An adaptive segmented stationary method for non-stationary signal is proposed to reveal the turbulent kinetic energy evolution during the entire sandstorm process observed at the Qingtu Lake Observation Array. Sandstorms, which are a common natural disaster, are mechanically characterized by a particle-laden two-phase flow experiencing wall turbulence, with an extremely high Reynolds number and significant turbulent kinetic energy. Turbulence energy transfer is important to the understanding of sandstorm dynamics. This study indicates that large-scale and very large-scale coherent structures originally exist in the rising stage of sandstorms with a streamwise kinetic energy of 75 % (at

Sandstorms are devastating natural hazards and one of the main global environmental problems which accelerate the expansion of desertification

At the beginning of a sandstorm, the local wind velocity gradually increases, and sand particles on the ground are carried away by the strong wind, which increases the particle concentration in the atmospheric surface layer (ASL). After the wind velocity gradually increases to reach a plateau, a steady state is usually maintained for a period of time, which is a steady turbulence signal that has been widely considered. Subsequently, the wind velocity decreases until it approaches zero, and the sand particles sink to the ground under the action of gravity

There are few analyses on the evolution of turbulence characteristics during the entire sandstorm process because the rising and declining stages are non-stationary signals whose statistical characteristics are a function of time. For non-stationary signals, researchers hope to utilize an analysis method that combines the time domain and frequency domain, which can reflect not only the frequency information but also the changes in frequency over time. Therefore, the local transform method is adopted to overcome the faults of the Fourier transform due to globality and thus solve the challenge of analyzing and processing non-stationary signals. In 1946,

Therefore, this study aims to propose a method that can be used to analyze the entire process of sandstorms, including the non-stationary rising and declining stage. On this basis, the difference in energy characteristics of sandstorms at different stages and their evolutionary laws are investigated using high-frequency wind velocity observation data during a complete sandstorm event obtained from long-term observations in the high Reynolds number ASL on the desert surface.

The sandstorm data used in this study were obtained from long-term observations conducted at the Qingtu Lake Observation Array (QLOA) site in western China. The site is located in a flat dry bed of Qingtu Lake, which borders the two deserts of Badain Jaran and Tengger, as shown in Fig. 1a. The area is perennially dry and rainless, with no vegetation covering the ground, and is on the path of cold air traveling northwest through China. Therefore, the cold front transit caused by the outbreak of cold air can form a strong wind in the region, which leads to frequent sandstorms in spring in the area. At the same time, the cold front transit is a regional weather process, and the control effect of the large weather system causes the strong wind to exhibit a relatively stable propulsion velocity and direction; thus, high-quality data for the entire sandstorm process can be obtained at the QLOA site.

The QLOA is composed of a 32 m high main tower and 22 lower towers that are 5 m in height. There are 10 streamwise towers in the prevailing wind of the main tower and 6 spanwise towers on the left and right sides of the main tower, as shown in Fig. 1b. Eleven sonic anemometers (Campbell CSAT3B, with a sampling frequency of 50 Hz) were installed on the main tower from 0.9 to 30 m in a logarithmic gradient, and 11 aerosol monitors (TSI, Dustrak II-8530-EP, with a sampling frequency of 1 Hz) for particles with sizes less than 10

To date, continuous ASL observations were performed at the QLOA over a duration of more than 8000 h. From 16 to 17 April 2016 a severe sandstorm occurred in the observation field. The QLOA captured the sandstorm event and obtained high-quality data during the complete process. The sandstorm started at 13:00 local time on 16 April and ended at 03:00 on 17 April, and lasted for 14 h, as shown in Fig. 2. The streamwise velocity at 5 m shown in Fig. 2a indicates that this sandstorm exhibits obvious rising, steady, and declining stages. The duration of these three stages is approximately 5, 7, and 2 h, respectively. At the steady stage, the average wind velocity was 11.26 m s

To clarify the cause of the sandstorm, the weather conditions and potential meteorological drivers were also investigated. From 16 to 17 April 2016, the average circulation in the midlatitudes to high latitudes of Eurasia turned into two troughs and one ridge. The midlatitudes to high latitudes from the Ural Mountains to Lake Balkhash were broad ridges, and northern Europe and the vicinity of the Okhotsk Sea were controlled by low-value systems. From the daily circulation evolution, affected by the westerly trough, plateau trough, and south branch trough, surface cyclones moved eastward and developed in Northwest China from 14 to 16 April. There was a cold air process with a low trough moving eastward from 16 to 17 April. Decreasing temperature occurred in the eastern part of Northwest China, accompanied by four to six northerly winds and seven to eight gusts. At the same time, under the influence of the ground cold front and the Mongolian cyclone, sandstorms occurred locally in northwestern and northern China.

