Não-estacionariedade de séries temporais turbulentas e a grande variabilidade dos fluxos nas baixas freqüências

Abstract

Turbulent flow high complexity makes it difficult to describe complex phenomena, such as the transport of vector and scalar quantities at the lower atmosphere, making the analysis of experimental data, such as time series, largely employed. The method mostly used by the micrometeorological community to quantify such turbulent transport is associated with the determination of the statistical covariance between two variables. It is known that the determination of statistical quantities for very long temporal windows leads to a large flux uncertainty. At the same time, the theory indicates that the association between fluxes and statistical covariance is only valid for temporally stationary series. The aim of the present study is to test the hypothesis that the estimate uncertainty is directly related to the series non-stationarity. To better understand this issue, we use a methodology based on a group of parametric and nonparametric statistical tests. The tests considered here are the T-test, F-test, median test, U-test and run test. Furthermore, the test results are compared with the outputs of two signal decomposition procedures: multiresolution analysis and empirical mode decomposition. The results suggest that the flux variability over large temporal scales characterizes the existence of temporal trends and low frequency components in the time series considered, so that it is more associated with an observational limitation of the analysis than with non-stationarity, as this concept should be the property of an ensemble, rather than of a single realization. Such limitation suggests the definition of a practical single order stationarity, associated with temporal trends and low frequency components whose energy is similar or larger to that of the turbulent fluctuations. For that reason, we affirm that the interactions test is, among all considered, the best suited for analyzing atmospheric data, because it is the most sensible to the existence of temporal trends. Furthermore, such test allows obtaining a temporal scale beyond which mesoscale events become important.