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):

+

+

0

2

0

0

0

1 1

= − −

(

)

(

)

(1)

where

0

is the observed backscattering coefficient,

0

is the

contribution from soil,

0

is the vegetation volumetric con-

tribution, and

0

is the contribution from land surface/

vegetation interaction. C is the vegetation fraction coverage

and

2

is the two-way vegetation transmissivity (incoming and

outgoing path). If all the area is covered by vegetation, we

have C = 1, therefore:

= +

0

0

0

2 0

+

(2)

and if the vegetation-soil interaction is neglected, then

observed backscattering coefficient results in:

= +

0

0

2 0

(3)

0

can be either the horizontal (

0

) or vertical (

0

) polariza-

tion backscatter coefficient;

also can be computed (Attema,

1978; Ulaby, 1986) as:

2

2

= −

exp

sec

(

)

(4)

and

0

2

1

=

−

cos (

)

(5)

where

is the local incidence angle,

is the vegetation

water content (kg/m

2

), and

and

are parameters which are

related to the canopy and vegetation type.

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):

0

2

2

2

2 4

0

2

2

=

−

( )

(

)

exp

tan

cos

(6)

where

= 2

/

is the root mean square (

RMS

) slope of surface

height,

is the standard deviation of the surface height, and

is horizontal distance between two different points on the sur-

face (a Gaussian correlation function can be assumed). |

(0)|

is soil Fresnel reflectivity (Peplinski 1995) which is an indica-

tor of soil wetness and can be expressed as (Morvan 2008):

0

2

2

,

(

)

=

− −

+ −

cos

sin

cos

sin

.

(7)

Also,

s

s

s

s

0

2

2

,

( )

=

− −

+ −

co

in

co

in

(8)

where

′

=

′

–

′′

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

0

,

0

,

,

, and

EC

; however,

solving the equations to obtain

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

., 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

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