A simplified hybrid model for radiation under discontinuous canopies

The hybrid geometric optical and radiative transfer (GORT) model (1995) for the radiation climate under a discontinuous canopy is simplified for easier application by approximation of the multiple scattering. The approximation involves decoupling the multiple scattering into path scattering within the canopy layer and multiple bouncing between the canopy layer and the ground surface. A three-stream approximation is used for multiple bouncing. The path scattering (including reflectance and transmittance) is approximated as functions of mean depth of single scattering source distribution and leaf albedo by extending the analytical solutions of path scattering parameters for a homogeneous layer with limited optical thickness. The approximated path scattering agrees reasonably well with the numerical solutions of the GORT model. By combining path scattering and multiple bouncing, the approximated downwelling radiation at the forest floor and upwelling radiation at top of the forest are close to the numerical solutions by the GORT model. The signature of the sunlit crown surface can also be approximated by the product of the canopy path reflectance parameter and the total gap probability in the discontinuous plant canopies. Through this, the signature of sunlit crown surface, a parameter required by the pure GO model can be derived. The calculated signature of sunlit crown surface agrees well with measurements made in a conifer forest in Howland, Maine.