The field observational site and measurement array:

The friction Reynolds number (

Given the complexity and uncontrollability of the atmospheric environment, specific pretreatment are performed on the raw data to obtain reliable results of turbulent characteristics in high Reynolds number ASLs. Following

The non-stationary index IST proposed by

Therefore, non-stationary signal processing methods are needed. The existing method of the non-stationary signal is used to analyze the time–frequency distribution, and it is not sufficient for exploring the turbulence signals. The statistical characteristics of turbulence are of greater concern, such as bispectrum

To extract the time-varying mean value, the EMD is a widely applied signal analytical method, which can decompose a multicomponent signal

The fluctuating streamwise velocity after removing the time-varying mean extracted by the EMD is shown in Fig. 2b. It is seen that the non-stationarity of the data is reduced, but it is not eliminated. Therefore, an adaptive segmented stationary method is proposed in this study based on the non-stationary index, which is detailed as follows.

After applying the data processing procedure, the sandstorm is divided into 14 segments, where the rising stage is divided into five segments (60, 55, 60, 80, and 45 min), the declining stage is divided into two hourly time series, and the steady stage is divided into seven hourly time series following standard practice in the analysis of ASL data

Turbulent coherent structures are responsible for the production and dissipation of wall turbulence and thus are important to understanding turbulence dynamics

Figure 3a–c show the pre-multiplied spectra of the streamwise velocity fluctuations

In addition, the spectral turbulent energy

Pre-multiplied spectra of streamwise velocity fluctuations

Figure 4a shows the wavelength variation in the lower wavenumber peak in pre-multiplied spectra with the height in the steady stage (blue solid circle). For comparison, Fig. 4a also includes the results in the laboratory turbulent boundary layer. The wavelength corresponding to the pre-multiplied spectral peak agrees well with the results in the laboratory turbulent boundary layer at low and moderate Reynolds numbers. Previously reported results indicated that the sand particles and Reynolds number exhibit negligible effects on the wavelength of the spectral peak

To analyze the differences in the energy contributions of the VLSMs at different stages of sandstorms, the variations in the energy fraction of the VLSMs with height at different stages is shown in Fig. 5, where the yellow cycle is the result in a sand-laden flow available in

In addition, Fig. 5 shows that the VLSM energy fraction increases with height in an approximately log-linear trend at different stages, which is qualitatively consistent with the results in the laboratory turbulent boundary layer

Variations in the energy fraction contributed by VLSMs to the total streamwise turbulent kinetic energy with height at different stages of sandstorms. The gray star is the result of

Affected by the cold front transit when a sandstorm occurs, the atmospheric flow in the local area changes dramatically, which could result in gales and unstable atmospheric stratification, and the particles at the surface are carried into the air. Moreover, the cold air mass transfers energy to the local atmosphere

The bispectra of the streamwise velocity fluctuations in different stages of a sandstorm are shown in Fig. 6a–c. It is seen in Fig. 6a–c that the contour maps of the bispectra in different sandstorm stages are basically the same. The large bispectrum values are concentrated in the low-frequency region. A large bispectrum value represents a strong nonlinear interaction between these frequencies of fluctuations, leading to a breakdown of the structure into smaller scales

Color contour maps of bispectra of the streamwise velocity fluctuations

As an example, the two-dimensional contour map of the evolution of the integral bispectrum with time at the height corresponding to the logarithmic region center (

Two-dimensional contour map of the evolution of the integral bispectrum with time at the height 8.5 m, where the height 8.5 m corresponds to the logarithmic region center and the blue dashed line represents the cutoff frequency converted from the wavelength of

The integral bispectrum shown in Fig. 7 is integrated again in the region below and above the blue dashed line to obtain the total nonlinear interaction occurring in LSMs and VLSMs and small-scale structures (

Figure 8a shows that the integral bispectra value of LSMs and VLSMs is relatively large and is positive during the rising stage of the sandstorm, which means that the LSMs and VLSMs gain energy from the nonlinear interaction. In the steady and declining stages, the integral bispectra value fluctuates around zero. That is, after the sandstorm gains energy in the rising stage and develops to a steady state, the energy maintains a balanced budget during the weakened nonlinear interaction process. Furthermore, when integrating the positive and negative bispectra values separately, Fig. 8b and c show that the absolute values of the input and output energy from the nonlinear interaction increase with height, but the increasing trend becomes less noticeable with the increased height. A plausible explanation for the varying bispectra values with height can be derived from the LSM and VLSM production mechanism. The LSMs and VLSMs in the ASL are dominated by the top–down mechanism. The larger synoptic-scale fluctuations input energy into the upper boundary layer and break down due to a strong quadratic phase coupling with downward transmission, which causes the nonlinear energy transfer between different scales to be more active. With decreasing height, the influence of the top–down mechanism gradually weakened, resulting in the decreased degree of nonlinear interaction.

