Chapter 5
Calculation of the Intensity of Self Heat
Radiation of the System “Surface-Atmosphere”
Abstract The radiative transfer equation for direct heat radiation is solved, that is
valid for clear atmosphere in IR spectral region. The cloud cover is taking into
account phenomenologically in calculation self heat radiation of the surface.
5.1 Concise Theory
The solution of the radiation transfer Eq. 1.17 by ignoring the scattering process
(that is valid in clear atmosphere for heat radiation in the long-wave spectral ranges
(l > 3 mm)) and taking into account the definition of the transmission function
P(n,x,y) according to the Eq. 1.22 that characterized the direct radiation looks as
follows:
J n; p t
ð
Þ ¼ e n
ð ÞB n; T s
½
ŠP n; p S ; p t
ð
Þþ
Z pt
p s
B n; TðxÞ
½
Š
@P n; x; p S
ð
Þ
@x
dx
þ 1 À e n
ð Þ
½
Š P n; p S ; p t
ð
Þ
Z p s
pt
B n; TðxÞ
½
Š
@P n; x; p S
ð
Þ
@x
dx;
(5.1)
Here J(n,p t ) is the intensity of the outgoing radiation at the wave number n, at the
level with the atmospheric pressure p t for nadir scheme of observation (viewing
angle y ¼ 0); e(n) is the emissivity of the surface; B[n,T] is the Planck’s function for
the blackbody radiation at the wave number n and temperature T; P(n,x,y) is the
transmission function of the monochromatic radiation from the level with pressure
y till the level with pressure x, which is the integration variable. It is fixed for
outgoing radiation y ¼ p t at the level of the atmosphere top with satellite scheme of
observations, for downward radiation y ¼ p S, where p S , is the atmospheric pressure
at the surface level. T S is the temperature of the surface. It is to point out that the
I. Melnikova et al., Remote Sensing of the Environment and Radiation Transfer,
DOI 10.1007/978-3-642-14899-6_5, # Springer-Verlag Berlin Heidelberg 2012
47