Evaluation of Linear Kernel-Driven BRDF Models over Snow-Free Rugged Terrain
Abstract
:1. Introduction
2. Model Development
2.1. RTLSR Kernel-Driven Model
2.2. TCKD Model
2.3. KDST-TCKD Model
3. Materials and Methods
3.1. Simulated Multi-Angle Reflectance of Rough Terrain with 3-D LESS
3.2. Multi-Angle Reflectance Data from the Terrain Sandbox
3.3. MODIS Satellite Observations
3.4. Evaluation Methods
4. Result
4.1. Evaluation of Kernel Shapes
4.2. Model Comparisons with 3-D LESS Simulations
4.3. Model Comparisons with Sandbox Measurements
4.4. Model Comparisons with MODIS Observations
5. Discussion and Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Models | DEM1 | DEM2 | DEM3 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
NIR | Red | NIR | Red | NIR | Red | |||||||
RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | |
RTLSR | 0.0358 | 7.859% | 0.0342 | 23.791% | 0.0392 | 9.665% | 0.0446 | 39.195% | 0.0471 | 15.7869% | 0.0516 | 61.869% |
TCKD | 0.0366 | 7.992% | 0.0337 | 23.337% | 0.0257 | 6.245% | 0.0324 | 28.049% | 0.0252 | 8.8421% | 0.0292 | 30.511% |
KDST-TCKD | 0.0192 | 4.409% | 0.0269 | 17.711% | 0.0167 | 4.522% | 0.0224 | 18.407% | 0.0169 | 5.1521% | 0.0180 | 18.930% |
Band | Models | Sandbox1 | Sandbox2 | Sandbox3 | Sandbox4 | ||||
---|---|---|---|---|---|---|---|---|---|
RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | ||
NIR | RTLSR | 0.0147 | 4.198% | 0.0346 | 14.797% | 0.0174 | 5.247% | 0.0265 | 12.343% |
TCKD | 0.0144 | 4.129% | 0.0298 | 14.002% | 0.0171 | 5.194% | 0.0251 | 11.699% | |
KDST-TCKD | 0.0137 | 3.878% | 0.0175 | 8.402% | 0.0133 | 4.441% | 0.0234 | 11.111% | |
Red | RTLSR | 0.0085 | 3.542% | 0.0156 | 18.666% | 0.0126 | 5.495% | 0.0165 | 12.023% |
TCKD | 0.0086 | 3.582% | 0.0127 | 17.866% | 0.0125 | 5.443% | 0.0154 | 11.297% | |
KDST-TCKD | 0.0082 | 3.368% | 0.0079 | 11.124% | 0.0116 | 5.167% | 0.0149 | 11.075% |
Model | Broad | Needleleaf | Savannas | Shrub | Glasslands | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | ||
a < 10° | RTLSR | 0.0309 | 6.161% | 0.0601 | 15.405% | 0.0603 | 16.128% | 0.0250 | 5.875% | 0.0300 | 6.261% |
TCKD | 0.0307 | 6.011% | 0.0600 | 15.285% | 0.0599 | 15.974% | 0.0231 | 5.268% | 0.0293 | 6.057% | |
KDST-TCKD | 0.0302 | 5.905% | 0.0580 | 14.721% | 0.0589 | 15.679% | 0.0223 | 5.058% | 0.0270 | 5.693% | |
10°–20° | RTLSR | 0.0360 | 7.443% | 0.0703 | 18.080% | 0.0682 | 16.792% | 0.0296 | 6.575% | 0.0340 | 7.413% |
TCKD | 0.0309 | 6.154% | 0.0649 | 16.446% | 0.0692 | 16.296% | 0.0248 | 5.124% | 0.0297 | 6.069% | |
KDST-TCKD | 0.0286 | 5.667% | 0.0602 | 14.964% | 0.0590 | 14.274% | 0.0202 | 4.641% | 0.0249 | 5.430% | |
