Earth observation modeling based on layer scattering matrices

Abstract

The differential equations describing radiative transfer in vegetative canopies as given by Suits are generalized and solved to derive a layer scattering matrix. Layer scattering matrices can be applied to the calculation of optical parameters for multilayer ensembles according to the Adding method. The application to atmospheric scattering is demonstrated by explaining path radiance, sky radiance, and other quantities in terms of elements from a layer scattering matrix and a surhce reflectance matrix. By combining scattering matrices originating from atmospheric layers with those from earth objects, earth observation models can be constructed. These may become valuable tools in the study of various remote sensing problems. Introductionwater bodies. This results in mathematical models that predict the intensity of Remote sensing of earth objects in the scattered or reflected radiation for given visible to middle infrared wavelength re-directions of sunlight and view as a funcgion is a powerful technique for providing tion of atmospheric and object parameinformation on earth resources rapidly and ters. In this way the quantitative relationover large areas. In the extraction of in-ships between object parameters and reformation from multispectral digital image motely sensed data can be established for data acquired by remote sensing missions, given conditions of observation. An excelseveral levels of sophistication can be dis-lent review of such models, with special tinguished. Some of these techniques, such emphasis on the applicability to remote as visual interpretation of enhanced color sensing problems, is given in Slater (1980). composite imagery or routines for auto-Of particular interest are the vegetation matic classification, already offer much canopy reflectance model of Suits (1972) valuable information for relatively little and the atmospheric model of Turner effort. In other cases, however, especially (1973), since these models are not too when quantitative data are to be ex-complex, require little computer proctracted, these techniques fall short be-essing power, and yet are reasonably recause the extraction of this type of infor-alistic. mation requires more insight into the The analytical model of Suits is based physical processes involved in the interac-on two extensions of the Kubelka-Munk tion of radiation with objects on earth (1931) theory, which describes the scatand with the atmosphere. These interac-tering and extinction of isotropic diffuse tions can be investigated by the appli-fluxes in upward and downward direccation of radiative transfer theory to prob-tion. The first extension is the addition of lems such as atmospheric scattering and specular sunlight with its associate extincnon-Lambertian reflection characteristics tion and scattering coefficients, which of objects like vegetation canopies and leads to the Dtmtley (1942) equations,

Estimation of crop gross primary production (GPP): II. Do scaled MODIS vegetation indices improve performance?

“…We used the PROSAIL2 model (Jacquemoud and Baret, 1990;Baret and Fourty, 1997;Braswell et al, 1996;Verhoef, 1984Verhoef, , 1985Zhang et al, 2005Zhang et al, , 2009Zhang et al, , 2012Zhang et al, , 2013, a coupled soil-canopy-leaf radiative transfer model, to retrieve fAPAR chl , the fraction of PAR absorbed by the foliage of the canopy (fAPAR foliage ), and the fraction of PAR absorbed by the non-photosynthetic foliage components (fAPAR non-chl ) (Zhang et al, 2014a). A pixel is composed of canopy and soil (Zhang et al, 2009(Zhang et al, , 2012(Zhang et al, , 2013.…”

Derivation of Soil Line Influence on Two-Band Vegetation Indices and Vegetation Isolines

“…Under this simplification, the radiative transfer problem in both covered and uncovered area can be simulated independently by modeling horizontally infinite homogeneous canopy and bare soil, respectively. Thus, the reflectance from a covered area can be simulated by a turbid medium canopy model such as the SAIL model [37,38]. Reflectance contributions from each fractional area are, therefore, obtained by a weighted sum of the two independent simulations.…”

Global terrestrial biogeochemistry: Perturbations, interactions, and time scales

“…In this study, we used the SAIL model (Verhoef 1984(Verhoef ,1985 because it is intermediate in complexity, and represents a compromise between physical realism and the number of input parameters.…”

“…A more general and concise formalism was introduced by Verhoef Verhoef (1984Verhoef ( ,1985 was not the solution, but the definition of the coefficients Mg in terms of the three primary angles (leaf inclination, solar zenith, and sensor zenith) and the leaf optical properties (reflectance and transmittance). So the set of model parameters P, along with the sun-sensor configuration 0 (see Section 5.3.3) are mapped into the coefficients Mu such that the reflectance is given by R=Rp(h, 0).…”