Abstract

The accuracy of the method of azimuth structure function for estimation of the dissipation rate of the kinetic energy of turbulence from an array of radial velocities measured by low-energy micropulse coherent Doppler lidars with conical scanning by a probing beam around the vertical axis has been studied numerically. The applicability of the method in dependence on the turbulence intensity and the signal-to-noise ratio has been determined. The method of azimuth structure function was applied for estimation of the turbulent energy dissipation rate from radial velocities measured by the lidar in the experiments on the coast of Lake Baikal. Two dimensional time–height patterns of the wind turbulence energy dissipation rate were obtained. Part of them were obtained in presence of the atmospheric internal waves (AIWs) and low-level jet streams. It is observed that the wind turbulence in the area occupied by jet streams is very weak. In the process of dissipation of AIWs the wind turbulence strength increases.

© 2017 Optical Society of America

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References

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  1. A. N. Kolmogorov, “Local structure of turbulence in incompressible viscous fluid at very large Reynolds numbers,” Doklady AN SSSR 30, 299–303 (1941).
  2. V. Banakh and I. Smalikho, Coherent Doppler Wind Lidars in a Turbulent Atmosphere (Artech House, 2013).
  3. A. Sathe and J. Mann, “A review of turbulence measurements using ground-based wind lidars,” Atmos. Meas. Tech. 6(11), 3147–3167 (2013).
    [Crossref]
  4. A. Sathe, R. Banta, L. Pauscher, K. Vogstad, D. Schlipf, and S. Wylie, “Estimating Turbulence Statistics and Parameters from Groundand Nacelle-Based Lidar Measurements:IEA Wind Expert Report,” (2015).
  5. A. Sathe, J. Mann, N. Vasiljevic, and G. Lea, “A six-beam method to measure turbulence statistics using ground-based wind lidars,” Atmos. Meas. Tech. 8(2), 729–740 (2015).
    [Crossref]
  6. I. N. Smalikho, V. A. Banakh, A. V. Falits, and Yu. A. Rudi, “Estimation of the turbulent energy dissipation rate from the data measured by the “StreamLine” lidar in the surface layer of atmosphere,” Atmos. Oceanic Opt. 28(10), 901–905 (2015).
  7. S. Wu, B. Liu, J. Liu, X. Zhai, C. Feng, G. Wang, H. Zhang, J. Yin, X. Wang, R. Li, and D. Gallacher, “Wind turbine wake visualization and characteristics analysis by Doppler lidar,” Opt. Express 24(10), A762–A780 (2016).
    [Crossref] [PubMed]
  8. V. A. Banakh and I. N. Smalikho, “Wind sensing in an atmospheric boundary layer by means of micropulse coherent Doppler lidars,” Opt. Spectrosc. 121(1), 152–159 (2016).
    [Crossref]
  9. R. G. Frehlich and M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar and lidar,” J. Atmos. Ocean. Technol. 11(5), 1217–1230 (1994).
    [Crossref]
  10. V. A. Banakh, V. A. Brewer, E. L. Pichugina, and I. N. Smalikho, “Measurements of wind velocity and direction with coherent Doppler lidar in conditions of a weak echo signal,” Atmos. Oceanic Opt. 23(5), 381–388 (2010).
    [Crossref]
  11. N. L. Byzova, V. N. Ivanov, and E. K. Garger, Turbulence in Atmospheric Boundary Layer (Gidrometeoizdat, 1989) [in Russian]
  12. B. J. Rye and R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I: Spectral accumulation and Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sens. 31(1), 16–27 (1993).
    [Crossref]
  13. I. N. Smalikho and V. A. Banakh, “Accuracy of estimation of the turbulent energy dissipation rate from wind measurements with a conically scanning pulsed coherent Doppler lidar,” Part I. Algorithm of data processing, Atmos. Oceanic Opt. 26(5), 404–410 (2013).
    [Crossref]
  14. V. A. Banakh and I. N. Smalikho, “Lidar observations of atmospheric internal waves in the boundary layer of atmosphere on the coast of Lake Baikal,” Atmos. Meas. Tech. 9(10), 5239–5248 (2016).
    [Crossref]
  15. I. N. Smalikho and V. A. Banakh, “Measurements of wind turbulence parameters by a conically scanning coherent Doppler lidar in the atmospheric boundary layer,” Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2017-140 (2017).
    [Crossref]
  16. I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Ocean. Technol. 30(11), 2554–2570 (2013).
    [Crossref]

