Analytical Method of Inverse Problem Solution for Cloudy Atmospheres - Short-Wave Solar Radiation in the Earth's Atmosphere - page 208

zenith solar or at the viewing angle in the range 45-50 ◦ fortheretrievalofthe
optical thickness and single scattering albedo. Otherwise, as has been pointed
out earlier (Boucher 1998; Kokhanovsky 1998) it is better to use other zenith
angles for estimating the phase function parameter, at which the radiance is
susceptible to the phase function.
The viewing direction during observations of the solar radiance reflected
from the ground surface is not of great importance for the orthotropic surface,
but the directions close to nadir are preferable for maximal excluding an effect
of the radiation scattering within the atmospheric layer below the cloud.

6.1.2
Problem Solution in the Case of Solar Radiation Observation
Within the Cloud Layer of Large Optical Thickness
In the general case, the stratus cloud is known to be vertically inhomogeneous.
The determination of the vertical structure of the stratiform clouds is of great
interest fromthe point of studying its physical characteristics and the processes
ofitsforming.Herewearepresentingtheapproachfortheopticalparameters
retrieval from the data of the airborne radiative observations within the cloud,
which could also serve to study the aerosol content and distribution.
While studying the scattered radiation field within clouds, it is necessary
to distinguish two essentially different cases: (1) a single optically thick cloud
layer with the optical properties, varyingwith vertical direction; and (2) a cloud
system consisting of several cloud layers separated from each other with clear
atmosphere.
In the case of vertically inhomogeneous clouds, the calculation uncertainties
of applying the formulas for the homogeneous clouds to the inhomogeneous
ones turns out to be sufficiently low because the information about the remote
points is “forgotten” due to the multiple scattering within the cloud. Therefore,
the photon, registered by the instrument, brings information only about the
last collision. Thus, while measuring the diffused irradiance, the information
collected by the instrument mainly concerns the points, remote from the in-
strument for the photon free path. In the case of stratus cloud this value is equal
to 20−50m. Soundings within the stratus cloud is usually accomplished at

every 100m, so it is possible to apply the results obtained below for the in-
terpretation of the airborne observations within the stratus cloud (Melnikova
and Mikhailov 2001).
It is possible to divide the process of the radiative transfer through the
optically thick cloud layer into three stages (Ivanov 1976), namely:
1. thetransferofradiationthroughtheupperboundarysublayeradjusting
the cloud top

∼

τ =

0( pumping );
2. the transfer through the inner layers ( diffusion );
3. the transfer through the layer adjusting the cloud bottom τ = τ 0 ( escap-

ing ).
Within the optically thick cloud, the processes of pumping, diffusion, and
escaping could be assumed independently. Consider consequently these stages.