An Integrated Analysis of Stationarity within Time Series

Time-averaged turbulence statistics from field observations are required to educe theoretical relationships and validate numerical simulations. Meaningful time averages rely upon stationary episodes. Previous studies employed various stationarity measures, whereas the relationship between one measure and another when applied to the same time series may vary from one time series to another. In this work, we provide an integrated analysis of four stationarity measures that remain invariant to applying a constant offset to the variable, including 1) the integral time scale, 2) the reverse arrangement test, 3) the run test, and 4) the nonstationarity ratio. We first investigate the response of each stationarity measure to two major causes of nonstationarity, mean trends and periodic variations. The reverse arrangement test only measures the presence of a mean trend, and is used to construct a technique that determines both the occurrence and duration of episodes containing negligible mean trends. Knowing the mean trends a priori enables reliable integral time scale estimates which characterize the most energetic turbulent motions. Combining mean trends with integral time scales provides insights into results from the run test and nonstationarity ratio measures. The integrated analysis of the Canopy Horizontal Array Turbulence Study (CHATS) data suggests that interpreting stationarity measures should always refer back to physical processes. Examples include: 1) turbulence anisotropy, 2) the time lag between a change in mean wind speed and a resultant change in mean shear stress, and 3) the internal gravity waves resulting from the interaction between canopy-shear-layer vortices and strongly stable temperature stratification.