THE USE OF 2-STREAM APPROXIMATIONS FOR THE PARAMETERIZATION OF SOLAR RADIATIVE ENERGY FLUXES THROUGH VEGETATION

Two-stream approximations have been used widely and for a long time in the field of radiative transfer through vegetation in various context s and in the last 10 years also to model the hemispheric reflectance o f vegetated surfaces in numerical of the earth-atmosphere system. For a plane-parallel and turbid vegetation medium, the existence of rotati onal invariance allows the application of a conventional two-stream ap proximation to the phase function, based on and expansion in Legendre Polynomials. Three conditions have to be fulfilled to make this reduct ion possible in the case of vegetation. The scattering function of sin gle leaves must be bi-Lambertian, the azimuthal distribution of leaf n ormals must be uniform, and the azimuthally averaged Leaf Area Normal Distribution (LAND) must be either uniform or planophile. The first an d second assumptions have been shown to be acceptable by other researc her and, in fact, are usually assumed explicitly or implicitly when de aling with radiative transfer through canopies. The third one, on the shape of the azimuthally averaged LAND, although investigated before, is subjected to a detailed sensitivity test in this study, using a set of synthetic LAND's as well as experimental data for 17 plant canopie s. It is shown that the radiative energy flux equations are relatively insensitive to the exact form of the LAND. The experimental Ross func tions and hemispheric reflectances lie between those for the synthetic cases of planophile and erectophile LANDs. However, only the uniform and planophile LANDs lead to canopy hemispheric reflectances, which ar e markedly different from one another. The analytical two-stream solut ions for the either the planophile or the uniform LAND cases may be us ed to model the radiative fluxes through plant canopies in the solar s pectral range. The choice between the two for any particular case must be made on the basis of experimental data.