Communications in Nonlinear Science and Numerical Simulation
Multi-scale entropy analysis of vertical wind variation series in atmospheric boundary-layer
Introduction
The atmospheric boundary layer is inherently non-stationary, turbulence time series collected in the atmospheric surface layer over land may often be non-stationary. It has been found that a stationarity test shows that about 40% of the turbulent heat fluxes at Summit, Greenland are classified as non-stationary. Three main factors are explored to account for the large fraction of non-stationary runs: (1) intermittency of turbulence in stable conditions, (2) changes in net all-wave radiation in response to cloud forcing, and (3) diurnal trends in stability [12].
The related concepts of stationarity and the existence and values of integral time scales are central to the ability of analyzing micrometeorological data within the framework of Monin–Obukhov similarity theory and other classical analysis. However, issues related to non-stationarity are not well understood and have only recently received more attention (e.g. Gluhovsky and Agee [15]; Dias et al. [13]; Mahrt [24], [25]). We know little about how to handle or even to judge non-stationarity that we cannot make progress in determining its consequences without a better way to characterize it.
Usually, the non-stationarity is closely linked to the coexistence of eddies of various scales, especially the coherent structures, in the turbulent flow. In studies of atmospheric turbulence, coherent structures are used to denote the distinct large-scale fluctuation patterns regularly observed in a given turbulent flow [31]. In the Ref. [1], the authors found that the preferred regime produces both first-order and second-order non-stationarity, which manifests a change in the series mean and in the variance for a segment of time series, is for the mean to increase while the variance simultaneously decreases. Such behavior is taken as evidence of coherent structures, often seen as ramps [2]. The ramp patterns in scalar traces such as temperature and vapor have been reported both in the unstably stratified surface layer and in the stably stratified surface layer, observations reveal the distinctive features of ramp structure in the turbulence records and surrounding the ramp are the regions of relatively quiescent fluctuations. Therefore, the issue of non-stationarity is also closely related to studies describing the occurrences of intermittent turbulence [14], [24], where intermittency is characterized by brief episodes of turbulence with intervening periods of relatively weak or small fluctuations of motion. In order to explain the turbulence intermittency, the synchro-cascade pattern theory [34] proposed that eddies of various sizes coexist and interweave with each other in each step of the cascade in the space occupied by the fluid, and their nonlinear interaction with each other strengthens or weakens their amplitudes. Thereby the interaction between eddies of various sizes causes strong fluctuations in amplitude with different scales, and then forms intermittency in the fluid turbulence. So the degree of organization of complex eddy motions of various scales is really crucial to the non-stationarity of fluid turbulence.
In this paper, we will seek to quantify the different degrees of organization of complex eddy motions using nonlinear dynamics method to contrast the non-stationarity effect in the vertical wind velocity (w) time series collected in the atmospheric surface layer (ASL). The wind in the atmospheric boundary layer is known to be distinctively turbulent and non-stationary. As a consequence the wind velocity varies rather randomly on many different time scales. In order to capture their multi-scale features, we will adopt the multi-scale entropy to quantify the differences resulted from the different degrees of organization of complex eddy motions, i.e. the non-stationarity effect.
The rest of the paper is organized as follows. In Section 2, we will make a short introduction of the analysis methods and the data sets we used. Results for relationship between Shannon entropy distribution and increments of different scales for stationary and non-stationary turbulent vertical wind-velocity series are provided in Section 3. In Section 4, we make some discussion and the conclusions are summarized.
Section snippets
Data
In this paper, atmospheric boundary-layer turbulence records collected during the experiment in Huaihe River Basin (HUBEX) between June 5 and June 22 in 1998 are used in the analysis. Huaihe River basin is situated between Yangtz River and Yellow River with a total area of 270,000 km2. It represents the typical climate condition in the East Asia monsoon region, and effects of human activity are relatively slight. The observation site was in the yard of the Shouxian Meteorological Observatory in
Non-stationary characteristics
First of all, we can see the obvious difference between the stationary and non-stationary turbulent vertical wind velocity records from the observational series directly, see Fig. 4, where both the original records and their increment records with different scale factors, where scale factor h defined as , , have been presented. For the original records, compared to stationary wind velocity variations, there are more dominant large scale structures in the non-stationary ones.
Conclusion and discussion
The wind in the atmospheric boundary layer is known to be distinctively turbulent and non-stationary. As a consequence, the wind velocity varies rather randomly on many different time scales. One of the most striking features is the PDFs of the observed atmospheric increment show robust (stretched) exponential tails that decay faster than a power-law and slower than a Gaussian distribution [7], [8], [11], [16], [21]. Nevertheless, for most technical and meteorological problems fluctuations as
Acknowledgement
Many thanks are due to supports from National Natural Science Foundation of China (No. 40975027). The valuable comments and suggestions from the anonymous reviewers are appreciated and helpful in further improving the manuscript.
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2018, Physica A: Statistical Mechanics and its ApplicationsCitation Excerpt :Therefore, characterizing the dynamic behavior underlying the wind field is still a challenging task in need of further studies. The experimental exploration of wind signals has attracted considerable interest on account of its significant importance, and many researchers have made fruitful achievements from different aspects [7–13]. In their studies, numerous methods have been applied to characterize the fluctuation of wind signals, such as power spectral density function [7], statistical analysis [8], support vector machine [9], clustering analysis [10], wavelet transform analysis [11], complexity analysis [12,13], etc.