Improved Estimation of Surface Biophysical Parameters From Kernel- driven BRDF models Upgrading workshop Mathias Disney UCL Geography

advent of EOS era - launch of Terra high repeat (e.g. 2-3 days for MODIS) moderate resolution (100s of m to km) angular sampling (e.g. POLDER) large quantity of multi-angular observations range of wavelengths, particularly visible/NIR good spatial/temporal coverage Context of project

vegetal functioning at regional/global scales - NDVI/LAI carbon cycle (NDVI/NPP) energy fluxes between surface  atmosphere fAPAR (absorbing) albedo (reflecting) hydrology, water cycle, soil relation to climate etc. Detailed characterisation of vegetated regions highly desirable

characterise surface directional reflectance (BRDF) different classes of model empirical physical (RT/GO/hybrid) computer simulation (MCRT/radiosity) semi-empirical GO/RT (kernel-driven) inversion of models optimisation, LUT inversion, linearising etc. Model development over last 20 years

Semi-empirical kernel-driven models (linear): appropriate for moderate resolutions driven by requirement for useful ‘products’ rather than reflectance or abstract parameters..... scale linearly (for linear additive combination) small number of parameters, easily inverted matrix inversion, order 3/4 say angular integration  interp./extrap. of BRDF spectral albedo/broadband albedo

Angular variation of semi-empirical RT/GO kernels

models treat physics very simply combine different components of surface scattering behaviour ­ relation of model parameters to biophysical parameters? ­ can any relations be treated simply? ­ parameter coupling? implications of model simplicity for derived products (e.g. albedo) ? BUT

assumptions behind kernel-driven models can  canopy be represented as linear combination of volumetric and GO components? can volumetric and GO components be separated by respective kernels? information contained in inverted parameters separation of soil/vegetation components spectral information remaining, coupling extension of kernel-driven concept from angular to spectral domain This project aims to address:

fieldwork - 3D measurements of canopy structure leaf zen./az. angles, lengths, widths, stems etc. measure LAI, directional reflectance, % cover etc. BPMS 3D canopy  simulate BRDF under assumptions made in kernel-driven models i.e.: single scattering only  leaf bi-Lambertian,  leaf =  leaf,  soil Lambertian direct illumination only Experimental method

Aerial photograph of Barton Bendish farm, 6/8/97. barley sugar beet wheat

Simulated barley canopy (slightly dodgy ears!)

Information obtained from simulations Proportions of sunlit/shaded leaf/soil (barley 18/4/97)

Shapes of separate components of simulated  canopy Volumetric component,  (barley, 15/5/97)

Shapes of separate components of simulated  canopy GO component,  (barley, 15/5/97)

components are separable, and predominantly independent of each other volumetric component > GO component volumetric - asymmetric upward bowl shape, corresponds to proportion of visible sunlit leaf GO - downward bowl shape, symmetric about nadir, corresponds to proportion of visible sunlit soil Analysis of components of  canopy show:

 leaf = 1 and  soil = 0 i.e. volume scattering.  leaf = 0 and  soil = 1 i.e. GO scattering.

for BPMS simulations volumetric component GO component so, if there is linear relation between components of simulated  canopy and k vol and k GO then: regress components of simulated  canopy ( ,  ) against k vol and k GO

Relationship between k vol and  Barley canopy 15/5/97

Relationship between k GO and 

volumetric and GO components of  canopy can be described by respective kernels, but.... relationship between k vol and  stronger than that between k GO and  disparity increases as canopy develops RossThick generally better than RossThin LiSparse generally better than LiDense r 2 k vol against  high when LAI is high, and vice- versa for k GO and  Demonstrates that:

 canopy can be split into volumetric and GO components there is a linear relationship between k vol and , k GO and  breaks down as canopy departs from assumptions of kernel-driven models (implications?) Next question: do kernels act independently? i.e. is volumetric component of  canopy described adequately by k vol alone, and GO component described by k vol alone? Coupling? Conclusions

substitute volumetric and GO components of simulated  canopy back into original expression for full kernel-driven model i.e. isotropic term purely volumetric term purely GO term plug a vol,GO and b vol,GO values in, plus appropriate  leaf and  soil

Retrieved parameters (as a fn of ) for barley canopy 15/5/97

agreement between parameters inverted from simulated  canopy, and those derived from regressed values of a vol,GO and b vol,GO ‘vegetation-like’ shape indicates spectral info. related to  leaf in volumetric parameter (expected) and isotropic (not so expected) for other dates,  soil seen in GO parameters (expected) -ve model parameters (meaning?) Results

volumetric and GO components of  canopy largely separable canopy develops  parameters increase  departure from expectations some of variation in  canopy due to volumetric scattering is described by  (k GO ) some of variation in  canopy due to GO scattering is described by  (k vol ) problems separating components entirely - again, implications for parameter retrieval Conclusions

2 PCs of model parameters, barley canopy, 15/5/97 Principal component analysis of parameters

PCA shows that PC1 >> PC2 i.e. always a dominant and secondary component (are separable) BUT volumetric parameter dominant even in some low LAI cases k vol cannot be interpreted straightforwardly here - not physically meaningful -ve parameters arise due to poor model choice for a particular canopy not important if parameters used for classification for e.g., but cannot be interpreted physically

 canopy can be separated into: volumetric component described by (and linearly related to) k vol GO component described by (and linearly related to) k GO breaks down when canopy departs from model assumptions (LAI, LAD, canopy type) some portion of each component described by other kernel parameters can contain spectral information (use for classification?) can take physically unrealisable values (constraint/auxiliary info.) Conclusions

Plan for completion development/application of linear spectral kernels Benefits? spectral interpolant for (narrow-band) albedo to broad-band combine samples from sensors with different spectral response e.g. POLDER + MSG potentially separate vegetation and soil components of  canopy - NPP/biomass etc. potentially VERY useful!

spectral kernels based on Price.... Price’s method -  soil represented by first 4 PCs of large data set of  soil lab spectra can same be done with  veg and combined with  soil to describe  canopy ? Assume.... mscatt terms sscatt soil term sscatt veg term

Price’s soil basis functions (scaled)

use lab spectra (LOPEX data) wet/dry  leaf,  leaf bark/needles, pastilles (layered media - mscatt) derive pcs from refl./trans. spectra OR sscatt albedo kernels - related to properties we require, physical constraints 1st basis function > 95% variance, 3 or more > 99% these + 2 or 3 of Price’s soil terms can describe wide range of  canopy behaviour

Examples of LOPEX spectra

‘Dry’ spectral kernels (scaled)

‘Dry’ spectral kernels (scaled) - continued....

Effectiveness of fresh sscatt albedo kernels, reconstructing original ,  and albedo

Results: 3-5 spectral kernels can describe > 99.5% variance in data sets from which they are derived visible cutoff at ~90% variance - RMSE rises rapidly after this 90% threshold occurs at (reflectance) RMSE (refl.) (trans) (sscatt albedo) albedo kernels better at reconstructing  +  or fresh+dry, or albedo than  or  kernels alone increase no. of kernels  RMSE decreases

Effectiveness of sscatt albedo kernels in reconstructing  leaf,  leaf, albedo

How to test/apply? invert spectral kernels against multi-angular airborne data (ATM) use params to recreate multi-spectral CASI data can then apply spectral directional kernels simultaneously require accurately co-registered data set, and good atmospheric correction (adapting MISR EOF algorithm) If successful, spectral directional kernels could be powerful tool, partic. for albedo/NPP