.3
CS650 time-domain reflectometer
The CS650 (Campbell Scientific, Logan, UT, USA) is a multi-parameter sensor that uses TDR to
measure the liquid water content and electrical conductivity of soils and other porous media.
Additionally, it measures the temperature of the medium via a thermistor in contact with one of
the rods. It consists of two 30-cm-long (3.2 mm diameter and 3.2 cm spacing) stainless steel rods
connected to a printed circuit board. The circuit board is encapsulated in epoxy, and a shielded
cable is attached to it for datalogger connection. A five conductor cable including the drain or
shield wire is used to provide power and ground as well as serial communication with the CS650.
The CS650 is intended to communicate with SDI-12 recorders, including Campbell Scientific
dataloggers (Scientific, 2016). The CS650 measures propagation time (converted to period),
electrical conductivity and signal attenuation, and temperature (Scientific, 2016). Dielectric
permittivity and liquid water content are then derived from these raw values. Period, electrical
conductivity, and signal attenuation are converted to dielectric permittivity (Scientific, 2016).
Liquid water content is obtained as a function of the medium’s dielectric permittivity with
empirical formulas. This is discussed in Section 6.5.
Because the CS650 is a time-domain reflectometer, its fundamental principle is that the velocity
of electromagnetic wave propagation along the probe rods is dependent on the dielectric
permittivity of the material surrounding the rods, as discussed in Section 6.2. In order for the
CS650 to perform a measurement, a differential emitter-coupled logic (ECL) oscillator on the
circuit board is connected to the two parallel stainless steel rods. The differentially driven rods
form an open-ended transmission line in which the wave propagation velocity is dependent upon
the dielectric permittivity of the media surrounding the rods. An ECL oscillator state change is
triggered by the return of a reflected signal from the end of one of the rods. Digital circuitry scales
the high-speed oscillator output to an appropriate frequency for measurement. CS650 accuracy
and precision for soil temperature, dielectric permittivity, and LWC measurements are presented
in Table 12.
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Table 12. CS650 operational specifications for soil temperature, dielectric permittivity, and LWC.
Parameter
Temperature
CS650 Operational Specifications
Accuracy
Precision
±0.5 °C
±0.02 °C
Dielectric permittivity ±(2% of reading + 0.6)
Liquid water content
6.4
±3%
<0.02
<0.05%
Snow Wetness Profiler setup
The SWP (Figure 13) was built with fourteen (14) CS650 soil water content reflectometers every
15 cm—all the way up to 90 cm—following, to some extent, the design by Lundberg (1997). The
assembly consists of reflectometers attached to steel rods and is made up of two (7 reflectometers
each) vertical profiles executing parallel measurements with a 1-h temporal resolution. The idea
of having parallel observations is mainly to have backup measurements in case of instrument
failure, but it also provides some spatial variability to the snow LWC measurements. The
development of the SWP provides, aside from a cost-efficient, non-destructive way to measure the
LWC of snow, the user with the capability to investigate the temporal variability of snow wetness
throughout the winter. The SWP has also the capability of measuring the snowpack temperature,
providing a vertically-distributed temperature profile.
The operational principle of the sensor is quite simple. When open to the air, the CS650 records
the air permittivity, which is one (1). However, when in contact with a porous medium, the
instrument records the permittivity (non-one number) of the medium, in this case snow. The
instrument was installed on 6 February 2014. At the time, there were around 60 cm of snow in the
ground at the station. The results shown in Section 6.8 comprise observations from (what are
considered) two winters: 6 February 2014 to 22 April 2014 (from installation to when the
snowpack melted in its entirety) and 24 November 2014 to 29 January 2015 (following winter
until datalogger stopped recording; this is discussed in Section 6.8). It should be noted that the
snowpack was disturbed during the installation process because some snow had to be removed in
order to set up the SWP. The removal of the snow left the snowpack open to the air. While the
specific day of installation was significantly cold (regularly conducive to a dry snowpack), this
exposure might have altered the snowpack’s moisture. Nonetheless, all CS650 reflectometers were
104
inserted into the snowpack during this process to make sure these were in contact with the snow,
not the air. However, it is acknowledged that this issue could potentially lead to errors due to the
presence of air bubbles between the probe rods and the snow, and cause additional snowmelt when
the air is warmer than the snowpack. This is discussed in detail in Sections 6.8 and 6.9.
Lastly, the CS650 information is stored on a datalogger (CR 3000) at CREST-SAFE. The CR 3000
was designed for stand-alone operation in harsh, remote environments. The orange Rx wire in the
reflectometers can be used to communicate by means of RS-232 Tx/Rx. The A200 USB-to-Serial
Module allows RS-232 serial communication between a computer and the CS650 by means of
Campbell Scientific’s Device Configuration Utility (DevConfig) software.
6.5
Obtaining LWC from dielectric constant measurements via empirical formulas
Campbell Scientific recommends the use of Topp’s equation (Equation 32) to obtain LWC
measurements as a function of the dielectric constant of the medium, as measured by the CS650
probes. Topp et al. (1980) describe (empirically) the relationship between dielectric permittivity
and LWC in mineral soils with a 3rd degree polynomial. With ߠ௪ the liquid water content and ‫ܭ‬
the dielectric permittivity of the soil, the equation presented by Topp et al. is:
ߠ௪ ൌ െͷǤ͵ ൈ ͳͲିଶ ൅ ʹǤͻʹ ൈ ͳͲିଶ ൈ ‫ܭ‬Ȃ ͷǤͷ ൈ ͳͲିସ ൈ ‫ ܭ‬ଶ ൅ ͶǤ͵ ൈ ͳͲି଺ ൈ ‫ ܭ‬ଷ.
Equation 32
To our knowledge, an equation of similar nature to Topp’s has not been developed for snow due
to its heterogeneity and metamorphic changes over time. The studies discussed previously have all
focused on developing their own empirical formulas (or using existing formulas) that relate snow
dielectric permittivity and density to its LWC. For most mineral soils, Campbell Scientific states
that Topp’s equation can be used to obtain LWC estimates using the CS650 dielectric permittivity
measurements. However, they suggest a user-derived calibration for other media by describing the
relationship between medium permittivity and liquid water content by a quadratic equation or a
third order polynomial, much like Topp et al., depending on the number of data points and
particular case. Data points should be spaced as evenly as practical over the expected range of
LWC and include the wettest and driest expected values. In this paper, Equation (32) was used
without any calibration due to the lack of in-situ LWC measurements at the CREST-SAFE station.
Because of this issue, and the fact that the equation presented by Topp et al. (1980) was developed
105
for mineral soils and does not take into account the effects of snow density on the dielectric
constant and, indirectly, the LWC of the medium, empirical equations by Denoth et al. (1984,
1989):
‫ܭ‬௥ ൌ ‫ ܭ‬െ ͳ െ ͲǤͲͲͳͻʹ ൈ ߩ௦௡௢௪ െ ͲǤͶͶ ൈ ͳͲି଺ ൈ ߩ௦௡௢௪ ଶ ,
Equation 33
ߠ௪ ൌ െʹͲǤ͹͹͹ ൅ ඥʹͲǤ͹͹͹ଶ ൅ ʹʹʹǤʹʹʹ ൈ ‫ܭ‬௥ ,
Equation 34
where ‫ܭ‬௥ is the dielectric constant reduced for variations in snow density ߩ௦௡௢௪ , and Tiuri et al.
(1984):
‫ܭ‬ௗ ൌ ͳ ൅ ͳǤ͹ ൈ ߩௗ ൅ ͲǤ͹ ൈ ߩௗ ଶ ,
ߠ௪ ൌ ହ
଻ଶ
ξʹͺͺͲͲ ൈ ο‫ ܭ‬൅ ͹ͻʹͳ െ ͺͻ,
Equation 35
Equation 36
where ‫ܭ‬ௗ is the dielectric constant under dry snow density ߩௗ conditions, and ο‫ ܭ‬is the increase
in permittivity due to wet snow conditions, were used as well. The empirical equations developed
by Denoth et al. and Tiuri et al. have been validated in more recent snow studies (Stein et al., 1997;
Lundberg, 1997; Schneebeli et al., 1998, Waldner et al., 2001, 2004). Their results have shown
that these empirical equations can, along with TDR, be used to provide LWC estimates within an
accuracy of 1%–2% when compared to in-situ observations. The comparison between LWC
estimates using Equations (32), (34) and (36) was done in order to remediate the fact that actual
in-situ LWC measurements were missing at the station, as discussed in Section 6.1. The general
idea is to cross-compare the three (3) LWC estimates obtained from these empirical equations with
SNTHERM-simulated LWCs to see whether the model simulations are precise by comparing them
with three different sources of LWC estimations.
6.6
Liquid water content simulations using SNTHERM
SNTHERM is a freely available, Fortran-written, one-dimensional snowpack physical model that
simulates snowpack properties and was first released on 1989. Since its origin, it has been
enhanced multiple times to improve its algorithms (Jordan, 1991). SNTHERM is energy and mass
balance-driven. It has been used in several validation studies such as: snowpack spectral signature
(Davis et al., 1993), snow melting processes (Rowe and Kuivinen, 1995), energy balances at
106
regional scales, as well as discrete point scales, and for “under the canopy” snow (Cline, 1997;
Hardy et al., 1998). A simplified version of the model is currently operational for snow mapping
and forecasting in the United States (Rutter et al., 2008; NOHRSC-ISI, 2016; Hardy et al., 2001)
and Bosnia (Melloh et al., 1997). SNTHERM was developed using as foundation the mass and
energy-balance snow model of Anderson (Anderson, 1976). The vertical water movement is based
on the work done by Colbeck (1979), in which the effective saturation of snow is a function of the
current saturation level and the irreducible water saturation. Colbeck developed a flow model that
accounts for multiple flow paths, transient ponding of water on ice layers, flow down distinct flow
channels, and background flow simultaneously. He considered that the infiltration of liquid water
through the ice layers is best described in a straightforward manner using his gravity flow theory
(Colbeck, 1972), but the movement of the water in the flow channels is somewhat more
complicated. Colbeck explained that flow channels are generated when water entering a dry, cold
snow develops “fingers” that propagate ahead of the background flow leaving areas of cold, dry
snow behind, and that the liquid water saturation in snow is too low for fingers to develop
spontaneously simply from a heavier fluid (water) displacing a lighter fluid (air). Therefore, he
hypothesized that the fingers are caused by the many crusts and ice layers normally present in
highly stratified snow covers. This situation occurs many times in most snow covers because wind
and melt crusts often mark the horizon between snow from separate storms. After flow fingers are
established by the first movement of water through a snow cover, these original flow channels
become preferential paths for future waves of infiltrating water due to the grain growth and
permeability increase associated with the presence of liquid water in snow. However, on the scale
of days or weeks leading to seasonal snow melt-off, the heterogeneous nature of the flow field is
an important feature of most seasonal covers. The problems of multiple flow paths are complicated
by the temporary ponding of water on individual ice layers. Hence, the volume of ponded water
per unit width is calculated for a horizontal ice layer undergoing a steady balance of inflow and
discharge to regularly spaced drains. He then concluded that, if the ice layer is sloping, if water is
seeping simultaneously through the ice layer, or if transient effects are important, the volume of
ponded water has to be adjusted accordingly. Thus, water in the snowpack propagates at a rate
dependent on the flux ahead and behind the flow going directly through the ice layers (Colbeck,
1979). However, the fluid flow model mentioned previously assumes horizontal homogeneity in
the snow cover. In reality, seasonal snow covers that are undergoing freeze-thaw cycles, or that
107
are subject to strong winds, develop crusts and ice layers, which complicate flow pattern. Thus,
perforations arise in the crusts through which fingers of water flow at a much faster rate than
through the crust itself (Colbeck, 1979). Field observations by Marsh and Woo (1984a) of runoff
rates from ripe snow in the Canadian Arctic showed that almost half the daily flow can be carried
by fingers or flow channels that move ahead of the background front. They also developed a
simulation model that incorporates the phenomenon of fingering (Marsh and Woo, 1984b). Later,
Schneebeli (1995) showed that the location of fingers may not be stable in time and space.
Additionally, more recent interpretations of preferential flow by Katsushima et al. (2013) and
Hirashima et al. (2014) have demonstrated that flow fingers can develop even in isothermal
conditions, and that ponding may allow to reach the necessary large concentrations of water.
Within SNTHERM, snowpack layer densification is calculated based on three (3) main processes:
destructive metamorphism or overburden compaction, constructive metamorphism or vapor
movement and grain size change, and melt metamorphism or the gravitational water movement
inside the snowpack (Anderson, 1976; Mellor, 1977; Kojima, 1967; Kattelmann, 1986). The first
two are merged into an overall compaction rate and the third metamorphism type is calculated
based on the water balance. Destructive metamorphism is calculated as a function of snow
viscosity (Mellor, 1977; Kojima, 1967). Constructive metamorphism is a function of temperature
and it is a process that has a faster rate when new snow density is greater than the density limit
constant (Anderson, 1976). As stated by the Special Report 91-16 of the United States Army Corps
of Engineers (1991), and later on reported by Melloh (1999), the SNTHERM numerical solution
is obtained using a variable grid of snow layers, each layer being governed by heat and mass
balance equations. The model uses a control volume numerical procedure (Patankar, 1980) for
spatial discretization that allows for the compaction of the snow. Lastly, a Crank-Nicholson central
difference scheme is used to solve the partial differential equations in the time domain.
CREST-SAFE experiment is a long-term field campaign where meteorological variables and
snowpack properties are measured. The measured meteorological variables at the station are: air
temperature, solar radiation, relative humidity, and wind speed and direction. The only
meteorological parameter that is not measured at CREST-SAFE (that is needed for simulation
purposes) is precipitation. Therefore, it was obtained from the National Weather Service (NWS)
Station named KCAR (NESDIS GHCN-D, 2016), located near (approximately 90 m away) the
CREST-SAFE site at the Caribou Municipal Airport in Caribou, ME. The NWS uses the All
108
Weather Precipitation Accumulation Gauge (AWPAG), instead of the traditional Heated Tipping
Bucket (HTB) technology, in their Automated Surface Observing System (ASOS) stations to
measure precipitation data. The AWPAG is essentially a weighing gauge where precipitation
continuously accumulates within the collector, and as the weight increases, precipitation is
recorded. The AWPAG has an 8-foot diameter outer shield to mitigate the wind effects on
precipitation readings. Additionally, a transfer function provided by the World Meteorological
Organization (WMO) is used to correct the precipitation measurements for undercatchment using
daily average wind speed and maximum temperature observations performed by the ASOS station
as well (Dover, 2007). SNTHERM needs two precipitation parameters as input: precipitation water
equivalent and precipitation type (rain or snow). Both variables were given to the model as
obtained from the NWS precipitation records—these provide both the liquid and solid precipitation
snowfall data. The precipitation deposition scheme to obtain the new snow height as solid
precipitation accumulates over the snow surface is performed by SNTHERM based on its built-in
algorithm (Jordan, 1991). Additional calibration parameters (i.e., irreducible water content for
snow (0.017), density of new snow (73 kg/m3), density limit for compaction of snow (96 kg/m3),
and the viscosity coefficient for overburden compaction (6.9 × 105 kg·s/m2)) needed by
SNTHERM to simulate the deposition scheme were established based on previous studies (Jordan,
1991; Anderson, 1976; Mellor, 1977; Kojiima, 1967; Kattelmann, 1986; Corona et al., 2015).
CREST-SAFE provides all of its meteorological data in an hourly time step via an automated
routine (Lakhankar et al., 2013), whereas the NWS provides precipitation data in 15-min time
steps. Naturally, the NWS precipitation data was aggregated to hourly time intervals. Hence, by
weather-forcing SNTHERM with the meteorological dataset at CREST-SAFE, layered hourly
simulated snowpack properties (i.e., LWC, depth, grain size, density, temperature, and SWE) for
the station were obtained for the period of this study.
It should be noted that Corona et al. (2015) validated SNTHERM snowpack simulations (forced
with CREST-SAFE in-situ meteorological data) with three years (2010–2013) of CREST-SAFE
in-situ snowpack observations. More specifically, the SNTHERM evaluation was performed on
properties such as: snow depth, SWE, density, temperature, and grain size, in addition to a layerby-layer comparison of the snowpack properties. SNTHERM outputs showed high agreement with
the observed data in properties like snow depth (R = 0.84), SWE (R = 0.77), density (R = 0.80),
snow surface temperature (R = 0.98), and average snowpack temperature (R = 0.75). Conversely,
109
the model was not very efficient when simulating properties like layer temperature (R = 0.54) and
grain size (R = 0.60). Generally, SNTHERM appeared to simulate all snowpack properties closer
to the snow surface better than those closer to the snow-ground interface. Additional studies by
Lakhankar et al. (2013) and Koivusalo and Heikinheimo (1999) have also shown good agreement
between various SNTHERM simulated snowpack properties and in-situ observations. Lakhankar
et al. demonstrated high agreement between bulk snow density (R = 0.97) and average grain size
(R = 0.96) SNTHERM simulations and CREST-SAFE in-situ observations. The differences in
agreement between the studies by Corona et al. and Lakhankar et al. can be attributed to the fact
that, in the former, the model vs. ground truth comparison was done at a layer-by-layer basis,
whereas, for the latter, it was done with snowpack averages. Averaging snowpack properties will
attenuate extreme (minimum and maximum) values in the dataset. Koivusalo and Heikinheimo
compared SNTHERM simulations with in-situ data from the Sodankylä Meteorological
Observatory in Northern Finland. The results demonstrated high agreement between simulated and
in-situ snowpack properties such as: snow albedo, temperature, depth, SWE, and melt outflow.
The proven good agreement between SNTHERM simulations and in-situ snowpack properties, the
CREST-SAFE-SNTHERM validation results by Corona et al., and the lack of in-situ LWC
measurements at the station led to the idea of using SNTHERM LWC simulations in this study.
While, to our knowledge, SNTHERM LWC simulations have not been validated directly, we
understand that the high agreement between SNTHERM and in-situ data for other snowpack
parameters (i.e., depth, SWE, and density) shown in previous validation efforts provides sufficient
evidence indicating that the SNTHERM LWC simulations (forced with in-situ meteorological
parameters) are, in fact, accurate. Firstly, because snow density has been described by snow
hydrologists as the ratio between SWE and snow depth (indicating an intrinsic relationship
between all three snow parameters), and, more importantly, because—in a simplistic approach—
SNTHERM LWC simulations at each node (layer) ߠ௪௜ are calculated using the ratio between nodal
liquid water bulk density ɏ௪௜ and nodal bulk snowpack densityߩ௦௜ :
110
ߠ௪௜ ൌ ஡ೢ೔
ఘೞ೔
,
Equation 37
both of which are reliant on the SNTHERM calibration parameters (irreducible water content for
snow, density of new snow, density limit for compaction of snow, and the viscosity coefficient for
overburden compaction) that produced good validation agreement with the CREST-SAFE snow
depth, SWE, and density observations, as stated previously. Each node containing a specific
thickness; all amounting up to the total snowpack depth (n is the number of nodes/layers) and,
consequently, LWC ߠ௪ at its pertinent time step (every hour, in this study):
ߠ௪ ൌ σ௡௜ୀଵ ߠ௪௜ .
Equation 38
Thus, accurate SNTHERM LWC simulations will be highly dependent on the already proven
accurate snow depth, SWE, and density simulations. However, the mass contribution of liquid
water in snow is small, albeit important for hydrology. Hence, good snow density reproduction
may be (at least partially) insufficient to infer that LWC and, equally important, liquid water
location within the snowpack are also well reproduced. Instead, these issues might generate
uncertainties in SNTHERM LWC simulations. For this reason, possible sources of model
uncertainty, as related to the results in Section 6.8, will be discussed in Section 6.9.
It should be mentioned actual SNTHERM node/layer (not bulk) snow LWC values were compared
with LWC estimates at single layer depths. The process consisted of finding the cumulative (sum
of node/layer thicknesses) snow depth that would lead to the specific SWP sensor height, then the
SNTHERM-simulated LWC at that node was extracted and used for comparison with LWC
estimates by the three empirical formulas. SNTHERM bulk snow density computations were only
discussed because these are part of its density simulation procedure.
Note: The irreducible water content for snow is the minimum amount of water that a layer of snow
can hold; controlling evaporation and sublimation in the snowpack. Density of new snow is the
assumed density for snow precipitation. Density limit for compaction of snow is the upper limit
on destructive metamorphism compaction. Lastly, the viscosity coefficient controls the
compaction rate of the snowpack due to overburden.
