The Level Crossing Method applied to mean wind speeds from “mixed” climates

Abstract

There is an ongoing need to develop alternative penultimate methods for analysing extreme wind speeds, i.e. methods not involving convergence to an asymptote. This need has sharpened given that it is now known that the wind climate is “mixed” at many more sites than previously thought. One penultimate method developed many years ago from work on random electrical noise signals, is the so-called Level Crossing Method. This was used for processing wind speeds without serious examination of the fundamentals.In the paper the original formulation is examined both theoretically and by testing with computer-generated synthetic data. It is found to be based on some incorrect assumptions, which lead to errors. A new theoretical expression is derived for level crossings of wind speeds which fits perfectly those measured from the synthetic data. Thus, given a parent distribution of the Forward Weibull type and the correlation coefficient between successive measured values, the Gumbel plot can immediately be derived.This process also uses the idea that rare crossings of high levels are a Poisson process. The correlation of the parent introduces systematic errors from this assumption, but these are small and have the advantage of decreasing as the wind speed level increases. Given a means of separating “mixed” wind regimes by the newly available OEN analysis, an up-dated version of the Level Crossing Method appears to be a possible new penultimate method for extremes.