On the Algorithms Used to Compute the Standard Deviation of Wind Direction

Abstract

The standard deviation of wind direction is a very important quantity in meteorology because in addition to being used to determine the dry deposition rate and the atmospheric stability class, it is also employed in the determination of the rate of horizontal diffusion, which in turn determines transport and dispersion of air pollutants. However, the computation of this quantity is rendered difficult by the fact that the horizontal wind direction is a circular variable having a discontinuity at 2p radians, beyond which the wind direction starts again from zero, thus preventing angular subtraction from being a straightforward procedure. In view of such a limitation, this work is meant to provide new mathematical expressions that simplify both the computational and analytical work involved in handling the standard deviation of wind direction. This is achieved by deriving a number of Fourier series and Taylor expansions that can represent the minimum angular distance and its powers. Using these expressions, the relation between two algorithms commonly used to determine the standard deviation of wind direction is analyzed. Furthermore, given that these trigonometric expansions effectively reduce the mathematical complexity involved when dealing with circular statistics, their potential application to solve other problems is discussed.

Surface Wind Direction Variability

“…These discontinuity crossings in the time series of wind direction become common with weak winds. Such problems are extensively discussed in Farrugia et al (2009) along with approximate solutions. The current study focuses on wind direction changes between subsequent time intervals, which do not encounter such difficulties.…”

The Performance of Different Boundary-Layer Parameterisations in Meteorological Modelling in a Southwestern Coastal Area of the Iberian Peninsula

“…The bias score (BIAS), which measures the tendency of a model to systematically overestimate or underestimate a parameter, was also calculated. To analyse the performance of each ABL scheme with regard to wind direction, the minimum angular distance of wind direction was calculated using the criteria described in [28]. A simulation of 3 days (72 hours) was performed for each scenario.…”

Uma Análise da Aplicação de Três Métodos Estatísticos para o Cálculo do Desvio Padrão da Direção do Vento na Região Tropical

“…Por isto, métodos estatísticos padrões comumente aplicáveis a conjuntos de dados lineares não devem ser utilizados, requerendo um tratamento especial. Para resolver este problema, diversos algoritmos já foram propostos para o cálculo da média e/ou do desvio padrão de variáveis circulares, tais como aqueles descritos em Verrall e Williams (1982), Ackermann (1983) e Yamartino (1984, citados, por exemplo, em Turner (1986), Weber (1997, Farrugia e Micallef (2006, 2009, Namboodiri et al (2014), entre outros. Apesar de se tratarem de publicações antigas, estes trabalhos devem ser valorizados como clássicos do tratamento matemático do vento.…”

“…Exemplos importantes de aplicabilidade do desvio padrão do vento estão relacionados em problemas de turbulência atmosférica e de transporte e dispersão de materiais devido à difusão inerente ao movimento do ar. (Weber, 1997;Farrugia et al, 2009). Segundo Mahrt (2011), é possível analisar a intensidade da turbulência pela variabilidade da direção do vento.…”