the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Turbulence Detection in the Atmospheric Boundary Layer using Coherent Doppler Wind Lidar and Microwave Radiometer
Abstract. The refractive index structure constant (C_{n}^{2}) is a key parameter in describing the influence of turbulence on laser transmission in the atmosphere. A new method for continuous C_{n}^{2} profiling with both high temporal and spatial resolution is proposed and demonstrated. Under the assumption of the Kolmogorov “2/3 law”, the C_{n}^{2} profile can be calculated by using the wind field and turbulent kinetic energy dissipation rate (TKEDR) measured by coherent Doppler wind lidar (CDWL) and other meteorological parameters derived from microwave radiometer (MWR). In the horizontal experiment, a comparison between the results from our new method and measurements made by a large aperture scintillometer (LAS) is conducted. Except for the period of stratification stabilizing, the correlation coefficient between them in the sixday observation is 0.8389, the mean error and standard deviation is 1.09 × 10^{−15} m^{−2/3} and 2.14 × 10^{−15} m^{−2/3}, respectively. In the vertical direction, the continuous observation results of C_{n}^{2} and other turbulence parameter profiles in the atmospheric boundary layer (ABL) are retrieved. More details of the atmospheric turbulence can be found in the ABL owe to the high temporal and spatial resolution of MWR and CDWL (spatial resolution of 26 m, temporal resolution of 147 s).
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RC1: 'Comment on amt2021288', Anonymous Referee #1, 12 Dec 2021
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt2021288/amt2021288RC1supplement.pdf

AC1: 'Reply on RC1', Haiyun Xia, 30 Jan 2022
Dear Referee #1:
Thank you for your valuable comments and suggestions which helped us significantly to improve our manuscript. We have considered all comments carefully and revised the manuscript. Our pointbypoint responses to all your comments are listed below in blue fonts and the changes in the manuscript are listed in blue italic fonts.
Anonymous Referee #1:
Manuscript presents the experimental results intending on demonstration of the possibility of vertical profiling the refractive index structure constant based on estimation of the turbulent kinetic energy dissipation rate and gradients of wind velocity and potential temperature from data of wind coherent lidar and microwave radiometer. For determining the refractive index structure constant, Eq. (4) in the manuscript is used. Eq. (4) follows from the formulae listed in Tatarskii, 1961 (see References in the manuscript).
General Comments:
The main remark to the manuscript is following. V.I. Tatarskii wrote in Tatarskii, 1961, that these formulae are true for the surface layer of the atmosphere. As to the heights above the surface layer, he noted, a lot of experiments are required to test applicability of these formulae. Actually, as it follows from the ground experiment described in the manuscript, Eq.(4) does not work even in the surface layer under the stable conditions, it gives the refractive index structure constant values which differ from the scintillometer results by two orders. The temperature stratification in the atmosphere is stable one at the heights exceeding the boundary layer height independently on the stratification in the boundary layer. Thus, Eq. (4) does not work over the boundary layer in any case.
Response: Firstly, thanks for your comments about the limitation of Eq. (4) under different circumstances. Based on our horizontal experiment, the reviewer points out that Eq. (4) doesn’t work under stable conditions even in the ground, then he/she mentions this method is limited in the atmospheric boundary layer (ABL).
Actually, in the ground experiment, the discrepancy between the method using Eq. (4) and the scintillometer mainly within the transition period around 16:0020:00 as shown in Fig. 2(g). When the stratification structure becomes stable at night, the TKEDR also gradually decreases, so the Cn2 obtained from them becomes consistent again. However, the results in the night coincide not as well as in the daytime. To study the limitation of this method, we added the uncertainty analyses in the revised manuscript by calculating the relative error of Cn2 and the integral scale of turbulence.
