Spectral Measurements of Solar Irradiance and Radiance in Clear and Cloudy Atmospheres - Short-Wave Solar Radiation in the Earth's Atmosphere - page 103

the standard deviation of the radiative flux divergence is close to the radiative
flux divergence mean value while calculating the uncertainty with the usual
methodology. However, the radiative flux divergence is a non-negative value
because it is a bounded value and its distribution differs from the Gaussian
one. Thus, the values of the mean radiative flux divergence and their standard
deviation obtained with the usual methodology do not correctly reflect the
distributionof the radiative flux divergence as a randomvalue. The application
ofthespeciallyelaboratedprocedureofempiricalsimulationoftheradiative
flux divergence with computing its mean value together with the standard
deviation removes this difficulty.
Letusconsideronelayerfrom P i +1 to P i for the appropriate determination
of the mean value and standard deviation of the radiative flux divergence.
We use the randomizer described in the topic by Molchanov (1970) with the
expectation and variance equal to the correspondent values for the irradiance
(Sect. 3.2). Irradiances F i +1 , F i , F i +1 , F i are simulated as random values. The
mean value of the radiative flux divergence and its standard deviation over
the layer are computed by their concrete realizations with (1.7) and (1.8),
excluding physically impossible cases of the negative radiative flux divergence
values. Then, after accumulating enough statistics we get the estimation of the
radiative flux divergence and its standard deviation. Moving on to the radiative
flux divergence simulation for all layers the demand of the physical property
of the radiative flux divergence additivity is necessary: the total radiative flux
divergence has to be calculated as a sum of the radiative flux divergences
of all layers during the layers merging. Hence, the multilayer situation is to
be rejected if either of one layer has the negative value of the radiative flux
divergence. It is also necessary to account that after the secondary processing
the irradiance values correlate with each other so all irradiances are to be
simulated at once as a randomly distributed vector with the fixed mean value
and with the covariance matrix according to the methodology described in the
topic by Ermakov and Mikhailov (1976).
According to the results of soundings accomplished in 1970-1980th, the
authors of various studies (Kondratyev and Ter-Markaryants 1976; Vasilyev O
1986; Vasilyev O et al. 1987) have revealed that it is possible to obtain the
radiative flux divergence with the appropriate accuracy for the atmospheric
layer of 100mbar thickness if only the following set of conditions coincides:
- strong aerosol absorption;
- stability of the atmospheric parameters during the observations;
- stable functioning of the instruments.
All these conditions are hardly realized in practice. Thus, it has been proposed
to consider the averaged irradiances in the atmospheric layer 1000-500mbar,
which are obtained as an arithmetic mean over the layers (with the corre-
sponded recalculation of standard deviations).
Figure 3.14 illustrates the typical values of the radiative flux divergence
above the Kara-Kum Desert and above Ladoga Lake. The molecular absorp-
tion bands of the atmospheric gases (ozone, oxygen and water vapor) are