111
6.7
Evaluation Criteria
Three criteria were used in order to eliminate certain erroneous conclusions that could result from
the use of one single evaluation criterion (James and Burges, 1982). These were: the Root Mean
Square Error (RMSE), Mean Absolute Error (MAE), and the correlation coefficient R. The
selected evaluation criteria are widely used throughout the scientific community. Simultaneous
analyses of these indexes will define the accuracy of the developed instrument. Generally, larger
RMSE and lower R values are associated with more significant errors and poor agreement between
the SWP and SNTHERM LWC estimates. Henceforth, there will be four (4) LWC annotations.
These are: LWCSNTHERM, LWCTopp, LWCDenoth, LWCTiuri; where each subscript makes reference
to the model or equation these come from, as described in Sections 6.5 and 6.6. The RMSE is
computed as shown below:
ܴ‫ ܧܵܯ‬ൌ ට
σሺ௒೚್ೞ ି௒ೞ೔೘ ሻమ
௡
Equation 39
,
where ܻ௢௕௦ is LWCTopp, LWCDenoth, or LWCTiuri, ܻ௦௜௠ is LWCSNTHERM, and ݊ is the number of
observations.
The MAE is calculated as follows:
ଵ
‫ܧܣܯ‬ሺΨሻ ൌ σ௡௜ୀଵหܻ௦௜௠ െ ܻ௘௫௣ ห,
௡
Equation 40
where ܻ௘௫௣ is LWCTopp, LWCDenoth, or LWCTiuri and ܻ௦௜௠ is LWCSNTHERM.
While the correlation coefficient R is obtained as follows:
ܴ ൌ
ത
ത
σ೙
೔సభሺ௑೔ ି௑ ሻൈሺ௒೔ ି௒ሻ
೙ ሺ௑
ത ሻమ ൈටσ೙ ሺ௒೔ ି௒ത ሻమ
ටσ೔సభ
೔ ି௑
೔సభ
,
Equation 41
where ܺ௜ is LWCTopp, LWCDenoth, or LWCTiuri, ܻ௜ is LWCSNTHERM, ܺത is the mean of the X dataset,
and ܻത is the mean of the Y dataset.
112
6.8
Results
6.8.1 Evaluating the SWP’s capability of estimating LWC and developing new statistical
relationships for different snow conditions
The CREST-SAFE Snow Wetness Profiler in-situ dielectric permittivity and snowpack
temperature measurements at different depths (15, 30, 45, 60, and 75 cm) above the soil surface,
along with snow depth and near-surface air temperature data from the station, and SNTHERM
melt rate and cold content simulations for winter (6 February–22 April) 2014 are illustrated in
Figure 36. It should be mentioned that the above isothermal temperatures (and respective dielectric
permittivity values) recorded by the sensors are attributed to these being over the snow surface and
exposed to the air temporarily. These observations are presented in Figure 36, but were eliminated
from the analysis, as temperature in snow can only be lower than or equal to 0 °C.
113
Figure 36. Snow Wetness Profiler snowpack dielectric permittivity (a) and temperature (b) measurements
at different depths (15, 30, 45, 60 and 75 cm) above the soil surface at CREST-SAFE for winter (6
February–22 April) 2014; The third panel (c) illustrates snow depth (ultrasonic depth sensor) and nearsurface air temperature (temperature and relative humidity probe) observations also collected at CRESTSAFE for the same period of time; The bottom panel (d) shows SNTHERM snowpack melt rate and cold
content simulations obtained by weather-forcing the model with CREST-SAFE in-situ meteorological data
for the same time interval. All data are hourly.
As shown in Figure 36, the SWP is capable of reflecting changes in dielectric permittivity (Figure
36a) due to some melting events (e.g., 6–15 April 2014) (Figure 36c; changes in snowpack depth)
and wetter periods with isothermal snowpack temperatures (most of April 2014) (Figure 36b).
Hence, increases in snowpack temperature were consistent with those in dielectric permittivity,
114
and vice versa. Snowpack temperature is affected because the seasonal snowpack grows in layered
structure, causing heterogeneity, with each layer having different physical and mechanical
characteristics. Then, the snowpack gets stratified because of successive snow events throughout
the winter season. Hence, each snow event encounters a different set of meteorological parameters
at the time of its occurrence and afterward. The snow continuously interacts with the environment
and exchanges energy with the atmosphere above it and the ground below. These energy exchange
processes set up the temperature distribution within the snowpack, which in turn is responsible for
its metamorphic changes (in dielectric permittivity and LWC) with time (Prihodko, 1997; Datt et
al., 2008; Lundquist and Lott, 2010). Hence, the combination of above freezing temperatures
during daytime with below freezing temperatures at night cause multiple freezing and melting
events within the snowpack during the melting period. Additionally, daytime solar radiation causes
snowmelt in the uppermost layer that produces higher dielectric permittivity and LWC in the
superior layers of the snowpack. Furthermore, snowpack condition is considerably affected by air
temperature. Previous studies (Techel and Pielmeier, 2011; Lu et al., 2012, Chen et al., 2013) have
shown that snow dielectric permittivity and LWC produce a significant and positive correlation
with air temperature changes. These studies demonstrated that the average water content
exponentially increased with the average air temperature and linearly increased with accumulated
air temperature. This is confirmed by comparing Figures 36a–c, where air and snowpack
temperature changes are significantly similar and linearly correlated, and dielectric permittivity
changes are positively correlated with these two parameters.
However, LWC (and permittivity) changes can only be partially explained by temperature
gradients. Hence, SNTHERM-simulated energy- (cold content) and mass-related (melt rate)
snowpack parameters were included in Figure 36d to expand this analysis. The cold content of the
snowpack is the energy required to bring the temperature of a dry snowpack to the temperature of
melt (0 °C) (Marks et al., 1999). This is a useful concept to interpret the delay between air
temperature raising above 0 °C and actual melt outflow of a snowpack. Snowpack melt rate is
associated with the amount of meltwater that will percolate through the snowpack and, ultimately,
reach the soil. Generally, the meltwater produced at the surface percolates downwards through the
snowpack. Because the speed of the percolation increases as the melt rate increases, water
produced during the peak melt period overtakes water produced earlier in the day, such that the
diurnal melt wave at successively deeper depths develops a sharp wave front. The time lag between
115
the timing of peak surface melting and peak water output through the bottom of the snowpack
increases with the depth of the snowpack (Dingman, 2002). Hence, e.g., a high cold content (and
non-existent or low melt rate) can explain constant permittivity values during the pre-snowmelt
period (no melt, just an increase in snowpack temperature). This is evidenced in Figure 36 by the
mostly constant dielectric permittivity values associated with significantly low melt rate and high
cold content from early-February to late-March. Conversely, increases in melt rate (combined with
a shallower snowpack) and low cold content can be identified with higher dielectric permittivity
values, and higher snowpack and near-surface air temperatures for the month of April.
According to Figure 36, during the pre-snowmelt periods, air temperature gradually increased and
dielectric permittivity variations were relatively small due to high cold content and low melt rate.
In this stage, the liquid water (at low melt rate) moves from the upper layer to the next layers and
accumulates in the coarse snow layer (Techel and Pielmeier, 2011; Lu et al., 2012; Chen et al.,
2013). Throughout the mid-snowmelt periods, the dielectric permittivity variation was drastic, as
well as the changes in melt rate. The dielectric permittivity from the bottom layers (15, 30, and 45
cm) of the snowpack were smaller than those in the upper layers (60 and 75 cm). The variation
was also smaller and more stable. During this period, liquid water is discharged from the snowpack
(Techel and Pielmeier, 2011; Lu et al., 2012; Chen et al., 2013). Dielectric permittivity seemed to
decrease during snowfall and the following one to two days. Lastly, during the late-snowmelt
periods, the dielectric permittivity and temperature distribution and variation of every snow layer
showed a uniform trend, and liquid water seemed to be moving to the next layer (at high melt rate).
Lastly, it is easy to identify warmer melting snow temperatures (close to or at isothermal)
consistent with higher dielectric permittivity (up to 1.6) values. Conversely, a low dielectric
permittivity (~1) is congruent with either colder (<0 °C) snowpack temperatures or sensor
exposure to air due to snow completely melting at that sensor height.
The next step was to evaluate whether or not the SWP dielectric permittivity measurements can be
translated into accurate LWC estimates. In Figure 37, Snow Wetness Profiler LWC (y axis)
(LWCTopp, LWCDenoth, and LWCTiuri) vs. LWCSNTHERM (x axis) scatter plots for different depths
(15, 30, 45, and 60 cm) above the soil surface at CREST-SAFE for winter (6 February–22 April)
2014 are illustrated. Table 13 describes the SWP performance by means of RMSE, MAE, and R
values. In general, results indicate higher agreement between LWCSNTHERM and LWCTopp,
LWCDenoth, and LWCTiuri at the lower snowpack layers. This is congruent with the melting of the
116
snow layers closer to the snow surface due to daytime solar radiation and warmer air temperatures.
Results also positive correlations for all LWC estimates. Moreover, LWCDenoth appears to better
capture the LWC changes in the snowpack.
Figure 37. Snow Wetness Profiler (y axis) (estimated using Topp, Denoth, and Tiuri empirical formulas
and developed statistical relationships) vs. SNTHERM (x axis) LWC scatter plots for different depths ((a)
15, (b) 30, (c) 45, and (d) 60 cm) above the soil surface at CREST-SAFE for winter (6 February–22 April)
2014.
117
Table 13. Results from Snow Wetness Profiler LWC (estimated using Topp, Denoth, and Tiuri empirical
formulas) vs. SNTHERM LWC comparison at different depths (15, 30, 45, and 60 cm) above the soil
surface at CREST-SAFE for winter (6 February–22 April) 2014.
Topp
Layer
Depth
RMSE
MAE
(cm)
(%)
(%)
15
1.76
1.70
30
1.93
1.87
45
1.78
60
1.88
Denoth
RMSE
MAE
(%)
(%)
0.89
0.96
0.86
0.69
1.24
1.12
1.75
0.74
0.88
1.86
0.62
0.87
R
Tiuri
RMSE
MAE
(%)
(%)
0.89
1.88
1.80
0.89
0.68
1.91
1.81
0.46
0.79
0.74
1.98
1.92
0.74
0.79
0.62
2.13
2.06
0.62
R
R
Because the results seem to be influenced by numerous low LWC estimates and the onset of the
melt period (LWC > 2%) increases the permittivity and LWC scatter considerably, the
LWCSNTHERM values were divided into three snowpack categories/conditions: dry, moist, and
wet. The idea being to provide insight as to whether or not the high agreement between
LWCSNTHERM and LWCTopp, LWCDenoth, and LWCTiuri is mostly due to dry snow conditions.
The categories were selected based on a study by Fierz et al. However, we used three (instead of
five) snow LWC categories. We decided to modify our snow LWC categories to fit specific LWC
ranges because Fierz et al. defined their categories based mostly on manual (and physical)
descriptions of the snow conditions (e.g., snow grains’ tendency to adhere to each other when
pressed together, water not visible even at 10X magnification), but our study was executed
remotely in automated fashion. This made it impossible for us to have specific knowledge on snow
conditions like grain size and wetness. Instead, we followed the LWC ranges provided by Fierz et
al. and made some adjustments. Because it seemed nearly impossible for SNTHERM to provide
exactly 0% LWC, we decided to consider dry snow as snow with a LWC below 2%. Due to this
modification, we proceeded to adjust moist snow from 0%–3% (Fierz et al., 2009) to snow with a
LWC between 2%–4%. Lastly, we defined wet snow as snow whose LWC is over 4%.
Additionally, categories like ‘very wet’ and ‘slush’ were also considered to be (because they are)
wet snow. The results (RMSE, MAE, and R) of the snow categorization comparison are shown in
Table 14 by comparing LWCSNTHERM with LWCTopp, LWCDenoth, and LWCTiuri for different
snow conditions. Results indicate that there is higher agreement between LWCSNTHERM and
LWCTopp, LWCDenoth, and LWCTiuri whenever the snow is dry or wet, with low agreement for moist
118
snow conditions. This clearly showed some limitations on all three empirical formulas that cannot
capture the different behavioural patterns between dry and wet snow.
Table 14. Results from Snow Wetness Profiler LWC (estimated using Topp, Denoth, and Tiuri empirical
formulas) vs. SNTHERM LWC comparison for different snowpack conditions (dry, moist, and wet) at
CREST-SAFE for winter (6 February–22 April) 2014.
Topp
Denoth
Tiuri
LWC (%)
RMSE (%)
MAE (%)
R
RMSE (%)
MAE (%)
R
RMSE (%)
MAE (%)
R
0–2 (dry)
2.03
1.78
0.54
0.85
0.84
0.54
2.11
1.81
0.55
2–4 (moist)
5.13
4.68
0.20
5.70
5.25
0.18
5.34
4.85
0.19
>4 (wet)
2.24
1.75
0.59
1.99
1.48
0.59
3.23
2.45
0.57
Figure 38. SNTHERM simulated LWC (y axis) vs. SWP dielectric permittivity (x axis) scatter plot for all
depths (15, 30, 45, and 60 cm) above the soil surface combined at CREST-SAFE for winter (6 February–
22 April) 2014. Third-degree polynomial regressions were found to be the best fit for dry (LWC < 2%) and
wet (LWC ≥ 2%) snow conditions.
119
However, because SNTHERM LWC simulations appear to be precise when compared to the LWC
estimates obtained using all formulas, this led to the notion that perhaps new statistical
relationships between in-situ snow dielectric permittivity and LWC simulations can be developed
for different snowpack conditions. This way, even if unable to quantify the exact snow LWC,
perhaps these new statistical relationships can detect the onset of melt, medium and maximum
saturation of the snowpack. In Figure 38, all LWCSNTHERM (y axis) were plotted against their
respective observed SWP in-situ dielectric permittivity (x axis) for winter (6 February–22 April)
2014 at CREST-SAFE. After analysing the results obtained in Figure 38, we came to the
conclusion that only one threshold and two general snow behaviours were apparent. There seemed
to be dry snow (<2%) for dielectric permittivity values below or equal to 1.2 and wet snow (≥2%)
for dielectric permittivity values above 1.2. This was the reasoning behind the selection of this
threshold. There was no clear statistical relationship between moist snow and dielectric
permittivity. Hence, our general recommendation is for the user to create two statistical
relationships based on this dielectric permittivity threshold value. Naturally, as demonstrated in
Figure 38, the snow condition/LWC (dry or wet) threshold will be implicit. However, the snow
LWC threshold has nothing to do (statistically) with the development of the statistical
relationships. These were strictly created and validated using the dielectric permittivity threshold
value of 1.2. Two cubic polynomial equations were found to be the best fit to describe the
relationship between snow dielectric permittivity values and LWC for dry (<2% and permittivity
≤ 1.2) and wet (≥2% and permittivity >1.2) snow conditions. The statistical relationships are:
ߠ௪ିௗ௥௬ ൌ ͶͺǤͻͻͳͷ ൈ ‫ܭ‬௔ ଷ െ ͳͷ͹Ǥͷ͵͵ͻ ൈ ‫ܭ‬௔ ଶ ൅ ͳ͸ͺǤʹ͸ͷͷ ൈ ‫ܭ‬௔ െ ͷͻǤ͸ͳ͹ͺǡ Equation
42
(perm. ≤ 1.2)
ߠ௪ି௪௘௧ ൌ ʹͲǤͳ͵ͻ͵ ൈ ‫ܭ‬௔ ଷ െ ͹͵ǤͲ͸͵ͻ ൈ ‫ܭ‬௔ ଶ ൅ ͺͻǤ͹Ͳ͸͵ ൈ ‫ܭ‬௔ െ ͵ͶǤʹͺ͵͹ǡ Equation
43
(perm. > 1.2)
where ߠ௪ିௗ௥௬ is the LWC of dry snow, ߠ௪ି௪௘௧ is the LWC of wet snow, and ‫ܭ‬௔ is the dielectric
permittivity. The regression models exhibited correlations of R = 0.63 and R = 0.65 for dry and
wet snow, respectively. The calibration results for these statistical relationships are shown in
Figure 37. Henceforth, the LWC obtained using the new statistical relationships presented will be
referred to as: LWCNEW.
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6.8.2 Validating SWP and new Statistical Relationships
This section intends to tackle on two subjects. The first being the validation of the SWP with
CREST-SAFE 2015 data due to the fact that the sensors might have been partially exposed to the
air in winter 2014. The second subject is the validation of the new statistical relationships shown
in Section 6.8.1.
Dielectric permittivity can be difficult to calculate when the parallel rods are not completely
covered by snow. If the rods are exposed to the air, this produces a major (decreasing) effect on
the dielectric permittivity of the snow and can increase the error in LWC estimations (Stein et al.,
1997). While CREST-SAFE SWP 2014 data might have been affected by this phenomenon due to
the removal of snow in order to install the instrument, 2015 data should not have been disturbed
because no snow was removed around the SWP during that winter. As such, snow deposited
around the SWP completely and the CS650 sensors were fully-covered in snow. To study the
possible effects this might have had on SWP LWC estimates, Snow Wetness Profiler LWCTopp,
LWCDenoth, LWCTiuri estimates were obtained and compared with LWCSNTHERM for different
depths (15, 30, 45 cm) above the soil surface at CREST-SAFE for winter (24 November 2014–29
January 2015) 2015. Table 15 shows the SWP performance by means of RMSE, MAE, and R
values. Additionally, it demonstrates the performance of the new statistical relationships
(LWCNEW) by comparing them with LWCSNTHERM as well.
Table 15. Results from Snow Wetness Profiler LWC (estimated using Topp, Denoth, and Tiuri empirical
formulas and new statistical relationships) vs. SNTHERM LWC comparison at different depths (15, 30,
and 45 cm) above the soil surface at CREST-SAFE for winter (30 November 2014–29 January 2015) 2015.
Topp
Layer
Depth
RMSE
MAE
(cm)
(%)
(%)
15
2.49
2.45
30
2.48
2.45
45
2.42
2.41
Denoth
RMSE
MAE
(%)
(%)
0.65
1.62
0.49
0.67
1.07
0.20
0.69
0.95
0.23
R
Tiuri
RMSE
MAE
(%)
(%)
0.87
3.66
3.58
0.85
3.74
3.72
0.88
3.80
3.80
R
New
RMSE
MAE
(%)
(%)
0.53
0.64
0.15
0.82
0.54
0.71
0.42
0.78
0.52
0.92
0.55
0.77
R
R
LWCTopp and LWCDenoth indicate general high agreement with LWCSNTHERM at all snowpack
layers, with LWCDenoth showing better overall results again. This might be attributed to the fact
that LWCDenoth are not only reliant on dielectric permittivity, but are also snow density dependent.
On the other hand, LWCTiuri exhibits significantly high errors. This might be credited to the first
121
assumption the user has to make for dry snow density (200 kg/m3 in this study). Additionally, the
dry snow density value used in the equation by Tiuri et al. was different from that calculated by
SNTHERM in its subroutine (160 kg/m3). Though the difference is not particularly large, it is still
a source of uncertainty when comparing LWC Tiuri to LWCSNTHERM. Lastly, while it is known
that dry snow density values will vary during a season and between winters, we decided to keep
the same value for both winters to avoid additional uncertainties. It should also be noted that
Equations (33) and (34) use bulk snow density values. The bulk snow density is the average density
of the snowpack (obtained via in-situ total snow depth and SWE values in this study), and not the
snow density at each specific layer. Although the LWC estimates obtained with the equations by
Denoth et al. displayed high agreement with SNTHERM LWC simulations, this could potentially
present another source of error. Ideally, the layer snow density would be used in Equation (33) to
obtain more accurate LWC estimates. Results display positive correlations for all LWC estimates.
It should be mentioned that the CR3000 datalogger to which the SWP is connected stopped
working after 29 January 2015 and had to be sent for repairment to its manufacturer. The SWP
remained operational, but was not collecting data. From 24 November 2014 to 29 January 2015,
the snow depth never reached 60 cm. This explains why only three snowpack layers (15, 30, and
45 cm) are shown in Table 5. There appears to be more variability between the LWC estimates by
all empirical formulas when compared to winter 2014. However, these changes are not drastic
enough (RMSE and MAE differences are between 1% and 2%, depending on the empirical formula
used) to suggest that there was sensor overexposure to the air in 2014, nor that this exposure
affected the dielectric permittivity values in any way. Furthermore, the MAE differences are
smaller than those reported (2% or higher) by Lundberg (1997) when the contact between the snow
and sensor probes is influenced by air-gap formations. Hence, it is possible that these are
interannual differences.
