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ρ
0
(0.67, 0.67) from unity
Tab l e 6 . 1 .
Deviation of the approximation of zeroth harmonic
g
0.3
0.5
0.75
0.8
0.85
0.9
ρ
0
(0.67, 0.67)
|
1−
|
0.0037
0.024
0.021
0.0059
0.013
0.0046
µ
0
)arecompletelydefinedbythecosineofthesolarzenithangle,i.e.bythe
time and place of the experiment, and functions
K
0
(
a
2
(
µ
µ
µ
)are
defined by the cosine of the viewing angle. Their values could be taken from
tables (Dlugach and Yanovitsky 1974; Hulst 1980; Minin 1988) or calculated
with (2.31), (2.34) and (2.35) presented inChap. 2, inaddition to the expressions
for constants
m
,
l
,
n
2
and
k
(2.29).
We need the value of the surface albedo to calculate function
K
0
(
),
K
2
(
)and
a
2
(
µ
=
)
µ
|
K
0
(
(1 −
A
). In the case of using the solar irradiance observations, value
A
could be inferred by dividing the upwelling irradiance by the downwelling one
at the bottom of the cloud. In the case of the radiance, the situation is not so
simple. Therefore, we propose a convenient approach. We should mention the
valueofthecosineofthezenithangle
)+
A
0.67 (it corresponds to 48
◦
), for
which the zeroth harmonic of reflection function is close to unity, especially
in the case of the Henyey-Greenstein phase function, the other harmonics
are close to zero and escape function
K
0
(
µ
=
µ
) is also equal to unity. Thus, the
reflected radiance, measured at the viewing angles close to 48
◦
is equal to
thereflectedirradiance(similarisalsotruefortransmittedradiation).Both
radiance and irradiance, measured at solar angle 48
◦
,approximatelycoincide
with the spherical albedo of the cloud layer. The value of
µ
0
)
|
in
the case of recent approximations ((2.37), (2.39) and Tables 2.3 and 2.4)
are presented in Table 6.1 for phase function parameter
g
ρ
µ
0
(
|
1−
,
=
0.3−0.9 and
µ
=
µ
0
=
0.67. The small deviation from unity shows rather low error of
the approach proposed here. The analysis of zeroth harmonic of reflection
function
ρ
0
(
µ
, 0.67) for different phase function parameter
g
demonstrates
that the deviation fromunity is about 8% for
g
≤
=
0.85−0.9.
ThereflectionfunctionhasbeencalculatedfortheMiephasefunctionthat
corresponds to the model of the fair weather cumulus (FWC) clouds (King
1983). These results indicate that the reflection function differs from unity by
2-5% at the zenith angles in the range 47-50
◦
.Hence,itispossibletoconclude
that the reflection function is close to unity at these zenith angles even for
the complicated phase function. It has been shown (Kokhanovsky et al. 1998)
that the impact of the phase function on the radiative forcing is almost the
same for different phase functions, if the solar incident angle is about 45-
50
◦
0.5 and 10% for
g
µ
0
=
0.643−0.707). The slightest influence of particle size distribution
on cloud phase function at scattering angles about 90
◦
has been also obtained
(Kokhanovsky et al. 1998); that approximately corresponds to cosines of zenith
angle
(
µ
0
=
µ
=
0.67. It is possible to explain these facts with the following:
the reflection function (and the escape function) more weakly depends on the
phase function at this angular range than at other angles. Thus, it is more
suitable to accomplish measurements of the reflected radiation either at the
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