20°–30° | RTLSR | 0.0421 | 10.684% | 0.0801 | 22.129% | 0.0677 | 17.138% | 0.0569 | 15.719% | 0.0396 | 9.480% |
TCKD | 0.0287 | 6.485% | 0.0691 | 18.817% | 0.0613 | 15.924% | 0.0465 | 12.289% | 0.0332 | 7.581% | |
KDST-TCKD | 0.0218 | 5.112% | 0.0633 | 17.360% | 0.0575 | 14.952% | 0.0377 | 10.518% | 0.0300 | 6.825% | |
a > 30° | RTLSR | -- | -- | 0.0842 | 27.130% | 0.0718 | 19.038% | 0.0602 | 19.127% | 0.0514 | 14.240% |
TCKD | -- | -- | 0.0843 | 26.971% | 0.0450 | 14.929% | 0.0498 | 14.558% | 0.0409 | 10.833% | |
KDST-TCKD | -- | -- | 0.0765 | 24.059% | 0.0384 | 11.752% | 0.0420 | 12.544% | 0.0340 | 8.625% |
Model | Broad | Needleleaf | Savannas | Shrub | Glasslands | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | ||
a < 10° | RTLSR | 0.0250 | 6.642% | 0.0544 | 19.478% | 0.0549 | 19.452% | 0.0209 | 6.587% | 0.0233 | 7.422% |
TCKD | 0.0243 | 6.343% | 0.0543 | 19.288% | 0.0542 | 19.260% | 0.0202 | 6.170% | 0.0224 | 6.909% | |
KDST-TCKD | 0.0238 | 6.147% | 0.0530 | 18.742% | 0.0531 | 18.721% | 0.0196 | 5.986% | 0.0216 | 6.684% | |
10°–20° | RTLSR | 0.0282 | 9.161% | 0.0557 | 21.029% | 0.0690 | 21.201% | 0.0213 | 7.632% | 0.0333 | 10.116% |
TCKD | 0.0238 | 7.221% | 0.0515 | 18.514% | 0.0634 | 18.849% | 0.0164 | 5.420% | 0.0274 | 7.849% | |
KDST-TCKD | 0.0221 | 6.621% | 0.0484 | 17.358% | 0.0595 | 17.188% | 0.0157 | 5.136% | 0.0236 | 7.008% | |
20°–30° | RTLSR | 0.0643 | 14.828% | 0.0664 | 24.813% | 0.0695 | 21.954% | 0.0416 | 17.608% | 0.0322 | 11.468% |
TCKD | 0.0579 | 11.395% | 0.0609 | 22.068% | 0.0566 | 17.112% | 0.0336 | 14.103% | 0.0272 | 9.016% | |
KDST-TCKD | 0.0470 | 9.869% | 0.0547 | 19.154% | 0.0536 | 16.064% | 0.0297 | 12.137% | 0.0247 | 8.014% | |
a > 30° | RTLSR | -- | -- | 0.0692 | 27.268% | 0.0774 | 23.279% | 0.0609 | 35.147% | 0.0429 | 19.369% |
TCKD | -- | -- | 0.0601 | 25.493% | 0.0533 | 19.120% | 0.0453 | 24.785% | 0.0334 | 14.436% | |
KDST-TCKD | -- | -- | 0.0584 | 25.733% | 0.0523 | 18.318% | 0.0358 | 19.428% | 0.0283 | 11.548% |
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Zhu, W.; You, D.; Wen, J.; Tang, Y.; Gong, B.; Han, Y. Evaluation of Linear Kernel-Driven BRDF Models over Snow-Free Rugged Terrain. Remote Sens. 2023, 15, 786. https://doi.org/10.3390/rs15030786
Zhu W, You D, Wen J, Tang Y, Gong B, Han Y. Evaluation of Linear Kernel-Driven BRDF Models over Snow-Free Rugged Terrain. Remote Sensing. 2023; 15(3):786. https://doi.org/10.3390/rs15030786
Chicago/Turabian StyleZhu, Wenzhe, Dongqin You, Jianguang Wen, Yong Tang, Baochang Gong, and Yuan Han. 2023. "Evaluation of Linear Kernel-Driven BRDF Models over Snow-Free Rugged Terrain" Remote Sensing 15, no. 3: 786. https://doi.org/10.3390/rs15030786