In the horizontal results, we find that the integral scale of turbulence L_{v} drops to the scale smaller than the length used to calculate the TKEDR during the transition period around 16:0020:00 (Fig. 3(b) in the revised manuscript). This verified the difference between the two instruments is mainly due to the state of the atmosphere changing from isotropic to anisotropic. In the vertical profiles, the L_{v} grows when the TKEDR decreases with height, which causes the larger relative error of the estimation of Cn2 in the high altitude (Fig. 8 in the revised manuscript).
According to the point of the reviewer, we tested the limits of this method and find the rationality within the ABL, especially within the convective boundary layer (Fig. 7 in the revised manuscript). Thanks again for your comments to make this manuscript more convincing and practical.
Specific Comments:
Comments 1: Lines 1516: "... the mean error and standard deviation is 1.09×1015 m2/3 and 2.14×1015 m 2/3, respectively."
That says about nothing. Relative units are more informative.
Response 1: Thanks for your suggestion, we have added the relative error in the revised Fig. 3(c). It should be mentioned that due to the value of the Cn2 being very small and normally changing between 23 orders of magnitude, the calculated relative error could be quite large even a small difference. For example, (2×10^{15} m^{2/3 }1×10^{15} m^{2/3})/(1×10^{15} m^{2/3})=100%. ^{}So, the relative error is calculated on a logarithmic scale.
Changes 1: Line 179: When using all data for analysis, the correlation coefficient, mean error, and relative error between the two methods are 0.6723, 1.34×10^{15} m^{2/3}, and 2.83%, respectively. When using the black dots, the correlation coefficient, mean error, and relative error are 0.8389, 1.09×10^{15 }m^{2/3}, and 2.04%, respectively.
Comments 2: Line 70. Eq. (1) is listed in Tatarskii, 1961, for the temperature structure constant. Relation between the refractive index structure constant and the temperature one is commonly known.
Response 2: Indeed, the method using the relationship between the Cn2 and CT2 is a common way to estimate the refractive index structure constant. As we discussed in the introduction, most of them acquire the Cn2 profiles through the sounding balloon with a Radiosonde. It normally takes a long time to obtain one profile. However, considering the fastchanging turbulence environment, our purpose and innovation are to seek a method that can detect the turbulence profiles with high temporal and spatial resolution at the same time. Therefore, we use Eq. (4), which contains the dynamics and thermodynamics part, to estimate the Cn2 profiles.
Comments 3: Lines 108109: " In the vertical direction of 02.17 km, 2.174.76 km, and 4.7611.26 km, the range resolution is 26 m, 52 m, and 130 m, respectively."
Pulsed lidars have dead zone, diapason "02.17 km" is not true. The same is for Figs. 2,4,6.
In Fig. 2e, instead of "8 2" should be "108 102". The same is for Figs.4g, 6d.
Response 3: Thanks for your reminder, the lidar we used has a pulse width of 200 ns, which has a blind zone of around 30 m. Now we have corrected the expression and the data in the figures are plotted from 51.96 m (first bin at 60 m and the elevation is 60 degrees).
The value of TKEDR ("8 2") are the units in log scale to simplify the expression and the same with Fig. 4(g), 6(d). And we have added the “log_{10}()” in these figures for convenience.
Changes 3: Line 115: The lidar has a pulse width of 200 ns, which has a blind zone of around 30 m. So, in the vertical direction of 0.032.20 km, 2.204.79 km, and 4.7911.29 km, the height resolution is 26 m, 52 m, and 130 m, respectively.
Comments 4: What means " the DAVIS weather station"?
Response 4: It means the weather station of model DAVIS6162: Wireless Vantage Pro2 Plus. We have added this information to the manuscript.
Changes 4: Line 130: the weather station (DAVIS6162: Wireless Vantage Pro2 Plus).
Comments 5: Line Lines 123,129: "The receiving and transmitting ends of LAS are located at the height of 55 m at site A and site B respectively. "… "temperature data recorded at the height of 2m, 8m, and 18m"
Difference in heights leads to difference in the refractive index structure constant about three times. The structure constant decreases with height.
