Identifying cloud, precipitation, windshear, and turbulence by deep analysis of the power spectrum of coherent Doppler wind lidar

Researches on the atmospheric boundary layer (ABL) need accurate measurements with high temporal and spatial resolutions from a series of different instruments. Here, a method for identifying cloud, precipitation, windshear, and turbulence in the ABL using a single coherent Doppler wind lidar (CDWL) is proposed and demonstrated. Based on deep analysis of the power spectrum of the backscattering signal, multiple lidar products, such as carrier-to-noise (CNR), spectrum width, spectrum skewness, turbulent kinetic energy dissipation rate (TKEDR), and shear intensity are derived for weather identification. Firstly, the cloud is extracted by Haar wavelet covariance transform (HWCT) algorithm based on the CNR after range correction. Secondly, since the spectrum broadening may be due to turbulence, windshear or precipitation, the spectrum skewness is introduced to distinguish the precipitation from two other conditions. Whereas wind velocity is obtained by single peak fitting in clear weather condition, the double-peak fitting is used to retrieve wind and rainfall velocities simultaneously in the precipitation condition. Thirdly, judging from shear intensity and TKEDR, turbulence and windshear are classified. As a double check, the temporal continuity is used. Stable wind variances conditions such as low-level jets are identified as windshear, while arbitrary wind variances conditions are categorized as turbulence. In the field experiment, the method is implemented on a micro-pulse CDWL to provide meteorological services for the 70th anniversary of the China’s National Day, in Inner Mongolia, China (43°54′N, 115°58′E). All weather conditions are successfully classified. By comparing lidar results to that of microwave radiometer (MWR), the spectrum skewness is found be more accurate to indicate precipitation than spectrum width or vertical speed. Finally, the parameter relationships and distributions are analyzed statistically in different weather conditions. © 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
The atmospheric boundary layer (ABL) plays an important role in many fields, including air pollution and the dispersal of pollutants, agricultural meteorology, aeronautical meteorology, mesoscale meteorology, and weather forecasting [1]. Accurate weather condition measurement and classification with high temporal and spatial resolutions are essential not only for engineering applications, but also for scientific research. For example, windshear and severe turbulence will cause aircraft loss of control and deviate from the intended flight path [2], and freezing precipitation may deteriorate the aircraft's aerodynamic performance [3]. To understand the microphysical process of the ABL, one needs knowledge of transport and mixing conditions including wind profiles, turbulence, windshear, precipitation, and cloud [4].
The CDWL has been used in some precipitation detection scenarios based on the power spectrum [21,22]. The common criterion for identifying rainfall is the spectrum broadening phenomenon, due to the velocity difference between rain drops and aerosol. This method is only valid for rain condition when the power spectrum shows two-peak structure clearly. However, it hard to recognize all rain conditions by spectrum broadening effect, such as drizzle or in the condition when aerosol is nearly washed out by the rain. In such cases, since one spectrum is dominated, the weaker one is submerged. Besides, other meteorological features can also lead to spectrum broadening, including windshear, turbulence, and multiple scattering of clouds [23][24][25][26].
Turbulence measurements using ground-based wind lidars are reviewed in [27]. Various parameters are used to estimate turbulence quantity using a lidar, including turbulent kinetic energy dissipation rate (TKEDR), radial velocity variance, coherence of the components of the wind field, etc. Compared with stable windshear, turbulence is caused by rapid irregular motion of air. Therefore, the distribution characteristics of wind variation provide an opportunity to distinguish turbulence and windshear.
In this work, a method using a single CDWL is proposed to detect and identify cloud, precipitation, windshear, and turbulence by deep analysis of power spectrum, to provide meteorological services for the 70th anniversary of the China's National Day. The sites, instruments are described in Sect. 2. Sect. 3 introduces the lidar products derived from power spectrum. In Sect. 4, observation, identification, and statistical results are present. Finally, a conclusion is drawn in Sect. 5. If not specified, local time is used.

Site and instruments
The field experiment is performed at Xilin Gol grassland, Inner Mongolia, China (43°54 ′ N, 115°58 ′ E), from 28 August to 1 October 2019. The site is in the hinterland of Xilingol grassland, with a typical temperate continental climate. Due to the frequent invasion of polar dry and cold air, the site is usually windy weather in autumn.

