Analysis of fetch-limited wave growth using high-frequency radars in the Gulf of Tehuantepec

Abstract

Fetch-limited wave growth was analyzed using high spatial and temporal resolution measurements obtained with high-frequency (HF) radars. To calculate the wave spectrum, the second-order echo (S_2N) was extracted from the Doppler spectrum and mapped to the wave frequency domain. The conversion of S_2N to the wave frequency spectrum was carried out using a linear parametric model dependent on wind speed. Wave growth, represented by the dimensionless energy and peak frequency as a function of dimensionless fetch, was determined from the spectra calculated for 25 cells (~400 km²) in the vicinity of a moored Air–Sea Interaction Spar buoy. The buoy data were used as reference and to provide the wind information required for the wave growth analysis. The simultaneous data from the buoy and HF radars showed a suitable agreement with the wave growth curves. The analysis of the 25 cells showed an adequate agreement and certain dispersion around the growth curves. Possible causes of this dispersion are related to errors in the estimation of the frequency spectrum and fetch, and the assumption of homogeneous wind conditions. From the limited data set used, it was not possible to prove any impact of swell on wave growth; however, it is possible that analysis over a wider range of swell heights may provide this evidence. Nevertheless, the results suggest that the linear parametric model is able to reproduce fetch-limited wave growth. This work represents the first effort focused on fetch-limited wave growth using HF radars.