In case of a partial cloud cover of the instrument’s field of view (cloud part is N c )
the outgoing radiation intensity J a (n,p t ) at the wave number n is defined by the
following:
J a n; p t
ð
Þ ¼ N c Á J c n; p c
ð
Þþ 1 À N c
ð
ÞÁJ n; p s
ð
Þ
(5.4)
The calculation of the integrals in expressions (5.1) and (5.2) uses numerical
approaches:
– the method spline-interpolation of the temperature profile at the same levels,
where the transmission function is fixed;
– the method of rectangles for the calculation of the definite integrals:
Z ’ðbÞ
’ðaÞ
f ðxÞd’ðxÞ ¼
X n
i¼2
f ðx iþ1=2 ÞD’ i ;
(5.5)
where
d’ðxÞ ¼
@’ðxÞ
@x
dx; h ¼
b À a
n
; x i ¼ ih; 1 i n;
x iÀ
1
2
¼
x iÀ1 þ x i
2
; 2 i n; D’ i ¼ ’ x iÀ
1
2 þ1
À ’ x iÀ
1
2
h
i
; 2 i n;
Table 5.1 The emissivity
of the surface different types
within IR ranges (8–12 mm)
Type of the surface
The emissivity e
Dry sand with small grains
0.949
Wet sand with small grains
0.962
Dry sand with large grains
0.914
Wet sand with large grains
0.936
Ice
0.980
Clean water
0.993
Quartz
0.712
Granite
0.815
Basalt
0.904
Dry peat
0.970
Wet peat
0.983
Dry sandy loam soil
0.954
Wet sandy loam soil
0.968
Conifer needles
0.971
Dry snow (t ¼À2.5
C)
0.996
Wet snow
0.997
Dirty snow
0.969
Fresh snow
0.986
5.2 Transmission Function
49