Efficient Emulation of Radiative Transfer Codes Using Gaussian Processes and Application to Land Surface Parameter Inferences
Abstract
:1. Introduction
2. Gaussian Process Emulator
Extension to Full Spectrum Emulation
3. GP Emulation Examples
3.1. Emulating Soil-Leaf-Canopy RT Models
Parameter | Symbol | Units | Minimum | Maximum | Transformation | Transformed Min | Transformed Max |
---|---|---|---|---|---|---|---|
Leaf layers | xleafn | – | 0.8 | 2.5 | – | – | – |
Leaf chlorophyll
concentration | Cab | μ g·cm | 0.2 | 77 | 0.46 | 1 | |
Leaf carotenoid concentration | Car | μ g·cm | 0 | 15 | 0.95 | 1 | |
Senescent fraction | Csen | – | 0 | 1 | – | – | – |
Equivalent water thickness | Cw | cm | 0.0043 | 0.0753 | 0.028 | 0.81 | |
Leaf dry matter | Cm | g·cm | 0.0017 | 0.0331 | 0.037 | 0.84 | |
Leaf area index | LAI | m ·m | 0 | 8 | 0.05 | 1 | |
Average Leaf Angle | ALA | 0 | 90 | 0.44 | 0.56 | ||
Soil brightness scalar | Bs | – | 0 | 2 | – | – | – |
Soil moisture endmember | Ps | – | 0 | 1 | – | – | – |
Weight of the first Price function | P1 | – | −0.5 | 1 | – | – | – |
Weight of the second Price function | P2 | – | −0.5 | 1 | – | – | – |
MODIS Band | Slope | Intercept | R | RMSE | MAE |
---|---|---|---|---|---|
1 | 1.002 | 1.222e-05 | 0.9995 | 9.774e-04 | 5.175e-03 |
2 | 0.999 | 1.562e-04 | 0.9998 | 5.602e-04 | 1.063e-02 |
3 | 1.004 | −3.362e-05 | 0.9996 | 9.181e-04 | 2.371e-03 |
4 | 1.000 | 2.784e-05 | 0.9999 | 5.255e-04 | 2.048e-03 |
5 | 0.993 | 1.591e-03 | 0.9990 | 1.437e-03 | 3.588e-02 |
6 | 0.998 | 4.182e-04 | 0.9995 | 9.490e-04 | 1.587e-02 |
7 | 1.000 | 1.183e-04 | 0.9997 | 8.194e-04 | 1.135e-02 |
MODIS Band | Slope | Intercept | R | RMSE | MAE |
---|---|---|---|---|---|
1 | 0.984 | 0.000 | 0.999 | 1.669e-03 | 3.679e-02 |
2 | 1.000 | −0.000 | 1.000 | 2.681e-04 | 1.307e-02 |
3 | 0.947 | 0.001 | 0.990 | 4.349e-03 | 4.678e-02 |
4 | 0.977 | 0.001 | 0.998 | 1.987e-03 | 5.585e-02 |
5 | 1.001 | −0.000 | 1.000 | 3.523e-04 | 1.722e-02 |
6 | 1.000 | 0.000 | 1.000 | 3.210e-04 | 7.791e-03 |
7 | 1.000 | 0.000 | 1.000 | 2.416e-04 | 2.392e-03 |
3.2. Emulation of a Coupled Soil-Leaf-Canopy-Atmosphere RT Model Combination: PROSAIL and 6S
MODIS Band | Slope | Intercept | R | RMSE | MAE |
---|---|---|---|---|---|
1 | 0.985 | 0.000 | 0.998 | 2.087e-03 | 3.889e-02 |
2 | 1.001 | −0.000 | 1.000 | 1.888e-04 | 5.694e-03 |
3 | 1.061 | −0.001 | 0.989 | 4.996e-03 | 2.635e-02 |
4 | 0.981 | 0.001 | 0.998 | 1.730e-03 | 5.136e-02 |
5 | 0.999 | 0.000 | 1.000 | 2.282e-04 | 5.256e-03 |
6 | 1.000 | 0.000 | 1.000 | 2.342e-04 | 4.954e-03 |
7 | 0.999 | 0.000 | 1.000 | 2.885e-04 | 1.857e-03 |
3.3. Spectral Emulation of a Coupled Soil-Leaf-Canopy RT Model Combination
3.4. Spectral Emulation of Atmospheric Effects
3.5. Full BRDF Coupling of a Soil-Leaf-Canopy Model and Atmospheric Spectral RT Model
4. Examples of the Use of GPs in Inverse Problems in Remote Sensing
4.1. The Synthetic “Satellite” Observations
Parameter | Value | ||||||
---|---|---|---|---|---|---|---|
N | 2.1 | – | – | – | – | – | – |
60 | 5 | 55 | -0.3 | 122 | 0.1 | 240 | |
7 | – | – | – | – | – | – | |
0.5 | – | – | – | – | – | – | |
0.0176 | 0.004 | 0.043 | −0.31 | 121 | 0.07 | 235 | |
0.002 | – | – | – | – | – | – | |
2 | 0.1 | 5 | −0.29 | 120 | 0.1 | 240 | |
70 | – | – | – | – | – | – | |
1.0 | – | – | – | – | – | – | |
0.3 | – | – | – | – | – | – |
Parameter | Sentinel2/MSI | Sentinel3/SLSTR | Proba-V |
---|---|---|---|
Number of bands | 12 | 5 | 4 |
Revisit frequency | 5 days | 2 days | 2 days |
Overpass time | 10:30 AM | 10:00 AM | 11:00 AM |
Variation in viewing zenith angle (VZA) | |||
Percentage valid observations | 30% | 30% | 30% |
Average temporal window | 12 days | 10 days | 11 days |
Noise model slope m | 0.0042 | 0.0075 | 0.108 |
Noise model intercept c | 0.0028 | 0.005 | 0.007 |
4.2. Generic Strategy for the Inverse Problem
Solving for the Posterior
4.3. Inversion Using Markov Chain Monte Carlo (MCMC)
4.4. Variational DA Solution: EO-LDAS Framework
4.5. Simple Particle Filter
5. Discussion and Outlook
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Gómez-Dans, J.L.; Lewis, P.E.; Disney, M. Efficient Emulation of Radiative Transfer Codes Using Gaussian Processes and Application to Land Surface Parameter Inferences. Remote Sens. 2016, 8, 119. https://doi.org/10.3390/rs8020119
Gómez-Dans JL, Lewis PE, Disney M. Efficient Emulation of Radiative Transfer Codes Using Gaussian Processes and Application to Land Surface Parameter Inferences. Remote Sensing. 2016; 8(2):119. https://doi.org/10.3390/rs8020119
Chicago/Turabian StyleGómez-Dans, José Luis, Philip Edward Lewis, and Mathias Disney. 2016. "Efficient Emulation of Radiative Transfer Codes Using Gaussian Processes and Application to Land Surface Parameter Inferences" Remote Sensing 8, no. 2: 119. https://doi.org/10.3390/rs8020119