Coherent Doppler wind lidar
A compact and integrated micro-pulse CDWL with high temporal and spatial resolutions is applied. The CDWL is shown in Fig. 1. It can work continuously in different weather conditions with an all-fiber structure and temperature control system. The CDWL is operated at an eye-safe wavelength of 1.5 µm. The pulse energy of the laser is 100 µJ. The key parameters are listed in Table 1. The CDWL supports multiple scanning modes, including plan position indicator (PPI), range height indicator (RHI) and velocity azimuth display (VAD). The reliability of the CDWL is demonstrated in previous works. [22,28,29]   uring the experiment, the lidar operates in the VAD scanning mode with a period of 2.5 min. The elevation angle is fixed at 60°. The azimuth angle changes from 0°to 300°, with a stepping angle of 5°. The radial spatial resolutions are set as 30/60/150 m in the range of 0-2.5/2.5-5.5/5.5-13.0 km. The resolution change is used to improve the detection probability in the high altitude where the aerosol concentration is usually low. Velocity components are retrieved by the filtered sine wave fitting (FSWF) method with radial wind velocities [30].

Microwave radiometer
A ground-based microwave radiometer (MWR) is used in the experiment, as shown in Fig. 1. The MWR provides atmospheric profiles of temperature, water-vapour, liquid water, and relative humidity, from the surface to a height of 10 km. The vertical resolutions are set as 50/100/250 m in the height of 0-0.5/0.5-2/2-10 km. The temporal resolution is 2 min. Application and detail specifications of the MWR are demonstrated in [31].

Characteristics of the power spectrum
The line of sight (LOS) velocity is determined by the mean Doppler frequency shift of the power spectrum. The sign is defined as positive when the movement is toward the lidar, and vice versa. The carrier-to-noise ratio (CNR) is the ratio of signal power to noise power. The accuracy of velocity estimation is mainly determined by the CNR [20,32]. The signal spectrum width is an indicator of velocity dispersion in a range bin. Adverse weather conditions can result spectrum broadening, such as windshear, turbulence, and precipitation. Besides the CNR and spectrum width, skewness is introduced to reveal how adverse weather conditions affect the power spectrum in this work. Skewness is a measure of the symmetry of the power spectrum. The skewness is expressed as: where v i and P i are the velocity and power spectrum value at sampling point i, respectively. v is the mean velocity. The negative skewness means that the spectrum is a left bias curve, and vice versa. In general, the spectrum has a single peak distribution with a small skewness of Sk 0 near to zero, because the shape of emitted pulse is not strictly Gaussian. Sk 0 can be estimated from spectra in clear air conditions with weak turbulence and windshear. Sk is not effective to identify the multi-peak structure. For example, Sk is close to zero for the spectrum having two similar intensity peaks in some precipitation conditions. Therefore, the skewness is modified in Eq. (1). v is set as the velocity associated with the maximum of signal intensity.

Calculation of turbulence and shear intensity
The TKEDR is a method for turbulence measurements using ground-based wind lidars [27]. The greatest advantage of estimation of TKEDR is that the universal behaviour of isotropy in the inertial subrange is used, either in the Fourier domain (using velocity spectrum) or in the temporal domain (using structure function). In this work, a method of azimuth structure function is applied to estimate the TKEDR in the VAD scanning mode. The method including error analysis are demonstrated in detail [18,33].
Windshear is the vector difference between the winds at two points. The shear intensity is calculated by dividing the magnitude of the vector difference between the two points by the distance, i.e. the velocity gradient of wind profiles [2]: where u i and v i are wind components at height z i , the shear intensity modulus of wind profiles has random fluctuations, due to the atmosphere turbulence.

