417
Microwave Vegetation Indices from Satellite Passive Microwave Sensors
Ku-band 18.7 GHz are plotted as the y-axis on the top and bottom rows, respectively.
From the left to right columns, the plots are for V, H, and V&H polarizations, respectively. The V&H plots are the plots where both simulated emissivities of the V and
H polarizations are on the same plot. Based on Figure 18.1, we noted the following
characteristics of the frequency dependence of the bare surface emission signals at
6.925, 10.65, and 18.5 GHz:
• Bare surface emissivity always increases as the frequency increases for
the same soil moisture and roughness properties. It was shown in a study
to develop a parameterized surface emission model (Shi et al. 2005) that
the surface roughness effect on bare surface emission signals has a similar
magnitude at our study frequencies. The change in surface emissivity as
a function of frequency is mainly due to the frequency dependence of the
dielectric properties of the soil liquid water properties. Higher soil moisture
will result in a larger difference in surface emissivities at different frequencies than for low-soil-moisture conditions. The larger frequency difference
will lead to greater surface emissivity differences than that at smaller frequency differences. This can be seen by comparing the top (10.65 GHz
versus 6.925 GHz with 3.625 GHz frequency difference) and bottom (10.65
GHz versus 18.7 GHz with 8.05 GHz frequency difference) row plots in
Figure 18.1.
• The bare surface emissivities at two adjacent frequencies of AMSR-E are
highly correlated and can be approximated by a linear function. These
relations are neither affected by soil moisture nor by surface roughness
properties. Therefore, they can be used for a wide range of soil conditions.
• These linear relations for soil emissivities at two adjacent AMSR-E
frequencies are minimally affected by the polarization status (right-side
column of Figure 18.1).
Therefore, we can describe the bare surface emissivities at two adjacent AMSR-E
frequencies as a linear function as
ε
ε
p
s
p
s
f
a f f
b f f
f
( )
( , ) ( , ) ( )
2
1 2
1 2
1
=
+
⋅
,
(18.5)
where the a and b parameters are independent of polarization and depend only on the
pair of frequencies used. They can be determined by the regression analyses using
the AIEM model simulated database. For the AMSR-E sensor
ε
ε
p
s
p
s
( .
)
.
.
( .
)
10 65
0 022 0 985
6 925
GHz
GHz
=
+
⋅
(18.6)
ε
ε
p
s
p
s
( .
)
.
.
( .
)
18 7
0 058 0 958
10 65
GHz
GHz
=
+
⋅
.
(18.7)
The errors generated by Equations 18.6 and 18.7 are generally negligible. The
root mean square errors of the relative error represented by Equation 18.6 when
Microwave Vegetation Indices from Satellite Passive Microwave Sensors
Ku-band 18.7 GHz are plotted as the y-axis on the top and bottom rows, respectively.
From the left to right columns, the plots are for V, H, and V&H polarizations, respectively. The V&H plots are the plots where both simulated emissivities of the V and
H polarizations are on the same plot. Based on Figure 18.1, we noted the following
characteristics of the frequency dependence of the bare surface emission signals at
6.925, 10.65, and 18.5 GHz:
• Bare surface emissivity always increases as the frequency increases for
the same soil moisture and roughness properties. It was shown in a study
to develop a parameterized surface emission model (Shi et al. 2005) that
the surface roughness effect on bare surface emission signals has a similar
magnitude at our study frequencies. The change in surface emissivity as
a function of frequency is mainly due to the frequency dependence of the
dielectric properties of the soil liquid water properties. Higher soil moisture
will result in a larger difference in surface emissivities at different frequencies than for low-soil-moisture conditions. The larger frequency difference
will lead to greater surface emissivity differences than that at smaller frequency differences. This can be seen by comparing the top (10.65 GHz
versus 6.925 GHz with 3.625 GHz frequency difference) and bottom (10.65
GHz versus 18.7 GHz with 8.05 GHz frequency difference) row plots in
Figure 18.1.
• The bare surface emissivities at two adjacent frequencies of AMSR-E are
highly correlated and can be approximated by a linear function. These
relations are neither affected by soil moisture nor by surface roughness
properties. Therefore, they can be used for a wide range of soil conditions.
• These linear relations for soil emissivities at two adjacent AMSR-E
frequencies are minimally affected by the polarization status (right-side
column of Figure 18.1).
Therefore, we can describe the bare surface emissivities at two adjacent AMSR-E
frequencies as a linear function as
ε
ε
p
s
p
s
f
a f f
b f f
f
( )
( , ) ( , ) ( )
2
1 2
1 2
1
=
+
⋅
,
(18.5)
where the a and b parameters are independent of polarization and depend only on the
pair of frequencies used. They can be determined by the regression analyses using
the AIEM model simulated database. For the AMSR-E sensor
ε
ε
p
s
p
s
( .
)
.
.
( .
)
10 65
0 022 0 985
6 925
GHz
GHz
=
+
⋅
(18.6)
ε
ε
p
s
p
s
( .
)
.
.
( .
)
18 7
0 058 0 958
10 65
GHz
GHz
=
+
⋅
.
(18.7)
The errors generated by Equations 18.6 and 18.7 are generally negligible. The
root mean square errors of the relative error represented by Equation 18.6 when