A simplified scheme of the generalized layered radiative transfer model

In this paper, firstly, a simplified version (SGRTM) of the generalized layered radiative transfer model(GRTM) within the canopy, developed by us, is presented. It reduces the information requirement of inputted skydiffuse radiation, as well as of canopy morphology, and in turn saves computer resources. Results from the SGRTMagree perfectly with those of the GRTM. Secondly, by applying the linear superposition principle of the optics andby using the basic solutions of the GRTM for radiative transfer within the canopy under the condition of assumedzero soil reflectance, two sets of explicit analytical solutions of radiative transfer within the canopy with anysoil reflectance magnitude are derived: one for incident diffuse, and the other for direct beam radiation. The explicitanalytical solutions need two sets of basic solutions of canopy reflectance and transmittance under zero soil reflectance,run by the model for both diffuse and direct beam radiation. One set of basic solutions is the canopy reflectance$alpha_{text f}$ (written as $alpha_1$ for direct beam radiation) and transmittance $beta_{text f}$ (written as$beta_1$ for direction beam radiation) with zero soil reflectance for the downward radiation from above the canopy (i.e.sky), and the other set is the canopy reflectance ($alpha_{text b})$ and transmittance $beta_{text b}$ for the upwardradiation from below the canopy (i.e., ground). Under the condition of the same plant architecture in the vertical layers,and the same leaf adaxial and abaxial optical properties in the canopies for the uniform diffuse radiation, the explicitsolutions need only one set of basic solutions, because under this condition the two basic solutions are equal, i.e.,$alpha_{text f}=alpha_{text b}$ and $beta_{text f}=beta_{text b}$. Using the explicit analytical solutions, thefractions of any kind of incident solar radiation reflected from (defined as surface albedo, or canopy reflectance),transmitted through (defined as canopy transmittance), and absorbed by (defined as canopy absorptance) the canopy andother properties pertinent to the radiative transfer within the canopy can be estimated easily on the ground surfacebelow the canopy (soil or snow surface) with any reflectance magnitudes. The simplified transfer model is proven tohave a similar accuracy compared to the detailed model, as well as very efficient computing.