# Use of ground based radar in hydrography

This article explains the basics of remote sensing by ground based radar in hydrography. Examples are given of measurements by microwave and High Frequency (HF) radar techniques.

### Introduction

Radar remote sensing in Earth observation does not only cover the global and regional survey of geophysical parameters by satellite- or airborne radars, it also includes local observations by ground based radar techniques. Due to their continuous measurement capabilities, the information provided by ground based instruments installed at the coast or on offshore platforms does not suffer from the episodic character of the satellite- or airborne radar observations. In contrast to the satellite systems, the incident angle of ground based radars is only a few degrees and near to zero (grazing) at far ranges. In this case, the working range of the radar strongly depends on the operating frequency. In this article we distinguish between:

• Microwave radars, which are limited by line-of-sight propagation to the horizon. Due to the large available bandwidth in the microwave frequency range, the spatial resolution can be as fine as 5 m at 5 km working range. By installing a microwave radar on-board a ship, the observation area can be extended along the ship track to a regional scale.
• Decameter wave radars, also known as High Frequency (HF) radars, make use of ground wave propagation far beyond the horizon. HF radars provide about 1.5 km at up to 200 km working range.

## Principles of ground based radar

By acquiring radar intensity or radar Doppler shift, an image of the related processes may be composed on a regional to local scale. By knowing the physics behind these modulations, the steering hydrodynamic processes may be assessed. In this article we will focus on the use of ground based X-band radar as tool for hydrographic observations. X-band radars operate in the frequency band 8-12.5 GHz In coastal management the regional and local survey by ground based radar provides a valuable completion to the in situ observations. Information on local wind, wave and current conditions as well as indirect parameters such as the local bathymetry, and even the coverage by ice, spills or slicks may be deduced routinely from radar products.

Although the microwave signal does not enter into the water, as almost 100% are reflected or scattered directly at the surface, it is possible to deduce additional information on the hydrodynamic from below the surface. For example the propagation of waves in shallow water allows deducing the local water depths out of the local wave propagation. Based on this relation it is possible to compose maps of the water depth (bathymetry), which can be used in monitoring the sand transport (see also section with "application and examples". Another example is the extrapolation of surface features down to the sea bottom as it is used by the operational model Vogelzang et al, (1997[2]).

#### Acquisition of radar Doppler shift

For the detection of Doppler shifts incurred to the microwave signal by the motion of the surface elements an acquisition time of at least some 100 milliseconds is necessary. During that time the antenna must be kept directed towards the individual surface elements. The longer the Doppler frequency information is integrated the greater the increases in its significance. As the frequency shift is sensitive to instantaneous local wind friction, the knowledge on the wind impact is crucial. We demonstrate an application of the Doppler measurements in chapter (see also the section with "application and examples").

Figure 2: Typical example of an antenna installation for WERA radar
Figure 3: Typical backscatter spectrum

HF radars are operated in the 3-30 MHz frequency range, where the electromagnetic waves can travel far beyond the horizon by ground wave propagation along a good conducting layer (salty ocean water) or due to reflections by the ionoshpere (sky wave propagation). Ground wave systems are installed at the coast close to the water to ensure a good coupling to the ocean and achieve working ranges up to 200 nautical miles, while sky wave radars are normally installed far off the coast, e.g. the JINDALEE radar in the centre of Australia and may reach thousands of nautical miles range. Only a few sky wave systems exist world wide, and in most cases are not used for oceanographic applications. The University of Hamburg recently developed a ground wave HF radar for coastal applications called WEllen RAdar (WERA), Gurgel et al. (1999[3]). Fig. 2 shows a typical example of an antenna installation set up for a WERA radar.

The development of HF radars in hydrography started in 1955, when Crombie[4] discovered that electromagnetic waves in the HF band were interacting with the ocean surface due to Bragg resonant scattering. The first radar for mapping of ocean surface currents was described by Barrick et al (1977[5])). A typical backscatter spectrum from a selected patch of the ocean at a given range and angle is shown in Fig 3: Two strong first-order Bragg peaks can be identified, which are generated by a resonant backscattering of the electromagnetic wave due to ocean waves of half the electromagnetic wavelength, e.g. 10 m long electromagnetic waves are scattered back by 5 m long ocean waves.

The phase speed C of these resonant ocean waves is given by the dispersion relationship. $C = \sqrt{\frac{g \lambda}{2 \pi} \tanh{\frac{2 \pi h}{\lambda}} }$

Where g is the acceleration due to gravity, λ is the ocean wave length, and h is the water depth. The shallow water term, $\tanh(\frac{2 \pi h}{\lambda})$ , approximates to 1 and can be neglected if the water depth is larger than the ocean wave length. As there are always ocean waves travelling towards and away from the radar, two strong first-order Bragg peaks can be observed. By changing the radar operating frequency, a specific ocean wavelength can be selected. Around the two first-order peaks, second-order side bands can be observed, which contain information on the ocean wave directional spectrum.

## Applications and examples of Microwave radar

This section describes to applications of Microwave radar. The first application is bathymetric survey and current field observation using local gravity wave dispersion. The second application is mapping of sea-surface currents by Radar Doppler Current Profiler.

