Abstract

We evaluate the mean velocity estimator performance for coherent Doppler lidar measurements of wind fields with wind shear and nonuniform system response as a function of target range. Performance of the velocity estimates is characterized by the bias and standard deviation that are determined by computer simulations. Results are for solid-state lasers with a Gaussian transmitted pulse. We consider data with high signal energy that produces negligible random outliers.

© 1997 Optical Society of America

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  1. J. W. Bilbro, C. DiMarzio, D. Fitzjarrald, S. Johnson, W. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 2952–2960 (1986).
    [CrossRef]
  2. W. L. Eberhard, R. E. Cupp, K. R. Healy, “Doppler lidar measurements of profiles of turbulence and momentum flux,” J. Atmos. Oceanic Technol. 6, 809–819 (1989).
    [CrossRef]
  3. R. T. Menzies, R. M. Hardesty, “Coherent Doppler lidar for measurements of wind fields,” Proc. IEEE 77, 449–462 (1989).
    [CrossRef]
  4. M. J. Post, R. E. Cupp, “Optimizing a pulsed Doppler lidar,” Appl. Opt. 29, 4145–4158 (1990).
    [CrossRef] [PubMed]
  5. T. Gal-chen, M. Xu, W. L. Eberhard, “Estimations of atmospheric boundary layer fluxes and other turbulence parameters from Doppler lidar data” J. Geophys. Res. 97, 409–418 (1992).
  6. R. L. Schwiesow, M. P. Spowart, “The NCAR airborne infrared lidar system: status and applications,” J. Atmos. Oceanic Technol. 13, 4–15 (1996).
    [CrossRef]
  7. M. J. Kavaya, S. W. Henderson, J. R. Magee, C. P. Hale, R. M. Huffaker, “Remote wind profiling with a solid-state Nd: YAG coherent lidar system,” Opt. Lett. 14, 776–778 (1989).
    [CrossRef] [PubMed]
  8. S. W. Henderson, C. P. Hale, J. R. Magee, M. J. Kavaya, A. V. Huffaker, “Eye-safe coherent laser radar system at 2.1 µm using Tm,Ho:YAG lasers,” Opt. Lett. 16, 773–775 (1991).
    [CrossRef] [PubMed]
  9. S. W. Henderson, P. J. M. Suni, C. P. Hale, S. M. Hannon, J. R. Magee, D. L. Bruns, E. H. Yuen, “Coherent laser radar at 2 µm using solid-state lasers,” IEEE Trans. Geosci. Remote Sensing 31, 4–15 (1993).
    [CrossRef]
  10. R. Targ, M. J. Kavaya, R. M. Huffaker, R. L. Bowles, “Coherent lidar airborne wind shear sensor: performance evaluation,” Appl. Opt. 30, 2013–2026 (1991).
    [CrossRef] [PubMed]
  11. R. G. Frehlich, S. Hannon, S. Henderson, “Performance of a 2-µm coherent Doppler lidar for wind measurements,” J. Atmos. Oceanic Technol. 11, 1517–1528 (1994).
    [CrossRef]
  12. R. G. Frehlich, S. Hannon, S. Henderson, “Coherent Doppler lidar measurements of winds in the weak signal regime,” Appl. Opt. 36, 3491–3499 (1997).
    [CrossRef] [PubMed]
  13. B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. I. Spectral accumulation and the Cramer-Rao lower bound,” IEEE Trans. Geosci. Remote Sensing 31, 16–27 (1993).
    [CrossRef]
  14. B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. II. Correlogram accumulation,” IEEE Trans. Geosci. Remote Sensing 31, 28–35 (1993).
    [CrossRef]
  15. R. G. Frehlich, M. J. Yadlowsky, “Performance of mean frequency estimators for Doppler radar and lidar,” J. Atmos. Oceanic. Technol. 11, 1217–1230 (1994).
    [CrossRef]
  16. P. Salamitou, A. Dabas, P. H. Flamant, “Simulation in the time domain for heterodyne coherent laser radar,” Appl. Opt. 34, 499–506 (1995).
    [CrossRef] [PubMed]
  17. R. G. Frehlich, “Simulation of coherent Doppler lidar performance in the weak signal regime,” J. Atmos. Oceanic Technol. 13, 646–658 (1996).
    [CrossRef]
  18. B. J. Rye, “Spectral correlation of atmospheric lidar returns with range-dependent backscatter,” J. Opt. Soc. Am. A 7, 2199–2207 (1990).
    [CrossRef]
  19. R. G. Frehlich, “Effects of wind turbulence on coherent Doppler lidar performance,” J. Atmos. Oceanic Technol. 14, 54–75 (1997).
    [CrossRef]
  20. S. M. Hannon, J. A. Thomson, “Aircraft wake vortex detection and measurement with pulsed solid-state coherent laser radar,” J. Mod. Opt. 41, 2175–2196 (1994).
    [CrossRef]
  21. R. T. Menzies, D. M. Tratt, “Airborne CO2 coherent lidar for measurements of atmospheric aerosol and cloud backscatter,” Appl. Opt. 33, 5698–5711 (1994).
    [CrossRef] [PubMed]
  22. K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
    [CrossRef]
  23. I. Gultepe, D. O.’C. Starr, A. J. Heymsfield, T. Uttal, T. P. Ackerman, D. L. Westphal, “Dynamical characteristics of cirrus clouds from aircraft and radar observations in micro and meso-γ scale,” J. Atmos. Sci. 52, 4060–4078 (1995).
    [CrossRef]
  24. R. G. Frehlich, S. M. Hannon, S. W. Henderson, “Coherent Doppler lidar measurements of wind field statistics,” Boundary-Layer Meteorol. (to be published).
  25. R. G. Frehlich, “Coherent Doppler lidar signal covariance including wind shear and wind turbulence,” Appl. Opt. 33, 6472–6481 (1994).
    [CrossRef] [PubMed]
  26. L. R. Bissonnette, “Multiple-scattering lidar equation,” Appl. Opt. 35, 6449–6465 (1996).
    [CrossRef] [PubMed]
  27. C. W. Helstrom, Statistical Theory of Signal Detection (McGraw-Hill, New York, 1968).
  28. R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30, 5325–5352 (1991).
    [CrossRef] [PubMed]
  29. B. J. Rye, R. G. Frehlich, “Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscattered target,” Appl. Opt. 31, 2891–2899 (1992).
    [CrossRef] [PubMed]
  30. G. M. Ancellet, R. T. Menzies, “Atmospheric correlation-time measurements and effects on coherent Doppler lidar,” J. Opt. Soc. Am. A 4, 367–373 (1987).
    [CrossRef]
  31. V. Cizek, “Discrete Hilbert transform,” IEEE Trans. Audio Electroacoust. AU-18, 340–343 (1970).
    [CrossRef]
  32. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing (Cambridge U. Press, London, 1987).
  33. J. M. Geist, “Computer generation of correlated Gaussian random variables,” Proc. IEEE 67, 862–863 (1979).
    [CrossRef]
  34. D. S. Zrnic, “Estimation of spectral moments of weather echoes,” IEEE Trans. Geosci. Electron. GE-17, 113–128 (1979).
    [CrossRef]

