relationship between the surface slope angle B and its X -, X - 
components is given by Eq.(4). 
B= an’ (4/2 tZ (4) 
The sea surface reflection matrix is composed of a reflection matrix 
specifying the radiation reflected directly by the sea surface , and 
a water column reflectance which is the transmitted radiation from 
the sea. In other word, itisthe radiation reflected diffusely by 
water molecules and hydrosols within the sea. It is very difficult 
to evaluate the under water radiation, because of many uncertainties 
in estimating the underwater radiative transfer model. In this 
paper we assume that the water column reflectance can be 
expressed by r,_, for the simplicity. The angular dependence of 
r,. may be neglected because of the observational difficulty in the 
measurements as discussed in Bréon and Deschamps [2]. In short 
wavelength (0.45um) r may be a few percent , whereas it is 
very close to zero in the near infrared (0.85um)[7]. Then , 
according to the formulation by Takashima [8] with some 
modifications of his original form , the sea surface reflection matrix 
R,, can be given approximately by Eq.(5). 
se 
TG 
RG 
4uu cos B 
R. (t, Hd ~ $ ) = 
where Rot( a) is the rotation matrix for a given rotation angle 
and it is given in Eq.(6) . The angles, ó and y are the rotation 
angles defining the reflection matrix with respect to the local 
meridian plane as a common reference for the Stokes vector. 
1 0 0 0 
0 cos20 . —sin2Ce. 0 
Rot(a) — 
0 sinc . cos2€ (6) 
0 0 0 1 
Furthermore, R(20) is the specular reflection function and @ is 
the incident or reflection angle to the facet . 
2. AIRBORNE POLDER DATA ANALYSIS 
We compute the theoretical reflectance and the degree of linear 
polarization curves against the viewing zenith angle in the principal 
plane at the wavelength of 0.85um for a two layer atmospheric 
model of mixed atmosphere, consisting of aerosols and gaseous 
molecules, bounded by a rough sea surface layer. The principal 
plane is a plane containing both the solar and the viewing 
directions. For the analysis of the airborne POLDER data , the 
internal upwelling reflectance zl/u,F and the degree of linear 
polarization 4 lQ' TU / at the flight altitude of the aircraft 
338 
(h-4700m) are computed in the principal plane by using the 
internal reflection function R in stead of R at the top of the 
atmosphere. The quantities of. 7, , Q, and U, are the 1st, 2nd, ang 
3rd components of the upwelling Stokes vector at the altitude of 
h, respectively. 
In the computations of the theoretical reflectance and the 
degree of linear polarization the Junge type size distribution 
function was assumed. The size distribution of the Junge type 
aerosol model is given by Eq.(7) [6]. 
Cio" 0.02um <r < 0.1um 
lr) = c poo 0.1um € r € 1Oum a 
0 r <0.02um, r > 10um 
pin 
r.z002um,r 
min max 
The theoretical calculations of reflectance at 0.85um in the 
= 10pm. 
principal plane were made for the Junge type functions with v= 
3.5,4.0 and 4.5. In this analysis we assumed that the radiation 
contribution from the underwater is negligible , i.e., r y =00a 
0.85um [7]. Since we considered 9 different refractive indices 
(m z 1.33, 1.33-10.01, 1.33-10.05 : mz 1.5, 1.5-0.01, 1.5-10.05; 
mz 1.75, 1.75-10.01, and 1.75-0.05 ), and 15 wind speeds ( from 
V = 8.0 m/sec to V=15.0 m/sec with an increment of 0.5 m/sec), 
there are 135 different combinations of the refractive index and 
wind speed. We should note that the measured wind speed and its 
direction were V=14.4 m/sec and W =220° at the time of the 
Medimar experiment. The refractive indices of m=1.33, 1.5, and 
1.75 correspond to those of water, dust, and soot aerosols, 
respectively. For each of aerosol size distribution functions, 135 
cases were examined whether the corresponding theoretical 
reflectance curves can satisfy the observed reflectance data or 
not. In this examination the surface wind direction of Wz220 
was fixed. We adopted a simple rule that the theoretically 
computed reflectance values should be at least within the range of 
observed error bars (+3 0) at all viewing zenith angles. We found 
Junge type size distribution functions can satisfy the observed 
reflectance data when an appropriate wind speed is assumed. They 
are as follows: the Junge type function with v = 3.5 and mel 
i0.01 ( referred to the aerosol model A ) for 10.5 m/sec SV 
13.5 m/sec, that with v = 4.0 and m=1.33 ( referred to the aerosol 
model B ) for 10.5 m/sec = V =< 11.5 m/sec, that with v=40 
and m=1.75-i0.05 ( referred to the aerosol model C ) for 11.0 m/ 
sec € V X 12.5 m/sec, that with v = 4.5 and_m=1.33-i0.01 
(referred to the aerosol model D ) for 10.0 m/sec € V é 1251 
sec, and that v 2 4.5 and m=1.75-i0.05 ( referred to the aerosol 
model E ) for 10.0 m/sec € V X 12.5 m/sec. In other words, tlt 
Junge type aerosol models, A-E could be candidate models, 
because they can satisfy the observed reflectance curve when à? 
appropriate wind speed is assumed. We also found that the Jung 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996