LWCNEW RMSE and MAE values range from 0.64–0.92 and 0.15–0.55, respectively. While R
values varied from 0.77 to 0.82. All indicative of high agreement between LWCNEW and
LWCSNTHERM and in agreement with previous studies (Stein et al., 1997; Lundberg, 1997;
Schneebeli et al., 1998; Waldner et al., 2001). In general, LWCNEW appears to provide LWC
estimates with better accuracy than the other empirical formulas. However, since it is more
important to know whether or not the newly developed statistical relationships can estimate LWC
accurately for dry and wet snow conditions, the LWCSNTHERM values were divided into three (dry,
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moist, and wet) snowpack categories/conditions again, and the results were compared with
LWCTopp, LWCDenoth, LWCTiuri, and LWCNEW. The results (RMSE, MAE, and R) of the snow
categorization comparison are shown in Table 16. Results indicate that there is higher agreement
between LWCSNTHERM and LWCTopp, LWCDenoth, and LWCTiuri whenever the snow is dry or wet,
and lower agreement is exhibited for moist snow conditions. All three formulas yielded similar
results. Additionally, interannual comparisons do not demonstrate significant changes in
agreement between LWCSNTHERM and LWCTopp, LWCDenoth, and LWCTiuri on a yearly basis. Lastly,
when comparing LWCSNTHERM with LWCNEW, results indicated improvements over all LWC
estimations when using the new statistical relationships on different snow conditions. RMSE and
MAE values ranged from 1.95–2.97 and 1.71–2.73, respectively, and R values fluctuated from
0.33 to 0.67. These results demonstrated smaller errors and better correlations when compared to
the LWC estimates by all other empirical formulas for all three snowpack states. Furthermore, the
LWCNEW estimations displayed a must needed improvement over moist snow conditions; where
dielectric permittivity and LWC measurements tend to be less stable.
Table 16. Results from Snow Wetness Profiler LWC (estimated using Topp, Denoth, and Tiuri empirical
formulas and new statistical relationships) vs. SNTHERM LWC comparison for different snowpack
conditions (dry, moist, and wet) at CREST-SAFE for winter (30 November 2014–29 January 2015) 2015.
Topp
Denoth
Tiuri
New
LWC
RMSE
MAE
(%)
(%)
0–2
2.33
2.05
2–4
4.83
4.31
>4
2.51
2.19
(%)
RMSE
MAE
(%)
(%)
0.47
1.03
0.93
0.18
5.15
4.90
0.49
2.03
1.94
R
RMSE
MAE
(%)
(%)
0.51
2.17
1.83
0.20
5.27
4.92
0.53
3.05
2.56
R
RMSE
MAE
(%)
(%)
0.46
1.95
1.74
0.67
0.15
2.97
2.73
0.33
0.47
1.86
1.71
0.64
R
R
Lastly, a brief (TDR dielectric permittivity) cross-comparison (MAE and relative error (RE))
between the two SWP rods at different snowpack heights above the soil surface is illustrated in
Table 17. The general idea was to compare the two rods to—if the results were different—
potentially estimate the influence of contact loss between the snow and sensor probes (air gaps).
However, results indicate that both sensor arrays measured similar snow dielectric permittivity
values at different snowpack heights. In reality, the distance between the two sensor rods is
approximately 30–40 cm (quite a small margin to be considered conducive to significant spatial
123
differences). Naturally, it seems logical then to think that both sensor rods faced (close to) identical
conditions throughout the period of study. This was further evidenced by the online webcams we
have at the site that allow us to have a real-time feed of the station at all times. Lastly, dielectric
permittivity MAE/RE values for dry (permittivity ≤ 1.2) and wet (permittivity ≤ 1.2) snow
conditions were 0.02/0.017 and 0.03/0.024, respectively. These results demonstrate that there is a
possible heating (especially at heights closer to the snowpack surface due to solar radiation) of the
probes that might create local snow melt around them; forming an air-gap. Hence, this local snow
melting might not have happened for both sensor arrays at the same height. However, the MAE
and RE values are not large enough to suggest that each sensor rod encountered significantly
different conditions, such as contact loss between the snow and probes.
Table 17. TDR dielectric permittivity comparison (MAE and RE) between Snow Wetness Profiler rods at
different depths (15, 30, 45, and 60 cm) above the soil surface at CREST-SAFE for winters 2014 and 2015.
Layer Depth (cm) MAE RE (%)
15
0.031
2.6
30
0.033
2.9
45
0.037
3.1
60
0.043
3.3
It should be noted that the frequency distribution (Figure 39) for the three snow
categories/conditions was considerably different between years. This was expected due to the
difference in observational periods between 2014 (February–April) and 2015 (November–
January). At CREST-SAFE, the months of November and December are commonly associated
with a “warm” (close to or at isothermal) snowpack and warmer air temperatures (leading to
moist/wet snow) when compared to the months of January, February, and early-to-mid-March.
February is a particularly cold month with a typically dry snowpack. While early-to-mid-April
onwards commonly presents a warm, melting snowpack (associated with moist-to-wet snow).
Nonetheless, different frequency distributions might have affected the results obtained using the
new statistical relationships. Furthermore, because the results obtained using these new
relationships demonstrated that estimating actual snow LWC values remains a difficult task
(specifically for moist snow), we decided to evaluate the accuracy of these equations on a “hit-or-
124
miss” basis using a confusion matrix. This way, we can at least tell whether the SWP can describe
correctly the snow conditions (i.e., dry, moist, wet) even if it can’t provide the exact LWC value.
Hence, the idea is to validate the capability of the new statistical relationships to “hit” the
LWCSNTHERM dry/moist/wet delimited thresholds (defined previously in this study) using
CREST-SAFE 2015 data.
Figure 39. Frequency distribution for dry, moist, and wet snow conditions at CREST-SAFE for winters (a)
2014 and (b) 2015.
In general, a confusion matrix is a table that is often used to describe the performance of a model
(equation or set of equations) on a set of test data (SNTHERM, in this case) for which the true
values are known. In this confusion matrix, there are three predicted (new statistical relationships)
and actual (SNTHERM) classes (dry, moist, and wet snow). These make up a total of nine class
comparisons. In Figure 40, numbers represent the amount of observations that make up a class
comparison.
125
Figure 40. Confusion matrix (actual-SNTHERM vs. predicted-new statistical relationships) using three
snow conditions (dry, moist, wet) as classes for CREST-SAFE 2015 validation data.
Percentages define the percent value of the total number of observations for each class comparison.
Green percent values inside the dark grey boxes describe the percentage of correct predictions for
that particular row or column. Red percent values inside the dark grey boxes describe the
percentage of incorrect predictions for that particular row or column. Results indicate that the new
statistical relationships are capable of predicting the snow conditions with an accuracy of 70.7%.
The true positive rates (actual and predicted match) for dry snow and wet snow were 97.8% and
91.8%, respectively. However, as expected, the true positive rate for moist snow was 43.3%. This
demonstrates that the new statistical relationships were only correct (when compared to
SNTHERM) half the time. However, when it comes to model precision, it is worth mentioning
that whenever the new statistical relationships predicted moist snow, these predictions were correct
86.3% of the time. Model precision for dry and wet snow was 66.4% and 65.9%, respectively.
These results demonstrate that the SWP was able to capture the changes in snow conditions, even
when it was not able to provide exact LWC values.
6.9
Discussion
6.9.1 Advantages and limitations
The SWP is inexpensive, and easy to install and assemble. This experimental setup is capable of
detecting changes in LWC continuously and non-destructively over an entire melting period. This
126
means changes in the LWC, such as daily melt-freeze cycles, can be traced with an hourly
resolution. While it was not proven that the SWP can produce exact LWC measurements
(especially for wet snow), it was demonstrated that it can recognize changes in the snowpack state
(dry to wet conditions, and vice versa). Nonetheless, because the SWP provides the snowpack
LWC and temperature profile, is makes it possible for snow scientists to gain insight as to how the
water is seeping into the snowpack. However, all three empirical formulas (Equations (32), (34)
and (36)) from previous literature (Denoth et al., 1984; Topp et al., 1980; Tiuri et al., 1984) and
the new statistical relationships (Equations (42) and (43)) developed in this study showed that
capturing the variability in dielectric permittivity and LWC of wet snow accurately still remains a
challenging task using TDR. These limitations can also be attributed to model uncertainties
(Section 6.9.3), or be an intrinsic limitation of any instrument that lies in melting snow. While
there was an apparent dielectric permittivity threshold value of 1.2 that seemed to separate dry and
wet snow, it was still troublesome to provide exact LWC estimates for specific dielectric
permittivity values under moist snow conditions. For this reason, it can only be inferred that
dielectric permittivity values above 1.2 can produce LWCs between 2%–8%. This is shown in
Figure 38, with the onset of the melting period and LWCs higher than 2%, the dielectric
permittivity and LWC scatter increases considerably (1.2 < Ka < 1.5 and 2% < LWC < 5%). Thus,
it seems more realistic to use the SWP to detect the onset of melt, medium, and maximum
saturation of the snowpack, as demonstrated by the confusion matrix.
Lastly, the SWP can provide valuable information for hydrological applications, e.g., to detect the
melt-onset with high temporal resolution. Particularly, if installed in large numbers at different
locations; due to their cost efficiency and easy assembly. Sensor networks with large numbers of
SWPs could be installed, monitoring on a large scale, e.g., melting processes of an entire
hydrological catchment, or on a small scale, e.g., an avalanche prone slope, which is
heterogeneously covered by snow.
6.9.2 Uncertainties when estimating LWC using TDR
In general, uncertainties in LWC estimates using TDR are dependent on several components.
These are mainly snow density variations, temperature influences, and the contact between the
probe rods and snow.
Aside from the trivial impacts inaccurate snow depth and SWE in-situ data might have on snow
density values (as discussed in Section 6.6), the dry snow density assumption as an input parameter
127
for the formulas by Denoth et al. and Tiuri et al. may also be erroneous. Though the ultrasonic
depth sensor and snow pillows were installed quite close to the SWP setup, snow depth at the SWP
location can certainly deviate by a few centimeters. As such, an overestimation in snow depth leads
to an underestimation of the LWC and vice versa; the higher this error is, the lower the snow depth
is. A possible effect of snow depth (and density) variability could be reduced if the ultrasonic snow
depth sensor would have been directly mounted above the SWP instrument, which was not
physically possible. However, errors in snow depth larger than about ± 5 cm are rather unlikely at
CREST-SAFE. A dry snow density value of 200 kg/m3 before the snow became wet was held
constant over the entire melting period for the sake of the LWC determination using the snow
density dependent formulas by Denoth et al. and Tiuri et al., as suggested by Mitterer et al.
Nonetheless, it has been demonstrated that deviations in dry snow density (e.g., due to settling
during the melting period) have little effect on the calculation of the LWC, especially when
compared to those in wet snow density (Koch et al., 2014). Lastly, one possible alternative to avoid
uncertainties caused by the initial dry snow density assumption would be to conduct an
independent density measurement right before the start of the experiment. On the other hand, wet
snow density variations are quite impactful on LWC measurements using TDR. Lundberg (1997)
demonstrated that a change in density of 100 kg/m3 corresponds to a change in LWC of
approximately 1%. A recent study (Farzaneh et al., 2004) has shown that the higher the density,
the higher the dielectric permittivity of snow. Also, the electrical performance of a snow-covered
insulator string deteriorates as the density of the snow increases (CIGRE TF, 2000). Lastly, bulk
snow density was used in this study to provide some snow LWC estimates at different snowpack
layers. While this is not ideal, it is common practice because it is quite hard to obtain in-situ snow
density values at each snowpack layer without manual measurements. This type of observations
would hardly be continuous throughout 5–6 months of winter for obvious reasons. Naturally, this
presents another source of uncertainty when trying to estimate snow LWC with a snow density
dependent formula; especially when trying to obtain LWC estimates at specific locations within a
snowpack knowing of its spatio-temporal snow density changes.
A study by Lu et al. (2012) clearly demonstrated that the LWC of the snowpack is significantly
affected by air temperature, which, naturally, affects snowpack temperature. In this study, the snow
LWC showed a significant and positive correlation with the daily average, maximum, minimum,
and accumulated air temperature. However, there was higher correlation between accumulated air
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temperature and LWC than that between average air temperature and LWC. Furthermore, the
average LWC of a whole layer exponentially increased with the average air temperature and
linearly increased with accumulated air temperature. The study also mentioned that the LWC
scatter could only be partially attributed to different temperature indices, and that it was likewise
partly caused by the mass balance of the snowpack. Techel and Pielmeier (2011) even proved there
to be specific snowpack temperature regimes where snow tends to be dry (snowpack temperature
< −2 °C), probably moist (−2 °C ≤ snowpack temperature < 0.5 °C), or wet (−0.5 °C ≤ snowpack
temperature < 0.5 °C). However, they also stated that prior knowledge of the snow grain size is
needed to use these regimes in a snow study.
Lastly, it is important to make sure that there is contact between the probe rods and snow. As this
lack of contact has been proven to yield inaccurate dielectric permittivity and LWC estimates.
Sensor exposure to the air will decrease dielectric permittivity and LWC measurements drastically.
Furthermore, when probes are used in the field, sun radiation penetrates the uppermost l0 cm of
the snow and may heat the probes and thus create local melt around probes forming an air-gap.
These air-gaps will decrease the measured dielectric permittivity and, hence, the measured LWC.
Lundberg (1997) demonstrated that air-gap formations around the probes can decrease LWC
measurements using TDR by more than 1% when the diameter of the hole increased from the
diameter of the probe (5 mm) to 20 mm. The occurrence of air gaps can only be found during
prolonged field measurements and are often unavoidable, since these happen naturally.
6.9.3 Possible sources of uncertainty in SNTHERM simulations
In general, there are three characteristics that separate SNTHERM from most snow physical
models (e.g., Biosphere–Atmosphere Transfer Scheme (BATS), Variable Infiltration Capacity
(VIC)
2-L, National Operational Hydrologic Remote Sensing Center (NOHRSC) snow model (NSM),
Lynch-Stieglitz snow model, Snow-Atmosphere-Soil Transfer (SAST), Community Land Model
(CLM) snow model, Simplified Simple Biosphere model (SSiB), Noah). First, SNTHERM allows
an unlimited number of layers to represent the vertical structure and thermal characteristics of the
snowpack, whereas most snow models limit the number of snow layers to three. SNTHERM can
therefore potentially resolve more detail in the snowpack profile, and a larger number of thinner
layers can allow more accurate solution of vertical fluxes through the snowpack. Secondly,
SNTHERM makes forward estimates by subdividing hourly meteorological inputs into smaller
129
time steps, ranging between several seconds and several minutes, until convergence criteria for
mass and energy fluxes in each layer have been satisfied. Long-term accuracy is maintained by
ensuring the accuracy of each smaller time step. Lastly, SNTHERM uses the temperature and
liquid water content of each layer to estimate the thermal conditions of the snowpack. Thus,
SNTHERM accounts for the small fraction of liquid water that coexists in equilibrium with snow
at temperatures less than 0 °C. However, these advantages (over other snow physical models) do
not make SNTHERM uncertainty-free.
Over the years, SNTHERM has been used to simulate snow physical properties, validated with insitu snow observations, and compared with other snow models. Andreas et al. (2004) validated
SNTHERM with the snow, ice, and near-surface atmospheric processes on Ice Station Weddell
(ISW). Ice Station Weddell produced over 2000 h of nearly continuous measurements in the
atmospheric surface layer and in the snow and sea ice in the western Weddell Sea. Model results
demonstrated high sensitivity to the density of newly fallen snow, which is estimated using a
function dependent on wind speed and air temperature (Jordan et al., 1999). Furthermore, they
used
a
new
snow
density
value
of
150 kg/m3 (twice the value we used in this study) because snow pit observations at ISW did not
support values below this limit. Andreas et al. also reported misestimated heat fluxes in the snow
due to errors in thermal conductivity. These errors were also attributed to new snow density.
Additionally, SNTHERM, like most other one-dimensional snow models, assumes that the ice
matrix and the interstitial air are at the same temperature and that the air is at rest. However, results
by Andreas et al. suggested that the simulated near-surface temperatures and the measured snowsurface temperatures are often colder. Mote et al. (2003) compared daily first-order SWE
observations from five stations across the northern Great Plains with those estimated from passive
microwave remotely-sensed data and SNTHERM. While they concluded that SNTHERM seems
to adequately capture the seasonal mean SWE and seasonal cycle, there was a clear tendency for
SNTHERM to underestimate SWE when compared to surface observations. This is especially
significant given that surface observations are generally assumed to be underestimates of actual
SWE. Most importantly, this is of specific significance to this study because SNTHERM SWE
values affect bulk snow density and, ultimately, LWC simulations. Additionally, Mote et al.
established that agreement between SNTHERM simulations and in-situ observations increases
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substantially after applying an appropriate undercatch correction (also done in this study) to the
precipitation data used to weather-force SNTHERM. While Feng et al. (2008) studied the impacts
of snow model complexity at three Cold Land Processes Field Experiment (CLPX) sites. They
cross-compared simulations from the SSiB, Noah, VIC, CLM, and SNTHERM to field
measurements from CLPX. When it comes to SNTHERM, early runoff was noted, owing to
neglected water retention within the snowpack, potential to inaccurate LWC simulations.
Furthermore, high snow albedo values in SNTHERM were shown to cause less solar radiation
absorption, resulting in less energy for snowmelt. This could define the inaccuracy under wet
conditions, which peaks at LWCs between 2%–4%, demonstrated in Section 4 when comparing
SNTHERM-simulated with SWP-estimated LWC values. These values are usually measured at
the beginning of the snowmelt season, which is probably the most difficult period for both in-situ
measurements and model simulations. Additionally, Feng et al. demonstrated that SNTHERM was
unable to capture the observed runoff timing, even though the water storage and refreezing effects
are included in the model physics. This implies that some uncertainty is associated with snow
melting parameterization. They also reported that SNTHERM apparently overestimates snow
density, which is likely a result of predicted excessive overburden within the snowpack,
contributing to higher SWE values. Rutter et al. (2008) compared four parameters (SWE, snow
depth, average snowpack temperature, and snow surface temperature) estimated by the NSM with
snow pit observations from five CLPX sites in Colorado and SNTHERM simulations. They stated
that the methods used by SNTHERM to calculate thermal conditions and LWC in each layer of
the snowpack are important, as they control the dominant mass flux (meltwater), which creates the
SWE divergence that persists throughout ablation to create differences in melt-out times. These
processes are greatly influenced by the irreducible water saturation (water withheld in the
snowpack by capillary forces) and liquid water fraction. The former is a calibration parameter
(0.04, in this study) that has to be established at the beginning of simulations, the latter is calculated
by SNTHERM using a semi-empirical approach to calculate liquid water fractions within the
snowpack as a function of snow temperature. Frankenstein et al. (2008) carried out numerical
experiments of snow accumulation and depletion, and surface energy fluxes over four CLPX sites
in Colorado using SNTHERM and the Fast All-Season Soil Strength model (FASST). Their results
showed that SNTHERM performs better when allowed to calculate the reflected solar radiation
(done in this study), instead of being weather-forced by it. Shi et al. (2009) investigated the lateral
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and vertical variability of snow stratigraphy by comparing the measured profiles of snow density,
temperature, and grain size obtained during the Snow Science Traverse— Alaska Region
(SnowSTAR2002) 1200-km transect from Nome to Barrow by comparing it to SNTHERM
simulations. They explained that, because the SNTHERM soil model is simple and does not
include many of the energy transport processes common to soils, errors of the snow temperature
profiles increase closer to the snow–soil interface as a result of the simplified energy transport
across the snow–soil interface, which only includes the thermal conduction and excludes the
significant vapor diffusion. Additionally, SNTHERM snow density profiles failed to capture the
hard and thin wind slabs because of the limitation of point model structure in representing the wind
compaction effect.
Ultimately, even though SNTHERM has been proven to be one of the most complex and,
consequently, accurate snow physical models, it remains a model nonetheless. As such, it will
always remain a conceptualization of real snow physics and has to be treated accordingly. More
importantly, the user should always be aware that the model outputs will always be reliant on
accurate initial calibration and parametrization; as all study cases are and will be fundamentally
different. Lastly, because the movement of liquid water in snow is a complex process, differences
between SNTHERM and SWP LWC values might be due to both model errors and instrument
inaccuracy.