Cloud extraction
The Haar wavelet covariance transform (HWCT) method is used to retrieve boundary layer height (BLH) from aerosol concentration [34]. The HWCT method is less affected by signal noise, with good adjustability and robustness. Here, the HWCT method is adopted to extract the cloud based on CNR after range correction, which reflects the aerosol concentration. Clouds are characterized by a steep increase of the range corrected lidar signal at the cloud base followed by a strong decrease of the signal at the cloud top. The determination of the cloud base and top is discussed in details [35,36]. Since the detection probability in the high altitude is improved at sacrifice of range resolution as mentioned in section 2.1, the CNR increases above 2.2 km, as shown in Fig. 2(a). Therefore, the CNR is range corrected for cloud extraction. The spectrum width is shown in Fig. 2(b). Both turbulence and windshear can cause the velocity of aerosol to deviate from the mean value, resulting in spectrum broadenings. However, the value of skewness does not increase obviously, as shown in Fig. 2(c). The skewness is corrected by Eq. (1), and the estimated Sk 0 is 0.02. Low-level jet is detected during the night and early morning. The low-level jet altitude is identified using the method presented by [37], as shown both in Fig. 2(d) and (e). The surface turbulence is generated by the drag of the low-level jet, the TKEDR is shown in Fig. 2(g). However, the low-level jet is interrupted by the turbulence generated by solar heating during the day time [38]. Because turbulent motion is enhanced by updraft from the ground, due to the solar radiation enhancing. Convection characteristics of vertical velocity also characterize turbulence, as shown in Fig. 2(f). The cloud attenuates the solar radiation sometimes during the daytime, decreasing the updraft. Consequently, the turbulence is weakened, as shown in Fig. 2(g). The error of radial velocity should be smaller than 0.5 m/s for wind vector estimation by FSWF method [39], thus the data with CNR below -35 dB are abandoned [20,29]. Higher quality data is needed for TKEDR estimation [33,40]. The CNR criterion is set to -27 dB for TKEDR, where radial velocity error the CDWL is not exceeding 0.2 m/s [20]. Hence the retrieval possibility of TKEDR is below than that of shear intensity, as shown in Fig. 2(h). Low-level jet cases identified in Fig. 2(d) and (e) can estimate the max velocity position in the low-level jet, while the shear intensity can reflect the windshear intensity in temporal and spatial ranges. The shear intensity driven by turbulence is disorderly, while that of low-level jet is zonal in the time axis. Stable windshear such as low-level jet has the features of temporal continuity. Here, this phenomenon is selected as a criterion for distinguishing windshear from turbulence. Continuous observation results including four precipitation cases are obtained by the CDWL from 28 August to 1 October 2019, as appended in the dataset [41]. Figure 3 shows a precipitation process, during 19-20 September 2019. At 19 September, 0:00, clouds at the height of 7 km start sinking with a vertical speed about 1 m s-1, as shown in Fig. 3(f). The skewness deviates significantly from zeros, from 23:00 on 19 September to 5:30 the next day, a total of 6.5 hours, as shown in Fig. 3(c). In the meantime, the spectrum width is broadened obviously, as shown in Fig. 3(b), and large sinking speeds are observed, as shown in Fig. 3(f). Apparently, the precipitation occurred during this period. The skewness increasing indicates that multiple components exist in the power spectrum of precipitation, due to the different velocities of aerosol and raindrop. Comparing to the spectrum width or vertical speed, the skewness provides a more accurate criterion to distinguish precipitation from windshear and turbulence. The temperature, water-vapour, liquid water, and relative humidity observed by MRR are shown in Fig. 4. In the early stage of rainfall, the liquid water is below 0.1g m −3 , and the water-vapour is above 6 g m −3 , below 2 km. The raindrops are evaporated due to arid conditions, increasing water-vapour. After a period of rainfall, the water-vapour, liquid water, and relative humidity increase significantly. The MWR results are consistent with that of the lidar.

