BRDF Applications in Semiarid Grassland Monitoring with the AVHRRs

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Weight of Determination

The weight of determination (WoD) is quantity providing a measure of the noise incurred when reflectance is modelled at view and illumination geometries other than those of the observations. It is calculated using the inverse matrix which provides the solution to the least squares problem when observations are fitted to a BRDF model. Since this matrix depends upon the sampling scheme (angular distribution of observations), the WoD is also dependent on this as well as the modelling geometry chosen.

The first chart below shows the maximum, mean and mode WoD values for images generated by modelling scenes with the Roujean model alongside the total transformed divergence for 10 grassland community type classes when signatures are extracted from the modelled images. Note that the lowest mean and mode WoD values occur close to the point at which total transformed divergence is highest; and that the number of observations with very high WoDs is very low for most geometries.

Total Transformed Divergence (total for 10 grassland community type class pairs) and Maximum, Mean and Mode Weight of Determination (for entire modelled images) with Modelling to Different View Zenith Angles in the Principal Plane (Roujean model; solar zenith at 45 degrees). Numbers against data points for maximum WoD indicate no. of observations with WoD > 1.00, out of a total of 33,405 for the entire image.

Maximum, Mean and Mode Weight of Determination (for entire modelled images) with Modelling to Different View Zenith Angles for a solar zenith of 45 degrees, in the Principal Plane, with the Roujean (solid lines) and LiDenseMODIS/RossThick (dotted lines) models. Numbers against data points for maximum WoD indicate no. of observations with WoD > 1.00, out of a total of 33,405 for the entire image. Note the increase in mean and mode WoDs for the LiDenseMODIS/RossThick model to about 1 at the hotspot location (viewing at 45 degrees in the backscattering direction).

The training sites for the classes used are shown here.