Multi-scale entropy analysis of vertical wind variation series in atmospheric boundary-layer

• Classical methods can not quantify effect of non-stationarity on statistics.
• MSE is an indicator to distinguish stationary from non-stationary velocity data.
• MSE can quantify the organization level of multi-scale motions.

Turbulent vertical wind variation records in atmospheric boundary-layer have been analyzed in this study. By means of space time-index (STI for short) method, vertical wind variation records can be classified as stationary and non-stationary. And then among these vertical wind velocity records, ten most stationary and ten most non-stationary records are chosen as two contrast groups for further analysis. Multi-scale entropy (MSE for short) analysis has been applied to quantify the increments of these two groups of wind-velocity records with different time lags. And marked differences are detected between non-stationary and stationary series, the entropy for the increments of stationary vertical wind records is larger than that of non-stationary ones when the time lags are smaller. So over certain range with small values of scale factor, the MSE can be taken as an indicator to quantify the different levels of eddy organization between the stationary turbulent vertical wind records and those non-stationary ones.