Apr 19, 2017 - Emulator. (emulated SCOPE). Which model would you choose? Any difference? 3/53 .... Gaussian Processes Regression (GPR). ⢠Variational ...
Emulation of radiative transfer models (RTMs): new opportunities for spectroscopy data processing Jochem Verrelst, Juan Pablo Rivera, Jordi Muñoz-Marí, Neus Sabater, Jorge Vicent, Jose Moreno and Gustau Camps-Valls Image Processing Laboratory, Univ. of Valencia (Spain)
EARSeL Imaging Spectroscopy Workshop 19 April2017
0.7 0.7
0.5 310
500#
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9
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N
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LAI Cw
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Cab hc Cdm
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Any difference? 37 min
9s
Which model would you choose?
SCOPE
Emulator
(emulated SCOPE)
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BACKGROUND
Advanced RTMs: generation of a large LUT (>1000#) SCOPE
DART
MODTRAN
40
0.5 0.35
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0.25
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35 0.4 30 25 AOT
dif
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Hours
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days
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0 60 80 CC
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Advanced RTMs: more realistic but slow • RTMs are widely used in RS science, e.g. for development of new missions and retrieval (inversion). • When choosing an RTM, a trade-of between applicability and realism has to be made: simpler models are easier to apply but less realistic, while advanced models are more realistic but require a large amount of variables to be configured.
Examples of advanced RTMs: • Ray tracing models (e.g. FLIGHT, RAYTRAN) • Voxel models: DART • Soil-Vegetation-Atmosphere-Transfer (SVAT) models: e.g. SCOPE • Atmospheric transfer models: e.g. MODTRAN
• Main drawback of advanced RTMs involves their long processing time: the more advanced, the longer it takes to generate output. • Long processing time makes that advanced RTMs are of little use for operational tasks, e.g., pixel-by-pixel inversion schemes.
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Emulation of RTMs
Emulators are statistical models that are able to approximate the processing of a physical model (e.g. RTM) - at a fraction of the computational cost: making a statistical model of a physical model RTM
Machine learning
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Regression vs. Emulation: Classical use of machine learning in optical RS: 0.7 0.6
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Variable (e.g. LAI)
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Statistical method: •
Variable/data-driven, black box, 1 output, portability is questionable
Emulation in optical RS:
Replace RTM: •
Multiple applications, e.g. inversion Radiometric method: Spectral fitting Portable: generally applicable
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Emulation in practice: Spectra 0.7
Variables
regression
10 9
0.6
8 7 6
0.4 LAI
Reflectance
0.5
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Emulation
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(e.g. LAI, chlorophyll,…)
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• In principle any nonlinear, adaptive machine learning regression algorithm (MLRAs) can serve as emulator. MLRAs:
• However, to emulate RTM spectral output, the MLRA should have the capability to reconstruct multiple outputs, i.e. the complete spectrum. Only Few MLRAs possess multi-output capability (e.g. NN). • Multi-output resolved with dimensionality reduction techniques (e.g. PCA). “spectral redundancy” is a blessing
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Processing steps Input (variables + spectra)
Splitting into training/validation
PCA on spectra
MLRA training looping over components
Prediction of components
Prediction of components
Validation
Emulator
Sc = U · X
PCA on spectra
MLRA training looping over components
Reconstruction of spectra
W = (Y + λI)-1 · Sc Sp = Sc · W
Reconstruction of spectra
http://isp.uv.es/software.html
Xr = U⊤ · Sp 9/53
Emulator toolbox With ARTMO’s emulation processing chain any RTM can be converted into an emulator. Input (variables + spectra)
Splitting into training/validation
PCA on spectra
MLRA training looping over components
Prediction of components
Reconstruction of full spectrum
Validation
Emulator
Xr = U⊤ · Sp
(Rivera et al., 2015)
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Emulators great idea… what about accuracy? Various open questions: 1) Role of machine learning regression algorithm? 2) Role of dimensionality reduction (DR) method?
3) Role of LUT size training? 0.6 0.5 Reflectance
4) Role of data type?
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Is a small LUT of #500 samples sufficiently covering the parameter space? Latin Hypercube Sampling (LHS)
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Experimental setup: emulating SCOPE Experimental setup: • SCOPE: LUT 500# @ 1 nm; 400-2500 nm; 8 variables, R and SIF outputs • 6 machine learning methods tested: RF, SVR, KRR, NN, GPR, VH-GPR • # 10, 20, 30, 40 components tested; 70/30% Training/Validation (T/V) • LUT of # 500, 1000 samples SCOPE: N (1-3) LCC (0-100) Cw (0-0.5) Cdm (0-0.5) Cs (0-0.3 LAI (0-10) Hc (0-2) SMC (0-0.7)
Emulator 0.7 0.6 0.5 Reflectance
0.7 0.6 0.5 Reflectance
• • • • • • • •
Emulated SCOPE
37 min (500#)
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Role of machine learning • • • • • •
Random Forests (RF) Neural Networks (NN) Support vector regression (SVR) Kernel Ridge Regression (KRR) Gaussian Processes Regression (GPR) Variational Heteroscedastic GPR (VHGPR) 14/53
Validation SCOPE R emulation
1) Role of machine learning Relative errors for 30% validation data (#150) with 20 PCA. 16 RF NN SVR GPR
KRR RF
NN KRR
GPR SVR VH-GPR VHGPR
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NRMSE (%)
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Here, NN best performing (
