# Tsunami Detection by High-Frequency Radar Beyond the Continental Shelf

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## Abstract

Where coastal tsunami hazard is governed by near-field sources, such as submarine mass failures or meteo-tsunamis, tsunami propagation times may be too small for a detection based on deep or shallow water buoys. To offer sufficient warning time, it has been proposed to implement early warning systems relying on high-frequency (HF) radar remote sensing, that can provide a dense spatial coverage as far offshore as 200–300 km (e.g., for Diginext Ltd.’s Stradivarius radar). Shore-based HF radars have been used to measure nearshore currents (e.g., CODAR SeaSonde^{®} system; http://www.codar.com/), by inverting the Doppler spectral shifts, these cause on ocean waves at the Bragg frequency. Both modeling work and an analysis of radar data following the Tohoku 2011 tsunami, have shown that, given proper detection algorithms, such radars could be used to detect tsunami-induced currents and issue a warning. However, long wave physics is such that tsunami currents will only rise above noise and background currents (i.e., be at least 10–15 cm/s), and become detectable, in fairly shallow water which would limit the direct detection of tsunami currents by HF radar to nearshore areas, unless there is a very wide shallow shelf. Here, we use numerical simulations of both HF radar remote sensing and tsunami propagation to develop and validate a new type of tsunami detection algorithm that does not have these limitations. To simulate the radar backscattered signal, we develop a numerical model including second-order effects in both wind waves and radar signal, with the wave angular frequency being modulated by a time-varying surface current, combining tsunami and background currents. In each “radar cell”, the model represents wind waves with random phases and amplitudes extracted from a specified (wind speed dependent) energy density frequency spectrum, and includes effects of random environmental noise and background current; phases, noise, and background current are extracted from independent Gaussian distributions. The principle of the new algorithm is to compute correlations of HF radar signals measured/simulated in many pairs of distant “cells” located along the same tsunami wave ray, shifted in time by the tsunami propagation time between these cell locations; both rays and travel time are easily obtained as a function of long wave phase speed and local bathymetry. It is expected that, in the presence of a tsunami current, correlations computed as a function of range and an additional time lag will show a narrow elevated peak near the zero time lag, whereas no pattern in correlation will be observed in the absence of a tsunami current; this is because surface waves and background current are uncorrelated between pair of cells, particularly when time-shifted by the long-wave propagation time. This change in correlation pattern can be used as a threshold for tsunami detection. To validate the algorithm, we first identify key features of tsunami propagation in the Western Mediterranean Basin, where Stradivarius is deployed, by way of direct numerical simulations with a long wave model. Then, for the purpose of validating the algorithm we only model HF radar detection for idealized tsunami wave trains and bathymetry, but verify that such idealized case studies capture well the salient tsunami wave physics. Results show that, in the presence of strong background currents, the proposed method still allows detecting a tsunami with currents as low as 0.05 m/s, whereas a standard direct inversion based on radar signal Doppler spectra fails to reproduce tsunami currents weaker than 0.15–0.2 m/s. Hence, the new algorithm allows detecting tsunami arrival in deeper water, beyond the shelf and further away from the coast, and providing an early warning. Because the standard detection of tsunami currents works well at short range, we envision that, in a field situation, the new algorithm could complement the standard approach of direct near-field detection by providing a warning that a tsunami is approaching, at larger range and in greater depth. This warning would then be confirmed at shorter range by a direct inversion of tsunami currents, from which the magnitude of the tsunami would also estimated. Hence, both algorithms would be complementary. In future work, the algorithm will be applied to actual tsunami case studies performed using a state-of-the-art long wave model, such as briefly presented here in the Mediterranean Basin.

## Keywords

Radar Tsunami Wave Radar Signal Doppler Spectrum Radar Cell## Notes

### Acknowledgments

The authors gratefully acknowledge financial support for this study from Diginext Ltd. The reported results only represent the author’s views and interpretations.

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