Effect of wave spectrum width on the probability density distribution of wind-wave heights

Abstract

The probability distribution of wave heights under the assumption of narrowband linear wave theory follows the Rayleigh distribution and the statistical relationships between some characteristic wave heights, derived from this distribution, are widely used for the treatment of realistic wind waves. However, the bandwidth of wave frequency influences the probability distribution of wave heights. In this paper, a wave-spectrum-width parameter B was introduced into the JONSWAP spectrum. This facilitated the construction of a wind-wave spectrum and the reconstruction of wind-wave time series for various growth stages, based on which the probability density distributions of the wind-wave heights were studied statistically. The distribution curves deviated slightly from the theoretical Rayleigh distribution with increasing B. The probability that a wave height exceeded a certain value was clearly smaller than the theoretical value for Ba parts per thousand yen0.3, and the difference between them increased with the threshold value. The relation between the H (s)/sigma ratio and B was investigated statistically, which revealed that the H (s)/sigma ratio deviated from 4.005 and declined with B. When B reached 0.698 1, the H (s)/sigma ratio was 3.825, which is about 95.5% of its original value. This indicates an overestimation in the prediction of H (s) from H (s)=4.005 sigma, and provides a potential method for improving the accuracy of the H (s) remote sensing retrieval algorithm, critical for extremely large waves under severe sea states.