Geoscience Reference
In-Depth Information
Considering the vegetation and soil as double-component mixtures of dry matter
and water, the dielectric constants can be determined by the following expressions:
ejj
p
p
ejj
¼
q
P
p
Þ
p
¼
q
B
p
Þ
p
e
B
þ
1
q
P
ð
e
W
;
e
B
þ
1
q
B
ð
e
W
;
ð
8
:
16
Þ
where
ˁ
B
are the relative volumetric concentrations of water in the plants and
soil, respectively; and
ˁ
P
and
ʵ
B
and
ʵ
W
are the dielectric constants of dry soil and water,
respectively.
As was shown empirically by Engman and Chauhan, (1995)
0
3
and both
the real and imagery parts of the soil dielectric constant are increasing functions of
the volumetric moisture content. These functions can be approximated by the fol-
lowing formulae:
0
3
e
[
e
exp c
4
c
5
=k
e
0
3
c
1
þ
c
2
q
B
þ
c
3
q
2
B
ð
Þ;
exp d
3
d
4
=k
ð
8
:
17
Þ
e
0
3
d
1
q
B
þ
d
2
q
2
B
ð
Þ;
where
is the wavelength (cm), and ci
i
and d
i
are constants depending on the soil
type. For example, soil that consists of 30.6 % sand, 55.9 % silt and 13.5 % clay is
characterized by the dependencies (
8.17
) with c
1
= 2.35; c
2
= 52.4; c
3
= 31.1;
c
4
= 0.057; c
5
= 1.22; d
1
= 7.1; d
2
= 46.9; d
3
= 0.0097 and d
4
= 1.84.
Thus, taking into account the dependencies of (
8.17
) it becomes possible to
optimize the microwave range for passive remote sensing. Of course, a set of
unsolved problems exists relating to the model corrections necessary in order to
take into consideration the surface roughness and other obstacles distorting the
brightness temperature T
B
, as well as a set of special features which arises in the
inverse tasks solution. A basis for future model re
ʻ
nements is the correlation
between T
B
, the atmospheric transmissivity for a radiometer at height H above the
soil, the smooth surface re
ectivity R and the thermometric temperatures of the SPF
T
s-v
and atmosphere T
a
. This correlation can be expressed by the Schmugge-Shutko
formula (Schmugge 1990; Shutko 1986):
fl
þ
T
a
T
B
¼ t
ð
H
Þ
RT
sky
þð
1
R
Þ
T
s
v
ð
8
:
18
Þ
where T
sky
is the contribution from the re
ected sky brightness. Typical remote
sensing applications use microwave wavelengths
fl
1 cm and in this case the
atmospheric transmission approaches 99 % and T
a
+T
sky
≤
ʻ ≥
5
°
K (Engman and
Chauhan 1995).
The more precise correlation in (
8.18
) can be achieved considering the in
fl
uence
ectivity: R
0
¼ R exp
g
cos
2
of the surface roughness on the soil re
fl
ð
x
Þ
, where
ˉ
r
2
k
2
, where
˃
is the angle of incidence, and g is the roughness parameter (g =4
is
the root mean square height variation of the soil surface and k =2
ˀ
/
ʻ
).
ed with the use of the correlation between
the soil water content
ˁ
B
and the vegetation water content
ˁ
P
(DeWitt and Nutter
1988):
Formulae (
8.16
) and (
8.17
) are simpli
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