# Turbulence Detection in the Atmospheric Boundary Layer Using Coherent Doppler Wind Lidar and Microwave Radiometer

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{−16}m

^{−2/3}and 1.27 × 10

^{−15}m

^{−2/3}, respectively. In the vertical direction, the continuous profiling results of ${C}_{n}^{2}$ and other turbulence parameters with high resolution in the atmospheric boundary layer (ABL) are retrieved. In addition, the limitation and uncertainty of this method under different circumstances were analyzed, which shows that the relative error of ${C}_{n}^{2}$ estimation normally does not exceed 30% under the convective boundary layer (CBL).

## 1. Introduction

## 2. Principle

#### 2.1. Stable Stratification

_{0}and outer scale L

_{0}), where the refractive index structure function obeys the Kolmogorov “2/3 law” (${D}_{n}\left(r\right)={C}_{n}^{2}{r}^{2/3}$) [62], turbulent energy propagates from the outer scale to the inner scale without dissipation. According to Tatarskii’s theory [63], under stable stratification, by combining wind field data or the outer scale of turbulence L

_{0}with meteorological parameters, ${C}_{n}^{2}$ can be calculated by Equation (1) [64]:

_{m}is the eddy viscosity (coefficient of mixing of momentum), and $\partial \overrightarrow{U}/\partial z$ is the wind shear of the horizontal wind vector in the vertical direction. In the latter method, the calculation of L

_{0}is quite difficult. Usually, it is estimated by different outer scale models [65,66] based on Tatarskii’s theory, such as the Colman–Vernin (C-V) model [66], which expresses L

_{0}as a function of altitude only within 2–17 km. Moreover, the Dewan model [67] considers the effect of both altitude and wind shear of the horizontal wind, which has different expressions in the troposphere and stratosphere of the following:

_{θ}is the coefficient of mixing of heat. Therefore, combining Equations (3)–(6), ε can be rewritten as follows:

^{2}is the square of the buoyancy frequency.

_{m}and K

_{θ}, Equation (7) has a new expression of the following [69]:

_{t}is an indicator of discrepancy between turbulent transport by heat and momentum. With gradient Richardson number R

_{g}and flux Richardson number R

_{f}, Rr

_{t}can be shown as follows:

_{t}grows nearly linear with increasing R

_{g}and has an empirical function of the following [70,71,72]:

#### 2.2. Convective Boundary Layer

_{i}is the height of CBL), the source of turbulence becomes mainly buoyancy-driven. Then, due to the non-local large-eddy heat flux, Equations (4)–(6) and (10) that are based on K- theory failed to deal with the “zero/counter-gradient” region, where $\partial \mathsf{\Theta}/\partial z\ge 0$ while $\langle {w}^{\prime}{\theta}^{\prime}\rangle >0$ [68,74]. Likewise, temperature structure constant ${C}_{T}^{2}$ and refractive index structure constant ${C}_{n}^{2}$ are not proportional to ${\left(dT/dz\right)}^{2}$ and M

^{2}anymore. Therefore, ${C}_{n}^{2}$ should not be calculated with Equation (13) within CBL.

## 3. Experiments

#### 3.1. Instruments

#### 3.2. Verification Experiment

_{10}${C}_{n}^{2}$ that are estimated by different methods introduced in the principle part are drawn in Figure 2h. Since the height of the wind tower is about 18 m and near the ground, which represents the changes in a local area of the surface, the calculated temperature gradient can vary widely every day. In addition, the method used to estimate ${C}_{nTatarskii,1961}^{2}$ is suitable for stable conditions. Therefore, to reduce errors, in the process of calculating ${C}_{nTatarskii,1961}^{2}$ in the horizontal experiment, the temperature gradient is taken as the empirical value in the troposphere: −0.0065 K/m; the pressure gradient is −0.10 hPa/m.

^{2}calculated from the wind tower is shown in Figure 2i. It can be found that N

^{2}also turns from negative to positive after around 16:00, similarly to the temperature gradient, which means that atmosphere stratification becomes more stable and the laminar flow grows.

^{2}drop to near zero and can even approach negative values. Thus, the method derived from stable stratification is no longer applicable. It can be proved from the ${C}_{nTatarskii,1961}^{2}$ shown in Figure 2h that it becomes unstable and fluctuates around 1–2 orders of magnitude during these periods.

#### 3.3. Limitation and Uncertainty Analysis

_{v}is an indicator reflecting the rationality of the turbulence parameters retrieval [46]. The Kolmogorov “2/3 law” holds, and the lidar measurement is within an inertial subrange when the longitudinal and transverse dimensions of the sensing volume do not exceed the upper boundary of the inertial subrange (${L}_{v}>\mathrm{max}\left\{\Delta y,\Delta z\right\}$, Δy is the spatial distance between the centers of two neighbouring probing volumes, Δz is the longitudinal dimension of the probing volume, and $\Delta z=30$ m and 60 m in the vertical direction of 0.03–2.20 km and 2.20–4.79 km, respectively). It can be calculated from the radial velocity variance averaged over all azimuth angles (${\overline{\sigma}}_{r}^{2}$) and TKEDR [84]:

_{v}, the relative error of estimation of TKEDR ($R{E}_{TKEDR}$) becomes larger.

_{v}in Figure 3a, one can observe that it is bigger than Δy, Δz, and lΔy in most cases, which means that TKEDR and ${C}_{n}^{2}$ are measured and retrieved within the inertial subrange most of the time during the experiment. During the transition period around 16:00–20:00, the integral scale of turbulence L

_{v}drops to the scale smaller than Δz. Similarly to the results shown in the temperature gradient and N

^{2}, this verified the prominent motion state of atmosphere changes from convective to laminar flow and the sensing volume exceeding the integral scale of turbulence. Thus, the spatial resolution of CDWL Δz needs to be improved in near-surface observations in future studies. In addition, the results also indicate that it is reliable to use the ${L}_{v}>\mathrm{max}\left\{\Delta y,\Delta z\right\}$ criterion in measuring the credibility of the new method.

