Local estimates in Monte Carlo method for the ocean-atmosphere system with a random interface

Abstract

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 |

Modeling Atmosphere-Ocean Radiative Transfer: A PACE Mission Perspective

“…This code is based on the Monte Carlo technique, works in either plane-parallel or in spherical-shell geometry, and accounts for polarization. A local estimate variance reduction technique (Marchuk et al, 1980;Rakimgulov and Ukhinov, 1994) is implemented for the radiance calculations. In spherical mode, the change in photon path due to index of refraction variations with altitude is neglected, which reduces accuracy at grazing angles and in twilight conditions.…”