Atmospheric turbulence parameters, such as turbulent kinetic energy and dissipation rate, are of great significance in weather prediction, meteorological disasters, and forecasting. Due to the lack of ideal direct detection methods, traditional structure function methods are mainly based on Kolmogorov's assumption of local isotropic turbulence and the well-known

Turbulence is the main form of motion in the atmospheric boundary layer. It plays a major role in the transportation and exchange of momentum, heat, water vapor, and matter between the surface of the Earth and the atmosphere, directly affecting human life and production activities and playing a crucial role in atmospheric motion and weather evolution (Byzova et al., 1989; Stull, 1988; Gottschall and Peinke, 2008). At present, there are still many difficulties related to the study of turbulence, and addressing them requires improvements in observational technology. Therefore, the development of atmospheric turbulence detection technology can strengthen our understanding of atmospheric turbulent motion and accelerate the development of atmospheric turbulence theory. In atmospheric modeling in particular, it is of great significance to obtain the relevant parameters and structural characteristics of atmospheric turbulence (Banakh and Smalikho, 2013).

In the past, there were few detection methods for measuring or inferring low-level turbulence parameters, mainly through the installation of three-dimensional ultrasonic anemometers in meteorological gradient towers (Sathe and Mann, 2013). The detection height, density, and detection ability of the detectors were limited, which hindered the development of boundary layer turbulence theory. Fortunately, with the development of remote sensing technology, as an active remote sensing device with fast response speed and three-dimensional scanning ability, coherent Doppler wind lidar has gradually become the main means of obtaining low-level atmospheric turbulence intensity (Mann et al., 2010; Choukulkar et al., 2017; Bonin et al., 2017, 2016; Jin et al., 2022; Smalikho et al., 2005; Branlard et al., 2013; Banakh et al., 2021; O'Connor et al., 2010).

According to Kolmogorov's theory of local homogeneity and isotropy, the structure function can only be determined by the kinetic energy dissipation rate (Kolmogorov, 1941; Kolmogorov, 1991). Therefore, the structure function can be calculated based on the wind speed fluctuation term, and the kinetic energy dissipation rate can in turn be estimated based on the relationship between the structure function and the kinetic energy dissipation rate given by a statistical turbulence model (Sathe and Mann, 2013). It is called the structure function method, which is an indirect method. Based on this principle, researchers have proposed different acquisition methods. In 2002, Frehlich and Cornman obtained the spatial statistical characteristics of a simulated turbulent velocity field using radial velocity estimation from coherent Doppler lidar data and subsequently calculated the turbulent energy dissipation rate (Frehlich and Cornman, 2002). In 2005, Smalikho et al. (2005) used coherent wind lidar to invert atmospheric turbulence parameters with two methods, i.e., the Doppler spectral width and height structure function, using the range height indicator (RHI) scanning mode. The experimental results were numerically simulated, which confirmed the reliability of these two methods (Smalikho et al., 2005). In 2008, Frehlich and Kelley obtained turbulence parameters in the boundary layer using longitudinal and transverse structure function methods in the plane position indicator (PPI) scanning mode with fixed pitch angle and changing azimuth angle (Frehlich and Kelley, 2008). The inversion results were compared with the detection results of ultrasonic anemometers, and the data consistency was good. In 2012, Chan and Lee divided radial wind field data into subsectors under the PPI scanning mode and calculated the turbulence dissipation rate within each subsector using velocity structure functions, thus obtaining the spatial distribution of the turbulence dissipation rate (Chan and Lee, 2012). In 2017, Smalikho and Banakh used the azimuth structure function in the velocity azimuth display (VAD) scanning mode to invert atmospheric turbulence parameters and extended the applicability of this method from the convective boundary layer to the stable boundary layer (Smalikho and Banakh, 2017). From 2017 to 2019, Zhai et al. (2017) studied the vertical structure characteristics of turbulence in the atmospheric boundary layer using various lidar observation models such as the VAD, PPI, and RHI (Zhai et al., 2017). They analyzed interaction characteristics between a wind turbine wake and atmospheric turbulence under the influence of underlying surfaces with different roughness and explored the influence of atmospheric turbulence on the evolution process of aircraft wake vortices. In 2023, Wang et al. (2023) used shipborne coherent Doppler lidar to measure the energy dissipation rate and wind shear intensity of turbulent flows at sea based on the structure function method, achieving the classification of turbulent mixing sources (Wang et al., 2023). These previous studies are based on the indirect acquisition of atmospheric turbulence parameters using a structure function, which in turn relies on the assumptions of isotropy and a power-law exponent of

Due to the extremely complex turbulence in the atmospheric boundary layer, the assumptions of isotropy and the

Layout diagram

The Shenzhen Shiyan Observation Base (22.65562° N, 113.90586° E) has a 356

Performance parameters of the ultrasonic anemometer and wind lidar instrument.

