Methods for the inversion of surface current

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 Applications of HFR

As was mentioned in Section 1.2, the mechanism of HFR sea echo backscatter is Remote sensing of ocean swell and some other coastal processes by HF radar Bragg resonance scattering (Crombie 1955). The corresponding feature in the Doppler spectrum is two most significant symmetrically located sharp peaks, called Bragg peaks or first-order peaks (Barrick 1972a). The ocean waves interacting with electromagnetic waves have wavelengths of half radio wavelength as the incident angle is near grazing, and they propagate along the radar look direction. These ocean waves are called Bragg waves. Bragg peaks positions in the Doppler frequencies are irrespective of sea state and are determined exclusively by the frequency of Bragg waves in absence of surface currents. Without currents, radar transmitting frequency is the only factor determining Bragg peak frequencies as it determines the frequency of Bragg waves.
The existence of surface current brings additional Doppler shift of the Bragg peaks from their theoretical frequencies (Crombie, 1972). By measuring this quantity of current-induced Doppler shift, the velocity component of surface current in the radial direction of radar station, also simply called radial velocity, can be derived. Radial velocity by two or more of HFR stations can be combined to give surface current vector field by the law of vector.
The principle of the inversion of current is straightforward. Using the first-order spectra, HFR provides the most reliable sea surface parameter – the surface current field. Stewart and Joy (1974) validated the theory of current inversion using drogue measurements of the same currents in the pacific near California in January 1973. Barrick et al. (1977a) and Frisch and Weber (1980) did a series of experiments and gave the root-mean-square difference (RMSD) between radar-derived currents and in situ measurements of 15 cm/s – 27 cm/s. Paduan and Rosenfield (1996) obtained RMSD of 13 cm/s. Chapman et al. (1997) measured RMSD among different radar stations of 9 cm/s to 16 cm/s. Kosro et al. (1997) compared currents by ADCP with radar measurements and obtain the RMSD of 15 cm/s with the correlation coefficient of 0.8. Currently, HFR technique of sea surface current is well developed and is widely used in field observations of circulation in coastal waters (Shay et al. 2007; Kim et al. 2011; Zhao et al. 2011). Meanwhile, further separation of surface flow components has been investigated. With studies of local tides, the residual current field can be obtained (Ardhuin et al. 2009a; Sentchev et al. 2013). Moreover, the concept of measuring vertical structure of current by HFR, originally proposed by Stewart and Joy (1974), has been further developed. Different electromagnetic waves go through different depths on the surface layer of the sea. Thus the shear of vertical velocity of sea surface current can be measured by HFR (Shrira et al. 2001; Ivonin et al. 2004).
Barrick (1972a) derived the first-order equation of radar cross section based on the small perturbation assumption of surface waves. The equation describes not only the location of Bragg peaks in Doppler frequencies but also the relationship between the amplitude of Bragg peaks and the waveheight of Bragg waves. Long and Trizna (1973) carried out the first attempt to map winds over a large area by HFR. Researchers obtained different models relating the ratio of the strengths of first-order peaks in Doppler spectra and the sea surface wind direction (Tyler et al. 1974; Harlan and Georges 1974). Most analyses showed the accuracy of wind direction by HFR of around 20° (Stewart and Barnum 1975; Wyatt et al. 2006). Heron et al. (1985) discovered that the existence of swell decreased the accuracy of the measurement of wind direction. In that sense, the measurements of swell will contribute to the inversion of other surface parameters, such like wind direction. Wind speed is even more challengeable to be obtained from HFR (Cochin et al. 2005; Green et al. 2009; Shen et al. 2012). Approaches are mainly based on empirical relationship between wind and surface waves. However, the correspondence of surface waves and local winds are complex and may not be totally dependent. Wyatt et al. (2006) concluded that it is possible to derive wind directions with reasonably good accuracy when the first-order Bragg waves are perfectly driven by local wind but the inversion of wind speed is not sufficient accurate with HFR for operational use.
The less energetic continuum around first-order Bragg peaks is called the second-order spectra. Second-order spectra are generated by two wave trains with certain wavelengths propagating at certain angle. Rice (1961) described the random conductive ocean surface and the electromagnetic field above it as two-dimensional Fourier series. Hasselmann (1971) pointed out the correlation between the ocean surface and radar sea echo by interpreting the HFR Doppler spectrum as the product of wave spectrum multiplied by a weighting function. Barrick (1972b) derived the resolved integral relationship between ocean wave spectrum and second-order sea echo spectrum. In principle, ocean wave spectrum can be inverted from second-order spectrum of HFR sea echo (Wyatt 1986; Howell and Walsh 1993; Hisaki 2005; Lipa and Nyden 2005). However, the correspondence between the two is complex and wave measurement is highly dependent on the quality of data (Forget 1985; Wyatt et al. 2011). At present, most inversions of ocean wave spectrum use empirical or semi-empirical models, and are mainly used to compute integral ocean parameters like significant waveheight of the total sea surface (Lipa and Barrick 1986; Wyatt 1990; Gill et al. 1996; Gurgel et al. 2006; Lipa et al. 2014).
There are other applications of HFR, such as recently implemented detection of tsunami (e.g. Lipa et al. 2006).

