Effects of non-stationarity on the magnitude and sign scaling in the multi-scale vertical velocity increment

We study the scaling properties of multi-scale increment series from the stationary and non-stationary vertical velocity records by the detrended fluctuation analysis (DFA) and series decomposition methods, and show the impact of non-stationarity on the magnitude and sign scaling properties. Firstly, we show it is difficult to define a significant scaling range for stationary records themselves. Secondly, for increment series with lag one, the nonlinear correlation found in magnitude fluctuation (i.e. volatility fluctuation) is obvious for both cases. And over the smaller scale range, the linear correlation found usually in the sign series is the same for both cases. However, over the larger scale range, the difference is sharp and marked nonlinear correlation is also incorporated for the non-stationary sign series. Thirdly, with the lags in increment increasing, there exist two scaling ranges in both the magnitude and sign fluctuations. The nonlinear correlation in the magnitude series over both small and large scale ranges decreases with the lags increasing. For the sign series, the linear correlation is dominant over both small and large scale ranges for stationary case; however, the nonlinear correlation can be found over the large scale ranges for non-stationary case and will decrease with lags increasing. The nonlinear correlation found in the sign series over large-scale range is resulted from the modulation of the large scale structures found in the non-stationary data, which will incorporate parts of the magnitude information into the sign series.