Stochastic Modeling of Radiation Regime in Discontinuous Vegetation Canopies

A stochastic radiative transfer equation for the mean l( → X), cosine of polar angle of direction → X d( → X2 → X0), Dirac delta function field and its solution for the case of discontinuous vegetation canopies is discussed in this article. The equation set v(→r ), indicator function Fdir(k), extraterrestrial solar radiance at the top of satisfies the law of energy conservation and is amenable to numerical solution by the method of successive orders the atmosphere Fdir1dif(k, → X0), extraterrestrial solar irradiance at the of scattering approximations. Special attention is given to analytical analysis of the effect of spatial discontinuity on top of the canopy I(→r , → X), radiance (intensity) at spatial point →r and the radiation field. Research indicates that a complete description of the radiation field in discontinuous media is in direction → X I(z , → X), mean radiance, averaged over the possible, using not only average values of radiation over total space, but averages over space occupied by abhorizontal plane at depth z U(z, → X), mean radiance, averaged over the sorbing elements is also required. A new formula for absorbtance, which extends the formula for a homogeneous vegetated portion of a horizontal plane z SR(x0,y0), cylinder of height H, with vertical axis case, was obtained for the general case of discontinuous media. The internal as well as the emergent radiation located at point (x0,y0) and radius R Tz, area of horizontal plane z, zP[0; H] covered fields were validated using available radiative transfer models (oneand three-dimensional) and Monte Carlo by vegetation Tz(x0,y0), manifold Tz, shifted by vector {x0,y0} model of computer-generated maize canopy. Additionally, the canopy reflectance simulation is assessed by compariSR∩Tz, common area of manifold SR, Tz Mes(S), measure of area S sons with field data from shrublands. In all cases, the p(z), horizontal density of vegetation (HDV) at simulations compare well with both the Monte Carlo relevel z sults and the field data. Elsevier Science Inc., 2000 uL(r ), foliage area volume density (FAVD; m2/m3) k, wavelength rD(k), spectral hemispherical reflectance of the NOMENCLATURE leaf H, total depth (height) of canopy tD(k), spectral hemispherical transmittance of the → X5{Xx,Xy,Xz}, unit vector of the solid angle leaf → X0, direction of direct solar radiation x(k), single-scattering leaf albedo qsoil(k), soil hemispherical reflectance G(→r , → X), mean projection of leaf normals in the *Department of Geography, Boston University Boston direction → X †INRA Bioclimatologie, Site Agroparc, 84914 Avignon Cedex 9, France 1