Remote Sensing of Forest Biophysical Structure Using Mixture Decomposition and Geometric Reflectance Models

Abstract

Using geometric shadow and linear mixture models we develop and evaluate an algorithm to infer several important structural parameters of stands of black spruce (Picea mariana), the most common boreal forest dominant. We show, first, that stand reflectances for this species can be represented as linear combinations of the reflectances of more elemental radiometric components: sunlit crowns, sunlit background, and shadow. Secondly, using a geometric model, we calculate how the fractions of these radiometric elements covary with each other. Then, using hand‐held measurements of the reflectances of the sunlit background, sphagnum moss (Sphagnum spp.), and assuming shadow reflectance to be that of deep, clear lakes, we infer the reflectance of sunlit crowns from the geometric shadow model and low‐altitude reflectance measurements acquired by a helicopter‐mounted radiometer. Next, we assume that the reflectance for all black spruce stands is simply a linear combination of shadow, sunlit crown, and sunlit background reflectance, weighted in proportion to the relative areal fractions of these pixel elements. We then solve a set of linear equations for the areal fractions of these elements using as input helicopter observations of total stand reflectance. Using this algorithm, we infer the values for the areal proportions of sunlit canopy, sunlit background, and shadow for 31 black spruce stands of varying biomass density, net primary productivity, etc. We show empirically and theoretically that the areal proportions of these radiometric elements are related to a number of stand biophysical characteristics. Specifically, the shadow fraction is increasing with increasing biomass density, average diameter at breast height, leaf area index (LAI), and aboveground net primary productivity (NPP), while sunlit background fraction is decreasing. We show that the end member fractions can be used to estimate biomass with a standard error of ≈ 2 kg/m2, LAI with a standard error of 0.58, dbh with a standard error of ≈ 2 cm, and aboveground NPP with a standard error of 0.07 kg·m‐2·yr‐1. We also show that the fraction of sunlit canopy is only weakly correlated with the biophysical variables and are thus able to show why a popular vegetation index, Normalized Difference Vegetation Index (NDVI), does not provide a useful measure of these biophysical characteristics. We do show, however, that NDVI should be related to the fraction of photosynthetically active radiation incident upon and absorbed by the canopy. This work has convinced us that a paradigm shift in the remote sensing of biophysical characteristics is in order–a shift away from direct inference of biophysical characteristics from vegetation indices and toward a two‐step process, in which (1) stand‐level reflectance is approximated in terms of linear combinations of reflectance‐invariant, spectrally distinct components (spectral end members) and mixture decomposition used to infer the areal fractions of these components, e.g., shadow, sunlit crown, and sunlit background, followed by (2) the use of radiative transfer models to compute biophysical characteristic values as a function of the end member fractions.