The values of turbulence parameters are extremely dependent on the precision of wind speed measurements, obtained as a time series, and the presence of too many abnormal signals can lead to the inference of abnormal turbulence parameters. Therefore, it is necessary to conduct data quality control to ensure the reliability of the observed data. For the wind lidar data, an overall inspection was conducted on the wind speed measurements every 30

The analysis of atmospheric boundary layer turbulence fluctuations, such as correlation analysis and spectral analysis, is based on the assumption that atmospheric turbulence fluctuations are stationary. The actual atmospheric turbulence field is influenced by various factors and does not have stationarity characteristics (Massman, 2006). However, if a shorter observation time is used, under relatively stable weather conditions and flat underlying surface conditions, atmospheric turbulence can be approximated as static. Turbulence stationarity requires that the main statistical variables of turbulence remain stable within the observation time; that is, the mean of the variance of the entire time period within an observation time period is roughly equal to the mean of the sum of variances of each period (Massman, 2006). In this study, data screening is conducted by determining whether the deviation between the mean variance within a 30

Comparison of the turbulence spectra obtained with the wind lidar and the ultrasonic anemometer in three directions:

The three-dimensional wind speed measured by the wind lidar and ultrasonic anemometers can be represented as

Comparison of the turbulent kinetic energy obtained from the wind lidar and three-dimensional ultrasonic anemometer on 1 January 2022 in the

By taking the logarithm of both sides of Eq. (

According to Eq. (

The slope can be obtained by performing linear fitting on

When

Temporal and spatial variations in the turbulent kinetic energy obtained by wind lidar on 1 January 2022 in the

Compared with traditional structure function methods that rely on the assumption of isotropy and the

We compared the wind speed data of the wind lidar at a height of 330

Power-law exponent profile of the wind speed in different directions with altitude on 1 January 2022 at

Temporal and spatial variations in the turbulent kinetic energy obtained by wind lidar on 11 September 2022 in the

Comparison of the turbulent kinetic energy obtained by the wind lidar and three-dimensional ultrasonic anemometer on 11 September 2022 in the

Using the method proposed in Sect. 3.2, based on the high-resolution wind lidar data, we obtained the kinetic energy and power-law exponent at different heights; here a height of 330

Temporal and spatial variations in the turbulent kinetic energy obtained by wind lidar on 14 January 2022 in the

On this basis, we produced spatiotemporal distribution maps of the turbulent kinetic energy and power-law exponent, as shown in Fig. 4, where panels Fig. 4a–c correspond to wind speed components

Furthermore, we present the derived power-law exponent profile in the three different directions at different local times on 1 January 2022 in Fig. 5. From the graph it can be seen that the power-law exponent changed similarly in the

Comparison of turbulent kinetic energy obtained by the wind lidar and three-dimensional ultrasonic anemometer on 14 January 2022 in the

To verify the effectiveness of the proposed method under different weather conditions, Fig. 6 shows the spatiotemporal variations in the turbulent kinetic energy and the power-law exponent on 11 September 2022. The weather on this day was clear and cloudless, with an average temperature of 27

Comparison of the turbulent kinetic energy obtained from the wind lidar and three-dimensional ultrasonic anemometer from 2 to 10 January 2022 in the

Figure 8 shows the spatiotemporal variations in the turbulent kinetic energy and power-law exponent on 14 January 2022. On that day, the weather was cloudy with an average temperature of 13

Figure 10 shows a comparison of the long-term, continuous turbulent kinetic energy obtained from the wind lidar and three-dimensional ultrasonic anemometer from 2 to 10 January 2022, where Fig. 10a–c and d–f correspond to the heights of 160 and 320

Correlation between the turbulent kinetic energy obtained with the wind lidar and three-dimensional ultrasonic anemometer in the

We proposed a method for directly measuring atmospheric turbulence parameters using coherent Doppler wind lidar from the perspective of spectral analysis without assuming isotropy and the

The data are available from the authors upon request.

Conceptualization, JX; methodology, JX; software, JX; validation, CL; formal analysis, JX; investigation, XL; resources, CL; data curation, LZ; writing – original draft preparation, JX; writing – review and editing, HY and NZ; visualization, XL; supervision, HY and NZ; project administration, HY and NZ; funding acquisition, HY and NZ.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

We thank Shenzhen Darsunlaser Technology Co., Ltd.

This work was supported by the National Key R&D Program of China (grant no. 2019YFE0124800), the Special Project for Sustainable Development of Shenzhen (grant no. KCXFZ20201221173412035), the National Natural Science Foundation of China (NSFC; grant nos. 42275065 and U2342221), the Guangdong Province Science and Technology Department project (grant no. 2021B1212050024), the scientific research projects of the Guangdong Provincial Meteorological Bureau (grant no. GRMC2020M29), and the Science and Technology Innovation Team Plan of the Guangdong Meteorological Bureau (grant no. GRMCTD202003).

This paper was edited by Yuanjian Yang and reviewed by Hao Yang and two anonymous referees.