and the following value lights at the radiometer panel:
T r ¼
bn
ln e
ðwÞ
n
an 3
J
"
n
þ1
h
i;
(7.8)
which is not equal to the real temperature value because of inequality emissivity of
water surface to emissivity of other studied surface e n
(w)
6 ¼ e n .
Actually we have
J
"
n ¼ e n B n; T s
½
Š;
(7.9)
where e n and T s are the emissivity and temperature of studied surface. It is evident
that:
e
ðwÞ
n B n; T r
½
Š¼ e n B n; T s
½
Š;
(7.10)
where T r is the radiometer reading and T s is the surface temperature. Then the
following relation is obtained with assuming known values e
ðwÞ
n , T r and T s :
E n ¼ e
ðwÞ
n
B n; T r
½
Š
B n; T s
½
Š
(7.11)
With substituting Planck’s function expression to the Eq. 7.10 the formula for
calculating the real emissivity value is derived:
e n ¼ e
ðwÞ
n
exp
bn
Ts
þ 1
exp
bn
Tr
þ 1
;
(7.12)
where n ¼1,000 cm
À1 (the centre of radiometer filter transmission); e
ðwÞ
n ¼0.993;
b ¼ 1.438786 K/cm
À1
. The Eq. 7.12 is used in the computer program « RAD.exe »
for the determination of emissivity e n .
7.3 Remote Measurement of the Surface Temperature
The direct radiometer reading is used for remote measurement of water surface
temperature.
Radiometer reading is not sufficient for observation above other surfaces (sand,
soil, et al.) for surface temperature T s retrieval. Value of emissivity e n of
corresponding surface (that are measured independently following the previous
section) is necessary. The recalculation radiometer reading T r to real value T s is
7.3 Remote Measurement of the Surface Temperature
65