Response 5: Thanks for reminding, actually the temperature data were recorded at the height of 2m, 8m, and 18m of the wind tower which was placed on the top of a 6story building about 30 meters high. So, the height difference is quite small and now we explained in the paper.
Changes 5: Line 134: The wind tower is placed on the top of a 6story building about 30 meters high at site C to record the continuous data of temperature and for the calculation of temperature gradient.
Comments 6: Figs. 2f, 5 say about nothing. The potential temperature and its gradient should be instead of temperature and temperature gradient to see the temperature stratification and its variations with height.
Response 6: Thanks for your advice, the temperature and its gradient were plotted in Fig. 2(f) to discover the temperature inversion phenomenon and the strong negative correlation with the Cn2. And the BruntVäisälä frequency squared N^{2} in Fig. 2(g) was drawn to reflect the temperature stratification structure. As shown in the green line in the following: the potential temperature gradient has a similar trend with the temperature gradient, especially with the N^{2}. So, to avoid giving redundant information and reveal the negative correlation between temperature inversion and the Cn2, we kept the temperature gradient result in the horizontal experiment.
Besides, we have added the potential temperature and its gradient profiles to see the temperature stratification in Fig. 5 in the revised manuscript according to your suggestion.
Changes 6:
Figure 5. The results of temperature profiles (a)(b), temperature gradient profiles (e)(f), potential temperature profiles (c)(d), and potential temperature gradient profiles (g)(h) derived from MWR and the barometric formula at different times on September 0607, 2019, local time.
Comments 7: The Richardson number in Fig. 6c is positive. That means, during measurements there was stable temperature stratification in the atmosphere. The applicability of Eq. (4) in such conditions is under question. As well as correctness of the profiles in Fig.7. Figs. 2g, 3 (green dots) demonstrate that at stable conditions there is large difference between the results of the scintillometer and calculations based on Eq. (4).
Response 7: Firstly, the Richardson number was calculated using the “bubble sort” algorithm proposed by Thorpe (Thorpe, 1977) to resort the potential temperature in a monotonically increasing order, which caused the positive value of the Richardson number. From Eq. 11, one can see that the sign of the Ri should be the same as N^{2}. Secondly, the Ri is the ratio of N^{2} to wind shear S^{2}. When 0<Ri<1, turbulence is easy to occur due to the domination of wind shear. So, the positive Ri doesn’t mean a stable layer, and a more specific illustration about Ri can be found in Line 281 in the revised manuscript. Thirdly, the differences in Fig. 2(g), 3 (green dots) have been explained in the general comments, which are mainly within the transition period around 16:0020:00 rather than all of the stable conditions at night. Moreover, the green lines in Fig. 7 are the HAP turbulence model that takes into account the powerlaw relationship with height near the ground. So, they are drawn here mainly to compare the surface layer and the model cannot represent a specific local feature. Finally, we have supplemented the analysis of the applicability and uncertainty of this method under different circumstances in the revised manuscript.
Changes 7: There are several changes related to the analysis of the limitation of this method. Parts of them are listed in the following:
Figure 3. The relative error of the estimation of TKEDR and Cn2 (a), integral scale Lv (b), and comparative statistical analysis of LAS and CDWL observation results from September 26 to October 01, 2020, local time.
Figure 7. The relative error of the estimation of TKEDR (a), Cn2 (b), and integral scale Lv (c) calculated from CDWL and MWR in the observations from September 06 to September 07, 2019, local time.
