Vectorial statistics for the standard deviation of wind direction

The standard deviation of wind direction is an important parameter in atmospheric pollution management. It can be used to calculate the rate of horizontal diffusion and from this the transport and dispersion of air contaminants can be determined. The standard deviation of wind direction cannot be calculated directly from customary linear statistics, mainly because of its periodic nature which makes the zero position arbitrary. Various algorithms have been proposed to estimate its value. The methodologies adopted in meteorology implicitly assume that the wind angle can be treated independently of the wind speed. Such an assumption might not be appropriate in some instances, as will be shown in this work by means of an example. To overcome this limitation, a new algorithm that takes into account both the periodic and the vectorial nature of the wind direction will be proposed. This is done by weighing each sample value with the corresponding wind speed. The results obtained from the new method were compared to those determined from algorithms available in literature using measured data. The comparison indicates that while the behavior is similar, differences do exist. Further investigation indicated that while the differences can be small, they might be physically important.

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