# The Characteristics of Wind Velocity that Favor the Fitting of a Weibull Distribution in Wind Speed Analysis

Stanton E. Tuller University of Victoria, Victoria, British Columbia, Canada V8W2Y2

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Arthur C. Brett University of Victoria, Victoria, British Columbia, Canada V8W2Y2

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## Abstract

The derivation of the Weibull distribution from the bivariate normal distribution provides theoretical justification for its use in wind speed analysis if four conditions are met. These conditions are that the orthogonal components of horizontal wind velocity transformed by raising them to the power k/2 are normally distributed, have zero means, have equal variances, and are uncorrelated. These four conditions specify a circular normal distribution for the transformed wind velocity components. Real world wind velocity patterns, however, are seldom, if ever, circular normal. Instead, the effects of topography and frontal systems produce a different wind speed distribution from each direction. This helps explain why the Weibull distribution gives only an approximate fit to the observed wind speed frequency distribution. The fit, at seven British Columbia coastal stations, was best at those stations with the most nearly circular wind velocity patterns and the lowest proportions of calms. It is suggested that these two characteristics, readily available in published wind normals, might provide a useful preliminary indication of the utility of attempting to fit a Weibull distribution.

## Abstract

The derivation of the Weibull distribution from the bivariate normal distribution provides theoretical justification for its use in wind speed analysis if four conditions are met. These conditions are that the orthogonal components of horizontal wind velocity transformed by raising them to the power k/2 are normally distributed, have zero means, have equal variances, and are uncorrelated. These four conditions specify a circular normal distribution for the transformed wind velocity components. Real world wind velocity patterns, however, are seldom, if ever, circular normal. Instead, the effects of topography and frontal systems produce a different wind speed distribution from each direction. This helps explain why the Weibull distribution gives only an approximate fit to the observed wind speed frequency distribution. The fit, at seven British Columbia coastal stations, was best at those stations with the most nearly circular wind velocity patterns and the lowest proportions of calms. It is suggested that these two characteristics, readily available in published wind normals, might provide a useful preliminary indication of the utility of attempting to fit a Weibull distribution.

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