43
Storm Impact on the Coastal Geomorphology and Current Field
3.3.1 Signal PRoceSSing algoRithM
3.3.1.1 Polar to Cartesian
The transformation of the coordinates in the radar data from polar to Cartesian was
realized by the use of the nearest neighbor interpolation method on the polar grid
(Seemann and Senet 1999). The polar coordinates (distance from radar and angle
from north) for each radar cell are matched to the Cartesian grid. All the radar image
sequences analyzed are geocoded and oriented northward. The exact geographical
coordinates are known, because the radar antenna’s position, height, and viewing
directions are determined by a differential global positioning system.
3.3.1.2 Directional-Frequency Decomposition
The frequency decomposition of the field of the imaged waves is accomplished with
the fast Fourier transformation (FFT) algorithm. Using a 3-D FFT, the sequence of
wave images (Figure 3.3ia) is transformed from the spatial–temporal to the wavenumber frequency (Figure 3.3ib). The 2-D frequency slices are filtered directionally
(red ellipse in Figure 3.3ib) and transformed to the spatial-frequency domain using
a 2-D inverse FFT, resulting in a complex-valued single-(wave) component image.
Figure 3.3ic shows the phase pattern of one wave component after the directionalfrequency decomposition. The phase image outlines a pattern with spatially varying
wavelength.
3.3.1.3 Wave Number and Dispersion Regression
The basic idea of the local wave number determination from a complex-valued singlecomponent image relies on the idea that the local wave number is given, except for
the imaginary number i, as the proportionality factor between the local slope and
image value (Havlicek and Bovik 1995). In a local neighborhood, this dependency is
solved in the least squares sense.
The final step of the DiSC algorithm consists of the calculation of the local water
depth and near-surface current (Figure 3.3id). The dispersion relation defines a surface in the wave number-frequency domain (Figure 3.3ii). The form of the dispersion
relation depends on the water depth and the near-surface current vector.
Each wave number-frequency component of the wave field represents a point in
the wave number-frequency space. The long, small-wave number waves (relative to
water depth) contain information about the water depth (Figure 3.3iia and iib), and
the short, large-wave number waves allow the retrieval of the current. The directional spread of the wave field allows the determination of the current vector component perpendicular to the main wave propagation direction (Figure 3.3iic). These
dependencies allow the retrieval of the parameter water depth and current vector
from the wave component using the least squares regression method.
3.3.2 aPPlicaBle Sea wave ModelS
The analysis of the image sequence by DiSC for the extraction of the wave field
properties is independent of the inverted theory. This means that any dispersion
model could be applied for the estimation of the bathymetry and current field. Bell
Storm Impact on the Coastal Geomorphology and Current Field
3.3.1 Signal PRoceSSing algoRithM
3.3.1.1 Polar to Cartesian
The transformation of the coordinates in the radar data from polar to Cartesian was
realized by the use of the nearest neighbor interpolation method on the polar grid
(Seemann and Senet 1999). The polar coordinates (distance from radar and angle
from north) for each radar cell are matched to the Cartesian grid. All the radar image
sequences analyzed are geocoded and oriented northward. The exact geographical
coordinates are known, because the radar antenna’s position, height, and viewing
directions are determined by a differential global positioning system.
3.3.1.2 Directional-Frequency Decomposition
The frequency decomposition of the field of the imaged waves is accomplished with
the fast Fourier transformation (FFT) algorithm. Using a 3-D FFT, the sequence of
wave images (Figure 3.3ia) is transformed from the spatial–temporal to the wavenumber frequency (Figure 3.3ib). The 2-D frequency slices are filtered directionally
(red ellipse in Figure 3.3ib) and transformed to the spatial-frequency domain using
a 2-D inverse FFT, resulting in a complex-valued single-(wave) component image.
Figure 3.3ic shows the phase pattern of one wave component after the directionalfrequency decomposition. The phase image outlines a pattern with spatially varying
wavelength.
3.3.1.3 Wave Number and Dispersion Regression
The basic idea of the local wave number determination from a complex-valued singlecomponent image relies on the idea that the local wave number is given, except for
the imaginary number i, as the proportionality factor between the local slope and
image value (Havlicek and Bovik 1995). In a local neighborhood, this dependency is
solved in the least squares sense.
The final step of the DiSC algorithm consists of the calculation of the local water
depth and near-surface current (Figure 3.3id). The dispersion relation defines a surface in the wave number-frequency domain (Figure 3.3ii). The form of the dispersion
relation depends on the water depth and the near-surface current vector.
Each wave number-frequency component of the wave field represents a point in
the wave number-frequency space. The long, small-wave number waves (relative to
water depth) contain information about the water depth (Figure 3.3iia and iib), and
the short, large-wave number waves allow the retrieval of the current. The directional spread of the wave field allows the determination of the current vector component perpendicular to the main wave propagation direction (Figure 3.3iic). These
dependencies allow the retrieval of the parameter water depth and current vector
from the wave component using the least squares regression method.
3.3.2 aPPlicaBle Sea wave ModelS
The analysis of the image sequence by DiSC for the extraction of the wave field
properties is independent of the inverted theory. This means that any dispersion
model could be applied for the estimation of the bathymetry and current field. Bell