1997 (2)

R. G. Frehlich, S. Hannon, S. Henderson, “Coherent Doppler lidar measurements of winds in the weak signal regime,” Appl. Opt. 36, 3491–3499 (1997).
[CrossRef] [PubMed]

R. G. Frehlich, “Effects of wind turbulence on coherent Doppler lidar performance,” J. Atmos. Oceanic Technol. 14, 54–75 (1997).
[CrossRef]

1996 (3)

L. R. Bissonnette, “Multiple-scattering lidar equation,” Appl. Opt. 35, 6449–6465 (1996).
[CrossRef] [PubMed]

R. G. Frehlich, “Simulation of coherent Doppler lidar performance in the weak signal regime,” J. Atmos. Oceanic Technol. 13, 646–658 (1996).
[CrossRef]

R. L. Schwiesow, M. P. Spowart, “The NCAR airborne infrared lidar system: status and applications,” J. Atmos. Oceanic Technol. 13, 4–15 (1996).
[CrossRef]

1995 (2)

I. Gultepe, D. O.’C. Starr, A. J. Heymsfield, T. Uttal, T. P. Ackerman, D. L. Westphal, “Dynamical characteristics of cirrus clouds from aircraft and radar observations in micro and meso-γ scale,” J. Atmos. Sci. 52, 4060–4078 (1995).
[CrossRef]

P. Salamitou, A. Dabas, P. H. Flamant, “Simulation in the time domain for heterodyne coherent laser radar,” Appl. Opt. 34, 499–506 (1995).
[CrossRef] [PubMed]

1994 (5)

R. G. Frehlich, “Coherent Doppler lidar signal covariance including wind shear and wind turbulence,” Appl. Opt. 33, 6472–6481 (1994).
[CrossRef] [PubMed]

S. M. Hannon, J. A. Thomson, “Aircraft wake vortex detection and measurement with pulsed solid-state coherent laser radar,” J. Mod. Opt. 41, 2175–2196 (1994).
[CrossRef]

