Empirical Models of the Probability Distribution of Sea Surface Wind Speeds

Abstract

This study considers the probability distribution of sea surface wind speeds, which have historically been modeled using the Weibull distribution. First, non-Weibull structure in the observed sea surface wind speeds (from SeaWinds observations) is characterized using relative entropy, a natural information theoretic measure of the difference between probability distributions. Second, empirical models of the probability distribution of sea surface wind speeds, parameterized in terms of the parameters of the vector wind probability distribution, are developed. It is shown that Gaussian fluctuations in the vector wind cannot account for the observed features of the sea surface wind speed distribution, even if anisotropy in the fluctuations is accounted for. Four different non-Gaussian models of the vector wind distribution are then considered: the bi-Gaussian, the centered gamma, the Gram?Charlier, and the constrained maximum entropy. It is shown that so long as the relationship between the skewness and kurtosis of the along-mean sea surface wind component characteristic of observations is accounted for in the modeled probability distribution, then all four vector wind distributions are able to simulate the observed mean, standard deviation, and skewness of the sea surface wind speeds with an accuracy much higher than is possible if non-Gaussian structure in the vector winds is neglected. The constrained maximum entropy distribution is found to lead to the best simulation of the wind speed probability distribution. The significance of these results for the parameterization of air/sea fluxes in general circulation models is discussed.