remotely sensed radiance L is described by the summation of (1) 
the atmospheric path radiance L, (2) the directly transmitted 
radiance reflected by the surface L, and (3) the scattered 
radiance by the local environment Le. 
L,, L, can be written as: 
E: i (1) 
Lom pe Cue 
X 
  
L. «x z4uH.JT LM. ) 
: z p A „CA . (2) 
where r^ is the global irradiance at the inclined surface, p and 
<p> are the target and averaged environment reflectance, 7 is 
the sum of Rayleigh and aerosol optical depth, e" and £44) 
are upward direct and diffuse transmittances respectively due to 
scattering of molecules and aerosols, 7,(u, is upward 
atmospheric transmittance due to gas absorption like O3 , H20, 
CO2 and O2 etc, and 44 is the cosine of viewing zenith angle. 
The global irradiance E, is the sum of beam irradiance En 
diffuse irradiance E',, adjacent slope reflected irradiance EL 
and the irradiance EL due to multiple reflection between 
atmosphere and ground. — E^; is expressed by: 
E; -SQ(n.E.e TAM.) (3) 
where Sy is the cast-shadow function which is binary, say 0/1 if 
the direct path between the sun and the target is/isn't intercepted 
by the surrounding terrain (Proy et al. 1989). y is the cosine 
of incidence angle / between the solar direction and surface 
normal. Æ, is the earth/sun distance-corrected exoatmospheric 
irradiance (Moran et al. 1992). pu is the cosine of solar zenith 
angle. e" and T,(44) are the same as equation (1) except for 
downward path. 
In determining diffuse irradiance E';, Hay's model is used (Hay 
1979, Hay and McKay 1985, Hay et al. 1986, Iqbal 1983): 
E, 7 E mu, / u, £050 - 203 coss)]. (4) 
where Ej is the diffuse irradiance for horizontal surface. 7 is 
the anisotropy index which defines as the ratio of beam 
irradiance at the horizontal surface Æ, to E,. As it accounts for 
the anisotropic distribution of diffuse radiation (Conese et al. 
1993b),  Hay's model is better than the isotropic model 
(Kondratyev 1977) adopted by some researchers. e.g. Yang and 
Vidal (1990). s is the slope of the terrain. 
E aa and E ,, are expressed respectively by (Iqbal 1983, Duguay 
and LeDrew 1992): 
El 208 p s (E; H^E,)(T- coss): (5) 
ue (ETE VES) 
I= <p> i (6) 
where ris the spherical albedo of the atmosphere. 
After combining equations (1)~(6), the satellite remotely 
sensed radiance L is written as: 
Le (tL, * a E dS, Qu, / u)e ^ t Qus) ! i) * 9x0 + coss)] . 
[1+05< p> d - oss [or^ ot 0| [00 0) T Qa (7) 
where /4(u) and r, can be approximated by Eddington method 
(Liu et al. 1996). 
Path radiance L, is also determined as the sum of molecular and 
aerosol path radiances as in the previous study (Liu et a/. 1996). 
The altitude-dependences of molecular optical depths, such as 
Rayleigh, O3, H2O and uniform gas, are determined by firstly 
calculating from LOWTRAN 7 (Kneiyzs et al. 1988) with 
radiosonde data and then being well regressed to be exponential 
decay model. 
Before determining surface reflectance p, uniform target is 
assumed, i.e. <p>=p=p,. Equation (7) is then written as: 
E I E Is, Qu, ! a )e "^ t Qu pru, / 1) 050 — MI + coss)} ° 
[1+050,(1-coss)}og[e 7 +126) /[A1= pur), GT, 04, + 8) 
From above equation, one can see remotely sensed radiance L is 
a function of reflectance po, altitude z, slope s, shaded reflief 
Sal and atmospheric parameters. z and s can be determined 
for a given terrain, such as digital terrain model (DTM). Su 
can also be determined from the given terrain and solar 
geometry for a specific image. The molecular optical depths 
can be computed from the regressed equation with known 
radiosonde data. The left unknowns are then po as well as the 
aerosol characteristics, i.e. single scattering albedo w,, 
scattering phase function P,(®) and optical depth z, which are 
implicit in equation (8). 
Junge size distribution is assumed as in the previously 
developed atmospheric correction model of horizontal surface 
(Liu et al. 1996). It should be emphasized that the Junge 
parameter v is assumed to be a mean value 3.3 (Iqbal, 1983) in 
the following proposed robust algorithm, whereas it can be 
iteratively retrieved from the image itself based on DDV by the 
image-based iterative algorithm in the flat surface (Liu e/ al. 
1996). The reason why we didn't use DDV to retrieve aerosol 
characteristics is that NDVI image determined from raw image 
of a rugged terrain demonstrated highly correlated with the 
topography (Liu 1995). In this study, the aerosol type is 
assumed to be continental. The radius size ranges from 
106 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996 
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