_{k}being the distance from the lidar to the center of the sensing volume, ${\theta}_{m}=m\Delta \theta $ is the azimuth angle, and Δθ is the azimuth angle resolution. $l=1,2,3,\dots ,L$ and $L\Delta \theta \ll \pi /2$. In addition, function $A\left(l\Delta {y}_{k}\right)$ can be expressed as follows:

_{W}is the temporal window width. $\Delta {y}_{k}=\Delta \theta {R}_{k}\mathrm{cos}\phi $ is the transverse size of the sensing volume.

#### 3.4. Continuous Observation of ${C}_{n}^{2}$ Profile

_{i}can be derived by using the following equation:

_{i}and ${h}_{i-1}$; g is gravitational acceleration (9.8 m/s

^{2}); M is the molar mass of Earth’s air (0.029 kg/mol); R is the universal gas constant (8.314 J/(mol·K)). Using the temperature profile measured by MWR and the recorded surface pressure, the pressure profile can be calculated from the bottom (the experimental site is 1160 m above sea level) to the top by using the differential method.

#### 3.5. Results Analysis

_{c}) of 0.25 in order to refer to [90,91]. When ${R}_{g}<{R}_{c}$, this indicates the small-scale perturbation of turbulence. We point out that R

_{g}is used in stably stratified turbulence, and it becomes much less meaningful when ${N}^{2}<0$. Therefore, the calculation of R

_{g}in this paper using the “bubble sort” algorithm proposed by Thorpe is meant to re-sort potential temperatures in a monotonically increasing order. Moreover, one should mainly focus on stable stratification conditions. The result of R

_{g}is shown in Figure 6c. Similarly to N

^{2}, it also has a stably stratified structure outside of CBL and increases after night falls. Significantly, the overall distribution features are quite consistent with ${C}_{n}^{2}$.

^{2}and R

_{i}can be found outside of CBL, especially on 6 September. In addition, there are several vertical structures in the daytime of ${C}_{n}^{2}$ on 6 September. By performing comparisons with Figure 6e–h, one can find that they are closely related to the wave structures of ${T}^{\prime}$, ${U}^{\prime}$, and ${w}^{\prime}$. Unlike gravity waves, these waves are more likely driven by the cloud’s ability to block solar radiation, which causes temperature fluctuations. When ${T}^{\prime}<0$, then ${w}^{\prime}>0$, indicating that the atmosphere is depositional; on the contrary, the atmosphere is uplifting. These phenomena generate the perturbation of TKEDR directly, which in turn affects the value of ${C}_{n}^{2}$.

^{2}indicates that stratification is quite stable. Therefore, the buoyancy term suppresses the generation of convective activity (vertical wind perturbation is near to zero) and results in a reduction in ${C}_{n}^{2}$. In addition, in the area above 1 km from 9:00 to 12:00 on the seventh, the discrepancy between ${C}_{n}^{2}$ and R

_{g}can also be better understood by the stationary ${w}^{\prime}$.

_{g}and ${C}_{n}^{2}$, since the spatial resolution of MWR is lower than CDWL, the original temperature profile is interpolated according to the spatial resolution of CDWL first. The profiles of potential temperature and potential temperature gradient at different times acquired from MWR on 6–7 September are shown in Figure 7a,b,e, and f. The thin lines in Figure 7e,f represent the original profiles of potential temperature gradient calculated by adjacent points. Thick lines represent the potential temperature gradient profiles that are estimated by the moving linear fit in a height range of 200 m. Using these thick lines, the profiles of Brunt–Väisälä frequency squared are shown in Figure 7c,d, which all have a similar characteristic with potential temperature gradient results, as excepted. Then, the gradient Richardson number profiles are depicted in Figure 7g,h.

^{2}during the daytime, one can observe that they are normally small and close to zero in the well-mixed part of CBL (Figure 7e,f). Meanwhile, the R

_{g}profiles also have a relatively small value that is less than 1. On the contrary, $d\mathsf{\Theta}/dz$, N

^{2}, and R

_{g}usually have a larger number at night, except for the region where LLJ occurred (Figure 7g,h).

_{v}are calculated vertically in Figure 8. The region with a relative error greater than 50% is marked in light yellow in Figure 8a,b. From the results, it can be observed that when using this combination method to obtain the profiles, a small relative error (Figure 8b, where $R{E}_{{C}_{n}^{2}}$ is mostly within 30%) can be maintained under CBL. In the meantime, L

_{v}is under 1 km in this area; thus, ${R}^{\prime}>{L}_{v}$ is satisfied mostly, which results in a low $R{E}_{\mathrm{TKEDR}}$ (Figure 8a). After 18:00, with a decrease in the height of the boundary layer, TKEDR drops rapidly at high altitudes, and L

_{v}becomes larger than 2 km. As a result, the calculated $R{E}_{\mathrm{TKEDR}}$ and $R{E}_{{C}_{n}^{2}}$ also grow, as shown in the figure. During the period of atmosphere changes from convection to laminar flow (around 18:00 to 21:00), a sudden increase in relative error can be observed, similarly to the horizontal experiment. After the atmosphere stabilized at night, the relative error of TKEDR and ${C}_{n}^{2}$ began to gradually decrease, but this occurred mainly within the mixing layer.

_{v}, lΔy, and ${R}^{\prime}$ profiles averaged in 12 min of the corresponding row. Δz profiles are not drawn here because they are smaller than lΔy when the height is above 297.7 m.