6.9.4 Comparing the CS650 (and its precision) to other non-destructive LWC-measuring
instruments
When it comes to TDR snow LWC measurements, there are two widely-known instruments: the
Denoth meter and Finnish Snow Fork (Techel and Pielmeier, 2011). The Denoth meter is a
capacitance probe which measures an area of 13 × 9 cm2, operates at 27 MHz, and requires a
separate density measurement to solve for the imaginary part of the permittivity. The Finnish Snow
Fork samples an area of 6 × 2 cm2, operates at 1 GHz, and simultaneously measures both parts of
the medium permittivity. Another commonly-used and -known TDR snow LWC measuring
instrument is the Tektronix model 1502C (Stein et al., 1997; Lundberg, 1997). The Tektronix
model 1502C and its Tektronix PB30-58 balanced probes sample an area of 5 × 30 cm2, the system
operates from DC to 1 GHz and also measures both parts of the medium permittivity. Other less
used, yet still relevant TDR snow measurement instruments include: the automatic network
analyzer (ANA) type R&S ZPV with tuner unit E3 (50 MHz to 1.5 GHz, 12.5 × 13.5 cm2)
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(Achammer and Denoth, 1994) and The Resonator (200 MHz to 1.4 GHz, 7 × 20 cm2) (Matzler,
1996). Additional non -TDR and -destructive related instruments commonly used to obtain snow
LWC estimates are the SPA and upGPR. The SPA consists of two (2) SPA sensing bands with one
installed horizontally 10 cm above the ground and the other installed at an angle (referred to as the
sloping band), an impedance analyzer, an ultra-sonic snow depth sensor, and mounting accessories
to assure proper tension of the SPA bands (Heggli, 2013). Each of the SPA bands sends frequencies
into the snowpack and measures the complex impedance. The returned signals allow for the
determination of liquid water, ice, and air percentages within the snowpack. The upGPR makes
use of impulse radar (10 MHz to 2.6 GHZ) and bipolar antennas to estimate snowpack properties
(e.g., LWC) (Heilig, 2009). Table 18 illustrates the accuracy and precision for snow LWC
measurements for all the instruments mentioned in this section, as well as those of the CS650
reflectometer (for soil).
Table 18. Operational specifications for snow and soil LWC measurements for different LWC-measuring
instruments.
LWC Operational Specs
Instrument
Accuracy (%)
Precision (%)
CS650 (soil)
±3
<0.05
Denoth meter (snow)
±2.5
<0.05
Finnish Snow Fork
±2.5
<0.05
Tektronix 1502C (snow)
±2.5
<0.05
ANA (snow)
±2
0.05
Resonator (snow)
±2
0.05
SPA
-
-
upGPR (snow)
±4–5
0.15
6.9.5 Comparing results with other studies
In this study, average MAE and R values for LWCTopp, LWCDenoth, LWCTiuri, LWCNEW
were 2.44, 0.31, 3.70, 0.37 and −0.67, 0.87, −0.53, and −0.79, respectively. As discussed
previously, the empirical formula by Denoth et al. seems to provide the more accurate LWC
estimates. Whereas the new statistical relationships show a slightly better performance over wet
snow conditions. In general, when compared to the study by Stein et al. (1997), the results are
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somewhat similar. Stein et al. reported average LWC MAE and R values of 1.3% and 0.81,
respectively. While the investigation by Lundberg (1997) reported LWC MAE values ranging
from 1%–2%. Lastly, the results by Denoth et al. (1984) displayed LWC MAE values of
approximately 1%. However, it is difficult to compare the accuracy between studies. Because,
although all of them used TDR to produce LWC estimates, the equipment used and general
approach to each experiment were different. Stein et al. used different probe diameters and lengths.
Additionally, the probes were aligned vertically (at the same height), not horizontally. Lundberg
used snow control volumes produced at a laboratory, and Denoth et al. used 6 different instruments.
6.10 Conclusion
We presented an approach to continuously determine snow LWC at different snowpack layers with
simple low-cost CS650 reflectometers using TDR. With this experimental setup, it was possible
to estimate (with deficiency for moist snow) the snow LWC as a function of its dielectric
permittivity. The Snow Wetness Profiler proof of concept demonstrates that it is possible to create
an automated, continuous, non-invasive, and non-destructive way of conducting snow LWC and
temperature profile observations to further improve our understanding of the interplay between the
dielectric permittivity, temperature, and LWC of a snowpack.
The accuracy of the SWP for estimating LWC was validated using empirical formulas by Topp et
al., Denoth et al., and Tiuri et al. These showed overall good agreement. However, all equations
demonstrated an inability to provide accurate LWC estimates for wet snow. Hence, two (for dry
and wet snow) new statistical (cubic polynomials) equations were developed between snow LWC
and dielectric permittivity using CREST-SAFE in-situ data. The equations displayed a better
capability to capture the LWC changes in wet snow. Though, not good enough to be used to
provide exact LWC estimates for specific dielectric permittivity values. Thus, at the moment, it
seems more realistic to use the SWP to detect the onset of melt, medium, and maximum saturation
of the snowpack. Uncertainties such as changes in snow density, snowpack and air temperature,
and the possibility of partial sensor exposure to the air remain concerns when dealing with TDR
field measurements. Nonetheless, the new statistical equations showed that formulas developed in
previous literature have to be reconsidered because most studies provide one general applicable
equation for LWC estimates, regardless of snow conditions. Dry and wet snow conditions should
be treated separately. Furthermore, those studies that try to consider the differences between dry
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and wet snow require initial dry snow density or ice content assumptions. Lastly, it should be
mentioned that, because these were developed using SNTHERM LWC values, the new statistical
equations have to be used with caution. Naturally, it is recommended to use manual in-situ LWC
measurements and either improve the new statistical equations shown in this study, or develop
alternate ones.
The main advantages of the SWP are its low cost and low power consumption, and that data
analysis is neither time-consuming nor labor intensive. Additionally, the easy assembly makes it
an appealing alternative for automated and continuous snow LWC measurements at a high
temporal resolution without destroying the snow cover. Moreover, due to the small size of the
instruments and the non-destructive measurement setup, these are virtually possible to install
anywhere. In light of these preliminary results, the sensors and SWP show promise to become an
alternative for in-situ continuous and long-term snow LWC monitoring. However, additional work
is needed to improve the accuracy of LWC estimations. As mentioned previously, the first
recommendation is to use manual in-situ LWC measurements to improve the new statistical
equations. Secondly, these equations could be further improved if snow density values are
incorporated as another independent variable. This was not done in this study because we think it
is ideal to provide an equation (or equations) that is only dependent on one snow parameter. In
reality, the reflectometers only provide dielectric permittivity values. Hence, if a snow density
dependent equation was created, the users will need additional instrumentation to perform those
measurements.
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7
Prediction of snow depth using Regression Tree algorithm
Snow depth is known as is the average depth of snow (including old snow and ice as well as new)
that remains on the ground at observation time, while the snow water equivalent is referred to as
the depth of water that would theoretically result if you melted the entire snowpack
instantaneously. Several snow physical properties influence snow depth. Snow surface and pack
temperatures have been demonstrated to affect snow depth (Gerland et al., 1999; C. Pérez Díaz,
Lakhankar, Romanov, Khanbilvardi, & Yu, 2015; Pérez-Díaz et al., 2017; Rango, 1993). Snow
wetness and grain size have been proven to significantly impact snow depth (Corona, Muñoz,
Lakhankar, Romanov, & Khanbilvardi, 2015; C. L. Pérez Díaz, Muñoz, Lakhankar, Khanbilvardi,
& Romanov, 2017; Schneebeli, Coléou, Touvier, & Lesaffre, 1998; Sun, Neale, & McDonnell,
1996; Techel & Pielmeier, 2011). Furthermore, passive MW RS has shown to be highly susceptible
to snow depth changes (Lakhankar et al., 2013; Macelloni et al., 2005; Mätzler, 1986; Rango,
1993). Because snow is a key component of the Earth’s energy balance, climate, and environment,
and a major source of freshwater in many regions, snow depth plays a significant role that
influences climate, culture, and commerce in significant ways (Brown & Robinson, 2011; Dominé
& Shepson, 2002; Frei et al., 2012). Knowledge of the snow depth is essential in water resources
management because it affects the hydrologic cycle, since water is stored over the winter and
released in a pulse during the spring melt. More importantly, snow cover plays a critical role in
the regional to global scale because rain-on-snow with warm air temperatures accelerates rapid
snow melt, which is responsible for the majority of the spring floods that damage property and
affect human lives (Chen et al., 2012). Spring floods present difficulties for water managers and
is partially the reason for the existence of man-made reservoirs. Additionally, avalanches impact
backcountry and mountain residents with property damage, injuries, or death. Hence, adequate
knowledge of the snow depth and water equivalent can lead to better management of our water
resources, resulting in more efficient energy production and the mitigation of human impacts on
river ecosystems (Barnett et al., 2005; DeWalle and Rango, 2008; Hogan, 2002).
In this chapter, a methodology is proposed to predict snow depth and SWE using in-situ snow
physical and radiative observations. A machine learning algorithm called a decision tree is used in
order to model the snow depth and SWE at CREST-SAFE using snow physical and radiative
properties as predictor variables. Decision trees are divided into two categories: classification and
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regression trees. Classification and regression trees are machine-learning methods for constructing
prediction models from data. The models are obtained by recursively partitioning the data space
and fitting a simple prediction model within each partition. As a result, the partitioning can be
represented graphically as a decision tree. Classification trees are designed for dependent variables
that take a finite number of unordered values, with prediction error measured in terms of
misclassification cost. While regression trees (RTs) are for dependent variables that take
continuous or ordered discrete values, with prediction error typically measured by the squared
difference between the observed and predicted values. This chapter is aimed at presenting the
results of the exhaustive analysis that was conducted in order to evaluate the performance of the
developed RTs. To validate the model, the RTs ingested new data from CREST-SAFE and the
snow depth and SWE predictions were compared to actual observations. In the next chapter, a
methodology will be presented to take this RT algorithm and apply it on a global scale.
7.1
Response and predictor variables
In this study, in-situ snow depth observations and SNTHERM SWE simulations were used as the
response variable. These data were obtained from the CREST-SAFE data records. This data set
includes snow depth, snow surface and pack temperature, and MW TB (10, 19, 37, and 89 GHz at
horizontal and vertical polarizations) observations from 2012 to present. The training and testing
data set was limited to data from 2012 to 2015. While 2016 data was used to validate the model.
Twelve predictor variables that were considered to significantly influence snow depth and SWE
were used (Table 19). These variables can be categorized in two distinct groups: physical and
radiative. Some predictor variables had to be modeled on account of the instrumentation not being
available at CREST-SAFE for years 2012 and 2013. These variables were: snow wetness (obtained
via SWM using grain size and snowpack temperature) and MW TBs at 10 GHz (acquired using
HUT Snow Emission Model).
Table 19. Predictor variables used to build the RT algorithm for snow depth prediction.
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7.2
Variable
Abbreviation
Units
Source
Category
Snow depth
SD
cm
CREST-SAFE
response
Snow water equivalent
SWE
cm
SNTHERM
response
Snow surface temp.
T-skin
K
CREST-SAFE
predictor
Snowpack temp.
T-pack
K
CREST-SAFE
predictor
Grain size
GS
mm
SNTHERM
predictor
Snow wetness
LWC
-
SWM
predictor
MW TB 10H
MW10H
K
HUT
predictor
MW TB 10V
MW10V
K
HUT
predictor
MW TB 19H
MW19H
K
CREST-SAFE
predictor
MW TB 19H
MW19V
K
CREST-SAFE
predictor
MW TB 37H
MW37H
K
CREST-SAFE
predictor
MW TB 37H
MW37V
K
CREST-SAFE
predictor
MW TB 89H
MW89H
K
CREST-SAFE
predictor
MW TB 89H
MW89V
K
CREST-SAFE
predictor
Data exploration
The first step for the development of a predictive model and the use predictor variables is to explore
the data to make sure that it complies with the assumptions that are necessary to consider any
conclusions valid (i.e. changes to predictor variables affect response variable). In RT there is no
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probabilistic model, just a binary split. Therefore, there are no assumptions about the relationships
between the variables or their distributions.
In order to explore the response and predictor variables at CREST-SAFE, a scatterplot matrix will
be used. This tool is useful for assessing the statistical distributions of the variables, the
relationships between variables, how correlated they are, and the shape of the correlation (Zuur,
Ieno, & Smith, 2007). It consists of a matrix of plots with one row and one column for each
variable. The labels for the variables are printed in the diagonal panels. In this chapter, twelve
predictor variables and one response variable will be analyzed, thus the scatterplot is a 13x13
matrix of plots. In the diagonal, histograms are also shown. The purpose of plotting the histogram
is to show the center and distribution of the data.
No histogram shows bimodality in Figs. 41 and 42. The response variable and all predictor
variables are unimodal. That means that it is quite common for the distribution of the predictor
variables to cluster around a single mode. The lower panels display a scatterplot for each possible
pair of fields. These plots are useful for visualizing and assessing the shape and direction of the
correlation between variables. Figure 41 suggests a relationship between snow depth and snow
surface temperature, grain size, and MW TBs at 19, 37, and 89 GHz. Furthermore, there appears
to be collinearity between snow surface and pack temperatures, and grain size and snow wetness.
Figure 42 suggests a relationship between SWE and grain size and MW TBs at 19, 37, and 89
GHz. The upper panels display Spearman's rank correlation coefficient (rho) for each possible pair
of fields. Pearson Correlation was not considered appropriate because the data failed the
assumptions necessary for conducting the Pearson's product-moment correlation. These
requirements are that the relationships between the fields are linear and that each field is normallydistributed. However, the Spearman’s correlation will only be valid in cases where there is a
monotonic relationship between the variables. A monotonic relationship exists when the values of
the variables increase at the same time, or when one variable value increases, the other one
decreases (Zuur et al., 2007). The way to check for monotonicity was by visually inspecting the
scatterplots. For instance, in Figure 41, Spearman’s correlation for snow surface and pack
temperatures, as well as the relationship between horizontal and vertical polarizations for all MW
TBs, is valid and can be analyzed using this coefficient, whereas Spearman’s correlation for grain
size and MW10V violates the assumption that there has to be a monotonic relationship between
139
variables. Thus, in this case our analysis will not focus in the value of the coefficient but instead
in the visual inspection of the scatterplot.
Figure 41. Scatter plot matrix for the response variable snow depth and twelve selected predictor variables
at CREST-SAFE.
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Figure 42. Scatter plot matrix for the response variable SWE and twelve selected predictor variables at
CREST-SAFE.
7.3
Regression Tree Algorithm
Tree models were introduced by (Breiman, 1984) in the Classification and Regression Tree
(CART) software. CART are machine learning methods for construction of prediction models
from data. These methods have been used extensively around the scientific community. In a
decision tree, a regression or classification model is constructed in the form of a tree. Classification
trees are used when the response variable is categorical in nature. On the other hand, regression
trees are required when the response variable is numeric or continuous. In this study, snow depth
and SWE observations are continuous. For this reason, RTs will be needed. The purpose is to break
down the data into smaller subsets while concurrently an associated decision tree is incrementally
created. The result is a tree with root nodes, decision nodes, and leaf nodes. A root is the first or
topmost node which represents the best predictor variable. A decision is a node that splits in two
or more branches, each representing values for the variable tested. A leaf is a node depicting a
decision on the target. Some of the advantages associated with CART are (Miner, Nisbet, & Elder,
2009):
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x CART is not significantly affected by outliers present in the variables that are used as
input data.
x CART is nonparametric. Therefore, it does not assume that the data belongs to a
particular distribution.
x CART conducts cross-validation to evaluate the goodness of fit more accurately.
x CART is able to make use of the same variable several times during tree construction.
This capability is advantageous to uncover intricate interdependencies between predictor
variables.
The objective in RT is to partition the predictor space into boxes and assign a value to each box
using the observations of the response variable that fall within that box. At each stage of the
regression tree, a predictor variable and a split point for that variable has to be selected in order to
continue with the recursive partitioning of the data. This is achieved by assessing all possible
predictor variables and split points using a fit criterion. For regression, the fit criterion is the
residual sum of squares (RSS). These are the main steps in the construction of a RT (Weiss, 2010):
x Estimate the null RSS Estimate the null RSS which is located at the root node.
This RSS is the sum of squared deviations of the individual values of the response variable about
their overall mean.
x Select a variable and a split point
Start the recursive partitioning process. For a continuous variable with m values ξ1, ξ2, ξ3,……,
ξm, consider each value. In the selection of the variable and split point, each predictor variable is
examined. Therefore, for a predictor variable x, a partition would yield {x≤ ξi} and {x> ξi},
i=1,2,3,….m. Since splits only happen between consecutive data values, the possible partitions to
consider for each predictor variable are m-1.
x Calculate the impurity measure for each possible partition
142
After examining each predictor variable and possible split points, compute the average value of
the response variable and the RSS in each of the areas resulting after the partition. The RSS for
the current split is defined as:
ଶ
ܴܵܵሺ‫ݐ݈݅݌ݏ‬ሻ ൌ ܴܵܵଵ ൅ ܴܵܵଶ ൌ σோଵሺ‫ݕ‬௜ െ തതതሻ
‫ݕ‬ଵ ଶ ൅ σோଶሺ‫ݕ‬௜ െ ‫ݕ‬
തതതሻ
ଶ
Equation 44
Where: y= response variable and R= region
Before the split, the overall residual sum of squares for the current split is calculated with the mean
of all values of the response variable.
ܴܵܵ଴ ൌ σோଵሺ‫ݕ‬௜ െ ‫ݕ‬തሻଶ
Equation 45
The predictor variable and split point selected will maximize the difference between ܴܵܵ‫ ݋‬and
ܴܵܵ (‫)ݐ݈݅݌ݏ‬.
x Try to divide the groups further
For all the groups that were formed in the previous step, inspect each predictor variable and
possible split points again to decide if it can be divided further. If it can be further divided, repeat
step 2 until the stopping criterion is met.
7.3.1 Details of the tree construction
A graphical summary of the unpruned snow depth RT built is shown in Figure 43. The partition
structure of the algorithm can be more easily explained using this plot. In each node the split
condition and variable corresponding to that node is shown. As it was discussed previously, the
unpruned RT in Figure 43 had to be pruned to find the optimum RT. To optimize a RT the
intersection between prune level and leaf size that produces the minimum cross-validated error has
to be found. As illustrated in Figure 44, a pruning level of 100 and leaf size of 20 yielded the
lowest cross-validated error for the unpruned tree in Figure 43. The resulting pruned snow depth
RT is shown in Figure 45.
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Figure 43. Unpruned snow depth regression tree at CREST-SAFE.
Figure 44. Snow depth regression tree cross-validated error as a function of pruning level and minimum
leaf size.
144
Figure 45. Pruned snow depth regression tree at CREST-SAFE.
The RT built has 100 terminal nodes produced by 99 splits. The RT initially divided the data into
two sets of MW37V above and below 244 K. The second partition consisted in GS radius above
and below 0.75 mm. The third partition took the MW89V values above and below 222 K. This is
an illustration of one of the advantages of decision trees, their interpretability. This recursive
partitioning is continued until the tree reaches the stopping rule specified. In this case, the
additional amount of explained deviance accomplished with a new split was less than the threshold
set of 1% of the null deviance. Figure 46 shows the pruned SWE RT.
145
Figure 46. Pruned SWE regression tree at CREST-SAFE.
The pruned SWE RT built has 100 terminal nodes produced by 99 splits. The RT initially divided
the data into two sets of MW37H above and below 230 K. The second partition consisted in
MW10H above and below 260 K. The third partition took the MW89H values above and below
217 K. A comparison between RTs indicates that SD is more dependent on GS and the 37 GHz
and 89GHz MW frequencies at vertical polarization. On the other hand, the SWE RT appears to
be more sensitive to 10, 37, and 89 GHz MW frequencies at horizontal polarization.
7.3.2 Residual plots
Another interesting assessment to examine the performance of the model is to plot the residuals
against the predicted values SD and SWE values. This graph is shown in Figures 47 and 48. The
distance from the line located at zero represents the difference between the observed and predicted
values (how bad the prediction was for that value). For the most part, it can be seen that a large
number of predictions were accurate because the majority of the points are closely located at the
0-line. Based on this plot, it is possible to conclude that RTs can be used to accurately predict SD
and SWE. This is mainly because the residuals are symmetrically distributed, implying balanced
predictions.
146
Figure 47. Residuals plot depicting the predicted SD values on the x-axis and the residuals on the y-axis.
Figure 48. Residuals plot depicting the predicted SWE values on the x-axis and the residuals on the y-axis.
7.3.3 Variable importance
The predictor ranking (also called variable importance) calculation is useful for understanding the
contribution that each variable makes to the construction of the tree (Saldford Systems, 2017). The
importance is determined by adding the reduction in sum of squares across all nodes in the tree for
147
which that predictor acts as a splitter. As mentioned in the previous section, for the SD RT, the
three most important variables are GS, MW37V, and MW89V. For the SWE RT, MW10H,
MW37H, and MW89H are the most important variables. See Figures 49 and 50.
