The parent wind speed distribution: Why Weibull?

• The Offset Elliptical Normal model (OEN) is derived for the joint PDF of wind vectors.
• The OEN justifies the Weibull distribution as the CDF for parent wind speeds.
• The assumptions in the OEN are verified using wind observations.
• The OEN model is extended to apply in “mixed” wind climates.

Part 1: The Weibull distribution has been used for many years to fit parent wind data. It is a particularly good fit to mean wind speed data arising from a wind climate dominated by temperate depressions. This good fit is practically useful, but intellectually not very satisfactory, because the familiar or Forward Weibull distribution is a purely empirical construct and there have seemed to be no reasons, grounded in either atmospheric physics or probability theory, why wind speeds should conform to this model. This paper introduces another distribution, the Offset Elliptical Normal (OEN) model, which has some justification in terms of probability theory and appears to form a more plausible model for mean wind speeds. It is shown that, over the entire practical range from everyday values to 1:10,000 year extremes and beyond, this new distribution matches a Weibull distribution so closely, that the Weibull can be regarded as not just empirical, but as an effective surrogate for the new distribution. One Weibull distribution corresponds to a whole family of the new distribution.Part 2: The assumptions of Harris’ Offset Elliptical Normal (OEN) model are verified using direct vector analysis of hourly wind observations at two, widely separated UK stations. The Jenkinson–Lamb index is found not to be effective in separating UK wind observations by causal mechanism for individual analysis. Fitting to the marginal distributions of wind speed and direction is shown not to be practicable owing to the information on their joint action that has been lost. Instead, an optimisation methodology is used to fit multiple disjoint OEN models to the joint PDF of the observed wind vectors, without prior separation of the observations. For Marham, Norfolk, a single OEN is sufficient, but two is marginally better. For Tiree, Inner Hebrides, two disjoint OENs are sufficient, but three is marginally better. For Changi, Singapore, three disjoint OENs correspond well with the three seasonal climates (inter-monsoon, “wet” NE monsoon and “dry” SW monsoon). For Rome (Ciampino) the component that dominates in the upper tail is shown to include downbursts from thunderstorms or other strong convective events.

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