_{s}is the height above the sea level, w is the average wind speed in high-altitude (normally 21 m/s), and h

_{0}and ${C}_{n}^{2}\left({h}_{0}\right)$ are the height above the ground of the instrument and the measured ${C}_{n}^{2}$, respectively. Power law p typically takes 2/3 at night, and it varies around 4/3 depending on the time during the day (the same as ${C}_{nTatarskii,1971}^{2}$).

_{v}profiles, one can observe that the ${L}_{v}>\mathrm{max}\left\{\Delta y,\Delta z,l\Delta y\right\}$ criterion is satisfied under normal conditions, which indicates the credibility of this method in ${C}_{n}^{2}$ profiling. The $R{E}_{{C}_{n}^{2}}$ in lower altitudes (especially with CBL) is relatively small due to the high value of CNR, TKEDR, and the low instrumental error of the radial velocity. In these regions, condition $l\Delta y<{L}_{v}\ll {R}^{\prime}$ is usually satisfied, especially during the daytime. In contrast, in the second and third rows or the high altitude in the fourth and fifth rows, when ${R}^{\prime}$ is comparable with or smaller than L

_{v}, the relative error of the estimation of ${C}_{n}^{2}$ can increase dramatically. ${C}_{n}^{2}$ can fluctuate between two orders of magnitude above CBL, as shown in the figure.

## 4. Conclusions and Discussion

_{v}, $\mathrm{max}\left\{\Delta y,\Delta z\right\}$, lΔy, and ${R}^{\prime}$, we analyzed the uncertainty and limitations when using this method at different time periods and altitudes. In the horizontal results, the ${L}_{v}>\mathrm{max}\left\{\Delta y,\Delta z\right\}$ criterion was proven valid in measuring the credibility of the new method. The compared ${C}_{n}^{2}$ results showed a great agreement between them most of the time in the six-day experiment, except for the period when the integral scale of turbulence L

_{v}reduces to a value smaller than Δz or lΔy. In the vertical profiles, ${C}_{n}^{2}$ can be estimated within the inertial subrange and with a low relative error under CBL. Moreover, L

