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1. BASIC FORMULATIONS
Assuming an atmosphere-ocean system with a rough anisotropic sea surface of Cox-Munk
type reflection model , the theoretical upwelling intensity / can be computed by the doubling and
adding method [2]. Let us assume an incident solar flux tcF 0 , per unit area normal to the direction
of propagation, illuminates a plane parallel atmosphere with the optical thickness of rfrom the
direction of ( fi 0 ,0 O ) , where symbols p 0 and (¡> 0 are the cosine of the solar zenith angle and the solar
azimuthal angle , respectively. The upwelling intensity at the top of the atmosphere in the direction
of (f.i ,(p ) can be expressed by Eq.(l) in terms of the reflection function of the atmosphere-ocean
system .
/(t: ^,^ o , 0-0 o ) = ii 0 R(r:ii,ii 0 ,(p-(t) Q )F 0 (1) .
By using adding method, R can be expressed in terms of the reflection and transmission
functions of the atmosphere, R A and T A , and the reflection function of the sea surface R sf [5] .
For a given atmospheric model, it is possible to compute R A and T A by the doubling and adding
method [2].
Since the reflectance data analysis in the perpendicular plane [61 rejected an isotropic Cox-
Munk model, we consider only an anisotropic Cox-Munk model in this study. A general
wave slope distribution ( an anisotropic Gaussian ) relating with both the surface wind speed and
direction can be expressed in terms of a Gram-Charlier series as described in [1].
G(Z C ,Z U ) = (Ijrcj'CrJ- 1 exp[-(£ 2 + rj 2 )/ 2]
* [1-c 21 (£ 2 -1)ti/ 2 -c 03 (rf -3*7)/6
+ c 40 (§ 4 ~ 6§ 2 +3)/24
+ c 22 (| 2 -l)(r/ 2 -l)/4 (2) ’
+ c 04 ( ? ? 4 ~ 6r/ 2 + 3)/ 24 + • • •]