### Bathymetric survey and current field observation

Figure 4: Gravity wave dispersion shell in wave frequency domain
Figure 5:Derived bathymetries

This Microwave radar techniques uses using local gravity wave dispersion Special challenge in coastal protection management is provided by the management of sandy coastlines. Here humans interact with the dynamic processes of the ocean with the shore line and undertake measures for their stabilization by measures such as beach nourishment. The interference of humans with nature must be attended by intense observations. The increase of sand to the coastal system means the survey of the sand’s residence on the one side, but on the other side the observation of the forces causing erosion, transport and deposition of sand. For this it is not enough to acquire time series of physical parameters at single observation points. It requires area mapping observations to identify the response within the system and to assign the process to their origins, either occasional forcing by storms or to continuous forcing by the tidal cycle, for instance. We will point out in the following the methods of radar hydrography allowing area covering and continuous survey of the forcing as well as the response of the bathymetry. The area of investigation is List West at the north end of the Island Sylt in the German bight.

In the current paragraph we present the assessment of the bathymetry and the current field by imaging the wave backscatter using marine radar. Time series of these images are inversed locally where the linear wave theory is valid and the surface wave dispersion holds. The algorithm used is known as “Dispersive Surface Classificator” (DiSC). The method has been developed at the Radar Hydrography Department of GKSS and is licensed as commercial product by Vision 2 Technology GmbH, partner of the Geesthachter Innovations- und Technologie-Zentrum (GITZ). The method is based on the linear wave theory that allows, by tracking of wave crest in space and time, the determination of the parameters water of depth and current vector. The dispersion relation of sea-surface waves is derived from the Eulerian equations of motion, the continuity equation and the dynamic and kinematic boundary conditions at the sea surface and the sea floor. A detailed description of the derivation of the dispersion relation is given in Senet et al., (2001[6]). The analysis of the image sequences of the inhomogeneous wave field provides a set of physical parameters on a local spatial scale. The basic idea of the method is that, in shallow waters, the waves vary their propagation (phase speed and wave number) locally and thus impresses the local bathymetry into the image series. The same mechanism acts via the local current that may be assessed by the DiSC as well.

The water depth and the current vector are free parameters influencing the shape of the dispersion shell in the wave-number frequency domain (see figure 5). An important characteristic of this application is that the radar has not to be calibrated, as the wave height is not influencing the wave dispersion. From the three dimensional radar observation the three dimensional power spectra in wavenumber -frequency domain is calculated by a Fourier Transformation. Next the shape of the actual effective dispersion is deduced by fitting the detected power values to a plane approximating the dispersion. Deviations from the undisturbed dispersion are used to determine the local water depth and current vector, Senet et al., (2007[7]). The local results are composed in spatial hydrographic-parameter maps.

Figure 6: Main analysis steps
Figure 7: Current field

The method is illustrated in figure 6 and the main steps of analysis are the following:

• preservation of the complex-valued 3D FFT image spectrum,
• filtering techniques of complex spectrum to separate the wave signal from noise, in contrast to the global method that the power spectrum is filtered
• directional and dispersion separation of the complex-valued spectrum into spectral bins at 2D wavenumber planes of constant frequency,
• 2D inverse Fast Fourier Transformation(2D FFT-1) of the spectral bins, yielding complex-valued, one-component spatial maps in the spatio-frequency domain,
• calculation of spatial maps of local wavenumbers from the one-component images of constant frequency,
• composition of the one-component local wavenumber maps of constant frequency to local 3D spectra and
• calculation of spatial hydrographic-parameter maps from the local 3Dspectra.

The result of the DiSC is the instantaneous local depth, the bathymetry, and the estimation of the current field. Figure 2a and 2b illustrate the bathymetries averaged over a tidal cycle each before and after a storm (wind conditions 8-9 Bft.). The two maps have common reference, corrected by gauge measurements.

The difference of the sediment volume between the beginning and end of the storm, which under the conditions could be considered as the sediment net increase of the area of investigation, is estimated in 50.000m3, with ±10% of accuracy for each grid cell, under the assertion that the accuracy of the method is higher than 90% per cell as it is given in Flampouris et al., (2007[8]). In general, the assumption of the constant difference between two periods, of the mean sea level, is not strong enough and decreases the accuracy of the calculation.

Fig. 7 illustrates an example of the current field in the same area as above. The wind conditions are approximately 5 Beaufort and the date of the data acquisition is the 12th July of 2001. The false current values, which are too high close to the shore and over the shoal at the north west corner of the observation area, indicate grid cells for which the linear dispersion is not valid.

### Mapping by Radar Doppler Current Profiler (RDCP)

The radar Doppler shift from the sea surface is used for the detection of the sea surface currents. With a coherent radar system it is possible to measure the scatterers speed directly. The ground based coherent X-band radar system can be mounted either onshore or onboard a ship to observe sea surface scatterer velocities. The azimuthal antenna view direction and data acquisition is computer controlled and defined by the user. Three different operating modi are possible and necessary for different applications: rotating antenna (also with different rotating speeds), stepping (changing view directions by set observing time) and the third mode is to permanently observe permanently a chosen direction. At a shore based permanent radar station the stepping mode is used for current and small scaled feature measurements like convergences/divergences or small eddies. Using the fixed view direction and a second radar antenna a full current vector can be achieved by moving the ship and the covered area increases versus a shore set up. This method of scanning the horizontal current profiles we called Radar Doppler Current Profile (RDCP). The transmitters are synchronized to acquire the two orthogonal components of the sea surface current during a single pass of the ship.

