# Universal families of Johnson distributions and their use for analysis of time series of surface wind speed

• G.P. Ivus
• E.V. Ahayar
• А.В. Semergei-Chumachenko
• L.M. Hurska
Keywords: Johnson′s family of distributions, series wind speed, statistical parameters, method of moments

### Abstract

Introduction. During the last decades in connection with rapid development of numerical methods of weather forecasting insufficient attention is given physical and statistical regularities. Nevertheless, climate change and its implications for the various sectors of the economy requires information about the probability characteristics of meteorological variables and phenomena, including wind anomaly. In the article it was considered experience of application Johnson′s distributions to equalize time series of surface wind speed in the meteorological station of Odessa-port in the central months of the seasons. Were found a number of regularities that take into account not only the seasonal and diurnal variation of parameters this distribution, but also the impact of physical and geographical conditions of the location meteorological station on the formation of surface wind regime.

The purpose of publication is to substantiation application of Johnson′s law to approximate series of wind speed at the surface on the meteorological station Odessa-port.

Methods and results. To describe the experimental data in various analytical models of the distribution law increasingly applied the family of Johnson's distributions. Its advantage compared to the distribution of the Pearson consists in the fact, that after some transformations, it leads to a normally distributed random variable. Approximation methods based on universal families of distributions provide flexibility solving the problem of alignment of distributions. The most common approaches to the construction of universal families are approaches based on the method of moments, and the replacement of the original sample the other, the distribution of which is the standard. Statistics wind is presented by following parameters: average values of wind speed, standard deviations, coefficients of asymmetry, excess, coefficient of variation and their error. Conducted alignment time series of surface wind speed using Johnson's distribution for station Odessa-port during a period 1981-1990 y.y., which managed to pick up when ε from -0.51 to -8.00. The parameter  λ, which determines the scale of change of the random variable seasonal ranges from 63.56 in January (18 UTC) to 15.77 in October (18 UTC). Estimating shape parameters of wind speed curves η and γ, can reveal some features of the surface wind regime at the st. Odessa port during the year. The less γ, the less slope of the curves. The values of η and γ varies within 0,82-3,54 and 0,24-4,81, respectively. In all cases, λ > 1, indicating that the family of curves belonging SL. The values of Q, which vary from 0.01 to 0.07, confirm the possibility of equalization the series of wind speed at the st. Odessa-port, Johnson's distribution family of SL.

Conclusion. For unimodal distributions of time series wind speed at the meteorological station Odessa-port in almost all cases, possible to use the universal distribution of the Johnson's family SL. The parameters of this distribution allow to reveal regularities, that take into account impact of physical and geographical conditions of the location stations on the formation of surface wind regime.

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Published
2015-11-26
How to Cite
Ivus, G., Ahayar, E., Semergei-ChumachenkoА., & Hurska, L. (2015). Universal families of Johnson distributions and their use for analysis of time series of surface wind speed. Ukrainian Hydrometeorological Journal, (16), 59-66. https://doi.org/10.31481/uhmj.16.2015.08
Section
Meteorology and Climatology