For the nonlinear energy transfer of the small-scale motions (

In addition, by summarizing the phenomenon shown in Fig. 8b, c, e, and f, it is found that the overall integral bispectrum value being positive is a phenomenon unique to the rising stage of sandstorms, and the monotonic decrease in the absolute value of positive or negative bispectrum integrals with time is a unique phenomenon in the declining stage of sandstorms. Therefore, a new criterion for dividing the sandstorm into different stages may be presented, that is, when the overall integral bispectra value is positive, which is the rising stage of the sandstorm, and when the bispectra absolute value integral decreases monotonically with time, which is the declining stage of the sandstorm.

Evolution of the total integral bispectra.

The positive and negative integral bispectra for LSMs and VLSMs and small scales at different stages are averaged to investigate the variations in the average integral bispectrum with the height, as shown in Fig. 9, where Fig. 9a shows the LSM and VLSM results and Fig. 9b shows the small-scale motion results. As expected, the absolute of the average integral bispectra for LSMs and VLSMs exhibits a gradually slowing increase with height; i.e., the increase in the average integral bispectra is pronounced near the surface and appears to level off as the center of the logarithmic region (

Variations in the average integral bispectra.

Combined with the previously documented reports on sandstorms from the perspective of meteorology, the dynamic characteristics in the entire sandstorm process can thus be summarized. The larger synoptic-scale fluctuations input energy into the upper boundary layer. This heralds the beginning of a sandstorm. With the sandstorm occurring, the cold air would sink close to the surface

This work studies the evolution of turbulent characteristics during an entire sandstorm process and establishes a relationship between turbulent characteristics and the macro-dynamic characteristics in meteorology. It is a new perspective for further insight into sandstorms, and thus needs more systematic and comprehensive research, such as other turbulence characteristics including the morphology and dynamics of turbulent structures and the interaction between multi-scale turbulent motions, rather than just energy. Moreover, experimental uncertainties are inevitably associated with these ASL measurements; however, it appears that the ASL measurements can be used as a representation of the very high Reynolds number behavior.

To investigate the entire sandstorm process (including the rising stage, the steady stage, and the declining stage), i.e., a typical complex non-stationary wind-blown-sand two-phase flow, an adaptive stationary segmentation method based on the IST index and the EMD is proposed, and this method is applied to separate the wind velocity series of a sandstorm. On this basis, the pre-multiplied spectra and bispectrum are obtained from the streamwise velocity fluctuations during the sandstorm.

In the rising stage of the sandstorm, the large coherent structures originally exist rather than gradually forming. The energetic structure in the flow field is dominated by VLSMs, and the turbulent kinetic energy fraction of the VLSMs may reach up to 75 % (at

In the steady stage, there is still quadratic phase coupling in the low-frequency large-scale fluctuations, but it is relatively weaker than that in the rising stage. The weakened nonlinear interaction process does not change the energy budget of turbulent motions of different scales. In addition, the results of the pre-multiplied energy spectrum agree well with the existing results in the laboratory turbulent boundary layer and the ASL, which confirms the reliability of the analysis method proposed in this study.

During the declining stage, the wind velocity decreases, and the VLSMs cannot retain their coherence. The energy fraction of VLSMs is the smallest during the sandstorm, accounting for only approximately 40 % (at

The data that support the findings of this study are available in the Zenodo data repository (

The supplement related to this article is available online at:

XZ designed and organized the research and its approach. HL analyzed the results, wrote the paper, and carefully modified the paper. YS carried out the field observations, analyzed the data, and performed the spectrum calculations. All authors contributed to the paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This study was supported by grant from the National Natural Science Foundation of China (92052202). The authors would like to express their sincere appreciation for the support.

This research has been supported by the National Natural Science Foundation of China (grant no. 92052202).

This paper was edited by Peter Haynes and reviewed by Hosein Foroutan and one anonymous referee.