2b has Bermuda grass which is mostly green and the height
is 3 to 5 cm (100 percent vegetation cover).
AOI
-3 displayed
in Figure 2c is a mix of bare soil (20 percent) and weeds (80
percent). The weed height is also short ranging from 5 to 10
cm. Figure 2d illustrates
AOI
-4 which covers areas that have
been mowed, and the dead cut grass is on the surface, which
are lying flat on top of the green short (3 to 5 cm) Bermuda
grass (100 percent vegetation cover).
Vegetated Backscatter Modeling
Since the levee area is covered with vegetation, in this section
we review backscatter models for vegetated areas. Various
empirical, theoretical, and semi-empirical models have been
developed for radar backscatter from vegetation canopies (At-
tema, 1978; Ulaby, 1984; Paris, 1986; Ulaby, 1986; Bindlish,
2001; De Roo, 2001; Wen, 2003). Attema and Ulaby (Attema,
1978) developed a semi-empirical model called water-cloud
in which the vegetation layer could be considered as cloud
droplets where the droplets are held by dry matter. That is,
the vegetation layer is modeled as many small discrete par-
ticles which scatter and absorb the radar signal. The param-
eters of this model are derived from experimental data. Some
variables such as height and water content of vegetation have
a significant effect on the model. The original water-cloud
model was modified and extended by various authors (Ulaby,
1984; Paris, 1986; Oh, 1992). In the water-cloud model, the
radar backscatter from a vegetated surface is expressed as
summation of volume scattering and surface scattering by the
underlying ground surface, and multiple interactions between
the canopy and ground surface. Therefore, we have (Frison,
1997; Wen, 2003):
+
+
C
C
σ
τ σ
σ σ
0
2
0
0
0
1 1
= − −
(
)
(
)
soil
veg
interaction
(1)
where
σ
0
is the observed backscattering coefficient,
σ
0
soil
is the
contribution from soil,
σ
0
veg
is the vegetation volumetric con-
tribution, and
σ
0
interaction
is the contribution from land surface/
vegetation interaction. C is the vegetation fraction coverage
and
τ
2
is the two-way vegetation transmissivity (incoming and
outgoing path). If all the area is covered by vegetation, we
have C = 1, therefore:
= +
σ σ σ
τ σ
0
0
0
2 0
+
veg
interaction
soil
(2)
and if the vegetation-soil interaction is neglected, then
observed backscattering coefficient results in:
= +
σ σ τ σ
0
0
2 0
veg
soil
(3)
σ
0
can be either the horizontal (
σ
0
HH
) or vertical (
σ
0
VV
) polariza-
tion backscatter coefficient;
τ
also can be computed (Attema,
1978; Ulaby, 1986) as:
τ
θ
2
2
= −
exp
sec
(
)
Bm
v
(4)
and
σ
θ τ
veg
v
Am
0
2
1
=
−
cos (
)
(5)
where
θ
is the local incidence angle,
m
v
is the vegetation
water content (kg/m
2
), and
A
and
B
are parameters which are
related to the canopy and vegetation type.
A
is the maximum
attenuation from the vegetation canopy (or vegetation density
parameter: 0 for bare soil and the highest for forests).
For bare soil surfaces, the radar backscatter coefficient can
be computed for
HH
and
VV
polarization by (Woodhouse 2000):
σ
θ
θ
soil
S
S
0
2
2
2
2 4
0
2
2
=
−
( )
(
)
Γ
exp
tan
cos
(6)
where
S
= 2
h
/
l
is the root mean square (
RMS
) slope of surface
height,
h
is the standard deviation of the surface height, and
l
is horizontal distance between two different points on the sur-
face (a Gaussian correlation function can be assumed). |
Γ
(0)|
is soil Fresnel reflectivity (Peplinski 1995) which is an indica-
tor of soil wetness and can be expressed as (Morvan 2008):
Γ
0
2
2
,
H
(
)
=
− −
+ −
cos
sin
cos
sin
θ ε
θ
θ ε
θ
.
(7)
Also,
s
s
s
s
Γ
0
2
2
,
V
( )
=
− −
+ −
ε θ ε
θ
ε θ ε
θ
co
in
co
in
(8)
where
ε
′
=
ε
′
–
j
ε
′′
is dielectric constant; The imaginary part
of the dielectric constant is proportional to conductivity and
volumetric moisture content (Hallikainen, 1985; Ulaby, 1986;
Dubois, 1995; Du, 2000). The above equations show that
there is a relationship among
σ
0
HH
,
σ
0
vv
,
ε
,
m
v
, and
EC
; however,
solving the equations to obtain
ε
and
EC
over a vegetated area
is difficult. In the following, we describe a machine learning
algorithm to obtain
EC
estimates from
SAR
data.
Methodology
In this section the method to estimate soil conductivity from
the TanDEM-X
SAR
image based on a machine learning algo-
rithm is explained. A block diagram of the algorithm is shown
in Figure 5. The
EEC
image of the
HH
and
VV
polarizations are
used as the input data. In addition, we use a
DEM
to estimate
the local incidence angle along with conductivity reference
data for training and validation. Since the soil conductivity
was surveyed as discrete samples, we use the kriging tech-
nique to interpolate the conductivity over the area of study. In
the feature extraction step, the backscatter and texture features
are extracted from
SAR
images. These features along with the
local incidence angle are input to an estimator. Two neural net-
work models, a back propagation neural network (
BPNN
) and a
wavelet basis neural network (
WBNN
) are examined. In training
mode, the parameters of the neural networks are obtained.
Feature Extraction
Based on different scenarios (detailed in the Results Sec-
tion), different sets of features such as backscatter coefficients
and texture features (the spatially distribution pattern of
the radar backscattering images) are extracted. The texture
features include window statistics and wavelet features. The
statistical features are the mean and standard deviation of the
backscatter coefficients over a sliding window with a size of
3 × 3 and also 5 × 5 pixels. The wavelet features are obtained
from two decomposition levels by employing a 7 × 7 sliding
window and the Daubechies wavelet family (“db1”)(Burrus
et
al
., 1997). Note that we examined different sliding windows
for the statistical and wavelet features and found the above
windows (3 × 3 for mean, 5 × 5 for standard deviation, and 7
× 7 for wavelet features ) had better performance than others.
The wavelet features are the local mean and standard devia-
tion of the horizontal, vertical, and diagonal detail coefficient
energies of the sub bands for both levels.
Local Incidence Angle Calculation
Despite having relatively consistent slope within a levee sec-
tion a system of levees can present significant variations in
512
July 2016
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
