On estimating the return values for wind speed and wind-wave heights

To estimate the return values for wind and wind-waves time series, we propose to use the extrapolation of a polynomial approximation built for a small part of the tail of provision function estimated for the series considered. A possibility of optimizing an accuracy of the polynomial approximation is stated, which is realized by varying both the length of the proper part for provision function and the exponent of the polynomial. The quality criteria for constructing approximation are proposed, allowing to increase the approximation accuracy. On example of the wind-reanalysis data and the results of numerical modeling of wind-wave heights in the Indian Ocean for the period 1980-2010, the proposed method was applied to obtain estimates of the return values at a number of fixed points in the ocean. It is shown that the method of polynomial approximation has a distinct advantage in estimating the return values with respect to the well-known method of initial Weibull distribution, taken for comparison.