On-the-Go Measurements of the Wind Waves with Shipborne Radar

The state of the sea surface, specifically the wind waves, is of a great importance for both fundamental geophysical research and safety of the marine navigation. In situ precise observations of the wind waves are critical for the data assimilation and validation of the general circulation and weather prediction models of both ocean and atmosphere. Wave forecasts and on-the-go wave observations are also critical for navigation of the vessels in the open ocean and maritime safety.
While there is a long history of the wind wave’s parameters measurements (significant wave height (SWH), peak period, wave period, frequency spectrum, etc.) with marine navigational radars, including commercial solutions that contribute to the safety of coastal platforms and vessels operating in the open ocean, there is still a significant methodological difficulty in the analysis of radar data while the ship is cruising with various speeds. These difficulties arise from the Doppler correction in the dispersion relation for waves in the deep water:
ω = (gk)^1/2 + k · V (1),
ω - frequency, g - gravity acceleration, k - wave vector, V - vessel's velocity relative to the water surface. Since the speed of the vessel can reach up to 9 m/s or even more, the second term in (1) can significantly exceed the first in modulus. Also, the large negative Doppler term (the case of the short oncoming waves) adds an extremum to the dispersion function ω(k) which is not related to the actual wave signal and creates false ambiguity for calculation of the frequency spectrum with the standard procedure.
In this study, we present an algorithm that allows to account for V and to processes radar images in real time with a three-dimensional Fourier transform. The algorithm uses the corrected relation (1) for calculation of the frequency spectrum, this results in accurate determination of the period of the wave peak in the stationary reference frame. In the case of a negative second term, the frequency spectrum is calculated from the wave number, which eliminates a ambiguity. In addition, we propose an original method for the directional analysis of wave systems. The polar diagram of the orthogonality of wave crests to the line of the sight allows to determine the direction of the main wave systems even in the case of a swell and a wind wave systems presence simultaneously.
The algorithm was validated in six research expeditions in the open ocean – two in the North Atlantic, two in Tropical Atlantic, one in the Arctic and one in the cross expedition from the North Atlantic to the South Atlantic and Antarctic. We validate algorithm both with satellite altimetry data and synchronous observations with the Spotter wave buoys when weather conditions in expeditions allowed.
We achieve standard deviations of less than 0.5 meters for the SWH, 3 seconds for the peak period and 30 degrees for the wave system direction - both for the stationary or low speed of the vessel case and for the cases of the vessel speeds up to 9 m/s.
Our broader mission is efforts towards significant increase of the number wave observations in real-time along ship routes in the open ocean with already inbuilt in every vessel standard X-band radar. This creates a huge potential for broadening of the wave observational network with direct benefits for maritime industries, environmental monitoring and climate science.