Jantine Rutten

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1. Goal

Estimate temporal and spatial quality differences of wave characteristics in marine X-band radar images to determine the appropriateness of radar images as validation tool for waves in a numerical model for an area with a complex bathymetry. 

The study site is the Ameland Inlet and ebb delta. The waves are modelled in the numerical wave model of Gautier and Westhuysen (2010) in SWAN. Currents will be incorporated in the wave model, since they interact with waves. The current input is provided from the flow model Delft3D. Temporal and spatial differences of wave characteristics in radar image quality will be tested by using radar data of the storm in October 2010 and the validated wave model.

2. Research questions

Model optimization (using radar data from January 2010)
1. How do waves deform over the Ameland ebb tidal delta into the tidal inlet during a high-energetic, stormy tidal cycle and what is the spatial and temporal evolution for wave deformation?
1.1.    In the wave model of Gautier and Westhuysen (2010)
1.2.   In the radar images of January 2010
2. Where and when the radar images (of January 2010) do not show realistic wave characteristics and consequently should be filtered out?
3. What are the wave characteristics extracted from the radar images after filtering?
3.1.   Wave length, wave period, wave angle?
3.2.   Significant wave height?          
3.2.1.      How is the empirical based Modulation Transfer Function?
4. Which hydrodynamic processes seem to be under-, overestimated or neglected spatially and temporally in the model; when comparing to radar wave characteristics (of January 2010) and buoy measurements?
5. Which model parameters can be adjusted spatially and temporally to optimize the numerical model (SWAN) of the Ameland Inlet for waves and to what extent should the model parameters be adjusted?
6. How do waves deform over the Ameland ebb tidal delta into the tidal inlet during a high-energetic, stormy tidal cycle in the optimized model?

Radar quality
7. How does the quality of the Ameland radar images differ spatially and temporally for waves over the ebb delta during a stormy tidal cycle?
7.1.   Comparing to the optimized model
7.2.   Evaluating the radar-inferred wave characteristic filter
8. When and where does the radar-inferred wave characteristic quality reduce and can this be related to certain quality lowering factors?
9. Can radar appropriateness for model validation be predicted for waves and currents over the Ameland ebb delta?

2. Methods

To use marine X-band radar images as validation tool for waves in a numerical model for a complex bathymetry, the spatial and temporal variable radar wave characteristic quality should be determined. From radar image to validated model, several data processing steps have to be taken. The marine X-band radar images were processed into hydrodynamic characteristics (wave length, wave period, wave angle) by Radar processing company SeaDarQ. The significant wave height can be approached by an empirical-based Modulation Transfer Function. Spatial and temporal patterns in these hydrodynamic (radar) characteristics have to be analyzed and not reliable data has to be filtered out. The (radar) wave characteristic quality has to be evaluated for the October 2010 storm (by comparing to an optimized model and by quantifying the filtered out radar wave characteristics) and a quality estimator (for the best predicted wave characteristic) has to be developed and tested for both storms. The model, needed to estimate the radar image quality, will be optimized (beforehand) to the radar data of the January 2010 storm and to the wave buoys.

2.1 Study site

This study builds on the study of Swinkels (2011) and Gautier and Westhuysen (2010). Their (Gautier and Westhuysen, 2010) wave model (SWAN) of the ebb tidal delta and into the inlet of the Dutch barrier island Ameland is used here as well. Swinkels (2011) and Gautier and Westhuysen (2010) improved their numerical models by comparing modelled current and wave characteristics to current and wave data extracted from an X-band marine radar at the northwest part of the Dutch barrier island Ameland of a storm in January 2010. Images of the same storm in January 2010 of the same radar are used in this study, but also images are used of a storm in October 2010.

