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ATMOSPHERIC PARAMETER ESTIMATION USING THE REFLECTANCE 
AND POLARIZATION DATA 
Y. KAWATA AND A. YAMAZAKI 
Environmental Information Research Laboratory 
Kanazawa Institute of Technology 
Nonoichi, Ishikawa 921, Japan 
KEY WORDS: Atmospheric Parameter, Reflectance, Polarization, Multiple Scattering. 
ABSTRACT: 
In this paper we have made the atmospheric optical parameter estimation using the reflectance and polarization data measured over 
Mediterrenean Sea ( referred as the Medimar data ) by the airborne POLDER sensor [1],[2]. Assuming an atmosphere-ocean system 
with a Cox-Munk type reflecting sea surface [3], the reflectance and polarization , including radiance contributions from multiple 
scatterings within the atmosphere and multiple reflections between the atmosphere and the sea surface, have been computed by using 
the adding and doubling method [4],[5] for several different atmospheric models. In this study the Junge type aerosol size distribution 
function was considered [6]. Our results based on this study are summarized as follows: 
1) We found five Junge type aerosol models which can explain the observed reflectance data at 0.85um in the principal plane. 
2) However, none of these model explained the observed polarization patterns in the backward scattering direction. 
3) Further study on other types of aerosol size distribution function are needed to find a aerosol model which can satisfy both the 
reflectance and polarization data. 
1. BASIC FORMULATIONS 
Assuming an atmosphere-ocean system with a rough 
anisotropic sea surface of Cox-Munk type reflection model , the 
theoretical upwelling Stokes vector / can be computed by the 
doubling and adding method [4]. Let us assume an incident solar 
flux zF, , per unit area normal to the direction of propagation, 
illuminates a plane parallel atmosphere with the optical thickness 
of 7 from the direction of ( I4, 0) , where symbols u, and 6, are the 
cosine of the solar zenith angle and the solar azimuthal angle , 
respectively. The upwelling Stokes vector at the top of the 
atmosphere in the direction of (u ,@) can be expressed by Eq.(1) 
in terms of the reflection matrix of the atmosphere-ocean system 
Kr, 6-6)» uie: uu. - 0.)F (1) 
By using adding method, R can be expressed in terms of the 
reflection and transmission matrices of the atmosphere, R, and 
T, , and the reflection matrix of the sea surface R_, . For a given 
atmospheric model, it is possible to compute R, and T, by the 
doubling and adding method. 
337 
Since the reflectance data analysis in the perpendicular plane 
rejected an isotropic Cox-Munk model by us [5] , we consider 
only an anisotropic Cox-Munk model in this study. A general 
wave slope distribution ( an anisotropic Gaussian ) surface wind 
speed and direction can be expressed in terms of a Gram-Charlier 
series as described in [3]. 
G(Z ,Z ) = (270,6 )' ex[-(E + n°)/2] 
x[1-c (8 -1m/2- e (n. -30)/6 
+e (8-66 +3)/24 
2 
*e (8 -1)(n =1)/4 a 
+ c, (n° - 61° +3)/24+-<] 
ES Elo aiu Al, © 
where 6, 7] are the standardized slope components and Z_, Z, are 
the slope components along the crosswind ( X ) and upwind (X) 
directions , respectively. Furthermore , 0., 0, are the root mean 
squares of Z , Z, , respectively. The explicit dependence of 6. , 0, 
and c j 9n the wind speed is given by Cox and Munk [3]. The 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996