A simulation method for the macro-meteorological wind speed and the implications for extreme value analysis

摘要

This paper provides a contribution to the testing of existing methods of analysis of extreme wind speeds and to the development of better alternatives. A method is developed for synthesising a correlated random time series with a Rayleigh amplitude distribution and an arbitrary auto-correlation. The auto- correlation is selected to be the Von Karman model because the method is then used to generate 20,000 years of simulated hourly mean wind speeds. Annual maxima are extracted and exhibited on Gumbel plots. Familiar problems with convergence to asymptotic forms are confirmed and a new problem is revealed in that the annual rate parameter, previously believed to be constant, is found to vary significantly in the range of the measured data encountered in practical extreme value analyses. With the exception of newly developed penultimate methods, all the existing methods of analysis depend implicitly on either convergence to an asymptotic form, or invariance of the annual rate parameter, or both. This has serious implications for the accuracy of these methods, not only for the analysis of annual maxima, but also for extensions of these methods developed to use more data from each year.