«Îïòèêà атмосферы и îêåàíà», 23, ¹ 4 (2010)
ОПТИКА КЛАСТЕРОВ, АЭРОЗОЛЕЙ И ГИДРОЗОЛЕЙ
УДК 519.216.24, 519.6
Monte Carlo simulation of angular characteristics
for polarized radiation in water-drop and crystal clouds
Sergey M. Prigarin1, Ulrich G. Oppel2
1 Institute of Comp. Mathematics and Math. Geophysics, SB RAS,
pr. Academician Lavrentyev, 6, Novosibirsk, 630090, Russia
Novosibirsk State University, Pirogova str., 2, Novosibirsk, 630090, Russia
2 Institute of Mathematics, Ludwig-Maximilian University of Munich,
Theresienstr., 39, Ä80333, Munich, Germany
Поступила в редакцию 20.12.2009 ã.
In the paper we present the results of computational experiments aimed to define the angular distributions
for the polarized radiation scattered in a cloudy layer. The angular distributions for Stokes parameters were
computed by Monte Carlo method for different optical models of water-drop and crystal clouds. The ulterior
objective of the research is to develop effective techniques to study the particles shape and size by measuring
angular characteristics of the scattered radiation emanating from clouds.
Key words: polarized radiation transfer, water-drop and crystal clouds, Monte Carlo simulation, angular
distributions, particle shape and size.
Introduction
The role of clouds in the global climate system is
important but not well studied. Cloud feedbacks are
the largest source of uncertainty in estimates of radiation
balance and climate sensitivity, therefore
a better understanding and representation of radiation
transfer processes in clouds is of paramount importance
for climate science. On the other hand, the
adequate optical models of clouds are necessary to
investigate properties of cloudiness by active and
passive optical remote sensing. Our paper deals with
numerical modeling of the solar radiation transfer in
the atmosphere clouds taking into account specific
features caused by polarization of light. By computational
experiments we studied angular distributions
for the polarized radiation scattered upward and
downward by water-drop and crystal clouds. The
angular distributions were computed for the Stokes
parameters, degree of polarization, and direction of
preferable polarization. For computations we used
Monte Carlo method and several optical models of
clouds. The ultimate aim of the research is to develop
effective techniques to study phase structure of
clouds, shape and size of particles by measuring characteristics
of the scattered radiation.
1. Mathematical model
and Monte Carlo algorithms
Assume that an optically isotropic scattering
medium consists of particles randomly oriented in
space, extinction coefficient and single scattering
albedo in the medium does not depend on light polarization,
and a field of reference-vectors ()
ρω is
fixed, i.e. for every direction ω ∈ Ω = {(a, b, ñ} ∈
∈ R3: a2 + b2 + c2 = 1} there is defined a unit vector
ρ(ω) orthogonal to ω. Then the process of stationary
polarized radiation transfer in the scattering medium
may be described by integral equations of the second
kind with the generalized kernel
S[ρ](r, ω) =∫∫ rr
3
e
Ω
×ρ ω δ ω −
′ ′
R
−τ ′rr
− ′
(, )
2
S rdr drr
′′ ′−
[](, ) ω′ ′ + S0[ρ](r, ω),
− '
rr
r′, r ∈ R3, ω′, ω ∈ Ω, ρ = ρ(ω), ρ′ = ρ(ω′). (1)
Here S[ρ](r, ω) is the Stokes vector (we shall consider
Stokes vectors of the type (I,Q,U,V)) with respect
to the reference vector ρ = ρ(ω) for the radiation
at the point r spreading in the direction ω, q(r′)
is the single scattering albedo at the point r′, σ(r′) is
the extinction coefficient at the point r′, δ is the
delta-function, S0[ρ](r,ω) is the Stokes vector of the
source at the point r in the direction ω,
τ(r′, r)= ∫σω
( ( ), )
l
segment [r′, r], r(s) = r′ + s(r – r′)/l, l = rr ,
− ′
0
M[ρ′, ρ](ω′, ω, r′) is the 4¥4-phase matrix of the medium
at the point r′ (ω′ is the direction before scattering,
and ω is the direction after scattering):
M[ρ′, ρ](ω′, ω, r′) = L[ρ, ρ*]–1M(ω′, ω, r′) L[ρ′, ρ*],
Monte Carlo simulation of angular characteristics for polarized radiation in water-drop and crystal clouds
243
rs ds is the optical length of the
qr r M r
() () [ , ]( ′,
′′ ′σρ ′ Ч
ρ ω ω, )
Стр.1