A note on the correlation between circular and linear variables with an application to wind direction and air temperature data in a Mediterranean climate

Abstract

There are several cases where a circular variable is associated with a linear one. A typical example is wind direction that is often associated with linear quantities such as air temperature and air humidity. The analysis of a statistical relationship of this kind can be tested by the use of parametric and non-parametric methods, each of which has its own advantages and drawbacks. This work deals with correlation analysis using both the parametric and the non-parametric procedure on a small set of meteorological data of air temperature and wind direction during a summer period in a Mediterranean climate. Correlations were examined between hourly, daily and maximum-prevailing values, under typical and non-typical meteorological conditions. Both tests indicated a strong correlation between mean hourly wind directions and mean hourly air temperature, whereas mean daily wind direction and mean daily air temperature do not seem to be correlated. In some cases, however, the two procedures were found to give quite dissimilar levels of significance on the rejection or not of the null hypothesis of no correlation. The simple statistical analysis presented in this study, appropriately extended in large sets of meteorological data, may be a useful tool for estimating effects of wind on local climate studies.