orientation angle, which in our case changes to closely follow

the orientation of the Mississippi River. The radar backscatter

is influenced by the local angle of incidence, which will thus

vary as the levee orientation changes with respect to the beam

direction. In order to compute the local incidence angle, we

used the geometric parameters of the satellite orbit combined

with the elevation data from lidar data. The local incidence

angle (

) is the angle between the incident radar beam and the

vertical (normal) to the intercepting surface.

Kriging Interpolation

Kriging is the interpolation method we used to compute

a continuous surface out of the discrete sampling of the

soil conductivity. Such interpolation was needed because

the sample distance for the

EC

measurement points varied,

sometimes being much smaller than the radar resolution cell

and sometimes greater. Kriging is a geostatistical interpola-

tion technique that takes into account both the distance and

the degree of variation between known data points when

an unknown area is estimated. The technique is based on a

weighted linear combination of the identified samples around

the points to be estimated, controlled by a semi-variogram.

By minimizing the error variance, it tries to prevent over or

under estimates (Cressie, 1990).

Back Propagation Neural Network (BPNN)

A back propagation neural network is a multilayer, feed-for-

ward network trained by the error back propagation algorithm

(Fausett, 1993). It is defined by the input, output, and hid-

den layers, and also the weight parameters and the transfer

function. The first layer has weights (W) which are applied to

the input feature values. Depending on the application, dif-

ferent numbers of hidden layers are selected. The weights of

each hidden layer are applied to the outputs of the previous

layer. These parameters are obtained in the training phase,

during which the training data are fed into the input layer

and propagated to the hidden layer and then the output layer

(forward pass). The nodes in the hidden and output layer sum

the inputs from all neurons of their previous layer multiplied

with appropriate weights. The values from the output layer

are compared with the corresponding target values and the

error value between them is back propagated into the hidden

layer (backward pass). This error is used to update the weight

matrices between the layers using the delta rule, which is a

gradient descent method that minimizes the total squared

error of the net output (Fausett, 1993). The

BPNN

used in this

work includes one hidden layer with three neurons, and one

output neuron. Note that we used this simple hidden layer

because some of the

AOIs

have limited reference data samples,

and also for preventing over-fitting. The learning rate was

selected as 0.01. The layer’s weights and biases were initial-

ized according to the Nguyen-Widrow initialization algorithm

(Nguyen, 1990). The tangent sigmoid transfer function was

used for the hidden layer and the linear transfer function was

used for the output layer (Mahrooghy, 2011). The number of

input neurons is equal to the number features used: three for

scenario 1; five for scenario 2; and 35 for the scenario 3 (the

scenarios are detailed in the Results Section). We have 1116,

190, 140, and 311 reference data samples (after interpolation)

for AOI1, AOI2, AOI3, and AOI4, respectively. The training

datasets for each

AOI

comprise 60 percent of the reference

data samples, and 40 percent used for validation and testing

of the

AOI

. The stopping criteria include 100 epochs, the mini-

mum performance gradient of 1 epoch to 6, and maximum

validation failures of 5.

Figure 5. Block diagram of the EC estimation algorithm (

gth

: ground truth soil conductivity; W: Weight for neural network; HH, VV: back

scattering coefficients; DEM: Digital Elevation Map; F: extracted features,

: local incident angle,

est

: estimated soil conductivity; BPNN:

back propagation neural network; WBNN: wavelet basis neural network; MGD: Multi-Look Ground Range Detected).

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