Identification procedure and results
An identification procedure of cloud, precipitation, windshear, and turbulence is introduced in this section. It incorporates the following lidar productions derived from the deep analysis of the power spectrum: CNR, spectrum width and skewness of power spectrum, TKEDR, and shear   intensity, as introduced in Sect. 3. Figure 5 is the flowchart of the identification procedure, as described below: 1. Firstly, the power spectrum is obtained from the CDWL raw data by using fast Fourier transform. And the CNR, spectrum width, and skewness are derived from the power spectrum.
2. Then, the cloud is extracted by CNR after range correction, using the HWCT method.
3. Except the method based on spectrum width, in previous works, precipitation cases are identified by the vertical velocity data using the assumption that all precipitations have a fall velocity greater than a threshold. The threshold is set as >1 m s −1 [19] and >1.5 m s −1 [15], respectively. Since precipitation is more coherent in the vertical dimension, using suitable time and vertical windows can obtain a robust result. However, could motion, large-scale vertical motion arising from orographic features or strong convection such as microburst can also cause a vertical velocity, which may introduce false precipitation identification. To improve the identification accuracy and capture the detail of precipitation features, skewness is introduced in addition to the spectrum broadening to identity the precipitation. The thresholds of spectrum width and skewness can be obtained, according to the precipitation results from Fig. 3, which are confirmed by MWR. The empirical thresholds of spectrum width and skewness are recommended to be >4.5 MHz and >0.2, respectively. After the identification of the precipitation spectrum, rain and wind velocity are simultaneously retrieved by double-peak fitting, as demonstrated in [21,22,29].  Figure 6 shows examples of the Doppler spectrum in precipitation conditions. The aerosol and rain spectra are obtained using double-peak fitting. The right spectrum is tagged as the rain signal, as discussed elsewhere [22].  (c) and (d) show spectra that the rain spectra are covered by that of aerosol. The Sw and Sk are the spectrum width and skewness of the raw spectrum. Fig. 6(b). Figure 6(c) and (d) show cases where the rain spectra are covered by aerosol ones. The spectrum width broadening of the raw spectrum in Fig. 6(d) is not obvious, compared with these of (a), (b), and (c), while the spectrum skewness reaches to 0.43, demonstrating the effectiveness of this method.
4. After recognizing of cloud and precipitation, the windshear and turbulence are identified by a threshold approach based on TKEDR and shear intensity. The turbulence is obtained with the TKEDR threshold >10 −4 m 2 ·s −3 , recommended in previous studies [42][43][44]. To expand the search band for turbulence, the irregular windshear is classified as turbulence, which could be wind-shear derived or cloud derived turbulence. The windshear region is identified when shear intensity is greater than 0.02 s −1 [4]. A time window recommend as 36 min is applied to filter the irregular windshear. Figure 7 shows the identification results of 27-28 September 2019 and 19-20 September 2019. The LOS velocity used to determine the velocity vector in Fig. 2 and Fig. 3, are obtained by one peak fitting. It is inaccurate for precipitation condition, since both aerosol and rain spectra exist. In precipitation, double-peak fitting is applied to separate the aerosol and rain components in the power spectrum. The separation results of wind and rain are shown in Fig. 8. The rain spectrum width is wider than that of aerosol as shown in Fig. 8(a) and (e). The spectrum width of aerosol in Fig. 8(a) is broadened during the precipitation, due to wind variances. The horizontal speed and direction of raindrops are close to that of wind, as shown in Fig. 8(b), (c), (f), and (j). It is caused by the drag effect of wind on raindrops in horizontal direction. Raindrops are obviously heavier than aerosol particles, thus the vertical speeds of raindrops are larger than that of wind, as shown in Fig. 8(d) and (h). The vertical speed of raindrops reflects the raindrop size [21]. Heavy rain is often accompanied by big raindrops that have large falling speed, while light rain usually consists of small drops. To analyse the characteristics of the identification results in Fig. 7, the parameter relationships are drawn in Fig. 9. The shear intensity, spectrum width, spectrum skewness, and vertical speed are selected. It should be specified that the shear intensity, spectrum width, and vertical speed of the precipitation are updated by two-peak fittings. The distribution centres of the precipitation, windshear and turbulence are marked as white inverted triangle, black circle, and white square.
The detailed values are listed in Table 2. Two precipitation clusters are shown in Fig. 9(a), (c), and (e). The right precipitation cluster with positive skewness represents cases that the aerosol component dominates. The left precipitation cluster with negative skewness represents cases that the rain component dominates. The skewness centres of precipitation clusters are -0.474 and 0.445, respectively. The spectrum width and vertical centres of precipitation are 8.413 MHz, and 3.367 m s −1 , significantly greater than that of windshear and turbulence. Combining the spectrum width and skewness, it is easy to identify precipitation from windshear and turbulence, as shown in Fig. 9(c). Strong shear intensity exists in precipitation, as shown in Fig. 9(a), (b), and (f), because significant changes in wind direction and velocity are often happened, as examples shown in Fig. 8(b) and (c). From Fig. 9(c), (d), and (e), it is hard to distinguish windshear from turbulence using the spectrum width, spectrum skewness, and vertical speed, since the distribution centres of them almost coincide. Nevertheless, the distribution of the shear intensity is obviously different, as shown in Fig. 9(a), (b), and (f). The shear intensity centre of 0.03 s −1 is obvious greater than 0.008 s −1 that of turbulence.  The probability density function (PDF) of parameters is estimated using the kernel density estimation (KDE), as shown in Fig. 10. The area of red shade in Fig. 10(a) is 98.9%, which reflects the identification rate for precipitation using the skewness threshold of 0.2. The spectrum width PDF of precipitation is a normal distribution, which is distinguished from that of windshear and turbulence, as shown in Fig. 10(b). From Fig. 10(c), the shear intensity PDF of windshear is distinct from that of turbulence. There exists an overlap between shear intensity PDF of windshear and precipitation, but the precipitation has been identified before windshear and turbulence, verifying rationality of the identification procedure. The PDFs of vertical speed are normal distribution, as shown in Fig. 10(d). Since the turbulence is accompanied with vertical air motion, the vertical velocity distribution of turbulence varies more widely than that of windshear.

Conclusion
A method for weather identification is introduced based on several CDWL products derived from the power spectrum. The method is verified on a field experiment, all mentioned weather conditions are successfully detected and identified. The spectrum skewness introduced in this work can indicates precipitation accurately. It reflects the difference in doppler shift of aerosol and precipitation particles, including cases where the weaker spectrum is submerged in the other one. The estimated recognition rate of precipitation using the skewness threshold of 0.2 is 98.9%. The skewness threshold can be updated by iteration to improve the identification rate, because the threshold may vary for different CDWLs or sites. Statistical results show that the precipitation is accompanied with strong shear intensity and large vertical speed. Therefore, it is important to identify precipitation before windshear and turbulence. After that, stable windshear can be distinguished from turbulence, since windshear is persistent in time with strong shear intensity. In summary, by deep analysis of the power spectrum of CDWL, the proposed method shows accuracy and robust in weather condition classification of the ABL. The current study contributes to our understanding the ABL, which is important for aviation safety, weather forecast and climate models.

Disclosures
The authors declare that there are no conflicts of interest related to this article.