The Use of the Weibull Distribution for Thunderstorm Parameters

T. Schütte Institute for High Voltage Research, Husbyborg, S-755 90 Uppsala, Sweden

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O. Salka Institute for High Voltage Research, Husbyborg, S-755 90 Uppsala, Sweden

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S. Israelsson Institute for High Voltage Research, Husbyborg, S-755 90 Uppsala, Sweden

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Abstract

Most observations in thunderstorm statistics are positive, having values between 0 and ∞. Since they are of a “duration-length” type. the normal distribution is not, in most cases, a satisfactory approximation. A widely used model is the lognormal distribution. It has the advantage of easy calculation of the distribution parameters, but, as most statistical distributions, it has the disadvantage of a nonanalytic cumulative distribution function.

In the present paper, we describe how the Weibull distribution can be used to estimate some characteristics related to thunderstorms. Examples of the calculation of some further properties assuming Weibull-distributed observations are also given.

From a theoretical point of view, the use of the Weibull distribution seems to be reasonable. It is a good model for describing electrical breakdown in insulating materials, and a lightning discharge is, indeed, such a breakdown.

Abstract

Most observations in thunderstorm statistics are positive, having values between 0 and ∞. Since they are of a “duration-length” type. the normal distribution is not, in most cases, a satisfactory approximation. A widely used model is the lognormal distribution. It has the advantage of easy calculation of the distribution parameters, but, as most statistical distributions, it has the disadvantage of a nonanalytic cumulative distribution function.

In the present paper, we describe how the Weibull distribution can be used to estimate some characteristics related to thunderstorms. Examples of the calculation of some further properties assuming Weibull-distributed observations are also given.

From a theoretical point of view, the use of the Weibull distribution seems to be reasonable. It is a good model for describing electrical breakdown in insulating materials, and a lightning discharge is, indeed, such a breakdown.

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