color 
lance 
ue is 
ional 
n the 
angle 
imuth 
ind à, 
These 
à set. 
1, the 
s are 
sen et 
tance 
sina 
In this study, we selected "Desert" ( 5x5 pixels) as a target 
area, over the Sahara in West Africa. POLDER observes 
target reflectances from up to 14 directions during a single 
satellite pass. "Desert" is in 12 successive framed images 
(Scene #21 to #32) of Path #287 data. 
3.1 Atmosphere - ground surface model 
A single atmospheric layer model is assumed. Let us 
assume an incident solar flux xF, illuminates a plane 
parallel atmosphere from the direction of (Jt, $)), where 
H, and 4, are the cosine of the solar zenith amgle 6, and 
the solar azimuth angle, respectively. Itis given by (1) in 
Stokes vector representation, 
F, = x[F 000]' (1), 
where a superscript t represents the matrix transposition. 
The upward Stokes vector I, (t, U, My, Ÿ-0,) - [IQ U VJ] 
at the top of the atmosphere in the direction of (u, ¢) can 
be expressed by (2) in terms of the reflection matrix of the 
atmosphere - ground surface model R 
atmos * surface? 
I (t, Hu, Bs $-0,) = HR somos surface (Ts H, Ho» 0-0) F, (2). 
As for the components of the Stokes vector, I is the 
intensity, Q, U, and V are related to the linear 
polarization, the plane of polarization, and the circular 
polarization respectively. R,...... ,,, Can be expressed in 
terms of the reflection and transmission matrices of the 
atmosphere, R,_ and T,_ , and the surface reflection 
matrix, R face For a given atmospheric model, it is 
possible to compute R,__and T, ___ by using the doubling 
and adding method. 
Level-1 products are given in unit of normalized Stokes 
vectors. All components of normalized Stokes vectors 
(I, Q, U, V. ]' where [= nl/nF = UF, Q = nQ/rF = Q/F, 
U = nU/nF = U/F and V = ( are normalized with respect 
to the extraterrestrial solar irradiance (nF). The fourth 
component V, is zero because POLDER does not 
measure the circular polarization. 
Table 1 shows the optical parameters in the computation. 
We adopted the molecular and aerosol optical thickness 
values based on the tropical model atmosphere of 
MODTRANG (Ontar Corp., 1995). The refractive index 
of aerosol, m = 1.55 - 10.005, as the desert dust (Tanre et 
al., 1988) and the Junge type aerosol size distribution 
function with v = 3 are adopted. 
For a natural surface, we assume that the surface 
reflection matrix consists of the diffuse and specular 
components. Then R. can be expressed as follows, 
Rome Ho 0-0) = OP ie * (1-00p,, (3), 
Table 1 Optical Parameters in the Atmospheric Model 
  
  
Band[nm] total fr ® 
443 0.616 0.389 0.999 
670 0.368 0.132 0.908 
  
t is the total optical thickness, f_is molecule gas - 
aerosol mixing ration, and Q is the scattering albedo 
of the atmosphere for each layer. 
where a is the mixing ratio of the specular to the diffuse 
components . In (3), p, represent the diffuse 
components in the polarized radiation by the target 
surface and p,, shows the specular components. The 
diffuse reflectance components are essentially equal to 
the surface reflectance of Lambertian surface. Then the 
simplified Rondeaux and Herman's model (Rondeaux et 
al., 1991) are adopted for the specular components. 
3.2 Results at 443 nm and 670 nm 
The theoretical reflectance and degree of linear 
polarization curves in channel 443 nm against viewing 
angles are presented for the atmospheric model with the 
ground surface of A = 0.05 and a = 1.0 in Figure 3 , 
together with observed values of "Desert". Figure 4 as 
well shows the case of A = 0.30 and a = 1.0 in channel 
670 nm. The relative reflectance is defined as (R= nl / 
H,RF 2 I/ uF - I,/ p). The degree of linear polarization 
is defined as (P 2 (Q?-U?)'2/ T). Scene #21 to #26 and 
#27 to #32 in the x-axis corresponds to cases of the 
surface reflection occurred in the backward and forward 
scattering directions respectively. In Figure 4 and 
Figure 5, we found a good agreement between the 
theoretical and observed values. This suggests that the 
assumption of Lambertian surface (a = 1.0) for this cover 
is acceptable at visible spectral channels. 
4. CONCLUSIONS 
In this paper, we have made a polarization analysis of 
ADEOS/POLDER image data over land surfaces, 
introducing the combined model with the atmosphere and 
ground surface. Our conclusions based on this study are 
summarized as follows: 
1) We found that the theoretical model can satisfy both 
the observed directional reflectance and linear polarization 
variations against zenith-viewing angles at 443 nm and 
670 nm. ; 
2) An assumption of Lambertian reflection of "Desert" 
seems to be valid in visible spectral regions. In this 
computation, we use the Junge model with v = 3 and 
refractive index m=1.55-0.005i as a typical desert aerosol. 
Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 45 
Bh Ms A EEE NEN EEE 
i 
E 
in] 
DLE I AL LE 
AUGUE. 
EEE