Line 315: Then, the relative error of estimation of TKEDR, Cn2, and the integral scale Lv are calculated vertically in Fig. 7. The region with a relative error greater than 50% are marked in light yellow in Fig. 7(a) and (b). From the results, it can be seen that when using this method to obtain the profiles, a small relative error ( is mostly within 30%) can be maintained in the ABL, especially in the CBL. In the meantime, is basically under 1 km in this area, so that R'>Lv is satisfied, which means a low RE_{TKEDR}. After 18:00, with the height of the boundary layer decreases, the TKEDR drops rapidly at high altitude, and the Lv becomes larger than 2 km. As a result, the calculated RE_{TKEDR} and RE_{Cn2} also grow as shown in the figure. During the period of the atmosphere changes from convection to laminar flow (around 18:00 to 21:00), a sudden increase in relative error can be found similar to the horizontal experiment. After the atmosphere stabilized at night, the relative error of TKEDR and Cn2 begin to gradually decrease, but mainly within the mixing layer.
Best regards!
Sincerely yours,
Haiyun Xia
School of Earth and Space Sciences,
University of Science and Technology of China.
96 Jinzhai rd. Hefei, Anhui, CHINA, 230026.


AC1: 'Reply on RC1', Haiyun Xia, 30 Jan 2022

RC2: 'Comment on amt2021288', Anonymous Referee #2, 13 Dec 2021
Pu et al. present an interesting study, which uses a combination of instruments which are increasingly used in operational observation of the ABL, i.e. Doppler wind lidar and microwave radiometer. They derive the structure parameter Cn2 from profile measurements, which is quite uncommon in boundarylayer meteorology profiling, but can be reasonable for the applications in optics and astronomy. Despite this novel approach the authors fail to convincingly show that their method really provides data that is valid and useful for the described applications. No uncertainty estimation is presented and confronted with the requirements. For these reasons, I cannot recommend the manuscript for publication in AMT unless major revisions are implemented.
General comments:
 Doppler wind lidar turbulence retrievals are always problematic in low turbulence regimes, because the volume averaging effect can only be corrected to a certain limit and smallscale turbulence cannot be captured. The cited work by Smalikho gives clear boundaries and criteria under which dissipation rates can be obtained with a reasonable uncertainty. It mostly depends on the integral length scale of turbulence. This should be considered in this study as well.
 Microwave radiometers are known to not be able to capture strong temperature gradients very well. This can be problematic at the tropopause, but also in nighttime inversion layers and at the top of the boundary layer. However, turbulence can particularly occur at these levels and Cn2 should be strongly affected. The authors do not discuss this and the implications on the accuracy of their retrievals.
 English language should be somewhat improved in the next revision. Some paragraphs are hard to understand.
Specific comments:
p.1, l.16: check units
p.3, Eq.2: $z$ is missing in the equation
p.4, l.100f: The MWR does not provide pressure profiles.
p.5, l.132f: so, I understand that the temperatre gradient is not measured, but Fig.2 says that Cn2 is calculated from wind tower as well.
p.6, l.169ff: I do not think that correlation coefficient and mean error are a good overall estimate here. It should probably be presented in some relation to the turbulence and stability regime.
p.8, l.212: I think this is a misinterpretation. I do not think that the smooth profiles reduce the error, but are actually a source of error, as described in the general comments. I am not sure what is meant by "jitter of the instrument" here.
p.8, l.235f: The Richardson number is not a parameter for rough prediction, but a comprehensive turbulence parameter that gives a value for the dynamic stability of the atmosphere. Equation 11 gives the gradient Richardson number, which is a simplification of the flux Richardson number.
p.20, fig.5: Pressure profile and pressure gradient is not really very interesting here.Citation: https://doi.org/10.5194/amt2021288RC2 
AC2: 'Reply on RC2', Haiyun Xia, 30 Jan 2022
Dear Referee #2:
Thank you for your valuable comments and suggestions which helped us significantly to improve our manuscript. We have considered all comments carefully and revised the manuscript. Our pointbypoint responses to all your comments are listed below in blue fonts and the changes in the manuscript are listed in blue italic fonts.
