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THE ACCURACY OF RADAR-DERIVED BATHYMETRY BY THE XMFIT ALGORITHM AND THE IDENTIFICATION OF ERROR SOURCES OF THIS ALGORITHM
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Understanding of the processes of the nearshore is of high importance for managing the coastal zone and
protection of the coastline. The coastal bathymetry might be the most essential input for understanding,
characterising,monitoring andmodelling this coastal environment. The present in situ bathymetry and current
measurement devices, however, have huge inherit disadvantages. Remote sensing may overcome these
disadvantages and has the advantage to obtain measurements with a high spatial and temporal resolution.
Marine radar is a promising remote sensing technique due to its potential to derive bathymetry hydrodynamics
and wave characteristics. Marine radar operates by sending and receiving an X-Band radar signal
from a high observation point at small incidence angles. These radar pulses interact with the centimetre
scale sea surface ripples. These centimetre-scale waves are modulated by the long waves' orbital motion,
and thereby influence the radar signal, from which the long waves can be identified. Wave characteristics
are obtained by performing a Fast Fourier Transformation (FFT) on these radar images. The FFT produces
pairs of wavenumbers and wave frequencies that can be linked to water depths and velocities by means of
the dispersion relation.
This process is implemented by multiple commercial products. A big drawback of these products is
their closed and fixed nature and unclear accuracy. Therefore an X-band radar depth inversion model(XMFit)
was recently developed by
Friedman (2014). This development was induced by a marine radar stationed near
the Sand Motor, a large scale nourishment, near Kijkduin in the Netherlands. As part of a measurement
campaign(MEGAPEX) accompanying this nourishment, a radar was stationed on a nearby dune.
However, XMFit is not yet a ready-to-use product. Present shortcomings are: the requirement of further
validation and verification of the XMFit algorithm, the lack to also determine wave heights with the algorithm,
but most importantly the present bias in the depth estimate. Therefore, the goal of this thesis was to
determine the accuracy of radar-derived bathymetry by XMFit a for the stormin October 2014 and determine
the cause for the present overestimation of the depth by XMFit at the SandMotor.
Three steps are outlined to arrive at this goal: First, XMFit is validated for the recent MEGAPEX storm
of October 2014. Second, the cause of the XMFit depth bias and other sources of accuracy are investigated
and possibly reduced. Third, a comparable study for the Ameland radar, may indicate whether the experienced
depth bias at the SandMotor is site specific.
An extensive validations study based on images of the Kijkduin radar presents that the present mean depth
bias of XMFit is 4.21 m at the Sand Motor. This study also shows that the XMFit error fluctuates over the
course of time and space. Even more, this study shows that the XMFit accuracy depends on waveheight,
wave period, precipitation and water depth. Filtering of inferior metocean conditions may reduce the depth
error at SandMotor to 3.04m.
The validation study shows that during calm weather XMFit velocities are very reliable, but during
storm deviate significantly from in situ measurements. XMFit is particularly good at predicting alongshore
flow velocities, though has a low skill in estimating the cross shore flow velocity. This may be partially improved
by the present work of (
Weijenborg, 2015, work in progress). The XMFit flow velocities at ADCP-F also
exhibit a small velocity bias in south-west direction. A small spatial analysis of these XMFit flow velocities
promisingly showed that sometimes a growing eddy can be observed on the lee side of the SandMotor.
A comparable validation study has been performed for radar images from the radar overlooking the
Amelander Zeegat. Here a mean depth bias of 1.04mis found. On the one hand, the Ameland results present
depth overestimation for large azimuths and on the Bornrif flat close to the radar. On the other hand, depth
underestimation is found on the outer edge of the ebb tidal flat. In contradiction with the Sand Motor, the
Ameland depth bias shows no dependency on the radar range. A metocean-filter to isolate reliable Ameland
results, is slightly effective when selecting on the waveheight and the precipitation.
A comparison of the known dispersion shell based on the in situ depth and velocity with the measured energy
in the 3D wavenumber frequency space has been the core of this study. It showed that the energy is observed
at a location off the theoretical dispersion shell. The XMFit fitting procedure is not the cause of the depth
bias, but the energy location is.