_{v}grows when TKEDR decreases with height, which leads to a larger $R{E}_{{C}_{n}^{2}}$ in high altitudes. Therefore, to meet the criterion and to reduce uncertainties as much as possible, the most appropriate scan angle resolution and spatial resolution of CDWL and MRW should be analyzed and adjusted according to the landscape, season, and even time period of the experimental site.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Ma, B.; Shang, Z.; Hu, Y.; Hu, K.; Wang, Y.; Yang, X.; Ashley, M.C.B.; Hickson, P.; Jiang, P. Night-time measurements of astronomical seeing at Dome A in Antarctica. Nature
**2020**, 583, 771–774. [Google Scholar] [CrossRef] [PubMed] - Storer, L.N.; Williams, P.D.; Gill, P.G. Aviation Turbulence: Dynamics, Forecasting, and Response to Climate Change. Pure Appl. Geophys.
**2019**, 176, 2081–2095. [Google Scholar] [CrossRef] [Green Version] - Ren, Y.; Huang, H.; Xie, G.; Ahmed, N.; Yan, Y.; Erkmen, B.I.; Chandrasekaran, N.; Lavery, M.P.J.; Steinhoff, N.K.; Tur, M.; et al. Atmospheric turbulence effects on the performance of a free space optical link employing orbital angular momentum multiplexing. Opt. Lett.
**2013**, 38, 4062–4065. [Google Scholar] [CrossRef] [PubMed] - Extance, A. Laser weapons get real. Nature
**2015**, 521, 408–410. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kumer, V.-M.; Reuder, J.; Dorninger, M.; Zauner, R.; Grubsic, V. Turbulent kinetic energy estimates from profiling wind LiDAR measurements and their potential for wind energy applications. Renew. Energy
**2016**, 99, 898–910. [Google Scholar] [CrossRef] [Green Version] - Wei, W.; Zhang, H.; Cai, X.; Song, Y.; Bian, Y.; Xiao, K.; Zhang, H. Influence of Intermittent Turbulence on Air Pollution and Its Dispersion in Winter 2016/2017 over Beijing, China. J. Meteorol. Res.
**2020**, 34, 176–188. [Google Scholar] [CrossRef] - Nootz, G.; Jarosz, E.; Dalgleish, F.R.; Hou, W. Quantification of optical turbulence in the ocean and its effects on beam propagation. Appl. Opt.
**2016**, 55, 8813–8820. [Google Scholar] [CrossRef] - Libich, J.; Perez, J.; Zvanovec, S.; Ghassemlooy, Z.; Nebuloni, R.; Capsoni, C. Combined effect of turbulence and aerosol on free-space optical links. Appl. Opt.
**2017**, 56, 336–341. [Google Scholar] [CrossRef] - Butterley, T.; Wilson, R.W.; Sarazin, M. Determination of the profile of atmospheric optical turbulence strength from SLODAR data. Mon. Not. R. Astron. Soc.
**2006**, 369, 835–845. [Google Scholar] [CrossRef] [Green Version] - Voyez, J.; Robert, C.; Conan, J.-M.; Mugnier, L.M.; Samain, E.; Ziad, A. First on-sky results of the CO-SLIDAR Cn2 profiler. Opt. Express
**2014**, 22, 10948–10967. [Google Scholar] [CrossRef] [Green Version] - Fusco, T.; Costille, A. Impact of Cn2 profile structure on Wide Field AO performance. Adapt. Opt. Syst. II
**2010**, 7736. [Google Scholar] [CrossRef] - Voyez, J.; Robert, C.; Michau, V.; Conan, J.-M.; Fusco, T. Accurate measurement of Cn2 profile with Shack-Hartmann data. Adapt. Opt. Syst. III
**2010**, 7736, 77360J. [Google Scholar] [CrossRef] [Green Version] - Otoniel Canuet, L.F. Atmospheric Turbulence Profile Modeling for Satellite-Ground Laser Communication; UPC, Escola d’Enginyeria de Telecomunicació i Aeroespacial de Castelldefels: Barcelona, Spain, 2015. [Google Scholar]
- Beland, R.R. Propagation through Atmospheric Optical Turbulence; SPIE: New York, NY, USA, 1993. [Google Scholar]
- Andrews, L.C.; Phillips, R.L.; Wayne, D.; Leclerc, T.; Sauer, P.; Crabbs, R.; Kiriazes, J. Near-ground vertical profile of refractive-index fluctuations. Proc. SPIE—Int. Soc. Opt. Eng.
**2009**, 7324, 732402–732412. [Google Scholar] [CrossRef] - Chen, X.; Li, X.; Sun, G.; Liu, Q.; Zhu, W.; Weng, N. Analysis of an optical turbulence profile using complete ensemble empirical mode decomposition. Appl. Opt.
**2016**, 55, 9932–9938. [Google Scholar] [CrossRef] - Wu, S.; Wu, X.; Su, C.; Yang, Q.; Xu, J.; Luo, T.; Huang, C.; Qing, C. Reliable model to estimate the profile of the refractive index structure parameter (Cn2) and integrated astroclimatic parameters in the atmosphere. Opt. Express
**2021**, 29, 12454–12470. [Google Scholar] [CrossRef] [PubMed] - Barletti, R.; Ceppatelli, G.; Moroder, E.; Paterno, L.; Righini, A. A vertical profile of turbulence in atlantic air mass measured by balloon-borne radiosondes. J. Geophys. Res.
**1974**, 79, 4545–4549. [Google Scholar] [CrossRef] - Martini, E.; Freni, A.; Cuccoli, F.; Facheris, L. Derivation of clear-air turbulence parameters from high-resolution radiosonde data. J. Atmos. Ocean. Technol.
**2017**, 34, 277–293. [Google Scholar] [CrossRef] - Zhang, J.; Zhang, S.D.; Huang, C.M.; Huang, K.M.; Gong, Y.; Gan, Q.; Zhang, Y.H. Latitudinal and topographical variabilities of free atmospheric turbulence from high-resolution radiosonde data sets. J. Geophys. Res. Atmos.
**2019**, 124, 4283–4298. [Google Scholar] [CrossRef] - Ko, H.C.; Chun, H.Y.; Wilson, R.; Geller, M.A. Characteristics of atmospheric turbulence retrieved from high vertical-resolution radiosonde data in the United States. J. Geophys. Res. Atmos.
**2019**, 124, 7553–7579. [Google Scholar] [CrossRef] - He, Y.; Sheng, Z.; He, M. The First Observation of Turbulence in Northwestern China by a Near-Space High-Resolution Balloon Sensor. Sensors
**2020**, 20, 677. [Google Scholar] [CrossRef] [Green Version] - Vyhnalek, B.E. Path Profiles of Cn2 Derived from Radiometer Temperature Measurements and Geometrical Ray Tracing. In Free-Space Laser Communication and Atmospheric Propagation XXIX; SPIE: New York, NY, USA, 2017; Volume 10096. [Google Scholar] [CrossRef] [Green Version]
- van Iersel, M.; Paulson, D.A.; Wu, C.; Ferlic, N.A.; Rzasa, J.R.; Davis, C.C.; Walker, M.; Bowden, M.; Spychalsky, J.; Titus, F. Measuring the turbulence profile in the lower atmospheric boundary layer. Appl. Opt.
