2 - MODEL 
To simulate the radiative transfer within the atmosphere, at the ocean surface, and within the 
ocean, we use a Monte Carlo model, an improved version of the model developed by Breon (1992) 
to simulate the bidirectional reflectance of clouds. The improved version accounts for the 
polarization of scattered and reflected radiance. 
The Monte Carlo model (hereafter referred to as MC) numerically simulates the path of 
photons interacting within the ocean-atmosphere system. The occurrence and type of interactions 
are determined by random numbers. In the atmosphere or in the water column, the pathlength L 
between two interactions is given by: 
L = — ln(£) 
k 
where e is a random number between 0 and 1 and kg# is the extinction coefficient. Two angles are 
then necessary to define the new direction of motion: the scattering angle a (the angle between the 
two motion vectors before and after scattering), and the rotation angle tp (the angle between the 
scattering plane and a reference plane containing the motion vector before scattering). The angle a 
is obtained from the equation: 
J q P(0) sin(0)r70 = e/^ ( 0 ) sin(0)(i0 
and the angle (p is randomly chosen between 0 and 2k. In (2), P( 6) is the scattering phase function. 
It depends on the scattering element, either molecules, aerosols, or hydrosols. 
At each scattering, the Stokes vector associated with a photon is modified according to 
(Chandrasekhar, 1960; Deirmendjian, 1969): 
f 
L 
PA «) 
h 
P 2 ( a ) 
1, 
U' 
PA a) -P 4 W 
u 
V' 
(°0 ^3 (°0 
_ v_ 
When a photon reaches the surface (either from the atmosphere or from the ocean), the wave 
slope, ft, is determined ramdomly according to wave slope statistics (Cox and Munk, 1954): 
tan(P) = a[- ln(e )]2 
where s depends on the wind speed. 
The photon is then either reflected or transmited through the interface. The Stokes vector 
associated to the photon becomes: 
/ 
L 
r_ 2 
/ ■ 
L 
r_ 2 
'7/ 
/ 
h 
U' 
= 
rl 
-r = r x 
I, 
U 
or 
/ 
h 
U' 
= 
-<J ± 
h 
U 
V' 
~ r = r l 
V 
V' 
-Ux 
V 
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