2016 (3)

V. A. Banakh and I. N. Smalikho, “Wind sensing in an atmospheric boundary layer by means of micropulse coherent Doppler lidars,” Opt. Spectrosc. 121(1), 152–159 (2016).
[Crossref]

V. A. Banakh and I. N. Smalikho, “Lidar observations of atmospheric internal waves in the boundary layer of atmosphere on the coast of Lake Baikal,” Atmos. Meas. Tech. 9(10), 5239–5248 (2016).
[Crossref]

S. Wu, B. Liu, J. Liu, X. Zhai, C. Feng, G. Wang, H. Zhang, J. Yin, X. Wang, R. Li, and D. Gallacher, “Wind turbine wake visualization and characteristics analysis by Doppler lidar,” Opt. Express 24(10), A762–A780 (2016).
[Crossref] [PubMed]

2015 (2)

A. Sathe, J. Mann, N. Vasiljevic, and G. Lea, “A six-beam method to measure turbulence statistics using ground-based wind lidars,” Atmos. Meas. Tech. 8(2), 729–740 (2015).
[Crossref]

I. N. Smalikho, V. A. Banakh, A. V. Falits, and Yu. A. Rudi, “Estimation of the turbulent energy dissipation rate from the data measured by the “StreamLine” lidar in the surface layer of atmosphere,” Atmos. Oceanic Opt. 28(10), 901–905 (2015).

2013 (3)

A. Sathe and J. Mann, “A review of turbulence measurements using ground-based wind lidars,” Atmos. Meas. Tech. 6(11), 3147–3167 (2013).
[Crossref]

I. N. Smalikho and V. A. Banakh, “Accuracy of estimation of the turbulent energy dissipation rate from wind measurements with a conically scanning pulsed coherent Doppler lidar,” Part I. Algorithm of data processing, Atmos. Oceanic Opt. 26(5), 404–410 (2013).
[Crossref]

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Ocean. Technol. 30(11), 2554–2570 (2013).
[Crossref]

2010 (1)

V. A. Banakh, V. A. Brewer, E. L. Pichugina, and I. N. Smalikho, “Measurements of wind velocity and direction with coherent Doppler lidar in conditions of a weak echo signal,” Atmos. Oceanic Opt. 23(5), 381–388 (2010).
[Crossref]

1994 (1)

R. G. Frehlich and M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar and lidar,” J. Atmos. Ocean. Technol. 11(5), 1217–1230 (1994).
[Crossref]

1993 (1)

B. J. Rye and R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I: Spectral accumulation and Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sens. 31(1), 16–27 (1993).
[Crossref]

1941 (1)

A. N. Kolmogorov, “Local structure of turbulence in incompressible viscous fluid at very large Reynolds numbers,” Doklady AN SSSR 30, 299–303 (1941).

Banakh, V. A.

V. A. Banakh and I. N. Smalikho, “Lidar observations of atmospheric internal waves in the boundary layer of atmosphere on the coast of Lake Baikal,” Atmos. Meas. Tech. 9(10), 5239–5248 (2016).
[Crossref]

V. A. Banakh and I. N. Smalikho, “Wind sensing in an atmospheric boundary layer by means of micropulse coherent Doppler lidars,” Opt. Spectrosc. 121(1), 152–159 (2016).
[Crossref]

I. N. Smalikho, V. A. Banakh, A. V. Falits, and Yu. A. Rudi, “Estimation of the turbulent energy dissipation rate from the data measured by the “StreamLine” lidar in the surface layer of atmosphere,” Atmos. Oceanic Opt. 28(10), 901–905 (2015).

