Computations from Elliptical Wind Distribution Statistics

A statistical model of the seasonal-diurnal wind climate at Adelaide

“…This also leads to five parameters: the means, ̅ , ̅ ; the uncorrelated standard deviations, , ; and the rotation angle, . These map directly to the Crutcher and Baer (1962) parameters, but are more physically representative of the elliptical form of the PDF: , is the angle of the major axis, and are the major and minor axis dimensions; and these are more convenient for developing the mathematical theory that leads to the Weibull distribution (Harris and Cook 2014). For convenience, the term "ellipse" is used throughout this paper to denote the elliptical one-standard deviation boundary defined in Figure 2 but also, by implication, the full distribution defined in Eqn.…”

“…In this model, contours of equal probability density appear as concentric ellipses, centred on the mean vector, with their principal axes rotated with respect to the W-S axes (Crutcher and Baer 1962). Joiner (1977a, 1977b) later extended this model to apply in mixed climates, employing the k-means clustering algorithm to sort the observations into k sets of non-overlapping clusters, before computing the five ellipse parameters for each cluster and their relative frequency, f. The k-means algorithm is iterative: (a) k clusters are assumed to exist; (b) initial values are assumed for the centre of each cluster; (c) each observed vector is assigned to the cluster with the closest centre; (d) new values are computed for the cluster centres and steps (b)-(d) are repeated until the parameters no longer change significantly.…”

Wind speed and power density analysis based on Weibull and Rayleigh distributions (a case study: Firouzkooh county of Iran)

“…Finding an appropriate statistical model to describe the frequency distributions of certain given wind regimes is important and for this reason numerous studies has been conducted such as the gamma distribution [9,10], two parameter gamma distribution [11], the three parameter generalized gamma distribution [9,[12][13][14], the inverse Gaussian distribution [15], the generalized normal [16], the log-normal distribution [13,14,[17][18][19], the three parameter lognormal [20], the kappa [16], the wakeby [21,22], the normal two variable distribution [23], the normal square root of the wind speed distribution [24], as well as hybrid distributions [25][26][27].…”

Surface Wind-Speed Statistics Modelling: Alternatives to the Weibull Distribution and Performance Evaluation

“…When wind components are used instead of wind speed, the zonal (west-east) and meridional (south-north) wind components (u and v) are derived from the wind speeds and directions. The wind components are often correlated so we use the procedure described by Crutcher and Baer (1962) to reduce component correlation to zero. The change of variable u → u , v → v , is obtained by a simple rotation of an angle ψ defined by…”