Determination of nonstationarity in turbulence time series using different methods

Stationarity is a fundamental assumption in the statistical investigation of turbulence and the development of similarity theories that are widely used in surface-layer parameterization schemes. Non-stationary time series should therefore be removed from the analysis before assessing turbulence statistics used in similarity theory. In this work we estimate degree of nonstationarity of first- and second-order statistical moments, i.e. means and (co-)variances. Many approaches have been developed over the years to determine nonstationarity of means and (co-)variances but there has been no systematic investigation of the differences and similarities between the approaches.

We contrast several approaches often used in investigation of nonstationarity of surface layer turbulence, including two statistical tests to determine trends, determination of a nonstationarity ratio and determination of differences in turbulence statistics calculated for different averaging times. We apply these approaches to time series of wind and temperature collected during the Terrain-induced Rotor Experiment in Owens Valley during spring 2006. Measurements were made on three 30m towers with 6 levels of ultrasonic anemometers allowing a detailed investigation of turbulence in an area of complex terrain. Our results show that the degree of nonstationarity varies considerably with the used approach. Investigation of the time series that have passed all the tests mentioned above reveals that in many cases such time series still show behaviour indicative of intermittent turbulence, both for stable and unstable conditions. When these tests are combined with an additional condition for intermittency level, rigorous approach for detection of nonstationarity is developed.