Upper winds over the world: Part I. The frequency distribution of winds at a point in the free air

Abstract

BROOKS, I).SC., c'. 5 . L)lRST, B.A., and N. C.\KKCiTHIiRS, c . 5~ 1 . INTHOI~TCTION FCEE AIKFor the greater part of tho world, data of wind direction and velocity in the free air a r e very scanty or non-existent. In many countries pilot balloon observations have been taken for many years, but the wind roses obtained lrom these are inaccurate and misleading for two reasons: (a) because data are obtained only for days on which the balloon was not hidden by cloud ; and (b) because with increase of height fewer and fewer occasions of strong winds are included owing to the disappearance of the balloon in the dis ta m e . l l i t h radio methods of observation the first of these limitations is completely and the second partially overcome, but as yet the radio wind stations are too few, and have been in operation for too short a time, to describe the general circulation of the atniospherc at great hcights. To collect the necessary information will take many years, but it is thought that in the meantime a n extrapolation can t e effected by the use of thc data at present available. The object of the present paper is t c show that, given the resultant direction and velocity of the wind a t i i point in the free air and sonic measure of the scatter of the individual observations about the resultant, it is practicable to coastruct a wind rose to show the frequency distribution of winds of different directions and velocities which \\.auld be given by a long series of observations. The resultant tlirection and velocity, and the scatter, can be derived from a relatively short series of data with much greater accuracy than the frequencies of observations falling i n individual cells of direction and velocity, which generally give a rather irregular distribution, so that such a reconstruction is in effect a "smoothing" process. It is strictly analogous to the representation of the ideal distribution of a series of, e.g. temperatures, by a frequency curve constructed from the mean and standard deviation o f the series. The quesiion of the estimation of the resultant wind and scatter, when no actual wind observations arc available in the free air, is left to a subsequent paper. 2.'I'IIE TYPE O F FREQVI-A'CY DISTIIIBVTIOS IX A N'VIKD ROS1,:

Parameterizing the seasonal–diurnal wind climate of Rome: Fiumicino and Ciampino

“…Carta et al (2008) and Han et al (2018) are amongst the few studies that assess wind speed and direction together as a vector using their joint distribution p(V,θ). Brooks et al (1946) were the first to suggest that the horizontal wind vector should be resolved into two orthogonal components which avoids issues with the circularity of θ. They assumed that each component was formed by the sum of random eddies and, hence, was Normally distributed.…”

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

“…Brooks et al (1946) parameterised short-duration balloon sonde and surface observations, by resolving the horizontal wind vector into orthogonal x and y components acting around the mean vector, on the assumptions that both components were normally distributed and uncorrelated, with means,  x and  y , and equal standard deviations,  x =  y . In the Brooks model, contours of equal joint probability density function (jPDF) appear as concentric circles around the mean vector in the vector plane.…”

Consolidation of analysis methods for sub-annual extreme wind speeds

“…An early attempt to formulate a model for this parent was made by Brooks et al (, ). They suggested that the wind vector be resolved into orthogonal x and y components relative to a set of arbitrarily oriented Cartesian axes, each component Normally distributed and mutually independent.…”