Analytical Method of Inverse Problem Solution for Cloudy Atmospheres - Short-Wave Solar Radiation in the Earth's Atmosphere - page 224

Even the small uncertainty of value g causes a significant error of the optical
thicknessasperexpression τ 0 = τ | [3(1 − g )] and is seen from Table 6.2. Model

= τ 0 = value g 24.36 with the uncertainty equal to

2.6%, while retrieved value g leads to the uncertainty equal to 14%. Hence, the
necessity of an accurate value of g is evident.
It is important to mention that a similar approach for the phase function
parameter has been considered in the topic by Yanovitskij (1997) for the case
ofconservativescatteringonthebasisoftherigoroustheory.Theapproach
for obtaining parameter g hasalsobeenproposedinthestudybyKonovalov
(1997) with the approximation of the reflection function.

0.85 allows obtaining

6.2.3
Parameterization of Cloud Horizontal Inhomogeneity

The simple approximate parameterization of the cloud top heterogeneity was
proposed earlier in the study by Melnikova and Minin (1977). The rough
cloud top causes an increase of the diffused radiation part in the incident
flux. Therefore, this obstacle turns out to be an essential one for calculating the
radiative characteristics dependingon solar incident angle. Both the escape and
reflection functions describe this dependence for the reflected radiance, and
theescapefunctiontogetherwiththeplanealbedoofsemi-infiniteatmosphere
describe this dependence for the reflected irradiance. Thus, it was proposed
(Melnikova and Minin 1977) to replace all functions depending on incident
angle cosine µ

0 with their modifications according to expressions:

ρ 0 ( µ µ 0 ) = ρ 0 ( µ µ 0 )(1 − r )+ ra ( µ , , ),

µ 0 ) = µ 0 )(1 − r )+ rn , K ( K (

(6.36)

µ 0 ) = µ 0 )(1 − r )+ ra ∞ a ( a ( ,

where spherical albedo a ∞ , plane albedo a ( µ 0 )andvalueof n are defined with

(2.27).

1 1 1

a ∞ = µ 0 ) µ 0 d µ 0 = µ 0 d µ 0 ρ

0 (

µ µ 0 ) µ µ 2 a ( 4 , d

0 0 0

(6.37)

1

= µ 0 ) µ 0 d µ 0

n 2 K (

0

and parameter r describes the diffused part of light in the incident flux.
The influence of the overlying atmospheric layers (including high thin
clouds), the difference between the reflection functions of the real cloud
(described by the Mie phase function) and model cloud (described by the
Henyey-Greenstein phase function), and other factors impacting the angular
dependence of radiation, are also partly corrected by parameter r .