Figure 49. Variable importance analysis for SD regression tree.
Figure 50. Variable importance analysis for SWE regression tree.
148
7.4
Model performance evaluation
In order to assess the quality of the algorithm, the holdout set method is used. Aside from providing
error estimates that render the selected model reliable, this method requires no theoretic or
parametric assumptions and, if enough data is provided, it is highly accurate. This method consists
in randomly splitting the data into two groups. For this research, the records are randomly split
into 70% training and 30% test (Figure 51).
Figure 51. Holdout set. 70% is used for training and 30 percent of the data is used for testing.
The training data will be used to fit the model; the test data portion will be used to measure the
model’s error. This error is called “true prediction error” because it provides information on how
well a model predicts on new data. Results for the SD RT are shown in Table 20. It is also helpful
to illustrate how well a developed model predicts on the data that was used for training. This error
is called training error. Results for the SWE RT are displayed in Table 21.
Results indicate that both RTs are capable of estimating SD and SWE accurately with high linear
correlation coefficient values fluctuating from 0.90 to 0.98, and RMSEs of 3.47 cm and 1.10 cm
for the SD and SWE RTs, respectively. The NRMSE values for both models demonstrate that there
is only and average error of 5%.
149
Table 20. Training and true prediction errors for SD regression tree model developed using CRESTSAFE data.
Regression procedure
Performance metric
Training error
True prediction error
(n = 9081)
(n = 3891)
Mean Absolute Error (MAE)
1.50
1.80
Mean Squared Error (MSE)
7.18
12.06
Root MSE (RMSE)
2.68
3.47
Normalized RMSE (NRMSE)
0.03
0.04
Pearson's r
0.99
0.98
Kendall's Tau
0.93
0.91
Spearman's Rho
0.99
0.98
R-squared (as squared Pearson's r)
0.98
0.96
Table 21. Training and true prediction errors for SWE regression tree model developed using CRESTSAFE data.
Regression procedure
Performance metric
Training error
True prediction error
(n = 9081)
(n = 3891)
Mean Absolute Error (MAE)
0.45
0.58
Mean Squared Error (MSE)
0.75
1.23
Root MSE (RMSE)
0.86
1.10
Normalized RMSE (NRMSE)
0.05
0.06
Pearson's r
0.98
0.97
Kendall's Tau
0.91
0.89
Spearman's Rho
0.98
0.97
R-squared (as squared Pearson's r)
0.97
0.95
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7.5
Model validation
The final step in the model development is its validation with new data. New data is referred to as
data that was not used to train the model. In this study, 4 years (2012-2015) of CREST-SAFE data
were used to train and test the model. The year 2016 was withheld from the training and test data
set in order to validate both the SD and SWE models. The validation results are shown in Table
22. Results indicate that both RT models provide reliable SD and SWE estimations when presented
with new data. This is further highlighted in Figure 52, where the observed SD and SWE at
CREST-SAFE from the year 2016 and the SD and SWE RT predictions for the same time span
were plotted in a time series.
Table 22. Validation results for the developed SD and SWE regression tree models using CREST-SAFE
2016 data.
Regression procedure
Performance metric
Snow depth
SWE
true prediction error
true prediction error
(n = 3032)
(n = 3032)
Mean Absolute Error (MAE)
6.07
1.92
Mean Squared Error (MSE)
64.71
6.41
Root MSE (RMSE)
8.04
2.53
Normalized RMSE (NRMSE)
0.13
0.17
Pearson's r
0.76
0.75
Kendall's Tau
0.50
0.55
Spearman's Rho
0.67
0.72
R-squared (as squared Pearson's r)
0.59
0.56
151
Figure 52. CREST-SAFE SD and SWE observations and RT SD and SWE predictions for the year 2016.
152
8
Global model implementation
The purpose of this chapter is to apply the methodology that was developed and presented in
Chapter 7 to the World. The result will be SD and SWE global maps that can be used by scientists,
hydrologists, and water resources managers to make educated decisions when it comes to
hydrological forecasts and monitoring climate change. Furthermore, it is important to recognize
and act accordingly to the possible threats that spring floods and avalanches pose in order to save
human lives. Moreover, these maps can also be integrated into regional-to-global-scale models to
determine snowmelt and the amount of water available in some regions, both of which are tied to
climate change. Lastly, as human requirements for reliable water supplies increase due to droughts,
accurate SD and SWE estimates are important for sustainable snowmelt runoff management.
8.1
Materials and methods
A data-based model is developed with the purpose of providing SD and SWE global maps at a 10km resolution. The product is based on the RT methodology developed and described in Chapter
7. The implementation of the methodology on a global scale is presented in this chapter. The
methodology involves the SD and SWE RTs and JAXA GCOM-W1 AMSR2 Level 3 TB products.
Because the RTs are dependent on snow physical properties (i.e. snow surface and pack
temperatures, grain size, and wetness) that are not available as satellite products, an approach to
estimate these at a 10 km resolution was developed using empirical formulas. The basic idea for
the creation of the SD and SWE models was to incorporate the most fundamental snow physical
and radiative properties into a data-based analysis that was able to discover and extract the complex
interactions between all system components and generate a model with the ability to accurately
predict SD and SWE on a global scale. Table 23 shows the predictor (independent) variables that
were used in the development of the SD and SWE global maps.
153
Table 23. Predictor variables used to create SD and SWE global maps using RTs developed in Chapter 7.
Variable
Abbreviation
Units
Source
Resolution
Snow surface temp.
T-skin
K
Empirical
10 km x 10 km
Snowpack temp.
T-pack
K
Empirical
10 km x 10 km
Grain size
GS
mm
Empirical
10 km x 10 km
Snow wetness
LWC
-
SWM
10 km x 10 km
MW TB 10H
MW10H
K
JAXA
10 km x 10 km
MW TB 10V
MW10V
K
JAXA
10 km x 10 km
MW TB 19H
MW19H
K
JAXA
10 km x 10 km
MW TB 19H
MW19V
K
JAXA
10 km x 10 km
MW TB 37H
MW37H
K
JAXA
10 km x 10 km
MW TB 37H
MW37V
K
JAXA
10 km x 10 km
MW TB 89H
MW89H
K
JAXA
10 km x 10 km
MW TB 89H
MW89V
K
JAXA
10 km x 10 km
AMSR2 is a multi-frequency microwave radiometer. It measures weak microwave emission (6.989.0GHz) from the surface and the atmosphere of the Earth. AMSR2 products are categorized
according to the processing levels. Level 1A (L1A) products consist of raw observation counts,
antenna temperature conversion coefficients, etc... While Level 1B (L1B) products contain
brightness temperatures which is converted from L1A count values using the conversion
coefficients. The Level (L2) products contain geophysical parameters which primarily related to
water and derived from the L1B products. L1 and L2 is swath data with geolocation information.
154
Lastly, Level 3 (L3) products are global gridded products at two different resolutions (0.1 and 0.25
degrees). Products make ground projections on the globe and in the North Pole and South Pole
regions by taking the time and spatial averages of the L1B and L2 standard products. In this study,
the Level 3 TB global products gridded at 0.1 degrees (10 km resolution) were used to estimate
SD and SWE globally. L3 TB maps contain 1800 (latitude) x 3600 (longitude) pixels. The JAXA
data providing service can be accessed at: http://gcom-w1.jaxa.jp/ and data can be either
downloaded manually or programmatically via File Transfer Protocol (FTP). JAXA provides
daytime and nighttime Level 3 TB products for all frequencies and polarizations. Missing values
are assigned the value 66535, while out-of-swath values are assigned a value of 65534. The scale
factor for the JAXA L3 TB products is 0.01 K.
As mentioned previously, there are four snow physical parameters needed by the RT to estimate
SD and SWE that are not available as satellite products. These are: snow surface and pack
temperatures, grain size, and wetness. Snow wetness will be obtained using the SWM, which is
dependent itself on snow grain size and pack temperature. Thus, using knowledge from previous
snow MW studies where relationships between snow physical and radiative properties were
defined, three empirical formulas were developed to estimate snow surface and pack temperatures,
and grain size. The data, relationships, and formulas are illustrated in Figures 53, 54, and 55,
respectively. The data used to develop these empirical equations was obtained from CREST-SAFE
data from 2012 to 2015. As discussed in Chapter 2, the MW penetration depth of the 89 GHz
channels is quite small. Hence, there is a direct relationship between snow surface temperature and
the V-H polarization gradient in this channel. When it comes to snowpack temperature, it is
common to use the 10 and 19 GHz bands because these penetrate further into the snowpack. The
MW10V-MW19V gradient displayed a clear relationship to snowpack temperature. Lastly, it has
been proven extensively that there is a relationship between GS and the MW channels at the 19
and 37 GHz frequencies. In this particular study, there was a clear relationship between the
MW19V-MW37V gradient and GS. The performance evaluation for all three empirical formulas
is shown in Table 24. Results indicate reliable accuracy for all empirical formulas. See Eqs. 46,
47, and 48. A more detailed explanation of the theory behind the development of these empirical
formulas is presented in Section 8.3.
155
ଶଷହ
ܶ௦௞௜௡ ሺ‫ܭ‬ሻ ൌ ʹ͹͵Ǥͳͷ െ ሺெௐ଼ଽ௏ିெௐ଼ଽுሻయ ሺ‫ܭ‬ሻ
Equation 46
ܶ௣௔௖௞ ሺ‫ܭ‬ሻ ൌ െͲǤͷʹͲͷ͵ሺ‫ ܸͲͳܹܯ‬െ ‫ܸͻͳܹܯ‬ሻ ൅ ሾʹ͸ͺǤ͹͹Ͷ͵ െ ͲǤͲͲͳʹ͹ͺͺ ‫ כ‬ሺ‫ ܸͲͳܹܯ‬െ ‫ܸͻͳܹܯ‬ሻଷ ሿሺ‫ܭ‬ሻ
‫ܵܩ‬௥௔ௗ௜௨௦ ሺ݉݉ሻ ൌ െͲǤ͵ʹʹ͹Ͷ݁ ଴Ǥ଴ହ଴ଷସ଺ሺெௐଵଽ௏ିெௐଷ଻௏ሻ ൅ ͲǤͷ͸ͶͷͶ݁ ି଴Ǥ଴଴ଵ଻ଷଽ଼ሺெௐଵଽ௏ିெௐଷ଻௏ሻ ሺ‫ܭ‬ሻ
Eq. 47
Equation 48
Figure 53. Relationship between snow surface temperature and the V-H polarization gradient at the 89
GHz MW frequency.
156
Figure 54. Relationship between snowpack temperature and the vertical polarization gradient between the
10 GHz and 19 GHz MW frequencies.
157
Figure 55. Relationship between snowpack temperature and the vertical polarization gradient between the
19 GHz and 37 GHz MW frequencies.
158
Table 24. Performance evaluation for the three empirical formulas developed to estimate GS, snow
surface and pack temperatures as a function of MW TBs.
Variable predicted
Performance metric
8.2
GS
Skin temp.
Snowpack temp.
(n = 3032)
(n = 3032)
(n = 3032)
MAE (mm, K, K)
3.68
6.76
8.71
MSE (mm2, K2, K2)
22.77
86.45
89.33
RMSE (mm, K, K)
4.77
9.30
10.11
NRMSE
6.85
0.28
0.34
Pearson's r
-0.66
0.65
-0.80
Kendall's Tau
-0.54
0.51
-0.62
Spearman's Rho
-0.70
0.70
-0.80
R-squared
0.43
0.42
0.64
Snow depth and SWE global maps
RT algorithm will be used to predict SD and SWE globally using snow physical and radiative
properties as predictors. Global SD and SWE prediction is accomplished by using regression trees.
The implementation of the RT algorithm to satellite MW TB products is performed using
MATLAB. MATLAB fits the developed regression tree to the input data layers using the Statistics
and Machine Learning and Mapping Toolboxes. Examples of the resulting maps are shown in
Figures 56 and 57.
159
Figure 56. RT developed SD global map using the JAXA GCOM-W1 AMSR2 MW brightness temperature
(10, 19, 37, and 89 GHz) products.
Figure 57. RT developed SWE global map using the JAXA GCOM-W1 AMSR2 MW brightness
temperature (10, 19, 37, and 89 GHz) products.
160
8.3
Validation of developed SD and SWE algorithms against existing RS products
8.3.1 JAXA AMSR2 SD and SWE products
The GCOM-W1 AMSR2 instrument constitutes a key component in the record of satellite passive
microwave observations of Earth from space. Continuing on from the Advanced Microwave
Scanning Radiometer for EOS (AMSR-E) launched in 2002, the Special Sensor Microwave
Imager (SSM/I) launched in 1987 and the Scanning Multichannel Microwave Radiometer
(SMMR) launched in 1979. AMSR2 is intended to extend the record beyond 35 years, enabling
significant insight into snow accumulation variability at regional to global scales.
The JAXA AMSR2 SD algorithm is an evolution of the original AMSR-E SWE algorithm and
takes advantage of the expanded range of channels available on the AMSR-E instrument compared
with the SSM/I and SMMR. In principle, the current algorithm is a frequency difference algorithm
approach that builds on the work of Chang et al. (1997). It undertakes a forest correction, retrieves
shallow snow using the 89 GHz channel, and retrieves moderate snow accumulation using the 37
GHz channel. In addition, a deep snow estimation method is implemented using the 19 and 10
GHz channel. To exploit the native resolution of the AMSR2 instrument, retrievals are conducted
at the original native spatial resolutions of the channels and then gridded to 0.25 x 0.25 degree and
0.10 x 0.10 degree grids. Using the study of Dewey and Heim (1982), locations where snow
accumulation is climatologically unlikely are masked out (e.g. at low latitudes and over the oceans)
and retrievals are not conducted over permanent terrestrial ice surfaces (ice sheets and glaciers).
8.3.2 JAXA AMSR2 SD and SWE algorithm theoretical description
The upwelling radiation measured by a satellite passive MW radiometer is called the apparent
temperature (ܾܶ), and can be expressed as:
ܾܶ ൌ ሺܴܾܶ௦௞௬ ൅ ൫ͳ െ ܴܾܶ௦௨௥௙ ൯݁ ିఛ ൅ ܾܶ௔௧௠
Equation 49
where ݁ ିఛ is the atmospheric transmissivity ܴ is the surface reflectivity, ܾܶ௦௞௬ is the sky radiation,
ܾܶ௦௨௥௙ is the surface emission and ܾܶ௔௧௠ is the atmospheric (Chang et al., 1997). Generally, ܾܶ௔௧௠
and ܾܶ௦௞௬ are quite small and ignored. Hence, ܾܶ is directly related to surface features and, if MW
atmospheric windows are used, atmospheric transmissivity is maximized (~1).
161
The wavelength-dependent intensity of radiation emitted from a snowpack depends on several
physical variables: kinetic temperature of the snow, snow GS distribution and the grain volume to
air fraction, the underlying surface conditions, and in-situ vegetation characteristics. At the satellite
scale, the fraction of water within the instantaneous FOV is important as well (Gunn et al., 2011).
For dry snowpacks deeper than 5 cm or SWE greater than 10 mm, isotropic scattering of naturally
emitted MW radiation by snow crystals occurs (Ulaby and Stiles, 1980). Below the 20 GHz
frequency threshold, snow is almost transparent. For RS snow applications, this emission behavior
is detected at frequencies greater than 20 GHz (e.g. Chang et al., 1987). This has become the
baseline approach for SD and SWE retrievals.
Generally, the strength of the scattering signal is proportional to the SWE or SD for snow-covered
terrain. Several algorithms for SD or SWE retrievals have been proposed in the past (e.g. Chang
et al., 1987). Later, these algorithms were updated for forested areas by Foster et al. (1997). These
approaches use the MW TB gradient between the 19 and 37 GHz channels as a scattering strength
estimate, calibrated statically to the SWE. Recent studies have shown improvement in SWE
estimations at regional scales through the use of numerical techniques for the inversion of semiempirical relationships (e.g. Tedesco et al., 2004). Grippa et al. (2004) used a dynamic algorithm
to estimate seasonal SWE in Siberia. Kelly et al. (2003) developed a dynamic algorithm that
demonstrated that the original statically-parameterized algorithms (Chang et al., 1987 and Foster
et al., 1997) can be improved by explicitly accounting for physical snowpack changes (e.g. grain
size and density). The current standard JAXA SD algorithm implemented for AMSR-E has
evolved from this approach, but with the parameterization of grain size based on TB polarization
signatures (Kelly, 2009). This is also the approach used as baseline for the AMSR2
implementation.
The algorithm considers snow to be either moderate to deep snow, or shallow snow. For moderate
to deep snow to be present, there are two criteria that have to be met. First, the difference between
non-scattering and scattering channels must be greater than zero. In order to do this, the following
equation is used:
MW19V – MW37V > 0
Equation 50
162
This approach has demonstrated that a positive TB difference between a non-scattering channel
(19 GHz) and a scattering channel (37 GHz) indicates the presence of a scattering medium (Chang
et al., 1987). Scattering effects can also be observed at the 18 or 19 GHz wavelengths for deeper
snowpacks (Tsang et al., 2000). The use of the 10 GHz channel on AMSR2 provides greater
insensitivity to SD. For moderate to deep snow accumulations to be detected, either of the
following two conditions must be satisfied:
MW10V – MW37V > 0
Equation 51
MW10H – MW37H > 0
Equation 52
The dominant physical mechanism used for estimating the presence and amount of snow is volume
scattering. Scattering can be caused not only by dry snow, but by rainfall hydrometeors. Thus, a
threshold must be identified to separate out these two scattering types (e.g. Grody and Basist,
1996). Normally, rainfall has a higher TB at 37 GHz than snow. Kelly (2009) suggested that at
MW37V and MW37H, the thresholds should be 255K and 245K, respectively.
Shallow snow is particularly challenging to detect, since it is mostly transparent at the MW37
frequencies. Hence, by using a combination of the 23 and 89 GHz channels at vertical and
horizontal polarizations, and a surface temperature estimator, Kelly et al. (2003) demonstrated
that:
ܶ௣௛௬௦ ൌ ͷͺǤͲͺ െ ͲǤ͵ͻ‫ ܸͻͳܹܯ‬൅ ͳǤʹͳ‫ ܸ͵ʹܹܯ‬െ ͲǤ͵͹‫͵ܹܯ‬͹‫ ܪ‬൅ ͲǤ͵͸‫ܹܯ‬ͺͻܸሺ‫ܭ‬ሻ
Equation 53
ܶ௣௛௬௦ , is the surface estimator, and is accurate to ±6 K. Locations where ܶ௣௛௬௦ is less than 267 K
are flagged as locations where shallow snow is possible, if moderate to deep snow has not been
previously detected. To ensure that shallow snow is present, the following condition is also
evaluated:
MW23V > MW89V & MW89V < 255 K & MW23H > MW89H & MW89H < 255 K
Equation 54
The 255 K threshold is a conservative value to ensure that only cold TBs related to snow cover
emission are used. By ensuring that MW89V and MW89H are less than the 255 K threshold in
(and that ܶ௣௛௬௦ is less than 267 K) the probability that atmospheric contamination is present is
minimized.
163
8.3.3 JAXA AMSR2 SD and SWE algorithm implementation
8.3.3.1 Implementation
The current standard retrieval is performed using L1R Global Swath data. SD retrievals are
performed on the instantaneous field of view (IFOV) samples. The procedure is defined by five
(5) steps.
1) Obtain TBs. AMSR2 TBs are acquired from L1R data and used at native channel resolution
with the exception of the 89 GHz channel, which is re-sampled to the 37 GHz channel resolution.
2) Calculateܶ௣௛௬௦ . The surface physical temperature (ܶ௣௛௬௦ ) in Kelvin using Eq. 53.
3) Test for moderate to deep snow presence. Thresholds are checked to ensure cold snow
conditions are potentially present in the 37 GHz TBs (MW37H < 245 K & MW37V < 255K). If
the condition is true then snow is possible and shallow or medium depth of snow is retrieved (see
step 5). If this condition is not met, then a shallow snow test is performed (step 4).
4) Test for shallow SD. If MW10V – MW37V > 0 K or MW10H – MW37H > 0 K, medium to
deep snow is assumed to be present (go to full retrieval, see step 5). Otherwise snowpack is
possibly shallow if: MW89V <= 255 K and MW89H <= 265 K and MW23V – MW89V > 0 K
and MW23H – MW89H > 0 K and ܶ௣௛௬௦ < 267 K. If shallow snow is detected, SD = 5.0 cm.