Giving more importance to longer waves will not help to improve the accuracy of the depth estimate,
and possibly even worsen it. This because the energy is often even further off the theoretical dispersion shell
for these longer waves. The energy is definitely not on the theoretical shell for these longer waves, an often
also inside of the XMFit fitted shell.
The XMFit derived 3D wavenumber frequency space shows energy on a location which can be attributed
to higher harmonics of the dispersion relation. During the storm of 21 October these harmonics
become visible. Other researches indicate that the inclusion of these higher harmonics and the aliased energy
is very important to improve the XMFit accuracy. These higher harmonics are not the cause for the XMFit
depth bias, since their energy level is only significant during the storm. However, these harmonics do cause
an onshore directed velocity error during the storm.
Multiple possible sources of the depth error were identified in this thesis. The in situ data, the fitting procedure
of the XMFit algorithm and the bottom slope are concluded to have a negligible contribution to the
XMFit depth bias. The metocean conditions including precipitation, the Rhine's fresh water plume, amplitude
dispersion and the water depth itself do have a considerable effect on the XMFit depth bias.
A great deal of effort has been put in the accurate determination of the validation data. This aims at
excluding that these validation data are a cause for the XMFit depth bias. Inaccuracies in the water level may
lead to a small error of 0.2mat the SandMotor and of 0.5mat Ameland.
Precipitation explains a lot of the huge outliers of the XMFit depth estimate. Large bias values during
precipitation or due to a too mild wave climate could be discarded if the radar images are filtered on based
on their contrast, like is done in other algorithms. Other extreme outliers have been related to opposing flows
inside the analysis cube. At certain time steps the passage of the fresh water plume, and the accompanying,
opposite directed flow, may cause an erroneous depth estimate. However this only happens at just a few
incidences.
The XMFit depth bias shows a large correlation with the radar range and the incidence angle of the
radar signal at predominantly the Sand Motor. However, it are not the incidence angle or the radar range
themselves that cause the increased depth bias. This correlation is caused by the correlation between the
depth bias and the deeper water depths. The increased bias for increased ranges is also caused by the increased
bias due to the larger azimuth in the edges in the radar domain.
This thesis also considered the validity of the dispersion relation. Depth inversion require the wave's
phase speed to be dependent on the water depth. Only long enough waves are able to feel the bottom. The
XMFit depth inversion is currently very dependent on shorter waves. A comparison of the in situ depth with
the depth that can actually be felt by the existing wave climate, showed that the applicability of the dispersion
relation might be stretched too far at the Sand Motor. The limited applicability of the dispersion relation
in deeper water correlates with the increased depth bias at this deeper water depth. However, there is no
evidence these are actually related. Other authors rather found underestimation for deeper water depths.
The increased depth error and scatter at the lower water depths could be attributed to the fact that
XMFit does not include amplitude dispersion in its calculation procedure. A test that included amplitude
dispersion for water depths up to 6m showed that this led to a significant reduce in the depth bias(3.54 m
compared to 5.33 m). However, results might be even further improved, if a local waveheight could be used
in stead of one waveheight for all gridpoints.
The determination of the accuracy of XMFit and its dependency on metocean conditions has helped to pinpoint
important error sources. After filtering the results for inferior metocean conditions, a depth bias of 2.30
m remains at the Sand Motor. It was found that this error is induced by a shift of the measured energy in the
3D wavenumber frequency spectrum. However, non of the researched error sources was able to explain this
shift. Therefore it becomes likely that the error is related to some cause outside of the XMFit Algorithm. The
only thing that is known for certain about the remaining depth bias, is that it is dependent on the water depth
and the size of the computational cube.
To find the cause of the depth bias at the Sand Motor, a sensible future step would be to further investigate
the local radar set-up and the image processing before the XMFit algorithm. Next to solving the
remaining depth bias other steps could be taken to increase the overall accuracy of XMFit. These would be
to reject contrastless radar images; include higher harmonic and aliased energy in the fit of XMFit; include
wave height estimation and amplitude dispersion into the algorithm; and improve the understanding of the
energy cutoff level.
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