Analysis of Radiative Observations in Cloudy Atmosphere - Short-Wave Solar Radiation in the Earth's Atmosphere - page 252

Fig. 7.13a,b. Vo l ume c o e f fi c i e n t s o f a -scatteringand b - absorption, transformed using
(7.2). The curve numbering corresponds to the experiments, listed in Table 3.2. The curve
marked with letter R characterizes the molecular scattering at altitude 1 km

equation of radiative transfer and corresponding asymptotic formulas solving
it are written for one component - droplet (in some cases for the droplet with
the absorbing particle within it). Item

q
0 in the second of (7.2) differs
from zero only within the molecular absorption bands. Remember that the
problem is considered only for

p
D

κ M τ ω

τ 0 >> 1.
Factor C turns out to be equal to unity. Powers p and q are equal to: p = 2and

0 , as per the estimations in several studies (Melnikova 1989, 1992, 1997;
Kondratyev et al. 1997; Melnikova and Mikhailov 2000). These magnitudes
correspond to the above-mentioned fact that the mean number of scattering
events in the cloud of optical thickness

= τ

q

0 (Minin 1981;
Yanovitskij 1997). We should point out that powers p and q were obtained from
the analysis of themagnitudes of volume scattering and absorption coefficients
for the data of two experiments at two wavelengths.
Transform values [

τ 0 is proportional to τ

α λ α κ λ ) (Tables A.8, Appendix A) using

(7.2) leads to the values obtained with Mie theory and usually attributed to
the cloud elementary volume (Grassl 1975; Nakajima et al. 1991). The spectral
dependence of the transformed values of both difference [

( )− (0.8)] and (

α λ α (0.8)] and

the volume absorption coefficient is presented in Fig. 7.13a,b. It is seen that the
magnitudes of the volume absorption coefficient demonstrated in Fig. 7.13b
practically coincide with the ones usually calculated with Mie theory for cloud
droplets (Grassl 1975). The molecular absorption bands become sharper. The
values of the single scattering albedo corresponding to the absorption coeffi-
cients presented in Fig. 7.13b are about 0.99998 that is close to the standard
magnitudes for the cloud layer. Difference [

( )−

α λ α (0.8)] converted with (7.2)

does not distinguishmuch fromRaleigh scattering coefficient for the clear sky.
The presented consideration concerns the external mixture ,i.e.thecase,
when aerosol particles are situated between the cloud droplets. When aerosol

( )−