Anonymous Referee #2:
Pu et al. present an interesting study, which uses a combination of instruments which are increasingly used in operational observation of the ABL, i.e. Doppler wind lidar and microwave radiometer. They derive the structure parameter Cn2 from profile measurements, which is quite uncommon in boundarylayer meteorology profiling, but can be reasonable for the applications in optics and astronomy. Despite this novel approach the authors fail to convincingly show that their method really provides data that is valid and useful for the described applications. No uncertainty estimation is presented and confronted with the requirements. For these reasons, I cannot recommend the manuscript for publication in AMT unless major revisions are implemented.
Response: Thank you for your recognition of the novelty in the manuscript. The purpose of our work is to obtain the turbulence profiles with high temporal and spatial resolution simultaneously. To make our results more convincing, we took the verification experiments horizontally with the scintillometer due to the difficulty of vertical experiments with high resolution. However, we become to realize the significance of results reliability evaluation thanks to your reminder. Now we have added the uncertainty analyses by calculating the relative error of TKEDR, Cn2, and the integral scale of turbulence in both horizontal and vertical experiments in the revised manuscript.
Changes: Line 368: Through the calculation of the relative error and integral scale of turbulence, we analyzed the uncertainty and limitation when using this method at different times and altitudes. In the horizontal results, the Cn2 retrieved by CDWL in the night (especially the transition period) coincides not as well as in the daytime when the integral scale of turbulence Lv reduces to a value smaller than mΔy. In the vertical profiles, the Cn2 can be estimated with a low relative error under the ABL. And the Lv grows when the TKEDR decreases with height, which leads to a larger RE_{Cn2} in the high altitude.
General Comments:
Doppler wind lidar turbulence retrievals are always problematic in low turbulence regimes, because the volume averaging effect can only be corrected to a certain limit and smallscale turbulence cannot be captured. The cited work by Smalikho gives clear boundaries and criteria under which dissipation rates can be obtained with a reasonable uncertainty. It mostly depends on the integral length scale of turbulence. This should be considered in this study as well.
Microwave radiometers are known to not be able to capture strong temperature gradients very well. This can be problematic at the tropopause, but also in nighttime inversion layers and at the top of the boundary layer. However, turbulence can particularly occur at these levels and Cn2 should be strongly affected. The authors do not discuss this and the implications on the accuracy of their retrievals.
English language should be somewhat improved in the next revision. Some paragraphs are hard to understand.
Response: Thanks for your constructive suggestions. Indeed, smallscale turbulence is hard to be found by Doppler wind lidar, especially at the high altitude in the nighttime. The criteria using the integral length scale of turbulence to estimate the uncertainty given by Smalikho is an effective way, and we have supplemented this part in the revised manuscript as we answered above.
Compare with the wind tower or radiosonde, the microwave radiometer (MWR) uses a remote sensing method to gain the temperature profiles. The MWR is indeed hard to capture strong temperature gradients layers, such as the tropopause, inversion layers, or the top of the boundary layer as the reviewer mentioned. However, these areas normally exist quite strong turbulence activities, which are vital in atmospheric turbulence research, especially in the boundary layer theory. Consequently, we have discussed this issue in the revised version.
Finally, we checked our revised manuscript and improved the grammar and sentences to make them more understandable. Thanks again for all your advice.
Changes: There are several changes related to the uncertainty analysis in the revised manuscript. The main principle is listed in the following:
Line 180210: To testify the applicability and its uncertainty of this method under different circumstances, the relative error of the estimation of Cn2 (RE_{Cn2}) is calculated according to Eq. (4) as follows:
(10)
where the RE_{TKEDR} is estimated based on the lidar system parameters, the value of TKEDR, and the instrumental error of the radial velocity (σ_{e}) (Banakh et al., 2017; Smalikho and Banakh, 2017). The σ_{e} is mainly affected by the CNR and it is calculated by the model of CramerRao lower bound (CRLB) with an assumption of a Gaussian laser pulse (Frehlich et al., 1994; Rye and Hardesty, 1993a, b). RE_{windshear} can be derived from the sum of relative error of horizontal wind in different altitudes divided by the distance between two layers. According to Eq. (8), the RE_{M(T, P)} is estimated by the relative error of temperature (RE_{T}) and pressure (RE_{P}). In this paper, RE_{T} takes ±1 K @ 280 K and RE_{P }takes ±1 hPa @ 800 hPa.
