Robin D. Morris, Athanasios Kottas, Matt Taddy, Roberto Furfaro and Barry D. Ganapol

12/31/2007 09:00 AM

Applied Mathematics & Statistics

Process models are widely used tools in geoscience and remote sensing, used both for studying the fundamental processes themselves, and as elements of larger system studies. A Radiative Transfer Model (RTM) simulates the interaction of light with a medium. Here we are interested in RTMs that model the light reflected from a vegetated region of the Earth. Such an RTM takes as input various biospheric and illumination parameters and computes the upwelling radiation at the top of the canopy. The question we address is: which of the inputs to the RTM has the greatest impact on the computed observation? We study the Leaf Canopy Model (LCM) RTM.

The LCM was designed to study the feasibility of observing leaf chemistry remotely. It takes as input leaf chemistry variables (chlorophyll, water, lignin, cellulose) and canopy structural parameters (leaf area index, leaf angle distribution, soil reflectance, sun angle).

We present a statistical approach to sensitivity analysis of RTMs, to answer the question posed above. The focus is on global sensitivity analysis, which studies how the RTM output changes as the inputs vary continuously according to a probability distribution over the input space (whereas local sensitivity analysis studies the behavior around a few fixed points.) The influence of each input variable is captured through the determination of the ``main effects'' and ``sensitivity indices''.

Direct computation requires extensive runs of the RTM, which is computationally expensive. We develop a Gaussian Process approximation to the RTM output to enable efficient computation.

We illustrate how the approach can effectively determine the input variables that are vital for accurate prediction. The methods are applied to the LCM with 7 inputs and output obtained at 8 wavelengths associated with specific MODIS bands that are sensitive to vegetation.