I. N. Smalikho and V. A. Banakh, “Accuracy of estimation of the turbulent energy dissipation rate from wind measurements with a conically scanning pulsed coherent Doppler lidar,” Part I. Algorithm of data processing, Atmos. Oceanic Opt. 26(5), 404–410 (2013).
[Crossref]

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Ocean. Technol. 30(11), 2554–2570 (2013).
[Crossref]

V. A. Banakh, V. A. Brewer, E. L. Pichugina, and I. N. Smalikho, “Measurements of wind velocity and direction with coherent Doppler lidar in conditions of a weak echo signal,” Atmos. Oceanic Opt. 23(5), 381–388 (2010).
[Crossref]

Banta, R.

A. Sathe, R. Banta, L. Pauscher, K. Vogstad, D. Schlipf, and S. Wylie, “Estimating Turbulence Statistics and Parameters from Groundand Nacelle-Based Lidar Measurements:IEA Wind Expert Report,” (2015).

Banta, R. M.

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Ocean. Technol. 30(11), 2554–2570 (2013).
[Crossref]

Brewer, V. A.

V. A. Banakh, V. A. Brewer, E. L. Pichugina, and I. N. Smalikho, “Measurements of wind velocity and direction with coherent Doppler lidar in conditions of a weak echo signal,” Atmos. Oceanic Opt. 23(5), 381–388 (2010).
[Crossref]

Brewer, W. A.

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Ocean. Technol. 30(11), 2554–2570 (2013).
[Crossref]

Falits, A. V.

I. N. Smalikho, V. A. Banakh, A. V. Falits, and Yu. A. Rudi, “Estimation of the turbulent energy dissipation rate from the data measured by the “StreamLine” lidar in the surface layer of atmosphere,” Atmos. Oceanic Opt. 28(10), 901–905 (2015).

Feng, C.

Frehlich, R. G.

R. G. Frehlich and M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar and lidar,” J. Atmos. Ocean. Technol. 11(5), 1217–1230 (1994).
[Crossref]

Gallacher, D.

Hardesty, R. M.

B. J. Rye and R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I: Spectral accumulation and Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sens. 31(1), 16–27 (1993).
[Crossref]

Kelley, N. D.

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Ocean. Technol. 30(11), 2554–2570 (2013).
[Crossref]

Kolmogorov, A. N.

A. N. Kolmogorov, “Local structure of turbulence in incompressible viscous fluid at very large Reynolds numbers,” Doklady AN SSSR 30, 299–303 (1941).

Lea, G.

A. Sathe, J. Mann, N. Vasiljevic, and G. Lea, “A six-beam method to measure turbulence statistics using ground-based wind lidars,” Atmos. Meas. Tech. 8(2), 729–740 (2015).
[Crossref]

Li, R.

Liu, B.

Liu, J.

Lundquist, J. K.

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Ocean. Technol. 30(11), 2554–2570 (2013).
[Crossref]

Mann, J.

A. Sathe, J. Mann, N. Vasiljevic, and G. Lea, “A six-beam method to measure turbulence statistics using ground-based wind lidars,” Atmos. Meas. Tech. 8(2), 729–740 (2015).
[Crossref]

A. Sathe and J. Mann, “A review of turbulence measurements using ground-based wind lidars,” Atmos. Meas. Tech. 6(11), 3147–3167 (2013).
[Crossref]

Pauscher, L.

A. Sathe, R. Banta, L. Pauscher, K. Vogstad, D. Schlipf, and S. Wylie, “Estimating Turbulence Statistics and Parameters from Groundand Nacelle-Based Lidar Measurements:IEA Wind Expert Report,” (2015).

Pichugina, E. L.

V. A. Banakh, V. A. Brewer, E. L. Pichugina, and I. N. Smalikho, “Measurements of wind velocity and direction with coherent Doppler lidar in conditions of a weak echo signal,” Atmos. Oceanic Opt. 23(5), 381–388 (2010).
[Crossref]

Pichugina, Y. L.

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Ocean. Technol. 30(11), 2554–2570 (2013).
[Crossref]

Rudi, Yu. A.