The sixday continuous results of RE_{TKEDR} and RE_{Cn2} are plotted in Fig. 3(a). Since the height set in the horizontal experiment is near the surface layer, the CNR is high and the instrumental error of estimation of the wind field is quite small. Therefore, the relative error of TKEDR and Cn2 are within 10% most of the time, which demonstrates the robustness of this method. The RE_{Cn2} is also shown in Fig. 2(g) with a shaded area error bar. However, since the Cn2 is usually compared on a log scale, a 10% relative error is not obvious in the figure.
The integral scale Lv is an indicator reflecting the rationality of the turbulence parameters retrieval (Smalikho and Banakh, 2020). It can be calculated from the radial velocity variance averaged over all azimuth angles (¯σ_{e}^{2}) and TKEDR (Smalikho and Banakh, 2017):
(11)
On the one hand, when the distance mΔy<Lv is satisfied (Δy is the spatial distance between the centers of two neighboring probing volumes, mΔy=5.24 m in the horizontal experiment), then the local isotropy of turbulence holds. On the other hand, if the radius of the scanning cone at a certain height (R'=30 m) is comparable with or even smaller than Lv, the relative error of estimation of TKEDR becomes larger.
From the results of Lv in Fig. 3(b), one can see that it is mainly distributed between the mΔy and R', which means this method work and remain a low relative error most of the time during the experiment. During the transition period around 16:0020:00, the integral scale of turbulence Lv drops to the scale smaller than the mΔy used to calculate the TKEDR. Like the results shown in the temperature gradient and N^{2}, this verified the difference between the two instruments are mainly due to the prominent motion state of the atmosphere changes from convective to laminar flow, which means the local turbulence translates from isotropic into anisotropic.
Specific Comments:
Comments 1: p.1, l.16: check units
Response 1: Thank you for your reminder, we have replaced the standard deviation with the relative error which is more informative.
Changes 1: Line 15: …the correlation coefficient between them in the sixday observation is 0.8389, the mean and relative error is 1.09×10^{15}m^{2/3} and 2.04%, respectively.
Comments 2: p.3, Eq.2: $z$ is missing in the equation
Response 2: Thanks a lot. We have corrected the intensity of the wind shear S into S(z) in the equation.
Changes 2: Line 82: Eq. 2
(2)
Comments 3: p.4, l.100f: The MWR does not provide pressure profiles.
Response 3: Thanks for reminding us. We have fixed it in a more precise way.
Changes 3: Line 107: …derived from microwave radiometer and the barometric formula.
Comments 4: p.5, l.132f: so, I understand that the temperature gradient is not measured, but Fig.2 says that Cn2 is calculated from wind tower as well.
Response 4: Sorry for the misunderstanding, the Cn2 was derived from the CDWL and LAS, instead of the wind tower. Now we have changed the expression.
Changes 4: Figure 2. The horizontal wind speed (a), wind direction (b), vertical wind speed (c), wind shear (d), log_{10}(TKEDR) (e), log_{10}Cn2 and its shaded area error bar (g) retrieved from CDWL, temperature, temperature gradient (f) and BruntVäisälä frequency squared (g) recorded by wind tower, log_{10}Cn2 (g, red) obtained from LAS in the observations from September 26 to October 01, 2020, local time.
Comments 5: p.6, l.169ff: I do not think that correlation coefficient and mean error are a good overall estimate here. It should probably be presented in some relation to the turbulence and stability regime.
Response 5: According to your suggestion, we have added the uncertainty analysis and explained it more reasonably in the revised manuscript.
Changes 5:

AC2: 'Reply on RC2', Haiyun Xia, 30 Jan 2022