**2019**, 58, 6934–6941. [Google Scholar] [CrossRef] [PubMed] - Odintsov, S.L.; Gladkikh, V.A.; Kamardin, A.P.; Nevzorova, I.V. Determination of the Structural Characteristic of the Refractive Index of Optical Waves in the Atmospheric Boundary Layer with Remote Acoustic Sounding Facilities. Atmosphere
**2019**, 10, 711. [Google Scholar] [CrossRef] [Green Version] - Ting-i, W.; Ochs, G.R.; Clifford, S.F. A saturation-resistant optical scintillometer to measure Cn2. J. Opt. Soc. Am.
**1978**, 68, 334–338. [Google Scholar] - Andrews, L.C.; Phillips, R.L.; Crabbs, R.; Wayne, D.; Leclerc, T.; Sauer, P. Creating a Cn2 Profile as a Function of Altitude Using Scintillation Measurements Along a Slant Path. In High Energy/Average Power Lasers and Intense Beam Applications VI Atmospheric and Oceanic Propagation of Electromagnetic Waves VI; SPIE: New York, NY, USA, 2012; Volume 8238. [Google Scholar] [CrossRef]
- Han, Y.; Gao, P.; Huang, J.; Zhang, T.; Zhuang, J.; Hu, M.; Wu, Y. Ground-based synchronous optical instrument for measuring atmospheric visibility and turbulence intensity: Theories, design and experiments. Opt. Express
**2018**, 26, 6833–6850. [Google Scholar] [CrossRef] [PubMed] - Belen’kii, M.S.; Roberts, D.W.; Stewart, J.M.; Gimmestad, G.G.; Dagle, W.R. Experimental validation of the differential image motion lidar concept. Laser Radar Technol. Appl. VI
**2001**, 4377, 307–316. [Google Scholar] [CrossRef] - Gimmestad, G.; Roberts, D.; Stewart, J.; Wood, J. Development of a lidar technique for profiling optical turbulence. Opt. Eng.
**2012**, 51, 101713. [Google Scholar] [CrossRef] - Brown, D.M.; Juarez, J.C.; Brown, A.M. Laser differential image-motion monitor for characterization of turbulence during free-space optical communication tests. Appl. Opt.
**2013**, 52, 8402–8410. [Google Scholar] [CrossRef] - Jing, X.; Hou, Z.; Wu, Y.; Qin, L.A.; He, F.; Tan, F. Development of a differential column image motion light detection and ranging for measuring turbulence profiles. Opt. Lett.
**2013**, 38, 3445–3447. [Google Scholar] [CrossRef] - Cheng, Z.; Tan, F.; Jing, X.; He, F.; Qin, L.A.; Hou, Z. Retrieval of Cn2 profile from differential column image motion lidar using the regularization method. Chin. Opt. Lett.
**2017**, 15, 020101. [Google Scholar] [CrossRef] - Aristidi, E.; Ziad, A.; Chabe, J.; Fantei-Caujolle, Y.; Renaud, C.; Giordano, C. A generalized differential image motion monitor. arXiv
**2019**, arXiv:1904.07093. [Google Scholar] [CrossRef] - Chabe, J.; Aristidi, E.; Ziad, A.; Lanteri, H.; Fantei-Caujolle, Y.; Giordano, C.; Borgnino, J.; Marjani, M.; Renaud, C. PML: A generalized monitor of atmospheric turbulence profile with high vertical resolution. Appl. Opt.
**2020**, 59, 7574–7584. [Google Scholar] [CrossRef] [PubMed] - Banakh, V.A.; Razenkov, I.A. Refractive turbulence strength estimation based on the laser echo signal amplification effect. Opt. Lett.
**2016**, 41, 4429–4432. [Google Scholar] [CrossRef] - Banakh, V.A.; Razenkov, I.A. Lidar measurements of atmospheric backscattering amplification. Opt. Spectrosc.
**2016**, 120, 326–334. [Google Scholar] [CrossRef] - Razenkov, I.A. Turbulent Lidar: II-Experiment. Atmos. Ocean. Opt.
**2018**, 31, 281–289. [Google Scholar] [CrossRef] - Whiteman, D.N.; Venable, D.; Landulfo, E. Comments on “Accuracy of Raman lidar water vapor calibration and its applicability to long-term measurements”. Appl. Opt.
**2011**, 50, 2170–2176. [Google Scholar] [CrossRef] [Green Version] - Shangguan, M.; Xia, H.; Wang, C.; Qiu, J.; Lin, S.; Dou, X.; Zhang, Q.; Pan, J.-W. Dual-frequency Doppler lidar for wind detection with a superconducting nanowire single-photon detector. Opt. Lett.
**2017**, 42, 3541–3544. [Google Scholar] [CrossRef] [PubMed] - Wang, C.; Xia, H.; Wu, Y.; Dong, J.; Wei, T.; Wang, L.; Dou, X. Meter-scale spatial-resolution-coherent Doppler wind lidar based on Golay coding. Opt. Lett.
**2019**, 44, 311–314. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zhang, Y.; Wu, Y.; Xia, H. Spatial resolution enhancement of coherent Doppler wind lidar using differential correlation pair technique. Opt. Lett.
**2021**, 46, 5550–5553. [Google Scholar] [CrossRef] - Banakh, V.A.; Smalikho, I.N.; Falits, A.V. Estimation of the turbulence energy dissipation rate in the atmospheric boundary layer from measurements of the radial wind velocity by micropulse coherent Doppler lidar. Opt. Express
**2017**, 25, 22679–22692. [Google Scholar] [CrossRef] - Banakh, V.A.; Smalikho, I.N.; Falits, A.V. Wind-Temperature Regime and Wind Turbulence in a Stable Boundary Layer of the Atmosphere: Case Study. Remote Sens.
**2020**, 12, 955. [Google Scholar] [CrossRef] [Green Version] - Banakh, V.A.; Smalikho, I.N.; Falits, A.V. Estimation of the height of the turbulent mixing layer from data of Doppler lidar measurements using conical scanning by a probe beam. Atmos. Meas. Tech.