5) Moderate to deep SD retrieval. For SD retrieval, the following general procedure is performed:
ܵ‫ ܦ‬ൌ ݂݂൫ܵ‫ܦ‬௙ ൯ ൅ ሺͳ െ ݂݂ሻሺܵ‫ܦ‬଴ ሻሺܿ݉ሻ
Equation 55
where SDf is the snow depth from the forest component of the IFOV and SDo is the snow depth
from non-forested component of the IFOV:
ሺெௐଵଽ௏ିெௐଷ଻௏ሻ
ܵ‫ܦ‬௙ ൌ ቂ
ቃ Ȁሺͳ െ ͲǤ͸݂݀ሻሺܿ݉ሻ
Equation 56
୪୭୥భబ ሺெௐଷ଻௏ିெௐଷ଻ுሻ
ܵ‫ܦ‬଴ ൌ ቂ
ሺெௐଵ଴௏ିெௐଷ଻௏ሻ
ቃ+ቂ
୪୭୥భబ ሺெௐଷ଻௏ିெௐଷ଻ுሻ
ሺெௐଵ଴௏ିெௐଵଽ௏ሻ
୪୭୥భబ ሺெௐଵଽ௏ିெௐଵଽுሻ
ቃ ሺܿ݉ሻ
Equation 57
164
where ff is the forest fraction (where a ff of 1.0 = 100% forest fraction and a ff of 0.0 = 0% forest
fraction) from the MOD12Q1IGBP product, and fd is the forest high spatial resolution (500 m)
forest density from University of Maryland Vegetation Continuous Field (VCF) data circular
smoothed at 15 km diameter and re-gridded to global 1 km. The polarization factors V-H are
constrained through optimization to vary conservatively throughout the season as the mean depthintegrated snowpack grain size increases (Kelly, 2009).
Note: The MW19 - MW37 gradient is used to maximize spatial resolution in forested areas,
whereas the MW10V - MW37V (increased dynamic range) and MW10V – MW19V gradients are
used for deep snow.
8.3.3.2 Input parameters
The input parameters are divided into two categories: dynamic swath granule TB file (L1R) and
static ancillary data files designed to characterize forest cover, land, oceans, coasts and ice cover
and snow climatology. JAXA AMSR2 L1R swath data form the basis of the SD retrievals and are
obtained at the Earth Observation Research Center (EORC) as part of the processing chain. The
output file for the first step is a swath product of four raster grid arrays. The first two are decimal
latitude and longitude grids (243 x 2100 floating point values), the third array contains snow depth
estimates in centimeters (243 x 2100 cell array of floating point values) and the fourth data layer
is a cell array of flags that identifies different surfaces or bad data. The following flags are
included:
Snow possible: 0
Water: 16
Climatologically snow impossible: 32
Permanent ice: 48
Tb out of range: 192
Bad spacecraft attitude: 208
Bad Tb: 224
165
The initial algorithm processing step, where the primary retrieval is performed, provides SD values
for all samples in the swath granule. Retrievals are conducted on the day and nighttime data. The
retrieval data are retained as swath data (scene data) before the processing suite computes daily
global (latitude and longitude) SD and north polar stereographical projected SD for day and night.
Finally, the data are composited to produce monthly global and polar projected SD estimates.
8.3.3.3 Ancillary data
The following data sets are used to parameterize the retrieval algorithm. These are static data sets
and are created for the algorithm and ingested at algorithm runtime.
1. Global forest fraction from Boston University data (MOD12Q1IGBP) circular smoothed
(15 km diameter) and mapped to 0.00833° grid (Hansen et al., 2003)
2. Global forest ‘spatial density’ from University of Maryland Vegetation Continuous
Fraction (VCF) (500m) circular smoothed (15 km diameter) and re-gridded to 0.00833°
3. Land, Ocean Coasts & Ice mask derived from MODIS MOD12Q1 IGBP land cover data
(collection V004)
If more than 50 % water cover is present in a 25 x 25 km EASE-Grid cell, the grid cell is flagged
as water. Additionally, the snow climatology data set (Dewey and Heim, 1982) is used to determine
the possibility/ impossibility of snow presence.
166
8.3.4 Results
In order to conclude if the models developed to estimate SD and SWE using MW RS products are
robust, validation using existing products is necessary. For this particular reason, JAXA’s own SD
and SWE global products were compared to the developed SD and SWE RT global maps. The
validation effort was performed from January 1st to April 30th, 2017, as these are months when
snow cover is undeniably present in many regions worldwide. This analysis was not only done for
the sake of validating the models, but to verify whether or not a bias correction needed to be
performed for the RT algorithms. The analysis was divided into three segments: World, World
minus Antarctica and Greenland, and Americas only. The main reason for these split analyses was
because there are many climatological and topographical differences in diverse regions of the
World that lead to inherently distinct snowpack types. The RT models were developed using data
from one in-situ station in the United States. No snowpack in the US resembles the snowpack
present in Antarctica nor Greenland, and both regions are large enough to skew the results in any
direction. The comparisons were split by daytime and nighttime satellite overpasses as well.
Scatter plots for all validation efforts between JAXA’s SD and SWE products (ordinates) and the
developed SD and SWE RTs (abscissas) are illustrated from Figs. 58 to 73. Each figure is
subdivided by month, overpass, and the three cases described above. The results corresponding to
each figure are shown by means of tables. See Tables 25 to 40. Additionally, Tables 41 and 42
display a summary of the results by combining all overpasses and months. Table 41 presents the
SD validation summary, while Table 42 highlights the summary for the SWE validation effort.
167
Figure 58. JAXA snow depth global map vs RT developed snow depth global map daytime comparison
for the month of January. There are three cases - top: World, middle: World minus Antarctica and
Greenland, bottom: Americas only.
Table 25. Results for the JAXA snow depth global map vs RT developed snow depth global map daytime
comparison for the month of January for each case: World, World minus Antarctica and Greenland, and
Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1978899)
(n = 379945)
(n = 153545)
R
0.42
0.50
0.64
Bias (cm)
33.10
21.69
13.48
RMSE (cm)
38.05
29.60
22.11
Std. dev. (cm)
18.75
20.15
17.52
Slope
0.33
0.43
0.55
Intercept (cm)
5.15
7.15
4.84
168
Figure 59. JAXA snow depth global map vs RT developed snow depth global map nighttime comparison
for the month of January.
Table 26. Results for the JAXA snow depth global map vs RT developed snow depth global map nighttime
comparison for the month of January for each case: World, World minus Antarctica and Greenland, and
Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 2052007)
(n = 471143)
(n = 241065)
R
0.46
0.59
0.67
Bias (cm)
32.11
20.68
15.22
RMSE (cm)
37.37
29.02
24.08
Std. dev. (cm)
19.12
20.35
18.67
Slope
0.34
0.47
0.53
Intercept (cm)
4.44
4.01
2.23
169
Figure 60. JAXA SWE global map vs RT developed SWE global map daytime comparison for the month
of January.
Table 27. Results for the JAXA SWE global map vs RT developed SWE global map daytime comparison
for the month of January for each case: World, World minus Antarctica and Greenland, and Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1684196)
(n = 364855)
(n = 153544)
R
0.24
0.38
0.46
Bias (cm)
9.37
5.88
3.50
RMSE (cm)
10.38
8.05
6.35
Std. dev. (cm)
4.45
5.50
5.30
Slope
0.25
0.30
0.37
Intercept (cm)
2.42
3.30
2.84
170
Figure 61. JAXA SWE global map vs RT developed SWE global map nighttime comparison for the month
of January.
Table 28. Results for the JAXA SWE global map vs RT developed SWE global map nighttime comparison
for the month of January for each case: World, World minus Antarctica and Greenland, and Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1761759)
(n = 456591)
(n = 240987)
R
0.35
0.54
0.62
Bias (cm)
9.09
5.72
4.03
RMSE (cm)
10.16
7.80
6.37
Std. dev. (cm)
4.54
5.30
4.93
Slope
0.31
0.40
0.46
Intercept (cm)
1.38
1.51
0.98
171
Figure 62. JAXA snow depth global map vs RT developed snow depth global map daytime comparison
for the month of February.
Table 29. Results for the JAXA snow depth global map vs RT developed snow depth global map daytime
comparison for the month of February for each case: World, World minus Antarctica and Greenland, and
Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1737270)
(n = 294487)
(n = 98604)
R
0.36
0.38
0.54
Bias (cm)
33.42
20.85
9.34
RMSE (cm)
38.32
30.33
21.27
Std. dev. (cm)
18.74
22.02
19.11
Slope
0.34
0.34
0.43
Intercept (cm)
6.00
14.46
14.68
172
Figure 63. JAXA snow depth global map vs RT developed snow depth global map nighttime comparison
for the month of February.
Table 30. Results for the JAXA snow depth global map vs RT developed snow depth global map nighttime
comparison for the month of February for each case: World, World minus Antarctica and Greenland, and
Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1826747)
(n = 401104)
(n = 191020)
R
0.43
0.58
0.69
Bias (cm)
32.20
19.77
13.74
RMSE (cm)
37.46
28.62
22.62
Std. dev. (cm)
19.15
20.70
17.97
Slope
0.38
0.50
0.61
Intercept (cm)
3.92
4.17
1.53
173
Figure 64. JAXA SWE global map vs RT developed SWE global map daytime comparison for the month
of February.
Table 31. Results for the JAXA SWE global map vs RT developed SWE global map daytime comparison
for the month of February for each case: World, World minus Antarctica and Greenland, and Americas
only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1465940)
(n = 281229)
(n = 98587)
R
0.18
0.24
0.35
Bias (cm)
8.91
5.26
1.85
RMSE (cm)
10.07
8.14
6.38
Std. dev. (cm)
4.69
6.21
6.11
Slope
0.21
0.18
0.24
Intercept (cm)
3.67
5.73
5.64
174
Figure 65. JAXA SWE global map vs RT developed SWE global map nighttime comparison for the month
of February.
Table 32. Results for the JAXA SWE global map vs RT developed SWE global map nighttime comparison
for the month of February for each case: World, World minus Antarctica and Greenland, and Americas
only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1562069)
(n = 387892)
(n = 190990)
R
0.34
0.53
0.63
Bias (cm)
8.57
5.13
3.23
RMSE (cm)
9.78
7.46
5.80
Std. dev. (cm)
4.70
5.42
4.82
Slope
0.34
0.42
0.52
Intercept (cm)
1.62
1.90
1.22
175
Figure 66. JAXA snow depth global map vs RT developed snow depth global map daytime comparison
for the month of March.
Table 33. Results for the JAXA snow depth global map vs RT developed snow depth global map daytime
comparison for the month of March for each case: World, World minus Antarctica and Greenland, and
Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1644678)
(n = 196442)
(n = 40281)
R
0.35
0.24
0.41
Bias (cm)
34.88
23.52
2.13
RMSE (cm)
39.17
33.38
22.22
Std. dev. (cm)
17.82
23.69
22.12
Slope
0.34
0.19
0.27
Intercept (cm)
5.62
20.09
24.97
176
Figure 67. JAXA snow depth global map vs RT developed snow depth global map nighttime comparison
for the month of March.
Table 34. Results for the JAXA snow depth global map vs RT developed snow depth global map nighttime
comparison for the month of March for each case: World, World minus Antarctica and Greenland, and
Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1802272)
(n = 320778)
(n = 127737)
R
0.36
0.49
0.72
Bias (cm)
32.52
16.44
4.44
RMSE (cm)
37.81
28.34
18.49
Std. dev. (cm)
19.30
23.08
17.95
Slope
0.35
0.44
0.67
Intercept (cm)
6.37
11.31
8.70
177
Figure 68. JAXA SWE global map vs RT developed SWE global map daytime comparison for the month
of March.
Table 35. Results for the JAXA SWE global map vs RT developed SWE global map daytime comparison
for the month of March for each case: World, World minus Antarctica and Greenland, and Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1354919)
(n = 182250)
(n = 40274)
R
0.16
0.12
0.44
Bias (cm)
9.15
5.57
-0.91
RMSE (cm)
10.23
8.78
5.91
Std. dev. (cm)
4.58
6.79
5.84
Slope
0.19
0.08
0.26
Intercept (cm)
3.91
6.63
6.41
178
Figure 69. JAXA SWE global map vs RT developed SWE global map nighttime comparison for the month
of March.
Table 36. Results for the JAXA SWE global map vs RT developed SWE global map nighttime comparison
for the month of March for each case: World, World minus Antarctica and Greenland, and Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1509881)
(n = 306119)
(n = 127714)
R
0.20
0.36
0.61
Bias (cm)
8.38
3.58
-0.14
RMSE (cm)
9.83
7.53
5.24
Std. dev. (cm)
5.15
6.63
5.24
Slope
0.21
0.28
0.53
Intercept (cm)
4.00
4.85
4.02
179
Figure 70. JAXA snow depth global map vs RT developed snow depth global map daytime comparison
for the month of April.
Table 37. Results for the JAXA snow depth global map vs RT developed snow depth global map daytime
comparison for the month of April for each case: World, World minus Antarctica and Greenland, and
Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1372527)
(n = 84832)
(n = 905)
R
0.44
0.44
0.31
Bias (cm)
34.83
28.79
-3.51
RMSE (cm)
38.61
34.68
21.88
Std. dev. (cm)
16.65
19.33
21.61
Slope
0.40
0.38
0.22
Intercept (cm)
0.96
6.03
23.24
180
Figure 71. JAXA snow depth global map vs RT developed snow depth global map nighttime comparison
for the month of April.
Table 38. Results for the JAXA snow depth global map vs RT developed snow depth global map nighttime
comparison for the month of April for each case: World, World minus Antarctica and Greenland, and
Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1462319)
(n = 142177)
(n = 13890)
R
0.41
0.45
0.44
Bias (cm)
33.14
18.58
-7.49
RMSE (cm)
37.81
30.38
22.20
Std. dev. (cm)
18.19
24.04
20.90
Slope
0.36
0.32
0.31
Intercept (cm)
4.42
12.95
24.22
181
Figure 72. JAXA SWE global map vs RT developed SWE global map daytime comparison for the month
of April.
Table 39. Results for the JAXA SWE global map vs RT developed SWE global map daytime comparison
for the month of April for each case: World, World minus Antarctica and Greenland, and Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1102412)
(n = 71481)
(n = 891)
R
0.30
0.24
0.43
Bias (cm)
9.31
7.27
-4.17
RMSE (cm)
10.20
9.34
5.64
Std. dev. (cm)
4.17
5.88
3.81
Slope
0.36
0.17
0.41
Intercept (cm)
0.99
4.48
5.57
182
Figure 73. JAXA SWE global map vs RT developed SWE global map nighttime comparison for the month
of April.
Table 40. Results for the JAXA SWE global map vs RT developed SWE global map nighttime comparison
for the month of April for each case: World, World minus Antarctica and Greenland, and Americas only.
Case
Performance metric
Globe
No AQ, GL
Americas only
(n = 1188684)
(n = 127771)
(n = 13829)
R
0.28
0.33
0.47
Bias (cm)
8.81
4.36
-4.45
RMSE (cm)
9.97
8.14
5.88
Std. dev. (cm)
4.66
6.88
3.84
Slope
0.29
0.21
0.45
Intercept (cm)
2.35
4.53
5.92
183
Table 41. Summary of the results for the JAXA SD global map vs RT developed SD global map comparison
for all overpasses and months combined for each case: World, World minus Antarctica and Greenland, and
Americas only.
Snow depth
Performance metric
Globe
No AQ, GL
Americas only
(n = 13876719)
(n = 2290908)
(n = 867047)
R
0.40
0.49
0.65
Bias (cm)
33.19
20.53
11.34
RMSE (cm)
38.04
29.79
22.15
Std. dev. (cm)
18.55
21.45
18.46
Slope
0.35
0.41
0.54
Intercept (cm)
4.71
8.93
6.34
184
Table 42. Summary of the results for the JAXA SWE global map vs RT developed SWE global map
comparison for all overpasses and months combined for each case: World, World minus Antarctica and
Greenland, and Americas only.
SWE
Performance metric
Globe
No AQ, GL
Americas only
(n = 11629860)
(n = 2178188)
(n = 866816)
R
0.26
0.39
0.55
Bias (cm)
8.95
5.24
2.52
RMSE (cm)
10.08
7.94
6.05
Std. dev. (cm)
4.63
5.90
5.17
Slope
0.27
0.30
0.43
Intercept (cm)
2.55
3.60
2.68
The summary of the results indicates that the inclusion of Antarctica and Greenland clearly skews
the validation, as was expected. Mostly because the RTs were trained using data from the United
States. The snowpack present in AQ and GL is most likely quite different from any snowpack in
the US. Results improved for both RT models when only the Americas were considered for the
validation. This further proves the hypothesis that in order for the RTs to fare better, these would
have to be trained using additional station data -preferably stations in other regions around the
World, not just AQ and GL. We can also notice systematic biases and random errors that can be
associated with the same issue. There are additional limitations to consider, these will be discussed
in Section 8.5. While JAXA’s SD and SWE algorithms and the developed SD and SWE RT
algorithms are not entirely different, both take different input parameters into account in order to
make predictions. This issue makes it difficult to compare them on a 1:1 basis, and thus, associate
the biases and errors to either one of them. In order to find a common ground between both
185
predictions, JAXA’s products and the developed RT algorithms were validated against in-situ
station data in the next section.
8.4
Validation of SD and SWE products against field-based data
In order to conclude if the developed RT models provide accurate SD and SWE estimates, field
measurement data was used for validation. Furthermore, these in-situ data was used as a reference
data set or “ground truth” because there were differences between the JAXA SD and SWE
algorithm and the RT algorithm. Hence, using field measurement data as the reference, we can
understand where the errors are coming from. The in-situ SD and SWE data was obtained from
Snow Telemetry (SNOTEL) stations.
8.4.1 SNOTEL
The U.S. Department of Agriculture (USDA) Natural Resources Conservation Service (NRCS)
forecasts water supply in 12 Western States where snowpack is the principle contributor to surface
water supplies. Basic data are collected for the purpose of developing water supply forecasts. Snow
survey data are available to the public. Snow survey data are collected manually and remotely.
Manual measurements are taken at snow courses and using aerial markers to collect SD and SWE
data. The scheduling of manual measurements varies, but is generally once a month, on or near
the first of each month during the snow season (January 1 to May 1).
Data are collected remotely using a large network of automated data collection platforms known
collectively as the SNOw TELemetry (SNOTEL) network. The standard data types collected at a
SNOTEL site are SWE, total accumulated precipitation, air temperature, and SD. Additional
sensors may be included to measure soil moisture, soil temperature, wind speed, wind direction,
solar radiation, relative humidity, barometric pressure and precipitation (tipping bucket). The
standard reporting period for SNOTEL data is once a day, at midnight, although it is recommended
that data be reported on an hourly basis when possible. Besides making the data more valuable to
more users for more applications, hourly report periods also make the data more consistent with
the guidelines for hydroclimatic stations of other agencies such as NOAA, World Meteorological
Organization (WMO), and NWS.
186
8.4.2 SNOTEL stations
Because the USDA NRCS provides SD and SWE data over 12 western U.S. states, the same
amount of stations were selected for this study. The twelve stations (one per state) were chosen
based on different topography, surface characteristics, and climatological conditions. See Table
43. Photographs for each SNOTEL station used in this study are illustrated in Appendix C.
Table 43. Summary of the twelve SNOTEL stations used in this study based on elevation, latitude,
longitude, ID, and Hydrologic Unit Codes (HUCs).
Location
Elevation (ft)
Latitude
Longitude
ID
HUC
Fairbanks, AK
450
64.85
-147.8
1174
190405060907
Hawley Lake, AZ
8300
33.97
-109.77
1271
150601020106
Blue Lakes, CA
8067
38.61
-119.92
356
180400120101
Copeland Lake, CO
8600
40.21
-105.57
412
101900050202
Moscow Mountain, ID
4700
46.81
-116.85
989
170603061002
Rocky Boy, MT
4700
48.17
-109.65
917
100500040101
Summit Lake, NV
7615
41.49
-119
1194
160402021301
Signal Peak, NM
8360
32.92
-108.15
755
150400010803
Miller Woods, OR
420
45.25
-123.28
1084
170900080606
Little Bear, UT
6548
41.41
-111.83
582
160102030103
Huckleberry Creek, WA
2250
47.07
-121.59
928
171100140307
Cole Canyon, WY
5910
44.49
-104.41
982
101202030102
187
8.4.3 SNOTEL SD and SWE measurements
The SNOTEL SD and SWE measurement types and equipment are described briefly below:
SWE (See Table 44 for criteria)
Purpose: To determine the amount of water content in the snowpack at a particular location
primarily for stream flow/water supply forecasting.