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Objectives and Contributions

Hydrodynamic environment in near shore area is much concerned for the safety of human activities, like fishing, navigation, rescue, etc. The ocean surface is a complex combination of many processes. Surface waves are critical objects to be investigated. In nearshore area, shallow water causes increase of waveheight by shoaling. Waves break and release much energy into the water column and thus play an important role in the impact on coastal and offshore infrastructures. The sea surface waves are usually divided into two groups: wind waves and swell. Wind waves are surface waves generated by local wind and contribute to the high frequency part of the total wave spectrum. Swell are surface waves generated by distant storms travelling across the ocean (Munk et al. 1963; Jiang and Chen 2013). Swell is usually located in the low frequency part of the total wave spectrum, with larger wavelengths and faster phase velocities. Wind waves dissipate much energy through wave breaking, whereas swell can spread over long distances due to smaller dissipation rate (Snodgrass et al. 1966; Collard et al. 2009; Ardhuin et al. 2010). In the ocean wave research, one of the interests is to separate wind wave and swell components from the complex total structure.
In recent years, contribution of swell in ocean processes has been much discussed. Laboratory studies by Phillips and Banner (1974) found that long-period waves inhibit growth of wind waves. Hara et al. (2003) used observations during two field programs to study the evaluation of the hydrodynamic modulation of wind waves by swell. Smedman et al. (2009) showed that the existence of swell accompanies variation of the profile of marine atmospheric boundary layer. Swell induces momentum and energy fluxes into the marine atmospheric boundary layer (Kudryavtsev and Makin 2004). Swell spread across the continental shelf and interacts with topography. Refraction and shoaling are caused by large-scale topography while the effects of intermediate scales and very small scales pose more difficulties to be understood (Ardhuin et al. 2003; Magne et al. 2007). The mechanisms behind the observed nonlinear propagation, attenuation that may be associated with bottom friction, local wave environment and other factors are still under study. Swell propagation and dispersion characteristics have been recently improved (Ardhuin et al. 2009b; Young et al. 2013; Gallet and Young 2014). The existence of swell affects the inversion of other oceanic parameters (Drennan et al. 1999). Mcwilliams et al. (2014) showed that the presence of swell amplifies and rotates Lagrangian-mean current.

Methods for the inversion of surface current

It was shown in Section 2.1 that Bragg frequencies are determined by radar transmitting frequency. However, this is based on the assumption that there are no surface currents. However, in practice the measured Bragg peaks are often displaced from the ideal positions. This additional displacement of Doppler frequency is due to the existence of surface current and is called current-induced Doppler shift, Df . A positive Doppler shift indicates a radial current velocity component towards the radar; a negative Doppler shift indicates a radial current velocity component off the radar. Fig. 2-3 shows a case of positive Doppler shift caused by surface current. This Doppler shift applies to all the Doppler frequencies. In an experimental Doppler spectrum, Df is measured via the more energetic first-order peak. The radial current velocity is computed by v = Df (2-13) cr 2.

Table of contents :

1 Introduction
1.1 HFR system
1.2 Development history
1.3 Applications of HFR
1.4 Objectives and Contributions
1.5 Organization of the thesis
2 Methodologies
2.1 Basic backscatter theory
2.2 Methods for the inversion of surface current
2.3 Methods for the inversion of wind direction
2.4 Methods for the inversion of swell
2.4.1 Swell frequency
2.4.2 Swell waveheight
2.4.3 Relative swell direction
3 Radar data processing
3.1 Locations and radar parameters
3.2 Beam forming
3.3 Averaging of Doppler spectra
3.4 Quality control
3.5 Statistics of qualified spectra
3.6 Summary
4 Results of surface currents
4.1 Radial current velocities
4.2 Total current vectors
4.3 Currents by SeaSonde
4.4 Summary
5 Results of wind directions
5.1 Radar inverted relative wind direction
5.2 Measurement of spreading parameter
5.3 Summary
6 Results of swell
6.1 Swell frequencies
6.1.1 Consistency of both radar measurements
6.1.2 Comparison with buoy data
6.1.3 Comparison with model data
6.2 Swell directions
6.2.1 Comparison between POS and LS methods
6.2.2 Comparison with model data
6.2.3 Absolute swell direction
6.3 Swell significant waveheights
6.3.1 Comparison with buoy data
6.3.2 Comparison with model data
6.3.3 Consistency of both radar measurements
6.4 Summary
7 Accuracy analysis
7.1 Radar intrinsic errors
7.1.1 Random error in radar-inverted frequency
7.1.2 Random error in radar-inverted relative direction
7.1.3 Random error in radar-inverted waveheight
7.2 Methodological discrepancies
7.3 Buoy and model intrinsic errors
7.4 Summary
8 Conclusions and perspectives
8.1 Main conclusions
8.2 Inadequate points and future work


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