**2021**, 14, 1511–1524. [Google Scholar] [CrossRef] - Smalikho, I.N.; Banakh, V.A. Effect of Wind Transport of Turbulent Inhomogeneities on Estimation of the Turbulence Energy Dissipation Rate from Measurements by a Conically Scanning Coherent Doppler Lidar. Remote Sens.
**2020**, 12, 2802. [Google Scholar] [CrossRef] - Banakh, V.A.; Smalikho, I.N.; Falits, A.V.; Sherstobitov, A.M. Estimating the Parameters of Wind Turbulence from Spectra of Radial Velocity Measured by a Pulsed Doppler Lidar. Remote Sens.
**2021**, 13, 2071. [Google Scholar] [CrossRef] - Smalikho, I.N.; Banakh, V.A.; Falits, A.V.; Sukharev, A.A. Experimental Study of Aircraft Wake Vortices on the Airfield of Tolmachevo Airport in 2018. Atmos. Ocean. Opt.
**2020**, 33, 124–133. [Google Scholar] [CrossRef] - Wang, C.; Jia, M.; Xia, H.; Wu, Y.; Wei, T.; Shang, X.; Yang, C.; Xue, X.; Dou, X. Relationship analysis of PM2.5 and boundary layer height using an aerosol and turbulence detection lidar. Atmos. Meas. Tech.
**2019**, 12, 3303–3315. [Google Scholar] [CrossRef] [Green Version] - Yang, Y.; Fan, S.; Wang, L.; Gao, Z.; Zhang, Y.; Zou, H.; Miao, S.; Li, Y.; Huang, M.; Yim, S.H.L.; et al. Diurnal Evolution of the Wintertime Boundary Layer in Urban Beijing, China: Insights from Doppler Lidar and a 325-m Meteorological Tower. Remote Sens.
**2020**, 12, 3935. [Google Scholar] [CrossRef] - Wang, L.; Qiang, W.; Xia, H.; Wei, T.; Yuan, J.; Jiang, P. Robust Solution for Boundary Layer Height Detections with Coherent Doppler Wind Lidar. Adv. Atmos. Sci.
**2021**, 38, 1920–1928. [Google Scholar] [CrossRef] - Yuan, J.; Wu, K.; Wei, T.; Wang, L.; Shu, Z.; Yang, Y.; Xia, H. Cloud Seeding Evidenced by Coherent Doppler Wind Lidar. Remote Sens.
**2021**, 13, 3815. [Google Scholar] [CrossRef] - Jia, M.; Yuan, J.; Wang, C.; Xia, H.; Wu, Y.; Zhao, L.; Wei, T.; Wu, J.; Wang, L.; Gu, S.-Y.; et al. Long-lived high-frequency gravity waves in the atmospheric boundary layer: Observations and simulations. Atmos. Chem. Phys.
**2019**, 19, 15431–15446. [Google Scholar] [CrossRef] [Green Version] - Cao, C.; Xinzhao, C.; Jian, Z.; Roberts, B.R.; Zhibin, Y.; Weichun, F.; Xian, L.; Smith, J.A. Lidar observations of persistent gravity waves with periods of 3-10 h in the Antarctic middle and upper atmosphere at McMurdo (77.83degS, 166.67degE). J. Geophys. Res. Space Phys.
**2016**, 121, 1483–1502. [Google Scholar] [CrossRef] - Tuononen, M.; O’Connor, E.J.; Sinclair, V.A.; Vakkari, V. Low-Level Jets over Uto, Finland, Based on Doppler Lidar Observations. J. Appl. Meteorol. Climatol.
**2017**, 56, 2577–2594. [Google Scholar] [CrossRef] - Banakh, V.A.; Smalikho, I.N. Lidar Studies of Wind Turbulence in the Stable Atmospheric Boundary Layer. Remote Sens.
**2018**, 10, 1219. [Google Scholar] [CrossRef] [Green Version] - Wei, T.; Xia, H.; Hu, J.; Wang, C.; Shangguan, M.; Wang, L.; Jia, M.; Dou, X. Simultaneous wind and rainfall detection by power spectrum analysis using a VAD scanning coherent Doppler lidar. Opt. Express
**2019**, 27, 31235–31245. [Google Scholar] [CrossRef] [PubMed] - Yuan, J.; Xia, H.; Wei, T.; Wang, L.; Yue, B.; Wu, Y. Identifying cloud, precipitation, windshear, and turbulence by deep analysis of the power spectrum of coherent Doppler wind lidar. Opt. Express
**2020**, 28, 37406–37418. [Google Scholar] [CrossRef] [PubMed] - Wang, C.; Xia, H.; Shangguan, M.; Wu, Y.; Wang, L.; Zhao, L.; Qiu, J.; Zhang, R. 1.5 µm polarization coherent lidar incorporating time-division multiplexing. Opt. Express
**2017**, 25, 20663–20674. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wei, T.; Xia, H.; Wu, Y.; Yuan, J.; Wang, C.; Dou, X. Inversion probability enhancement of all-fiber CDWL by noise modeling and robust fitting. Opt. Express
**2020**, 28, 29662–29675. [Google Scholar] [CrossRef] [PubMed] - Pan, Y.; Zhang, S.; Li, Q.; Ma, L.; Jiang, S.; Lei, L.; Lyu, W.; Wang, Z. Analysis of convective instability data derived from a ground-based microwave radiometer before triggering operations for artificial lightning. Atmos. Res.
**2020**, 243, 105005. [Google Scholar] [CrossRef] - Kolmogorov, A.N. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high reynolds number. J. Fluid Mech.
**1962**, 13, 82–85. [Google Scholar] [CrossRef] [Green Version] - Tatarskii, V.I. Wave Propagation in a Turbulent Medium; McGraw-Hill: New York, NY, USA, 1961. [Google Scholar]
- Andrews, L.C.; Phillips, R.L. Laser Beam Propagation through Random Media; SPIE: New York, NY, USA, 2005. [Google Scholar]
- Han, Y.; Wu, X.; Luo, T.; Qing, C.; Yang, Q.; Jin, X.; Liu, N.; Wu, S.; Su, C. New Cn2 statistical model based on first radiosonde turbulence observation over Lhasa. J. Opt. Soc. Am. A—Opt. Image Sci. Vis.
**2020**, 37, 995–1001. [Google Scholar] [CrossRef] - Coulman, C.E.; Vernin, J.; Coqueugniot, Y.; Caccia, J.L. Outer scale of turbulence appropriate to modeling refractive-index structure profiles. Appl. Opt.
**1988**, 27, 155–160. [Google Scholar] [CrossRef] - Dewan, E.M.; Beland, R.; Brown, J. A Model for Cn2 (Optical Turbulence) Profiles Using Radiosonde Data; Directorate of Geophysics: Hanscom Air Force Base, MA, USA, 1993. [Google Scholar]
- Stull, R.B. An Introduction to Boundary Layer Meteorology; Springer Science & Business Media: Dordrecht, The Netherlands; Kluwer Academic: Alphen aan den Rijn, The Netherlands, 1988. [Google Scholar]
