Response of wind speed probability distribution parameters to urban expansion

Abstract

Recent studies have indicated that wind speed probability distribution can be described closely using three-param- eters Weibull distribution, which has come to be widely used in the description of wind speed probability distribution over the past several years. The fitting effect of probability density curve would be better than the universal three-parameter Weibull distribution in calm wind by changing the universal three-parameter Weibull distribution function definition domain condition [ r , ∞) to a limited three-parameter Weibull distribution function definition domain [0, ∞), which would be more applicable to actual wind speed distribution. Timely observation wind speed of Beijing, Nanjing, Guangzhou, and other 5 large urban stations and their comparative county stations, and corresponding NCEP/NCAR Reanalysis-1 wind speed data collected from 1985–2014 were divided into sets, each of which had an average of six periods. The three parameters ( k , c , r ) of Weibull distribution of wind speed probability distribution are fitted using numerical iteration to analyze the changes in wind speed probability distribution parameters with respect to differences in wind speed section, and synthetic variations of those parameters can reflect changes in different wind speed sections, such as calm wind, light wind, and strong wind probability under urbanization, which can provide thorough understanding of the relationship to city size indexes and wind speed probability distribution parameters. Data analysis and mathematical derivation were here used to draw the following conclusions: (1) the relationship of urban-rural wind speed difference D and rural wind speed V x can be expressed as D = b 1 V x + i . Under these conditions, city wind speed parameters k , c , and r and the corresponding rural wind speed parameters c x , k x , and r x have the following relationship: c =( b 1 + 1) c x , r =( b 1+1) r x + i , k = k x . (2) As shown, parameter c is affected by unitary surface friction function, parameter r by the combination of various kinds of factors, and the change in parameter k is only an expression of climatic random fluctuation produced by constructing relative variables of c / c x = b 1 + 1, r / r x = b 1+1+ ir x , k / k x =1. (3) It has a correlation with the degree of variation in wind speed probability distribution parameters and the speed of city expansion. Urbanization resulted in significant variations in location parameter r , scale parameter c comes second and shape parameter k did not show any significant changes. (4) Parameter c decreased with city build-up area enlarges. Seven stations’ regression equations pass the significant tests and the variation rates are between −0.0203–−0.0016 km−2, which means that the expansion of city scale will narrow the distribution range of the wind speed probability density curve. Parameter r presents a rising trend (the value changes from negative to positive) along with the extension of city build-up area. Six stations’ regression equations showed significant results, and the rates of variation were between 0.0014 and 0.0171 km−2, which indicated that the likelihood of calm wind decreased as the urban area expanded. Analysis also showed a close relationship between parameter r and latitude. (5) Using reanalysis data to fit the comparison parameters c x and r x produced the relative variable c / c x , and r / r x , analyses showed results similar to the consequences of c and r . Shape parameter k showed a non-significant relationship with the city size index in comparison.