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

• Published in: Journal of wind engineering and industrial aerodynamics Vol. 125; pp. 146 - 155
• Main Author: Ian Harris, R.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-02-2014
• Subjects: Annual maxima; Asymptotic properties; Autocorrelation; Constants; Convergence; Correlation; Extreme value analysis; Extreme values; Mathematical models; Maxima; Penultimate methods; Simulated time series; Time series; Wind speed; Simulated time series; Annual maxima; Extreme value analysis; Correlation; Penultimate methods
• ISSN: 0167-6105; 1872-8197
• DOI: 10.1016/j.jweia.2013.12.003

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.
•A method for synthesising a time series with a Rayleigh amplitude distribution and an arbitrary auto-correlation.•Synthesis of 20,000 years of simulated hourly mean wind speeds with a Von Karman auto-correlation.•Extraction of annual maxima and Gumbel plots which confirm known convergence problems and reveal a new problem – the variation of the rate parameter.•Implications for the validity of existing extreme value analysis methods.