- Tatarskii, V.I. The Effects of the Turbulent Atmosphere on Wave Propagation; Israel Program for Scientific Translations: Jerusalem, Palestine, 1971. [Google Scholar]
- Venayagamoorthy, S.K.; Stretch, D.D. On the turbulent Prandtl number in homogeneous stably stratified turbulence. J. Fluid Mech.
**2010**, 644, 359–369. [Google Scholar] [CrossRef] [Green Version] - Kantha, L.; Luce, H. Mixing Coefficient in Stably Stratified Flows. J. Phys. Oceanogr.
**2018**, 48, 2649–2665. [Google Scholar] [CrossRef] - Li, D. Turbulent Prandtl number in the atmospheric boundary layer—where are we now? Atmos. Res.
**2019**, 216, 86–105. [Google Scholar] [CrossRef] - Luce, H.; Kantha, L.; Hashiguchi, H.; Lawrence, D. Estimation of Turbulence Parameters in the Lower Troposphere from ShUREX (2016–2017) UAV Data. Atmosphere
**2019**, 10, 384. [Google Scholar] [CrossRef] [Green Version] - Ghannam, K.; Duman, T.; Salesky, S.T.; Chamecki, M.; Katul, G. The non-local character of turbulence asymmetry in the convective atmospheric boundary layer. Q. J. R. Meteorol. Soc.
**2017**, 143, 494–507. [Google Scholar] [CrossRef] - Deardorff, J.W. The Counter-Gradient Heat Flux in the Lower Atmosphere and in the Laboratory. J. Atmos. Sci.
**1966**, 23, 503–506. [Google Scholar] [CrossRef] [Green Version] - Luce, H.; Kantha, L.; Hashiguchi, H.; Doddi, A.; Lawrence, D.; Yabuki, M. On the Relationship between the TKE Dissipation Rate and the Temperature Structure Function Parameter in the Convective Boundary Layer. J. Atmos. Sci.
**2020**, 77, 2311–2326. [Google Scholar] [CrossRef] [Green Version] - DAVIS6162: Wireless Vantage Pro2 Plus Support Documents. Available online: https://cdn.shopify.com/s/files/1/0515/5992/3873/files/07395.234_Manual_VP2__RevZ_web.pdf?v=1647548782 (accessed on 16 June 2022).
- LAS MkII Scintillometer—Manual. Available online: https://www.kippzonen.com/Download/598/LAS-MkII-Scintillometer-Manual (accessed on 16 June 2022).
- Olofson, K.F.G.; Andersson, P.U.; Hallquist, M.; Ljungstrom, E.; Tang, L.; Chen, D.; Pettersson, J.B.C. Urban aerosol evolution and particle formation during wintertime temperature inversions. Atmos. Environ.
**2009**, 43, 340–346. [Google Scholar] [CrossRef] - Guo, J.; Chen, X.; Su, T.; Liu, L.; Zheng, Y.; Chen, D.; Li, J.; Xu, H.; Lv, Y.; He, B.; et al. The Climatology of Lower Tropospheric Temperature Inversions in China from Radiosonde Measurements: Roles of Black Carbon, Local Meteorology, and Large-Scale Subsidence. J. Clim.
**2020**, 33, 9327–9350. [Google Scholar] [CrossRef] - Sorbjan, Z.; Balsley, B.B. Microstructure of turbulence in the stably stratified boundary layer. Bound.-Layer Meteorol.
**2008**, 129, 191–210. [Google Scholar] [CrossRef] [Green Version] - Friedrich, K.; Lundquist, J.K.; Aitken, M.; Kalina, E.A.; Marshall, R.F. Stability and turbulence in the atmospheric boundary layer: A comparison of remote sensing and tower observations. Geophys. Res. Lett.
**2012**, 39, L03801. [Google Scholar] [CrossRef] [Green Version] - Balsley, B.B.; Lawrence, D.A.; Fritts, D.C.; Wang, L.; Wan, K.; Werne, J. Fine Structure, Instabilities, and Turbulence in the Lower Atmosphere: High-Resolution In Situ Slant-Path Measurements with the DataHawk UAV and Comparisons with Numerical Modeling. J. Atmos. Ocean. Technol.
**2018**, 35, 619–642. [Google Scholar] [CrossRef] - Smalikho, I.N.; Banakh, V.A. Measurements of wind turbulence parameters by a conically scanning coherent Doppler lidar in the atmospheric boundary layer. Atmos. Meas. Tech.
**2017**, 10, 4191–4208. [Google Scholar] [CrossRef] [Green Version] - Frehlich, R.; Hannon, S.M.; Henderson, S.W. Performance of a 2-µm Coherent Doppler Lidar for Wind Measurements. J. Atmos. Ocean. Technol.
**1994**, 11, 1517–1528. [Google Scholar] [CrossRef] - Rye, B.J.; Hardesty, R.M. Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I. Spectral accumulation and the Cramer-Rao lower bound. IEEE Trans. Geosci. Remote Sens.
**1993**, 31, 16–27. [Google Scholar] [CrossRef] - Rye, B.J.; Hardesty, R.M. Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. II. Correlogram accumulation. IEEE Trans. Geosci. Remote Sens.
**1993**, 31, 28–35. [Google Scholar] [CrossRef] - Venayagamoorthy, S.K.; Koseff, J.R. On the flux Richardson number in stably stratified turbulence. J. Fluid Mech.
**2016**, 798, R1. [Google Scholar] [CrossRef] - Banakh, V.A.; Smalikho, I.N.; Falits, A.V. Remote Sensing of Stable Boundary Layer of Atmosphere. In EPJ Web of Conferences; EDP Sciences: Les Ulis, France, 2020; p. 06015. [Google Scholar]
- Miles, J.W. On the stability of heterogeneous shear flows. J. Fluid Mech.
**1961**, 10, 496–508. [Google Scholar] [CrossRef] [Green Version] - Stull, R. An Introduction to Boundary Layer Meteorology; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1998; p. 176. [Google Scholar]
- Xu, G.; Xi, B.; Zhang, W.; Cui, C.; Dong, X.; Liu, Y.; Yan, G. Comparison of atmospheric profiles between microwave radiometer retrievals and radiosonde soundings. J. Geophys. Res.
**2015**, 120, 10313–10323. [Google Scholar] [CrossRef] - Andrews, L.C.; Phillips, R.L.; Crabbs, R.; Wayne, D.; Leclerc, T.; Sauer, P. Atmospheric Channel Characterization for ORCA Testing at NTTR. In Atmospheric and Oceanic Propagation of Electromagnetic Waves IV; Korotkova, O., Ed.; SPIE: New York, NY, USA, 2010; Volume 7588. [Google Scholar]

