Phase: RAMI 3
The 1-D approaches, such as the two-stream schemes implemented in Global Climate Models to represent the radiation transfer regimes occurring in 3-D structurally heterogeneous environments, impose the use of effective variables in order to 1) accurately model the three radiant fluxes (i.e., reflected, transmitted and absorbed) for realistic conditions 2) validate the GCM outputs against the values delivered by remote sensing algorithms and 3) ensure the consistency between various fluxes and state variable values when using assimilation techniques. The definition of effective variables follows from simple radiation transfer considerations, such as satisfying the classical Beer-Bouger-Lambert law for the extinction of the direct illumination while, in the mean time, ensuring a correct distribution between the reflected, diffusely transmitted and absorbed fluxes associated with 3-D structurally heterogeneous conditions. The inverse procedure to estimate the values of the effective variables is fully described in Pinty, et al. (2004) (see bottom of page)
The two-stream solutions, as well as their approximations, for estimating the three radiant fluxes accurately are decomposed into separate contributions, namely the Black Background (no scattering from the background), the Black Canopy (no scattering by canopy elements) and the remaining contribution involving multiple scattering events between the canopy and the background. This decomposition facilitates the identification of the physical processes intervening in the various components. The Black Background solutions follow exactly the Meador and Weaver's (1980) original two-stream solutions for direct illumination conditions.
The solution to the Black Canopy problem is accurately represented via an approximate function involving the value of the structure factor estimated at 60 degrees Sun zenith angle. Finally the coupled canopy-background scattering processes are parameterized on the basis of the same Meador and Weaver's (1980) two-stream solutions but extended to address the case of an external isotropic source of illumination.
The two-stream solutions were found to be in very good agreement with results from accurate and realistic simulations of 3-D heterogeneous canopies, as represented by a Monte-Carlo model, both for standard and extreme conditions, in both the red and near-infrared spectral regions.
The numerical accuracy of these two-stream solutions are conserved under conditions where the leaf reflectance and transmittance are not assigned the same value and where multiple scattering regimes dominate, e.g., presence of snow-covered background.
The proposed formulation of the two-stream problem favors its coupling with existing 1-D atmospheric radiation transfer schemes by simply adding one more layer, which scattering properties correspond to those of a vegetation canopy.
The source code for this model (together with detailed documentation) can be found here.
