The paper deals with a new Monte Carlo algorithm for the calculation of the field of optical radiation reflected and refracted by the sea surface. The algorithm allows one to take into account the effects of shadowing and re-reflecting of the radiation by the surface elements. In contrast to the known Monte Carlo methods the algorithm does not contain a cumbersome procedure of numerical construction of the random surface realizations. The paper provides the corresponding local estimates for the radiation intensity field in the ocean-atmosphere system.When elaborating and optimizing the sea remote sensing methods, and also when solving quite a number of fundamental and applied problems of the sea optics, one faces a problem of calculating the electromagnetic field of the radiation reflected and refracted by the sea surface. The mathematical essence of the problem is that one has to calculate certain functionals of the solution to the radiation transfer equation. The functionals are given on a random field which is an undulating sea surface.Evidently the Monte Carlo method was first applied to such a problem in [16]. In the work the simplest model was considered. The model assumes the air-water boundary to be a random surface formed by a set of elementary surface elements whose centers lie in a plane and whose normals are distributed according to a prescribed single-point distribution function. Calculations of the radiation field were made on the basis of the direct modelling of the radiation transfer process. Later on in [3] more effective weighting algorithms were proposed for the same model. Thus the results of calculations [3,16] were obtained without taking account of the effects of shadowing and re-reflecting of the radiation by the surface elements. To take account of these effects, two approaches were proposed in [9]. According to the first approach, one approximately constructs random realizations of the surface deviations in respect to a mean level, and then models the trajectories of radiation quanta (photons). Though the corresponding calculation algorithms (see [8,11]) are rather simple to realize, but their realization costs much computational time. The present work considers the second, more efficient, approach that is in essence a variant of the expectation method.
New estimates in the Monte Carlo method are considered for calculation of the field of optical radiation that is reflected and refracted by an undulating sea surface. Local estimates of the field of radiation intensity are developed for the 'facet' model of sea undulation and the model of random field of normals and elevations. POSING THE PROBLEMLet us consider a problem of radiation transfer in a plane-parallel ocean-atmosphere system, which is represented as a scattering and absorbing layer of depth H. Let 5 Q and S H denote the planes z = 0 and z = //, which are the ocean floor and the upper boundary of the atmosphere respectively. In addition, let S be the plane z = h, Ο < h < //, which is the water-air interface.The plane S Q is a diffusively reflecting one with the albedo A(r). The intensity of the reflected radiation at the point r e 5 Q in the direction ω e Ω + is expressed as where Ω_ = {coe , (co,k)<0}, = {coeR 3 , |ω| = 1}, k = (0,0,1).Henceforth we also use the set Ω + = {ω e β, (ω, k) > 0}. We use the 'facet' model [1,5,6] as a model for an undulating ocean surface. In this model, it is assumed that the water surface consists of surface elements whose centers are located at the same level and slopes are distributed with a given distribution density p(z 9 z). Here z and z are the tangents of the angles between a surface x, y x, y element and the axes OX and OY respectively. In the following we assume that slope distributions at two distinct points are independent of one another and the density ρ(ζ χ ,ζ) is normal, i.e.Then the distribution density of the normal s to a surface element is written as P(S) = in the spherical coordinate system, where φ stands for the azimuth angle and μ = (s, k) for the cosine of the zenith angle.' Computing Center, the Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia Brought to you by |
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