I. N. Smalikho, V. A. Banakh, A. V. Falits, and Yu. A. Rudi, “Estimation of the turbulent energy dissipation rate from the data measured by the “StreamLine” lidar in the surface layer of atmosphere,” Atmos. Oceanic Opt. 28(10), 901–905 (2015).

Rye, B. J.

B. J. Rye and R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I: Spectral accumulation and Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sens. 31(1), 16–27 (1993).
[Crossref]

Sathe, A.

A. Sathe, J. Mann, N. Vasiljevic, and G. Lea, “A six-beam method to measure turbulence statistics using ground-based wind lidars,” Atmos. Meas. Tech. 8(2), 729–740 (2015).
[Crossref]

A. Sathe and J. Mann, “A review of turbulence measurements using ground-based wind lidars,” Atmos. Meas. Tech. 6(11), 3147–3167 (2013).
[Crossref]

A. Sathe, R. Banta, L. Pauscher, K. Vogstad, D. Schlipf, and S. Wylie, “Estimating Turbulence Statistics and Parameters from Groundand Nacelle-Based Lidar Measurements:IEA Wind Expert Report,” (2015).

Schlipf, D.

A. Sathe, R. Banta, L. Pauscher, K. Vogstad, D. Schlipf, and S. Wylie, “Estimating Turbulence Statistics and Parameters from Groundand Nacelle-Based Lidar Measurements:IEA Wind Expert Report,” (2015).

Smalikho, I. N.

V. A. Banakh and I. N. Smalikho, “Wind sensing in an atmospheric boundary layer by means of micropulse coherent Doppler lidars,” Opt. Spectrosc. 121(1), 152–159 (2016).
[Crossref]

V. A. Banakh and I. N. Smalikho, “Lidar observations of atmospheric internal waves in the boundary layer of atmosphere on the coast of Lake Baikal,” Atmos. Meas. Tech. 9(10), 5239–5248 (2016).
[Crossref]

I. N. Smalikho, V. A. Banakh, A. V. Falits, and Yu. A. Rudi, “Estimation of the turbulent energy dissipation rate from the data measured by the “StreamLine” lidar in the surface layer of atmosphere,” Atmos. Oceanic Opt. 28(10), 901–905 (2015).

I. N. Smalikho and V. A. Banakh, “Accuracy of estimation of the turbulent energy dissipation rate from wind measurements with a conically scanning pulsed coherent Doppler lidar,” Part I. Algorithm of data processing, Atmos. Oceanic Opt. 26(5), 404–410 (2013).
[Crossref]

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Ocean. Technol. 30(11), 2554–2570 (2013).
[Crossref]

V. A. Banakh, V. A. Brewer, E. L. Pichugina, and I. N. Smalikho, “Measurements of wind velocity and direction with coherent Doppler lidar in conditions of a weak echo signal,” Atmos. Oceanic Opt. 23(5), 381–388 (2010).
[Crossref]

Vasiljevic, N.

A. Sathe, J. Mann, N. Vasiljevic, and G. Lea, “A six-beam method to measure turbulence statistics using ground-based wind lidars,” Atmos. Meas. Tech. 8(2), 729–740 (2015).
[Crossref]

Vogstad, K.

A. Sathe, R. Banta, L. Pauscher, K. Vogstad, D. Schlipf, and S. Wylie, “Estimating Turbulence Statistics and Parameters from Groundand Nacelle-Based Lidar Measurements:IEA Wind Expert Report,” (2015).

Wang, G.

Wang, X.

Wu, S.

Wylie, S.

A. Sathe, R. Banta, L. Pauscher, K. Vogstad, D. Schlipf, and S. Wylie, “Estimating Turbulence Statistics and Parameters from Groundand Nacelle-Based Lidar Measurements:IEA Wind Expert Report,” (2015).

Yadlowsky, M. J.

R. G. Frehlich and M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar and lidar,” J. Atmos. Ocean. Technol. 11(5), 1217–1230 (1994).
[Crossref]

Yin, J.

Zhai, X.

