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considering the sense of the main direction (Sect. 3.4):
ηη
+
c
(1 −
η
=
η
η
)
2
) cos(
∆ϕ
2
)(1−(
:
−
)
(5.3)
∆ϕ
=
π
ϕ
.
k
+
The formulas of the recalculation are analogous to (2.21) for the scattering
angle but in (5.3) azimuth
∆ϕ
ϕ
.
Parameter
k
in (5.3) is equal to zero for the case of the mirror reflection (water
surface) and to unity for the backward reflection (sand surface). Parameter
c
couldbeequaltotwodiscretemagnitudes+1and−1.Theconcretemagnitude
is selected from condition
is computed in the same coordinate system as
η
<
0, i. e. the photon moves up after the reflection
(if this condition fulfills for both alternatives of value
c
,oneofthemwillbe
selected randomly).
Thecomparisonofthecalculationresultswithasubjecttoreflectionaniso-
tropyandwithoutithasbeenaccomplishedforthecasesofthewaterand
sand surfaces, while the snow surface has been assumed as an orthotropic
one (Sect. 3.4). Note that these anisotropic models were constructed just for
the surfaces above which the sounding had been carried out. The results have
demonstrated that the influence of anisotropy on the observation uncertainty
is negligible in the UV region, and it is about the SD of the upwelling irradiance
(1-2%) in the VD and NIR regions. Thus, in the applied algorithm we ignore
anisotropy, however we are accounting for its influence on the accuracy. It
should be emphasized that the influence of anisotropy on the irradiance for
the highly anisotropic surface (water) turns out to bemuch weaker than for the
slightly anisotropic surface (sand). This phenomenon could be easily explained
with the following. The albedo of the water surface is small and decreases,
whilepassingfromtheUVtotheVDregion,hencetheinfluenceofthesurface
properties on the upwelling irradiance is also small. The albedo of the sand
surface is rather significant and increases from the UV to VD region, thus its
reflecting properties greatly affect the upwelling irradiance especially in the
VD and NIR regions.
Simulation of monochromatic radiative transfer has been considered in
Sect.2.1.However,accordingto(1.23)solarirradiancefortherealobservations
is the integral with instrumental function (3.1):
λ
∆λ
i
+
λ
i
)
=
λ
)
f
λ
(
λ
−
λ
i
)
d
λ
.
F
(
F
(
(5.4)
λ
∆λ
i
−
Theproblemofitscalculationwith(5.4)connectedwiththecomplicatedspec-
tralbehaviorofthevolumecoefficientofmolecularabsorption
κ
m
expressed
by (1.29) leads to the corresponding spectral behavior of monochromatic ir-
radiance
F
(
λ
), so the direct integration of (5.4) needs a lot of computing time.
The general scheme that allows us to avoid the calculations of the problems of
multiple light scatteringwith (5.4) is presented in several studies (Lenoble 1985;
Minin1988; Tvorogov 1994). This approach is basedonpassing fromthe solving
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