Table of Contents
X Linear model experiment
X.1 Introduction
X.2 Experimental method
X.3 Hypotheses behind the linear models
X.3.1 canopy as a linear combination of volumetric and GO scattering
X.3.2 Volumetric and GO components of canopy
X.3.3 Discussion of directional shapes and magnitudes of  and 
X.3.3.1 Volumetric component of canopy, 
X.3.3.2 GO component of canopy, 
X.3.4 Summary
X.4 Separation of canopy into constituent volumetric and GO components
X.4.1 Relationships between  and kvol, and  and kGO
X.4.2 Volumetric component 
X.4.2.1 Values of r2
X.4.2.2 Slopes and intercepts avol, bvol of  against kvol
X.4.3 GO component 
X.4.3.1 Values of r2
X.4.3.2 Slopes and intercepts avol, bvol of  against kGO
X.4.4 Summary
X.5 Hypothesis 2: seperability of volumetric and GO scattering components
X.5.1 Method
X.5.2 Results
X.5.3 Discussion
X.5.3.1 Barley – 18th April
X.5.3.2 Barley – 13th May
X.5.3.3 Barley – 4th June
X.5.3.4 Barley – 24th June
X.5.3.5 Wheat – 23rd March
X.5.3.6 Wheat – 23rd April
X.5.4 Implications of coupling
X.5.5 Implications of negative model parameters
X.6 Conclusions
Figures
X.1 Proportions of vegetation/soil in simulated canopies
X.2 Simulations of each canopy with soil DEM
X.3 Viewing and illumination geometry for simulations
X.4 Variation of simulated volumetric component of canopy with v
X.5 Variation of simulated GO component of canopy with v
X.6 Proportions of sunlit and shaded canopy components
X.7 LADs of selected canopies
X.8 Variation of  against the RossThick and RossThin kernels
X.9 Variation of  against the LiSparse kernels
X.10 Variation of  against the LiDense kernels
X.11 Schematic of how estimates of kvol,GO are obtained from two different sources
X.12 leaf and soil reflectance spectra used in the derivation of kvol,GO estimates
X.13 Comparison of isotropic, RossThick and LiSparse kernels derived from BPMSsimulated canopy and inversion of a full linear model.
X.14 Comparison of isotropic, RossThin and LiDense kernels derived from BPMSsimulated canopy and inversion of a full linear model.
X.15 PCA analysis of BPMS-simulated canopy
X.16 Comparison of kiso,vol,GO from inversion of 2 parameter with those derived from
3 parameter models – 24th June barley canopy.
X.17 Comparison of kiso,vol,GO from inversion of 2 parameter with those derived from
3 parameter models – 23rd April wheat canopy.
X.18 Scatter plots of two parameter kvol,GO against three parameter kvol,GO for 23rd
April wheat canopy.
X.19 Scatter plots of 2 parameter kvol,GO against 3 parameter kvol,GO for 24th June
barley canopy.
Equations
X.1 full linear kernel-driven BRDF model
X.2 canopy in terms of  and 
X.3 definition of 
X.4 kvol as a function of 
X.5 kGO as a function of 
X.6 definition of  in terms of P and G
X.7 kvol (RossThick)
X.8 kvol (RossThin)
X.9 kGO (LiSparse)
X.10 kGO (LiDense)
X.11 Slope of  against RossThick kernel
X.12 Slope of  against RossThin kernel
X.13 gradient of LiSparse kernel
X.14 gradient of LiDense kernel
X.15 canopy expressed as a function of leaf, soil, avol,GO and bvol,GO
X.16 a-c fiso,vol,GO expressed as functions of leaf, soil, avol,GO and bvol,GO
Tables
X.1 LAI and %cover values for the six canopies used in experiment
X.2 r2, avol and bvol values for  against kvol
X.3 r2, avol and bvol values for  against kGO