Spectral Measurements of Solar Irradiance and Radiance in Clear and Cloudy Atmospheres - Short-Wave Solar Radiation in the Earth's Atmosphere - page 92

taken as weights, for irradiances registered at the high solar zenith angles
having a smaller weight, the uncertainty caused by the deviation from the
cosine law is also included to the standard deviation as a random error.
The last stage of the preliminary analysis system is an accounting of indi-
vidual specific features of the flight scheme. Solar zenith angle

ϑ 0 ( µ 0 = ϑ 0 )

cos

= and a set of the atmospheric pressure values P i , i 1,..., N i are chosen at

this stage, which the final magnitudes of the irradiances will be obtained for as
a result of the secondary processing of the sounding data. There are six levels in
the ordinary flight scheme N i = 6 and the irradiances magnitudes are output

for the pressure levels from 1000 to 500mbar through every 100mbar.
After the above-described preliminary analysis, N j downwelling irradiances
f ↓ ( P j ,

µ 0, j )and N k upwelling irradiances f ↑ ( P k , µ 0, k ) are registered, fromwhich

µ 0 ). The algorithm of
this problem solution was described in Vasilyev O et al. (1987). However,
this algorithm was based on several physically poor assumptions, e. g. on the
supposition about the linear dependence of the irradiances upon solar zenith
angle, on the square approximation of the dependence of the irradiances upon
the atmospheric pressure, on the supposition about the monotonic increasing
of the upwelling irradiance with altitude. Thus, the new algorithm has been
elaborated for processing the results of soundings accomplished in the years
1983-1985. It is also based on certain assumptions but not so severe as before.
Let us present the dependence of the irradiance upon the solar zenith angle
cosine and atmospheric pressure using Taylor series limiting by the items of
second power:

µ 0 )and F ↑ ( P i , it is necessary to obtain N i values F ↓ ( P i ,

F i − Df j

= a 1 x j + a 2 y ij + a 3 x j + a 4 y ij + a 5 x j y ij ,

(3.6)

F i − Df k = b 1 x k + b 2 y ik + b 3 x k + b 4 y ik + b 5 x k y ik ,

where D is the correcting coefficient for the compensation of the systematic
calibration uncertainty (the calibration factor). Specifications

F i F ↓ ( P i , µ 0 ), F i F ↑ ( P i , µ 0 ), ≡ ≡

f j

j ), f k

f ↓ ( P j , µ f ↑ ( P k , µ k ), ≡ ≡

= µ 0 − µ j , = µ 0 − µ k , x j x k

= = y ij P i − P j , y ik P i − P k

are introduced for a brevity. The desired values are F i , F i , D , a 1 ,..., a 5 ,
b 1 ,..., b 5 .
The conditions for determining calibration factor D are to be added to solve
equation system (3.6). The extrapolation of the downwelling irradiance to the
level P i

= δ µ 0 , 0mbar and its comparison with known extraterrestrial flux F 0

δ where correction factor accounts for the deviations of the Sun-Earth distance

fromthemean value for the date of the observation. The spectral magnitudes of