Measurement types
Manual: Snow tube measurements and manometer measurements.
Approved equipment
• Standard Federal Sampler
• McCall cutter
• Snow pillow manometer
Automated: Snow pillow (hypalon or metal) and associated instrumentation to collect SWE on a
predetermined sampling and reporting interval.
Approved equipment
• Fluid based
• Flexible
• Snow pillow
Calculated: Any process that is used to determine SWE from other collected data.
Approved equipment
• Standard statistical procedures
188
Table 44. SNOTEL criteria for SWE measurements.
Attribute
Threshold
Units
Inches
Resolution
0.1 inches
Accuracy
Snow tube manual measurement (cutter teeth
+4% to +10% depending on snow conditions
sharpened flat)
Fluid base, flexible, snow pillow/
±4% over full scale
transducer based
Measurement range
0 to 250 inches of water
Sensor sampling interval
Minimum 1 hour
Sensor reporting interval
24-hour current SWE
SD (See Tables 45 and 46 for criteria)
Purpose: To aid in the determination of snow depth.
Measurement types
Manual: Visual observation of depth taken at regularly scheduled time intervals.
Approved equipment
• Standard Federal Sampler
• McCall cutter
• Snow stakes
• Snow board
189
• Aerial markers
Automated: Use of electronic equipment to measure and record snow depth on a scheduled time
frame.
Approved equipment
• Ultrasonic snow depth sensor
Calculated: Any process that is used to determine depth from other collected data.
Approved equipment
• Standard statistical procedures
Table 45. SNOTEL criteria for SD manual measurements.
Attribute
Threshold
Units
Inches
Resolution
0.5 inches
Accuracy
േ0.5 inches
Measurement range
0 to 30 feet
190
Table 46. SNOTEL criteria for SD automated measurements.
Attribute
Threshold
Units
Inches
Resolution
0.5 inches
Accuracy
±2 inches or 0.4% distance to target
Must have temperature compensation built into
Temperature correction
device
Beamwidth
22 degrees
Sensor operating range
–30 to +70 °C
Measurement range
0.5 to 10 meters
Sensor sampling interval
Minimum 1 hour
Sensor reporting interval
One reading of the current value reported in inches of
depth
191
8.4.4 Results
This section shows the results for the satellite (JAXA, SD and SWE RT) product vs in-situ
(SNOTEL) measurement validation. A comparison between satellite product and field
measurement SD and SWE data for the twelve SNOTEL stations described in Section 8.4.2 was
performed from January 1st to April 30th, 2017. As discussed previously, most SNOTEL SD and
SWE manual observations are performed once a day. Hence, these in-situ observations were
compared to the average (between daytime and nighttime overpasses) satellite product estimates.
The results between JAXA and SNOTEL for SD and SWE are shown in Tables 47 and 48, while
those between the developed SD and SWE RT algorithms and SNOTEL are illustrated in Tables
49 and 50.
Table 47. JAXA vs SNOTEL SD comparison for twelve SNOTEL stations from January 1st to April 30th,
2017.
Snow depth - SNOTEL vs JAXA
Metric
R
Bias
(cm)
RMSE
(cm)
AK
AZ
CA
CO
ID
MT
NV
NM
OR
UT
WA
WY
0.19
0.18
0.02
0.66
0.57
0.56
0.02
0.04
0.51
0.05
0.75
0.41
30.98
53.23
246.18
1.78
123.21
-0.99
90.73
7.02
-3.04
87.37
13.03
20.82
34.45
63.77
252.18
25.28
125.58
12.60
91.74
13.70
5.76
102.03
19.52
25.43
15.14
35.27
54.91
25.33
24.40
12.61
13.60
11.82
4.92
52.93
14.59
14.67
Std.
dev.
(cm)
192
Table 48. JAXA vs SNOTEL SWE comparison for twelve SNOTEL stations from January 1st to April
30th, 2017.
SWE - SNOTEL vs JAXA
Metric
R
Bias
(cm)
RMSE
(cm)
AK
AZ
CA
CO
ID
MT
NV
NM
OR
UT
WA
WY
0.35
0.17
-0.01
0.78
0.30
0.73
0.42
0.15
0.54
0.16
0.73
0.39
5.87
18.19
112.12
3.08
42.39
1.15
31.44
1.75
-0.73
29.78
5.01
4.91
6.68
21.55
119.09
7.02
43.44
2.84
31.92
3.32
1.39
34.33
6.72
5.91
3.21
11.59
40.31
6.33
9.50
2.61
5.53
2.84
1.18
17.14
4.50
3.29
Std.
dev.
(cm)
Table 49. SD RT vs SNOTEL SD comparison for twelve SNOTEL stations from January 1st to April 30th,
2017.
Snow depth - SNOTEL vs SD RT
Metric
R
Bias
(cm)
RMSE
(cm)
AK
AZ
CA
CO
ID
MT
NV
NM
OR
UT
WA
WY
0.18
0.26
0.07
0.57
0.50
0.49
-0.02
-0.05
0.30
0.15
0.67
0.52
5.81
35.79
235.91
-1.90
101.97
-17.57
75.06
-6.45
-19.15
74.91
-0.33
6.77
21.90
49.67
242.19
26.93
104.77
27.44
77.56
15.76
25.50
91.24
16.95
15.61
21.20
34.59
55.04
26.98
24.15
21.16
19.59
14.44
16.91
52.31
17.02
14.12
Std.
dev.
(cm)
193
Table 50. SWE RT vs SNOTEL SD comparison for twelve SNOTEL stations from January 1st to April
30th, 2017.
SWE - SNOTEL vs SWE RT
Metric
R
Bias
(cm)
RMSE
(cm)
AK
AZ
CA
CO
ID
MT
NV
NM
OR
UT
WA
WY
-0.29
0.08
0.03
0.77
0.27
0.92
0.51
-0.13
0.25
0.08
0.72
0.11
-1.31
15.37
109.30
1.84
37.51
-6.34
26.66
-1.92
-3.97
27.57
-0.64
2.80
6.96
19.33
116.44
7.02
38.70
7.44
27.17
4.14
5.21
32.43
4.92
4.79
6.87
11.76
40.32
6.81
9.54
3.91
5.27
3.69
3.39
17.16
4.90
3.91
Std.
dev.
(cm)
Results hardly indicate any difference between both algorithms (JAXA and RT) and the SNOTEL
in-situ data. However, the developed RTs seem to provide better results than JAXA’s algorithms
when compared to SNOTEL. The systematic biases and random errors appear to be smaller for the
SD and SWE RT algorithms for most stations. Hence, it seems inappropriate to correct the
developed RTs for biases using JAXA’s products, as these provided larger errors when compared
to in-situ data. Some possible sources of error for both algorithms are discussed in the next section.
8.5
Limitations
The simplicity of the algorithm implementation allows a fast inversion. However, it is also the
source of errors that are known to be related to SD retrievals from satellite passive MW
observations: (1) snow emission attenuation by atmospheric effects caused by variations in
atmospheric thickness (JAXA and SD RT); (2) snow emission attenuation by forest and tall stand
vegetation (SD RT); (3) grain size and density evolution (JAXA); (4) fractional emission effects
on mixing by water bodies (in frozen and liquid states) (JAXA and SD RT); (5) inability to map
the snow depth of wet snow (JAXA).
194
Atmospheric Attenuation: the MW signal emitted at the surface passes through the atmosphere
before being detected by a space-borne sensor, and thus it is subject to the effects of atmospheric
absorption and emission. This attenuation varies with the optical depth of the atmosphere (as a
function of variable land surface elevation), air mass type, and MW frequency. Consequently, the
MW19 – MW37 TB gradient from space-borne data can be different from those obtained using
TBs at the surface (Wang and Tedesco, 2007; Markus et al. 2006). The TBs observed by AMSR2
depend on the effective atmospheric temperature (Ta), optical depth (τ), surface emissivity (e), and
surface temperature (Ts). Rawinsonde data from different stations can be used to stratify Ta and τ.
Surface emissivity can be derived through an atmospheric absorption model (e.g. Rosenkranz,
1998), and the surface TB can then be obtained by the product of e and Ts. This works for clearsky conditions, and is the rationale for the work presented by Savoie et al. (2009) who simplified
this background science and corrected retrievals over the Tibetan plateau by simple atmospheric
TB corrections based on an empirical model and elevation information. For cloud-covered skies,
it is necessary to have information about the cloud thickness and LWC. Recent results show that
even under clear sky conditions, the atmospheric absorption could account for as much as ‫ ׽‬2550 % of SD or SWE estimations, depending on the reference TBs (Wang and Tedesco, 2007).
Forest Attenuation: forest cover represents a significant source of error for satellite passive MW
SD and SWE retrieval algorithms. The presence of forest attenuates the radiation emitted by the
underlying snowpack, thus affecting the retrieval accuracy of the algorithm. The problem is
complex: stem volume and canopy closure and gap fraction within a footprint are important
modulators of passive MW emission. At the northern edge of the boreal forest, stunted conifers
that are sparse might be considered forest and yield a reasonably accurate SD estimate. However,
in the middle of the taiga, a pixel covered by dense forest growth would yield much less SWE
using passive MW measurements. With newer high spatial resolution vegetation products
available, such as the Vegetation Continuous Fraction (VCF) product (Hansen et al., 2003) and
the global Landsat GeoCover data base at the University of Maryland, significant improvement in
forest (and other vegetation type) parameterization is possible. Recent work by Metsamaki et al.
(2005) demonstrates an effective approach to mapping snow in forested lands which could be of
benefit to improve forest parameterization.
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Snow microphysical properties: Kelly and Chang (2003) demonstrated that SWE retrieval errors
can be caused by not accounting for snowpack physical properties (i.e. GS and density) that
metamorphose during the snow season. Snow crystals metamorphose in response to vapor
gradients within the snowpack and as a result of melting and refreezing cycles, which alter the
bulk snowpack structure. Furthermore, snow bulk density changes during the season. These
physical properties control the snow MW response (Armstrong et al., 1993). While empirical and
physically-based models have been developed to predict the growth of the snow crystals and
density (e.g. Jordan, 1991), it is not trivial which model to select to account for regional-to-global
scale conditions. The current AMSR2 SD algorithm uses polarization information to attempt to
account for the temporal evolution of a snowpack (especially GS). The polarization gradient at 36
GHz (19 GHz for thicker snowpacks) changes as the snowpack GS metamorphoses (Matzler,
1987). However, it is known that the current standard algorithm’s performance is substandard in
the north east Siberian regions (Clifford, 2010).
Effect of terrestrial water bodies: Lakes and ponds affect the accuracy of passive MW SD and
SWE retrievals because the strong TB gradient between liquid and frozen water changes the TB
gradient between the 19 and 37 GHz channels. Analysis of airborne passive MW data acquired in
the Northwest Territories, Canada in April 2005 showed that the relationship between MW37V
and lake cover fraction is reversed across the northern boreal forest, compared to the open tundra
(Derksen et al., 2005). Over forested sites, lower MW37V measurements were observed over lakes
relative to land, while the MW19V data showed little sensitivity to lakes. Conversely, the MW37V
values at tundra sites were greater over lakes than over terrestrial surfaces. This difference in
response to lake ice at MW37V impacts SWE retrievals because the increase in TB at 37 GHz
across lake rich tundra areas reduces the MW37V – MW19V gradient. Based on this knowledge,
Derksen et al. (2010) led to a tundra-specific algorithm for SWE estimation.
Wet snow mapping: The presence of liquid water within the snowpack increases the absorption
and emission of radiation, reducing the emission depth from the surface. As a consequence the
MW19 – MW37 gradient approaches 0 K, completely terminating the sensitivity to SD or SWE.
Therefore, it is important to distinguish between dry and wet snow conditions, to exclude those
pixels containing wet snow in order to reduce the uncertainty on the SWE retrieval. Walker and
Goodison (1993) reported a wet snow discrimination technique based on the 37 GHz polarization
196
gradient while Sun et al. (1996) used a neural network to determine snow wetness in vegetated
terrain. Identification of wet snow is an important aspect of SD and SWE mapping with passive
MW observations.
8.6
CREST Snow Depth and SWE product
The resulting SD and SWE RT algorithms from this study were made into a satellite product named
CREST Snow Depth and SWE product. It operates by downloading AMSR2 MW TB data at 12
AM every day via JAXA’s FTP server and reading these MW TB data files into the RT algorithms
to create SD and SWE daily global maps. These maps are then uploaded into the product website:
https://noaacrest.org/snow/products/. All of these processes are fully automated. Figure 74
illustrates the CREST Snow Depth and SWE product website home page.
Figure 74. CREST Snow Depth and SWE product website home page.
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9
9.1
Conclusions and future work
Conclusions
Snow cover plays an important role at the regional-to-global scale because it represents a
significant portion of the insolation, thus maintaining the Earth’s radiation budget in balance.
Approximately 40–50% of the Northern Hemisphere is covered with snow during mid-winter,
making snow cover the most prevalent land cover type throughout the season. On a regional scale,
snow cover is important for local water availability, river runoff, and groundwater recharge;
particularly in middle to high latitudes. Furthermore, in countries like Norway and Switzerland,
where electricity is mainly generated through hydropower stations, snow cover plays a major role
in energy supply. Within this context, exact knowledge of the snow-covered areas is essential for
water resource management (e.g. snowmelt runoff models). Moreover, information about the snow
water equivalent is important for hydrological modeling and water resource management.
Additionally, snow depth changes influence the vegetation growth of certain land cover types.
Climate change has impacted snow-covered areas, as a decrease in snow cover has been observed
globally since the 1960s - when satellites first started to monitor the Earth’s surface. However, in
regions like China, an increase in snow cover has been observed. Climate change influences the
global snow cover conditions with earlier melting and less area coverage. Furthermore, snow
properties such as SD may also increase because of high temperatures depending on the geographic
location. SD has been decreasing south of 40°N and increasing north of 40°N. Analyzed SD and
climate data from previous studies corroborate this trend. Moreover, precipitation in the Northern
Hemisphere has increased up to 4%, causing increased snow accumulation during cold months
and the opposite throughout spring. For the complete Northern Hemisphere, the mean monthly
snow cover extent has decreased by 1.3% per decade. Hence, it is important to map snow cover,
SD, and SWE changes with high temporal and spatial coverage. Remote sensing presents the
perfect too for this task. For this reason, SD and SWE global maps that are spatially continuous
can provide very useful information for the water resource management and climate change
monitoring. In-situ SD and SWE observations are important because of the high confidence that
can be placed on values that are adequately collected. However, geospatial data sets have the
ability to store, analyze, and present data for large and remote areas.
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The spectral reflectivity and scattering characteristics of snow depend on many different factors
such as: snow grain size and shape, liquid water content, SD, impurity of snow, temperature, ice
content, depth hoar (result of snow metamorphism from low to moderate density) and the
consistency of the surface beneath the snow cover. Depending on the chosen sensor type and
resolution, the interference of all these factors on the retrieval of snow parameters may vary.
Snow reflects a high portion of the radiation in the visible wavelengths. Depending on the impurity,
grain size and age of the snow, this proportion can reach up to 90% for freshly fallen, pure snow.
When snow ages, the percentage of reflected insolation decreases. This decrease is due to various.
First, the impurity of the snow cover increases with time, leading to decreased reflectance.
Secondly, melting and refreezing processes within the snow lead to an increased grain size, which
then leads to reduced reflectance. For longer wavelengths, the reflectance of snow declines
significantly, reaching near-zero values in near-IR. One of the major challenges in snow mapping
is the discrimination between clouds and snow. Although other land cover classes can be easily
discriminated from clouds in the visible wavelengths, snow may behave similarly to clouds in the
reflective and thermal part of the spectrum. The major differences between the reflective
characteristics of clouds and snow have been described by Dozier (1989); water drops (10 μm) or
ice crystals (40 μm) within clouds are smaller than typical snow grains (300–500 μm. The smaller
particle size and the water content cause less absorption in the spectral region from 1.55 to 1.70
μm. However, ice-containing clouds cannot be discriminated from snow by this feature. Because
snow cover is usually optically thicker than cloud cover, it reflects a larger proportion of the visible
radiation. This criterion can help to distinguish between thin cirrus clouds and snow. The
characteristic decline of snow reflectance towards shortwave IR can be useful to distinguish
between the cloud and snow because most clouds reflect a higher proportion of the shortwave IR.
Sensors such as the Advanced Very High Resolution Radiometer (AVHRR), MODIS, or Landsat
provide the appropriate spectral channels to utilize the properties mentioned above. Usually, using
only one spectral channel to discriminate between clouds and snow can lead to errors. To identify
the low and high, thin and thick, warm and iced clouds correctly and avoid confusion with snow
cover, a combination of multiple spectral bands is advisable.
The Earth continuously emits microwave radiation from its surface that can be measured from
space using passive MW sensors. Such data have been collected by the SMMR, SSM/I and AMSR-
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E, thus providing a large and continuous time series on a global scale. Snow-covered areas
attenuate the emitted MW radiation from the underlying surface for wavelengths similar to the
snow GS. This attenuation of MW radiation depends principally on the snow mass of a respective
snowpack; the more the snow covers an area, the less the microwave radiation will reach the
satellite sensor. A snowpack consists of air, ice, and, in some cases, liquid water. Because the air
does not influence the MW signal, the propagation of microwaves in a snowpack depends on the
dielectric constants of ice and water, which are extremely different. Liquid water content, GS and
shape may influence the signal that reaches the sensor. For dry snow, the scattering is caused by
the dielectric discontinuities of snow grains and air. Microwave absorption within dry snow is low,
resulting in volume scattering of the snowpack. Passive MW sensors map the surface in different
frequencies and polarizations. Vertically-polarized data are more sensitive to the snow volume and
are therefore capable of mapping shallow snow cover. However, because there could be confusion
between snow and the underlying dry soil, horizontally-polarized data are usually used to map
snow cover. The frequency is crucial for the wavelength and the spatial resolution of the signal.
The higher the frequency, the finer the resolution of the resultant pixel. The maximum SD that can
be derived from passive MW sensors depends on the wavelength of the signal. The 37 GHz
channel, for example, which is often used to derive SWE, has a wavelength of 0.8 cm, limiting the
maximum SD that can be measured to 10–100 times the wavelength, thus ‫׽‬100 cm and a
respective SWE of 250 mm. Scattering effects are also decreased when the wavelength of the
signal becomes greater than the GS of the snow crystals. Increasing the wavelength of the sensors
will therefore not improve the ability to map deeper snow. At wavelengths greater than 5 cm, not
scattering but absorption will be the dominant process. The minimum SD that can be recognized
by passive MW sensors has been identified at 2 cm. The snow crystal properties can influence the
signal and may lead to an overestimation of the SWE. Initially, a fixed snow crystal diameter and
snow density was assumed for the calculations (e.g. 1 mm crystal size and 300 kgm -3 snow
density). Large divergences from these fixed values can lead to wrong assumptions. Furthermore,
studies have shown that the shape of the snow crystals has little to no impact on SD and SWE
estimations, and that crystal size is a more sensitive factor. Additionally, the analysis of passive
MW data is subject to some other major restrictions. Forests tend to mask out the snow cover,
leading to underestimation of SD and SWE. The vegetation absorbs microwaves in the 37 GHz
region, thereby suppressing the scattering signal emitted from the snow surface underneath. Liquid
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water increases the dielectric losses within the snowpack, which strongly increases the absorption
of microwaves within it. Volume scattering is therefore completely prevented leading to strongly
degraded SD estimation. Algorithms to estimate SD under wet snow conditions are, therefore, still
being researched. Furthermore, due to its coarse resolution, passive MW data are more suitable for
the global monitoring of snow properties rather than it is for regional scales. Lastly, while the
resolution may be the biggest disadvantage of passive MW sensors, their ability to map snow even
in the presence of clouds makes them a valuable tool for snow cover mapping. The possibility to
estimate SD and SWE is another big advantage of this sensor type.
In this study, a regression tree algorithm capable of providing SD and SWE estimates based on the
snow physical and radiative properties was developed. Contrary to existing algorithms, varying
snowpack properties such as grain size, surface and pack temperatures, and wetness were
integrated into the RT algorithm to provide a dynamic background. The investigation was subdivided into four main objectives: (1) a comparison and cross-validation between satellite land
surface temperature products with observed snow surface temperature readings. For this purpose,
automated and continuous in-situ snow surface temperature observations are conducted and
recorded at CREST-SAFE; (2) study the temporal evolution of snow wetness; (3) develop a
regression tree algorithm that ingests snow physical (snow surface and pack temperatures, grain
size, and wetness) and radiative (MW TBs at 10, 19, 37, and 89 GHz) properties to estimate snow
depth and SWE; and (4) to improve on global snow cover mapping by developing a free, publicly
accessible product capable of estimating snow depth using MW RS. Accurate retrievals about the
spatial/temporal distribution of snow depth are important for predicting meltwater runoff and
forecasting wet snow avalanches.