**Figure 1.**Illustration of two experiment sites in the satellite map and the instruments layout in the horizontal experiment (USTC, Hefei City).

**Figure 2.**The horizontal wind speed (

**a**), wind direction (

**b**), vertical wind speed (

**c**), wind shear (

**d**), log

_{10}(TKEDR) (

**e**), temperature and its gradient (

**f**), variances in vertical wind fluctuation and flux of potential temperature (

**g**), log

_{10}${C}_{n}^{2}$ estimated by different methods (

**h**), Brunt–Väisälä frequency squared, log

_{10}${C}_{n}^{2}$ and its shaded area error bar (

**i**) retrieved from CDWL, wind tower, and LAS in the observations from 26 September to 1 October 2020, local time.

**Figure 3.**The integral scale L

_{v}(

**a**), relative error of the estimation of TKEDR and ${C}_{n}^{2}$ (

**b**), and comparative statistical analysis of LAS and CDWL observation results (

**c**) from 26 September to 1 October 2020, local time.

**Figure 4.**The CNR (

**a**), horizontal wind speed (

**b**), wind direction (

**c**), vertical wind speed (

**e**), wind shear (

**f**), and log

_{10}(TKEDR) (

**g**) derived from CDWL. The temperature (

**d**) and pressure (

**h**) retrieved from MWR and the barometric formula in the observations from 6 September to 7 September 2019, local time.

**Figure 5.**The results of the variances of vertical wind fluctuation (

**a**), instantaneous flux of potential temperature (

**b**), log

_{10}${C}_{n}^{2}$ estimated by ${C}_{nTatarskii,1961}^{2}$ (

**c**), ${C}_{nTatarskii,1971}^{2}$ (

**d**), and ${C}_{nLuce,2020}^{2}$ (

**e**) in the observations from 6 September to 7 September 2019, local time.

**Figure 6.**The potential temperature (

**a**), Brunt–Väisälä frequency squared (

**b**), gradient Richardson number (

**c**), log

_{10}${C}_{n}^{2}$ (

**d**) profiles, perturbations of temperature (

**e**), horizontal wind speed (

**f**), vertical wind speed (

**g**), and averaged wind speed perturbations within 1–2 km (

**h**) derived from CDWL and MWR in the observations on 6–7 September 2019, local time.

**Figure 7.**The results of potential temperature (

**a**,

**b**), potential temperature gradient (

**e**,

**f**), Brunt–Väisälä frequency squared (

**c**,

**d**), and gradient Richardson number (

**g**,

**h**) profiles derived from CDWL, MWR, and the barometric formula at different times on 6–7 September 2019, local time.

**Figure 8.**The relative error of the estimation of TKEDR (

**a**), combined ${C}_{n}^{2}$ (

**b**), mixing layer height (MLH, (

**a**,

**b**)), and integral scale L

_{v}(

**c**) calculated from CDWL and MWR in the observations from 6 September to 7 September 2019, local time.

**Figure 9.**Profiles of log

_{10}${C}_{n}^{2}$ in raw data that are distance averaged and show a shaded area error bar, calculated from the HAP model and time averaged integral scale L

_{v}(

**a7**–

**e7**) during the period of 14:59:30–15:11:49 (

**a1**–

**a6**) and 20:59:22–21:11:41 (

**b1**–

**b6**) on 6 September and 02:59:02–03:11:21 (

**c1**–

**c6**), 09:01:17–09:13:36 (

**d1**–

**d6**), and 15:01:19–15:13:40 (

**e1**–

**e6**) on 7 September 2019, local time.

Parameter | Value |
---|---|

Wavelength | 1548 nm |

Pulse energy | 200 μJ |

Pulse width | 200 ns |

Repetition frequency | 10 kHz |

Temporal resolution | 2 s |

Azimuth scanning range | 0–360° |

Zenith scanning range | 0–90° |

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## Share and Cite

**MDPI and ACS Style**

Jiang, P.; Yuan, J.; Wu, K.; Wang, L.; Xia, H.
Turbulence Detection in the Atmospheric Boundary Layer Using Coherent Doppler Wind Lidar and Microwave Radiometer. *Remote Sens.* **2022**, *14*, 2951.
https://doi.org/10.3390/rs14122951

**AMA Style**

Jiang P, Yuan J, Wu K, Wang L, Xia H.
Turbulence Detection in the Atmospheric Boundary Layer Using Coherent Doppler Wind Lidar and Microwave Radiometer. *Remote Sensing*. 2022; 14(12):2951.
https://doi.org/10.3390/rs14122951

**Chicago/Turabian Style**

Jiang, Pu, Jinlong Yuan, Kenan Wu, Lu Wang, and Haiyun Xia.
2022. "Turbulence Detection in the Atmospheric Boundary Layer Using Coherent Doppler Wind Lidar and Microwave Radiometer" *Remote Sensing* 14, no. 12: 2951.
https://doi.org/10.3390/rs14122951