Zhang, H.

Atmos. Meas. Tech. (3)

V. A. Banakh and I. N. Smalikho, “Lidar observations of atmospheric internal waves in the boundary layer of atmosphere on the coast of Lake Baikal,” Atmos. Meas. Tech. 9(10), 5239–5248 (2016).
[Crossref]

A. Sathe and J. Mann, “A review of turbulence measurements using ground-based wind lidars,” Atmos. Meas. Tech. 6(11), 3147–3167 (2013).
[Crossref]

A. Sathe, J. Mann, N. Vasiljevic, and G. Lea, “A six-beam method to measure turbulence statistics using ground-based wind lidars,” Atmos. Meas. Tech. 8(2), 729–740 (2015).
[Crossref]

Atmos. Oceanic Opt. (2)

I. N. Smalikho, V. A. Banakh, A. V. Falits, and Yu. A. Rudi, “Estimation of the turbulent energy dissipation rate from the data measured by the “StreamLine” lidar in the surface layer of atmosphere,” Atmos. Oceanic Opt. 28(10), 901–905 (2015).

V. A. Banakh, V. A. Brewer, E. L. Pichugina, and I. N. Smalikho, “Measurements of wind velocity and direction with coherent Doppler lidar in conditions of a weak echo signal,” Atmos. Oceanic Opt. 23(5), 381–388 (2010).
[Crossref]

Doklady AN SSSR (1)

A. N. Kolmogorov, “Local structure of turbulence in incompressible viscous fluid at very large Reynolds numbers,” Doklady AN SSSR 30, 299–303 (1941).

IEEE Trans. Geosci. Remote Sens. (1)

B. J. Rye and R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I: Spectral accumulation and Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sens. 31(1), 16–27 (1993).
[Crossref]

J. Atmos. Ocean. Technol. (2)

R. G. Frehlich and M. J. Yadlowsky, “Performance of mean-frequency estimators for Doppler radar and lidar,” J. Atmos. Ocean. Technol. 11(5), 1217–1230 (1994).
[Crossref]

I. N. Smalikho, V. A. Banakh, Y. L. Pichugina, W. A. Brewer, R. M. Banta, J. K. Lundquist, and N. D. Kelley, “Lidar investigation of atmosphere effect on a wind turbine wake,” J. Atmos. Ocean. Technol. 30(11), 2554–2570 (2013).
[Crossref]

Opt. Express (1)

Opt. Spectrosc. (1)

V. A. Banakh and I. N. Smalikho, “Wind sensing in an atmospheric boundary layer by means of micropulse coherent Doppler lidars,” Opt. Spectrosc. 121(1), 152–159 (2016).
[Crossref]

Part I. Algorithm of data processing, Atmos. Oceanic Opt. (1)

I. N. Smalikho and V. A. Banakh, “Accuracy of estimation of the turbulent energy dissipation rate from wind measurements with a conically scanning pulsed coherent Doppler lidar,” Part I. Algorithm of data processing, Atmos. Oceanic Opt. 26(5), 404–410 (2013).
[Crossref]

Other (4)

I. N. Smalikho and V. A. Banakh, “Measurements of wind turbulence parameters by a conically scanning coherent Doppler lidar in the atmospheric boundary layer,” Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2017-140 (2017).
[Crossref]

N. L. Byzova, V. N. Ivanov, and E. K. Garger, Turbulence in Atmospheric Boundary Layer (Gidrometeoizdat, 1989) [in Russian]

V. Banakh and I. Smalikho, Coherent Doppler Wind Lidars in a Turbulent Atmosphere (Artech House, 2013).

A. Sathe, R. Banta, L. Pauscher, K. Vogstad, D. Schlipf, and S. Wylie, “Estimating Turbulence Statistics and Parameters from Groundand Nacelle-Based Lidar Measurements:IEA Wind Expert Report,” (2015).

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Figures (9)

Fig. 1
Fig. 1

Azimuth dependence of the average radial velocity (black curve), radial velocity at the center of the sensing volume moving over the scanning cone base (blue curve), and lidar estimate of the radial velocity (red curve).

