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µ
Tab l e 2 . 2 .
Values of second coefficient
a
2
(
) of the plane albedo expansion for the semi-
infinite layer and parameter 0.75
≤
g
≤
0.9
µ
g
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.75
1.310
2.220
3.118
4.078
5.126
6.256
7.475
8.786
10.19
11.70
13.29
0.80
1.267
2.236
3.151
4.117
5.163
6.289
7.494
8.796
10.18
11.66
13.23
0.85
1.201
2.242
3.181
4.148
5.198
6.320
7.512
8.798
10.17
11.63
13.18
0.90
1.092
2.244
3.208
4.193
5.237
6.350
7.529
8.808
10.16
11.60
13.12
and
1.6
1+
g
=
36
q
−6
g
−
a
3
µ
that gives errors 0.04 and 0.004%correspondingly. The values of function
a
2
(
)
computingforfourvaluesofparameter
g
are presented in Table 2.2.
Surface albedo
A
is assumed by the formulas:
K
0
(
µ
=
µ
|
)
K
0
(
)+
A
(1 −
A
),
3
K
0
(
+
n
2
,
µ
(2.35)
A
1−
A
)
3. 8
−2.7
1+
g
K
2
(
µ
=
K
2
(
µ
µ
)
)+
2.2.3
The Analytical Presentation of the Reflection Function
The following group of formulas is the approximations obtained from the
analysis of the numerical values of the reflection function. As is usually done
(Sobolev 1972; King 1983; Minin 1988; Yanovitskij 1997), let us describe the
reflection function with the above-mentioned expansion over the azimuth
angle cosine to separate the item independent of the azimuth angle:
µ
0
)+2
∞
ρ
ϕ
µ
µ
0
)
=
ρ
0
(
µ
1
ρ
m
(
µ
µ
0
) cos
m
ϕ
(
,
,
,
,
,
(2.36)
=
m
µ
0
) are the harmonics of the reflection function of
order
m
. Superscripts specify here the number of the azimuthal harmonics. As
has been mentioned above, we are using here the phase function described by
the Henyey-Greenstein formula (1.31).
The analysis of the numerical calculations (Yanovitskij 1972; King 1983;
King 1987; Yanovitskij 1997) shows that for the accurate description of func-
tion
ρ
µ
m
(
where functions
,
ρ
ϕ
µ
µ
0
) it is enough to know the zeroth and first 6 harmonics if either
(
,
,
µ
µ
0
are greater than 0.15 even for value
g
=
of cosines
0.9, unfavorable
for computing accuracy. This limitation does not restrict our consideration
and
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