Comparative analysis of estimators for wind direction standard deviation

P. S. Farrugia a1 and A. Micallef a1
a1 Department of Physics, University of Malta, Msida MSD 06, Malta Email:;

Article author query
farrugia ps   [Google Scholar] 
micallef a   [Google Scholar] 


Wind direction is a circular variable. This makes the algorithms used to find its standard deviation different from that of the linear variables. In particular, the requirement for storing all the data points before the standard deviation can be computed limits the storage capacity and puts great strain on remote data acquisition systems. Various algorithms have therefore been developed to estimate the standard deviation in order to reduce the number of terms stored. The following work consists of a comparative analysis of such estimators together with the parameters used. It emerges that some of the assumptions adopted to produce the equations being analysed do not hold in practice, even though this does not affect significantly the performance of the estimators that depend on them. On the other hand, the parameter that has the best trend with the algorithm adopted is the magnitude of the vector to the centre of gravity of the system. However, such a result gives rise to some concerns since it does not account for the ‘vectorial’ nature of the angle being treated.

(Received January 2004)
(Revised September 2005)

Key Words: wind direction; estimator; angular standard deviation; circular variables.