2.2 Radar data

Prior to describing the methods to determine wave deformation over the ebb delta using marine X-band radar imaging, some theoretical background is needed about how those radar images were processed into wave and current data by Radar processing company SeaDarQ. SeaDarQ processed the marine X-band radar images of the storms in January and October 2010 and extracted image spectra, frequency-directional spectra, wave length, wave angle, wave period, current speed and current direction. The methods to determine wave deformation (using wave length, wave angle, wave period and wave height) over the ebb delta and to improving those results by using a data filter, answer the questions 1 to 3 and follow after a short summary of SeaDarQ’s data processing.
The radar rotated around a vertical axis and recorded one (circular) image of each rotation. Image sequences arose for the time the radar rotated continuously (1.6min), with a repetition time of 13min. In the radar images wavy patterns (sea clutter) were observed, which arose by the interaction between the sent microwave and ripples and foam on the sea surface (Valenzuela, 1978). Wave (angular) frequency and wave number (and length) were estimated by a 3D Fourier Transform on the wavy patterns of the sea clutter in the radar image sequences (Young et al., 1985). The wavy pattern can be represented by a superposition of sine functions with different wave number and frequency. SeaDarQ did a 3D Fourier Transform over spatial computational cells of 960x960m (pixel size of 7.5m) and time sequences of 1.6min, which resulted in a set of wave numbers and corresponding frequencies or image spectrum I(k_x,k_y,ω) of each computational cell and radar rotation period. The spatial resolution of the image spectra is 300m, since the computational cells overlap partially. The temporal resolution equals the time between subsequent radar rotations (13min).
SeaDarQ determined current speed and direction by estimating the current vector in the dispersion relation (linear wave theory) using least squares regression (Hessner and Reichert, 2007) on the set of (radar) wave numbers and frequency. They used only the high frequency part of the frequency spectra to estimate the surface current speed and direction for the January storm (and probably also for the October storm). I will interpolate the radar current data to a grid (so radar grid points correspond to model grid points, with a spatial resolution of 300m) and then will filter the radar data of the January 2010 storm temporally (similar as Swinkels, 2011) and spatially for outliers. For the January 2010 storm Swinkels filtered out values (data points) with more than three standard deviations from the mean (value), values more than 0.5 standard deviation different from neighbouring values and values based on less than 10 data points. For remaining outlying values the data was filtered in space (pilot by Swinkels, 2011).
To describe the wave deformation over the ebb delta and into the tidal inlet of Ameland the wave characteristics wavelength, wave angle and wave height have to be known. SeaDarQ provides radar 2D frequency-directional spectra. The peak wave period, wave angle and wavelength follow from the radar intensity peak in the 2D spectra of SeaDarQ (answers question 1.2).
To answer question 2, outliers in the derived wave lengths, wave periods and wave angles should be located in space and time. Therefore, a filter equivalent to the time- and space filter of Swinkels (2011) will be applied. Dependent on the effect of the filter on the quality of the wave parameters the filter criteria will be adjusted.
To answer question 3.1, peak wave length, peak wave period and peak wave angle will be determined, but now for the filtered frequency-directional spectra.
Question 3.2 can be answered when the Modulation Transfer Function (question 3.2.1) is determined. The significant wave height is (roughly) approached by transforming the radar intensity spectrum I(f) to a energy density spectrum E(f) by multiplying I(f) with an empirically based Modulation Transfer Function (Young et al., 1985; Nieto Borge et al., 2004). The (frequency- and range- dependent) empirical Modulation Transfer Function will be found as the relation between the 1D radar intensity frequency spectrum of a computational cell (960x960m) and a wave buoy spectrum at the same location. A reliable Modulation Transfer Function will be obtained by averaging over time for the two storms (now radar intensity spectra are provided by SeaDarQ, covering the dataset spatially and temporally for both storms) and interpolating the MTF between the several buoy locations (because the range- dependency of the MTF) (answers question 3.2.1). However, spatial interpolation of the MTF will be difficult, because only four wave buoys are located in the Ameland Inlet (at a different range and azimuth with respect to the position of the lighthouse) and the complex bathymetry. From the resulting estimates of the energy density spectra (applying the range- and frequency- dependent MTF on all radar intensity spectra), the significant wave heights will be extracted (answers question 3.2).