In this study, the VIIRS LST EDRs were evaluated against T-skin and T-air ground observations
recorded at the CREST-SAFE, located in Caribou, ME, USA during the winters of 2013 and 2014.
The satellite LST corroboration of snow-covered areas is imperative because high-latitude regions
are often physically inaccessible and there is a need to complement the data from the existing
meteorological station networks. T-skin is not a standard meteorological parameter commonly
observed at synoptic stations. Common practice is to measure surface infrared emission from the
land surface at research stations across the world that allow for estimating ground-observed LST.
Accurate T-skin observations are critical for estimating latent and sensible heat fluxes over snow-
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covered areas because the incoming and outgoing radiation fluxes from the snow mass and T-air
make the snow surface temperature different from the average snowpack temperature. Precise
characterization of the LST using satellite observations is an important issue because several
climate and hydrological models use T-skin as input. Results indicate that T-air correlates better
than T-skin with VIIRS LST data and that the accuracy of nighttime LST retrievals is considerably
better than that of daytime. Based on these results, empirical relationships to estimate T-air and Tskin for clear-sky conditions from RS LST were derived. Additionally, an empirical formula to
correct cloud-contaminated RS LST was developed. Furthermore, the procedure and results of a
temperature-based validation approach for the MODIS LST product provided by NASA Terra and
Aqua satellites using in-situ LST observations recorded at CREST-SAFE during the years of 2013
(January–April) and 2014 (February–April) are presented. Additionally, different satellite
windows were studied to discuss whether a single pixel (1 km2) or several spatially averaged pixels
should be used for satellite LST validation by increasing the MODIS window size to 5 × 5, 9 × 9,
and 25 × 25 windows. Several trends in the MODIS LST data were observed, including the
underestimation of daytime values and night-time values. Results indicate that although all the
data sets (Terra and Aqua, diurnal and nocturnal) showed high correlation with ground
measurements, day values yielded slightly higher accuracy (about 1°C), both suggesting that
MODIS LST retrievals are reliable for similar land-cover classes and atmospheric conditions.
Increasing the MODIS window size showed an overestimation of in-situ LST and some
improvement in the daytime Terra and night-time Aqua biases, with the highest accuracy achieved
with the 5 × 5 window. A comparison between MODIS emissivity from bands 31, 32, and in-situ
emissivity showed that emissivity errors (relative error = −0.30%) were insignificant. Lastly,
because LST is a key parameter for hydrological, meteorological, climatological, and
environmental studies and satellite microwave-based retrievals provide the capability to measure
LST with near-global coverage and high temporal resolution for both clear and cloudy (nonraining) conditions, as opposed to infrared-based retrievals, the procedure and results of a
temperature-based validation approach between the MiRS LST product - retrieved from SNPP/ATMS measurements – and SURFRAD-derived LST observations from six locations
(Nevada, Illinois, Montana, Mississippi, Pennsylvania and South Dakota) across the coterminous
United States over a 13-month period (May 2016 – May 2017) were discussed. Results indicated
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high performance between all stations, despite their considerably different climates and surface
characteristics.
Because the temporal evolution of snow wetness’s plays a significant role in wet-snow avalanche
prediction, meltwater release, and water availability estimations and assessments within a river
basin and it remains a difficult task to measure the snowpack’s LWC and its temporal evolution
with conventional in-situ techniques, an approach based on the use of TDR and CS650 soil water
content reflectometers to measure the snowpack’s LWC and temperature profiles was proposed.
For this purpose, an easily-applicable, low-cost, automated, and continuous LWC profiling
instrument using reflectometers at the CREST-SAFE and tested it during the snow melt period
(February–April) immediately after installation in 2014 was created. Snow Thermal Model
(SNTHERM) LWC simulations forced with CREST-SAFE meteorological data were used to
evaluate the accuracy of the instrument. Results showed overall good agreement, but clearly
indicated inaccuracy under wet snow conditions. For this reason, two (for dry and wet snow)
statistical relationships between snow LWC and dielectric permittivity similar to Topp’s equation
for the LWC of mineral soils were developed. These equations were validated using CREST-SAFE
in-situ data from winter 2015. Results displayed high agreement when compared to LWC estimates
obtained using empirical formulas developed in previous studies, and minor improvement over
wet snow LWC estimates. Additionally, the equations seemed to be able to capture the snowpack
state (i.e., onset of melt, medium, and maximum saturation). Lastly, field test results show
advantages, such as: automated, continuous measurements, the temperature profiling of the
snowpack, and the possible categorization of its state. However, future work should focus on
improving the instrument’s capability to measure the snowpack’s LWC profile by properly
calibrating it with in-situ LWC measurements. Acceptable validation agreement indicates that the
developed snow LWC, temperature, and wetness profiler offers a promising new tool for snow
hydrology research.
The methodology to predict snow depth and SWE using in-situ snow physical and radiative
observations was developed. In-situ snow depth observations and SNTHERM SWE simulations
were used as the response variable. These data were obtained from the CREST-SAFE data records.
This data set includes snow depth, snow surface and pack temperature, and MW TB (10, 19, 37,
and 89 GHz at horizontal and vertical polarizations) observations from 2012 to present. The
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training and testing data set was limited to data from 2012 to 2015. While 2016 data was used to
validate the model. Twelve predictor variables that were considered to significantly influence snow
depth and SWE were used. Some predictor variables had to be modeled on account of the
instrumentation not being available at CREST-SAFE for years 2012 and 2013. These variables
were: snow wetness (obtained via SWM using grain size and snowpack temperature) and MW TBs
at 10 GHz (acquired using HUT Snow Emission Model). A machine learning algorithm called a
regression tree was used in order to model SD and SWE at CREST-SAFE using snow physical
and radiative properties as predictor variables. The model is obtained by recursively partitioning
the data space and fitting a simple prediction model within each partition. As a result, the
partitioning can be represented graphically as a decision tree. Regression trees used for dependent
variables that take continuous or ordered discrete values, with prediction error typically measured
by the squared difference between the observed and predicted values. To validate the model, the
RTs ingested new data from CREST-SAFE and the snow depth and SWE predictions were
compared to actual observations. Results demonstrated high agreement between SD and SWE
estimates by the RT algorithm and in-situ observations. Lastly, a data-based model was developed
with the purpose of providing SD and SWE global maps at a 10-km resolution. The product is
based on the RT methodology developed using CREST-SAFE data. The implementation of the
methodology on a global scale was presented. The methodology involves the SD and SWE RTs
and JAXA GCOM-W1 AMSR2 Level 3 TB products. Because the RTs are dependent on snow
physical properties (i.e. snow surface and pack temperatures, grain size, and wetness) that are not
available as satellite products, an approach to estimate these at a 10 km resolution was developed
using empirical formulas. The basic idea for the creation of the SD and SWE models was to
incorporate the most fundamental snow physical and radiative properties into a data-based analysis
that was able to discover and extract the complex interactions between all system components and
generate a model with the ability to accurately predict SD and SWE on a global scale. Naturally,
the SD and SWE estimations obtained using the RT algorithm were validated against JAXA’s SD
and SWE products with relative good agreement. Then, both algorithms (JAXA and RT) were
validated against SNOTEL in-situ SD and SWE data. The SD and SWE estimates by the RT
algorithm displayed better agreement with in-situ stations than JAXA’s algorithm.
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9.2
Future work
In summary, collection of field survey data is useful for the inventorying and mapping of SD and
SWE at a fine spatial scale. In-situ data is important because of the high reliability that can be
placed on variables, when adequately collected. For this reason, they are also crucial for validation
purposes as reference data sets when compared to RS retrievals. However, this type of data lacks
the temporal extent, spatial coverage, and cost-effectiveness that are found in RS data. On the other
hand, remote sensing has revolutionized the way in which environmental and hydrological data
are collected, stored, analyzed, and visualized. This work highlights the advantages of using MW
remote sensing and snow physical and radiative knowledge for SD and SWE mapping and
monitoring including the possibility of collecting data for large and remote areas, as well as the
synoptic perspective, and multi-temporal resolution. Remote sensing data have shown to be
extremely valuable because they provide spatially continuous data that is validated and
complemented by sample data points. Thus, remote sensing significantly assisted this work. The
successful use of remote sensing to map SD and SWE relies on knowledge about the behavior of
different snowpack properties (i.e. GS, T-skin, T-pack, and LWC) and in understanding the IR and
MW spectral signatures of snow. Furthermore, it shows how integrating both snow physical and
radiative properties into one algorithm provides more accurate results.
At a global scale, much work still remains in the creation of SD and SWE maps. The integration
of field survey data collection and remote sensing provides great potential because detailed data
can be used to understand the differences between snow physical and radiative properties. This
research shows that the poor spatial coverage of field observation data can be complemented by
satellite imagery, providing cost-effective ways to monitor large and remote areas. In places where
there is confusion between spectral signatures, or the quality of the available imagery is not
adequate, RS can provide assistance in the process of updating SD and SWE data. This integration
will result in more consistent and objective SD and SWE global maps. This integration is also
advantageous because field methods can prove useful to investigate the spatio-temporal variability
of SD and SWE at a local scale. However, satellite-derived data is a more suited alternative for the
determination and evaluation of hydrological processes that cover larger areas. This combination
of field-collected data and remote sensing is still a challenge for SD and SWE global mapping
because of the poor development of automated techniques to help during this integration and
205
scarcity of geospatial data with high spatial resolution. Data mining techniques are useful for the
non-trivial extraction of implicit information from predictor variables and should continue to be
investigated in the future for the purpose of SD and SWE mapping. Data mining algorithms might
be able to find hidden patterns between SD and SWE and different snow physical and radiative
predictor variables that may otherwise be missed because they are not expected. Ground-based
snow physical and radiative measurements can potentially be used as training data in models
developed to predict SD and SWE using remote sensing.
Lastly, the five major challenges related to SD and SWE MW-based retrievals are: atmospheric
attenuation, forest attenuation, snow microphysical properties, effects of terrestrial waterbodies,
and wet snow. This means that a better understanding of the coupling between these factors and
MW RS are necessary to accurately characterize the feedback between SD (and SWE) and
hydrological processes. The developed SD and SWE RT algorithm in this study takes care of some
of these challenges, but not all. Future work should consider the integration of IR LST as the snow
surface temperature, elevation as it impacts SD and SWE estimates significantly, and forest cover
attenuation. To work towards this initiative, the use of the following satellite RS products is
recommended:
x
Global forest fraction from Boston University data (MOD12Q1IGBP) circular smoothed
(15 km diameter) and mapped to 0.00833° grid (Hansen et al., 2003)
x
Global forest ‘spatial density’ from University of Maryland Vegetation Continuous
Fraction (VCF) (500m) circular smoothed (15 km diameter) and re-gridded to 0.00833°
x
NOAA’s Etopo1 Global Relief Model (Topography)
x
MODIS Land Surface Temperature/Emissivity Daily L3 Global 1km (Aqua satellite MYD11A1)
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Appendix A – Research publications and conference presentations
Peer-reviewed research publications
Pérez Díaz, C., T. Lakhankar, P. Romanov, R. Khanbilvardi, and Y. Yu. 2015. “Evaluation of VIIRS
Land Surface Temperature Using CREST-SAFE Air, Snow Surface, and Soil Temperature
Data.” Geosciences 5(4): 334–360. doi:10.3390/geosciences5040334.
Pérez Díaz, C., J. Muñoz, T. Lakhankar, R. Khanbilvardi, and P. Romanov. 2017. “Proof of Concept:
Development of Snow Liquid Water Content Profiler Using CS650 Reflectometers at Caribou,
ME, USA.” Sensors 17(3): 647. doi:10.3390/s17030647.
Pérez-Díaz, C., T. Lakhankar, P. Romanov, J. Muñoz, R. Khanbilvardi & Y. Yu. 2017. “Evaluation
of MODIS land surface temperature with in-situ snow surface temperature from CRESTSAFE.” International Journal of Remote Sensing 38(16): 4722-4740. doi:
10.1080/01431161.2017.1331055.
Pérez-Díaz, C., C. Grassotti, Q. Liu, S. Liu, J. Chen, T. Lakhankar, and R. Khanbilvardi. MiRSretrieved LST validation with in-situ SURFRAD measurements. 2017. Earth and Space
Science. Under review.
Pérez-Díaz, C., T. Lakhankar, and R. Khanbilvardi. Snow depth and SWE prediction using data
mining techniques (regression tree algorithm) and snow physical and radiative properties.
2017. Under preparation.
Sánchez, H., T. Lakhankar, C. Pérez Díaz, J. Nuñez, and R. Khanbilvardi. 2017. Impact of Snowpack
Temperature on Albedo and Radiation using CREST-SAFE Field Experiment Observation.
Geosciences. Under review.
Conference presentations
1. Pérez-Díaz, Carlos L., T. Lakhankar, J. Muñoz, P. Romanov, Y. Yunyue and D. R.
Khanbilvardi (2017) CREST-SAFE: Snow LST validation, wetness profiler creation, and
depth/SWE product development, 2017 AGU Fall Meeting at the New Orleans Ernest N.
Morial Convention Center, New Orleans, LA (December 12-16, 2017).
2. Pérez-Díaz, Carlos L., T. Lakhankar, J. Muñoz, P. Romanov, Y. Yunyue and D. R.
Khanbilvardi (2017) CREST-SAFE: Snow LST validation, wetness profiler creation, and
depth/SWE product development, Society of Hispanic Professional Engineers (SHPE)
Conference 2017 at Kansas City, MO (November 1-5, 2017).
3. Pérez-Díaz, Carlos L., C. Grassotti, Q. Liu, T. Lakhankar, and D. R. Khanbilvardi (2017)
MiRS-retrieved LST validation with in-situ SURFRAD measurements, STAR JPSS
207
Annual Science Team Meeting 2017 at the NCWCP, College Park, MD (August 14-18,
2017).
4. Pérez-Díaz, Carlos L., T. Lakhankar, J. Muñoz, P. Romanov, Y. Yunyue and D. R.
Khanbilvardi (2017) CREST-SAFE: Calibration, validation, and product development,
NOAA CREST Day 2017 at The City College of New York, NY, NY (April 30th, 2017).
5. Pérez-Díaz, Carlos L., T. Lakhankar, J. Muñoz, P. Romanov, Y. Yunyue and D. R.
Khanbilvardi (2016) Evaluation of MODIS land surface temperature with in-situ snow
surface temperature from CREST SAFE, 2016 AGU Fall Meeting at the Moscone Center,
San Francisco, CA (December 12-16, 2016).
6. Pérez-Díaz, Carlos L., T. Lakhankar, J. Muñoz, P. Romanov, Y. Yunyue and D. R.
Khanbilvardi (2015) Evaluation of MODIS land surface temperature with in-situ snow
surface temperature from CREST SAFE, 8th Biennial National Oceanic and Atmospheric
Administration (NOAA) Educational Partnership Program (EPP) Education and Science
Forum at the The City College of New York, NY, NY (August 28-31, 2016).
7. Pérez-Díaz, Carlos L., C. Grassotti, Q. Liu, T. Lakhankar, and D. R. Khanbilvardi (2016)
CRTM and HUT Snow Microwave Emissivity Comparison with In-situ Microwave
Emissivity from CREST-SAFE and SSMIS retrievals, STAR JPSS Annual Science Team
Meeting 2016 at the NCWCP, College Park, MD (August 8-12, 2016).
8. Pérez-Díaz, Carlos L., T. Lakhankar, J. Muñoz, P. Romanov, Y. Yunyue and D. R.
Khanbilvardi (2014) Evaluation of MODIS and VIIRS Land Surface Temperature Using
CREST-SAFE Air, Snow Surface, and Soil Temperature Data, Society of Hispanic
Professional Engineers (SHPE) Conference at Baltimore, MD (November 11-15, 2015).
9. Pérez-Díaz, Carlos L., T. Lakhankar, J. Muñoz, P. Romanov, Y. Yunyue and D. R.
Khanbilvardi (2015) Near−surface air temperature and snow skin temperature comparison
from CREST-SAFE station data with MODIS land surface temperature data, NOAA
Technical Meeting at the NCWCP, College Park, MD (May 7, 2015).
10. Pérez-Díaz, Carlos L., T. Lakhankar, J. Muñoz, P. Romanov, Y. Yunyue and D. R.
Khanbilvardi (2014) Near−surface air temperature and snow skin temperature comparison
from CREST-SAFE station data with MODIS land surface temperature data, 7th Biennial
National Oceanic and Atmospheric Administration (NOAA) Educational Partnership
Program (EPP) Education and Science Forum at the University of Maryland Eastern Shore,
Princess Anne, MD (October 26-29, 2014).
11. Pérez-Díaz, Carlos L., T. Lakhankar, J. Muñoz, P. Romanov, Y. Yunyue and D. R.
Khanbilvardi (2014) Near−surface air temperature and snow skin temperature comparison
from CREST-SAFE station data with MODIS land surface temperature data, 10th Annual
Science NOAA/NESDIS Cooperative Research Program (CoRP) Symposium on Satellites
and Society at the City College of New York of the City University of New York, NY
(September 9-10, 2014).
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Appendix B – Software and tools used for product development
The CREST Snow Depth and SWE product was developed using a combination of software and
programming language tools. To compute and perform math-intensive modeling, MATLAB was
used. More specifically, the MATLAB Statistics and Machine Learning and Mapping Toolboxes
were utilized. However, in order to acquire the remotely-sensed satellite retrievals via FTP, Linux
cronjobs were used. Lastly, the Windows Task Scheduler and WinSCP software were used to
transfer the local global maps files created using the RT algorithm to the product server via FTP.
Adobe Dreamweaver was used to develop the product website interface. All of these processes are
automated. The analysis workflow is shown in Figure 75.
The tool that was primarily used in this research was Statistics and Machine Learning and it
contains the tools that perform statistical analyses and/or modeling. Naturally, the Mapping
Toolbox was used to create the SD and SWE global maps. In this study, predictive modeling tools,
in particular tree-based models were selected for the analyses. The MATLAB Statistics and
Machine Learning Toolbox provides the option to use tree-based models.
The MATLAB Statistics and Machine Learning Toolbox was mainly used for these purposes:
1. Data exploration
2. Training regression trees
3. Evaluation of model’s performance.
209
Figure 75. Analysis workflow for the CREST SD and SWE product development and current process. The
blue ovals represent the inputs to the analysis. The yellow boxes correspond to the tasks carried out using
the MATLAB Statistics and Machine Learning and Mapping Toolboxes. Black boxes correspond to
miscellaneous tasks performed by additional software (i.e. Linux, Windows Task Scheduler, and WinSCP).
Green ovals correspond to model outputs. Cloud defines the product server and the box with green outline
is used to represent the software (Adobe Dreamweaver) used to create the user-friendly interface for the
product.
How can I fit regression trees using the MATLAB Statistics and Machine Learning Toolbox?
Open MATLAB and select the Statistics and Machine Learning Toolbox. Within the toolbox, click
on Machine Learning, then on Decision Trees, followed by Regression Tree Learner App. Here,
you will find the options to evaluate, explore, and model data. Alternatively, you can write a script
for you own regression tree, which is the way it was done in this study. See Figure 76 for example.
210
Figure 76. MATLAB regression tree creation example.
211
Appendix C – SNOTEL stations
All SNOTEL station images were downloaded from the SNOTEL website (https://www.wcc.nrcs.usda.gov/snow/).
Figure 77. SNOTEL station in Fairbanks, AK.
Figure 78. SNOTEL station in Hawley Lake, AZ.
212
Figure 79. SNOTEL station in Blue Lakes, CA.
Figure 80. SNOTEL station in Copeland Lake, CO.
213
Figure 81. SNOTEL station in Moscow Mountain, ID.
Figure 82. SNOTEL station in Rocky Boy, MT.
214
Figure 83. SNOTEL station in Summit Lake, NV.
215
Figure 84. SNOTEL station in Signal Peak, NM.
Figure 85. SNOTEL station in Miller Woods, OR.
216
Figure 86. SNOTEL station in Little Bear, UT.
Figure 87. SNOTEL station in Huckleberry Creek, WA.
217
Figure 88. SNOTEL station in Cole Canyon, WY.
218
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