Figure 8: Ship with mounted RDCP
Figure 9: Current situation within a tidal channel in the German bight

Figure 9a and 9b, show the speed and direction of the surface current field. An eddy with a diameter of about one nautical mile shows the outflow directed westward on the northern side of the gully and a counter current directed eastward on the south side. This is overlaid by a current modulation due to the change in the cross section over the submared sand dunes, which interact with the ebb current in a way that we observe acceleration over the crest of the dunes and slowing down where the cross section is widening. For the comparison with the satellite SAR data it is of high interest to see that the directionality within the current field interacts with the dunes as well. It is evident that the current direction rotates into the main gully direction (clockwise), where the current speeds up above narrowing cross sections. The direction rotates anti clockwise in cross gully orientation slowing down currents above widening cross sections.

## Applications and examples of High Frequency radar

This section describes how HF-radar is used for the measurement of maps of surface currents, ocean wave spectra and wind direction.

### Measurement of surface current maps

Figure 10: Example of surface current field (Brest, France)

If an ocean surface current is transporting the Bragg resonant waves (cf. the two first-oder Bragg peaks in Fig. 3) the first-order Bragg peaks are shifted in frequency, away from the value given by the dispersion relationship (Equ.1). This shift moves both peaks by the same amount and to the same direction and its amount can be used to calculate the radial component of the surface current. The surface current value measured represents the average from the surface down to about 16% of the ocean wave length, which is e.g. the top 160 cm of the ocean at 15 MHz radar frequency.

Because one HF radar measures the radial component of the current, a second HF radar some 10 km apart is required to calculate the 2-dimensional surface current from the two radial components. Fig. 10 shows an example of a surface current field measured off Brest, France.

### Measurement of ocean wave spectra maps

Figure 11: Example of measured wave field (Brest, France)

The second-order sidebands seen in Fig. 3 contain information about the ocean wave directional spectrum. Note, that these sidebands may be hidden by stronger first-order Bragg peaks shifted by a different current velocity from other directions in case of non-directive receiving antennas.

There are two kinds of algorithms to derive the ocean wave spectra from the second-order sidebands: Most are based on the inversion of the Barrick-Weber equations Barrick et al (1977[5], e.g. the method developed by Wyatt (2000[11]), which allows resolving bi-modal sea states. This theory reaches it's limitations when the length of the Bragg-resonant ocean wave raises to the order of the significant wave height. The other kind of algorithms is based on an empirical approach, finding calibration factors by linear regression. The algorithm described by Gurgel et al. (2006[12]) falls into this category. Fig. 11 shows an example of a wave field measured off Brest, France.

Due to problems associated with reliably identifying the first-order Bragg peaks when the significant wave height reaches the length of the Bragg-resonant ocean waves, both algorithms show saturation effects: At 27 MHz radar frequency, the wave measurement saturates at Hs ˜ 7.5 m, at 12.5 MHz, the limit is at Hs ˜ 16 m. During high sea state conditions, a lower radar frequency has some advantages, however, the lowest detectable sea state is higher in this case.

There are several papers discussing the accuracy of HF radar wave measurements. An extensive comparison has been published by Wyatt et al. (2003[13]) within the EuroROSE (European Radar Ocean Sensing, EU Mast-3, CT98-0168) project.

### Measurement of wind direction maps

Figure 12: Example of measured wind direction (Brest, France)

By exploiting the ratio of the two first-order Bragg peaks in the backscatter Doppler spectrum (cf. Fig. 3), the direction of the Bragg-resonant ocean waves can be calculated. As these are quite short and refer to the wind-induced part of the ocean wave spectrum, they give a good indication of the wind direction. The wind-induced ocean waves follow changes in the wind direction with some 10-15 min. delay. Fig. 12 shows an example of the wind direction measured off Brest, France.

The algorithm to calculate the wind direction is to fit the ratio of the amplitudes of the two first-order Bragg peaks to a $\cos^s(0.5 \theta)$ or $sech^s(1.0 \theta)$ angular distribution model Gurgel et al. (2006). As this distribution model has a symmetric shape, the solution is ambiguous if one Bragg line ratio is available. A second Bragg peak ratio from a different direction, provided by a second HF radar, solves this ambiguity. A second radar site is required to measure ocean currents, anyway.

Wind speed measurements by HF radar are still under investigation. The problem is, that with increasing winds the wave energy of the Bragg-scattering waves inceases less and less and nearly reaches a saturation. Instead of further inceasing the waveheight, the energy is tranfered to longer ocean waves by nonlinear wave-wave interaction. Exploiting the level of the first-oder Bragg peaks is not sufficient in this case, and the complete ocean wave spectrum must be considered.