Estimators for the Standard Deviation of Horizontal Wind Direction

The standard deviation of horizontal wind direction is a central quantity in the description of atmospheric turbulence and of great practical use in dispersion models. As horizontal wind direction is a circular variable, its standard deviation cannot be directly estimated by on-line methods. For a mathematically strict determination of the angular standard deviation, it is necessary to store all observations and perform off-line calculations. A more practical approach is to calculate on-line moments of linear variables and to parameterize angular standard deviation in terms of these moments. A variety of such estimators is compared by means of a large dataset from an ultrasonic anemometer. The paper systematically investigates which types of linear variables lead to the best estimators and which parameterizations are best within each group of linear variables. Estimators based on moments of the sine and cosine of the wind direction turned out to be most robust. The parameterizations based on an isotropic Gaussian model of turbulence gave the estimators with smallest error within the different groups.