Chapter 8
Study of Depending the Uncertainty
of the Remote Surface Temperature Retrieval
on the Initial Parameters Exactness
Abstract The inverse problem of the surface temperature retrieval is formulated.
The influence of the initial parameters uncertainties to the resulting temperature is
considered.
8.1 Remote Retrieval of the Surface Temperature
Remember the expression (2.9) for the outgoing intensity formed by the surface
with ignoring the atmosphere:
J
"
n ¼ e n B n ðT s Þ;
(8.1)
where T S is the surface temperature; B n is the Planck’s function; e n is the surface
emissivity.
Taking into account only the atmospheric absorption and neglecting scattering
(that is valid in IR spectral region l > 3 mm without cloud) the relation (8.1)
transformed to:
J
"
n ¼ e n B n; T s
½
ŠP n p s
ð Þ þ
ð p t
p s
B n; TðxÞ
½
ŠdP n ðxÞ:
(8.2)
Here P n (x) is the transmission function at the wave number n between levels
in the atmosphere with pressure p t (the atmosphere top) and x (the integrating
variable); p S is the pressure at the surface level.
The following expression is valid for the 2nd item in the Eq. 8.2: according to
mean value theorem:
ð
Pt
P s
B n; TðxÞ
½
ŠdP n ðxÞ ¼ B n; ~
T n
Â
Ã
1 À P n p s
ð Þ
½
Š ;
(8.3)
I. Melnikova et al., Remote Sensing of the Environment and Radiation Transfer,
DOI 10.1007/978-3-642-14899-6_8, # Springer-Verlag Berlin Heidelberg 2012
73