Fig. 2
Fig. 2

Difference structure functions ΔD(y) (blue curve), Δ D ¯ max (y) (red curve), and Δ D ¯ cnt (y) (green curve) at ε = 10−3 m2/s3 and L V = 300 m.

Fig. 3
Fig. 3

Relative error in the lidar estimate of dissipation rate as a function of the signal-to-noise ratio for ε = 10−6 (1), 10−5 (2) 10−4 (3), and 10−3 m2/s3 (4).

Fig. 4
Fig. 4

Signal-to-noise ratio as a function of the turbulence energy dissipation rate at E ε ×100% = 16% (solid red curve).

Fig. 5
Fig. 5

Time–height patterns of the wind speed U, vertical component of the wind velocity V z , turbulence energy dissipation rate ε, SNR, relative error of the dissipation rate E ε , and the radial velocity error σ e retrieved from the Stream Line lidar measurements on the coast of the Lake Baikal on August 23, 2015.

Fig. 6
Fig. 6

Vertical profiles of the turbulence energy dissipation rate (a), SNR (b), relative error of the dissipation rate estimate (c), and the radial velocity error (d) retrieved from the lidar measurements at 11:30 (black curve), 12:30 (red curve), and 13:30 (blue curve). Data are taken from Fig. 5. Dashed curves show results of calculation by Eqs. (12) and (6).

Fig. 7
Fig. 7

Vertical profiles of the turbulence energy dissipation rate (a), SNR (b), relative error of the dissipation rate estimate (c), and the radial velocity error (d) retrieved from the lidar measurements at 14:30 (black curve), 15:30 (red curve), and 16:30 (blue curve). Data are taken from Fig. 5. Dashed curves show results of calculation by Eqs. (12) and (6).

Fig. 8
Fig. 8

Results of spatiotemporal visualization of the wind speed (a), wind direction angle (b), and vertical component (c) from measurements by the Stream Line lidar on shore of Lake Baikal on 06.08.2016.

Fig. 9
Fig. 9

Dynamics of the wind speed (a), wind direction angle (b), vertical component of the wind vector (c), turbulence energy dissipation rate (d), and relative error of estimation of the dissipation rate (e) at a height of 300 m as obtained from measurements by the Stream Line lidar on shore of Lake Baikal on 06.08.2016.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

V ^ r ( R k , θ m ,n)= V ^ r ( R k , θ m ,n) S m V( h k ) ,
D ^ L ( m Δθ)= N 1 n=1 N (M m ) 1 m=1 M m [ V ^ r ( R k , θ m + m Δθ,n) V ^ r ( R k , θ m ,n) ] 2 .
V ^ r ( R k , θ m ,n)= V ¯ r ( R k , θ m ,n)+ V e ( R k , θ m ,n) .
D L ( m Δθ)= D ¯ ( m Δθ)+2 σ e 2 ,
E ε = 3 2 < [Δ D ^ L (y)Δ D ¯ (y)] 2 > Δ D ¯ (y) .
E ε =(3/2) σ D ¯ 2 + σ I 2 ,
σ I 2 = 8 (M M )N ( 1+ σ e 2 Δ D ¯ (y) ) σ e 2 Δ D ¯ (y) .
Δ D ¯ (y)=[A(mΔ y k )A(Δ y k )] ε 2/3 ,
A(z)= 4 3 C k z 2/3 G(z) ,
G(z)= [3 π Γ(5/6)] 1 0 d ξ 1 (1cos ξ 1 ) 0 d ξ 2 ( ξ 1 2 + ξ 2 3 ) 4 3 [ 1+ 8 3 ξ 1 2 ξ 1 2 + ξ 2 2 ]H( ξ 1 , ξ 2 ;z) ,
H( ξ 1 , ξ 2 ;z)=exp[ 2 ( Δp ξ 2 2z ) 2 ]sin c 2 ( Δq ξ 2 2z )sin c 2 ( Δ y k ξ 1 2z ).
σ e =( 1+ 1 SNR ) Δv N a ,

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