R. T. Menzies, D. M. Tratt, “Airborne CO2 coherent lidar for measurements of atmospheric aerosol and cloud backscatter,” Appl. Opt. 33, 5698–5711 (1994).
[CrossRef] [PubMed]

R. G. Frehlich, S. Hannon, S. Henderson, “Performance of a 2-µm coherent Doppler lidar for wind measurements,” J. Atmos. Oceanic Technol. 11, 1517–1528 (1994).
[CrossRef]

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

1993 (3)

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

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. II. Correlogram accumulation,” IEEE Trans. Geosci. Remote Sensing 31, 28–35 (1993).
[CrossRef]

S. W. Henderson, P. J. M. Suni, C. P. Hale, S. M. Hannon, J. R. Magee, D. L. Bruns, E. H. Yuen, “Coherent laser radar at 2 µm using solid-state lasers,” IEEE Trans. Geosci. Remote Sensing 31, 4–15 (1993).
[CrossRef]

1992 (2)

T. Gal-chen, M. Xu, W. L. Eberhard, “Estimations of atmospheric boundary layer fluxes and other turbulence parameters from Doppler lidar data” J. Geophys. Res. 97, 409–418 (1992).

B. J. Rye, R. G. Frehlich, “Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscattered target,” Appl. Opt. 31, 2891–2899 (1992).
[CrossRef] [PubMed]

1991 (4)

1990 (2)

1989 (3)

W. L. Eberhard, R. E. Cupp, K. R. Healy, “Doppler lidar measurements of profiles of turbulence and momentum flux,” J. Atmos. Oceanic Technol. 6, 809–819 (1989).
[CrossRef]

R. T. Menzies, R. M. Hardesty, “Coherent Doppler lidar for measurements of wind fields,” Proc. IEEE 77, 449–462 (1989).
[CrossRef]

M. J. Kavaya, S. W. Henderson, J. R. Magee, C. P. Hale, R. M. Huffaker, “Remote wind profiling with a solid-state Nd: YAG coherent lidar system,” Opt. Lett. 14, 776–778 (1989).
[CrossRef] [PubMed]

1987 (1)

1986 (1)

J. W. Bilbro, C. DiMarzio, D. Fitzjarrald, S. Johnson, W. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 2952–2960 (1986).
[CrossRef]

1979 (2)

J. M. Geist, “Computer generation of correlated Gaussian random variables,” Proc. IEEE 67, 862–863 (1979).
[CrossRef]

D. S. Zrnic, “Estimation of spectral moments of weather echoes,” IEEE Trans. Geosci. Electron. GE-17, 113–128 (1979).
[CrossRef]

1970 (1)

V. Cizek, “Discrete Hilbert transform,” IEEE Trans. Audio Electroacoust. AU-18, 340–343 (1970).
[CrossRef]

Ackerman, T. P.

I. Gultepe, D. O.’C. Starr, A. J. Heymsfield, T. Uttal, T. P. Ackerman, D. L. Westphal, “Dynamical characteristics of cirrus clouds from aircraft and radar observations in micro and meso-γ scale,” J. Atmos. Sci. 52, 4060–4078 (1995).
[CrossRef]

Ancellet, G. M.

Bilbro, J. W.

J. W. Bilbro, C. DiMarzio, D. Fitzjarrald, S. Johnson, W. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 2952–2960 (1986).
[CrossRef]

Bissonnette, L. R.

Bowles, R. L.

Bruns, D. L.

S. W. Henderson, P. J. M. Suni, C. P. Hale, S. M. Hannon, J. R. Magee, D. L. Bruns, E. H. Yuen, “Coherent laser radar at 2 µm using solid-state lasers,” IEEE Trans. Geosci. Remote Sensing 31, 4–15 (1993).
[CrossRef]

Cizek, V.

V. Cizek, “Discrete Hilbert transform,” IEEE Trans. Audio Electroacoust. AU-18, 340–343 (1970).
[CrossRef]

Cupp, R. E.

M. J. Post, R. E. Cupp, “Optimizing a pulsed Doppler lidar,” Appl. Opt. 29, 4145–4158 (1990).
[CrossRef] [PubMed]

W. L. Eberhard, R. E. Cupp, K. R. Healy, “Doppler lidar measurements of profiles of turbulence and momentum flux,” J. Atmos. Oceanic Technol. 6, 809–819 (1989).
[CrossRef]

Dabas, A.

DiMarzio, C.

J. W. Bilbro, C. DiMarzio, D. Fitzjarrald, S. Johnson, W. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 2952–2960 (1986).
[CrossRef]

Eberhard, W. L.

T. Gal-chen, M. Xu, W. L. Eberhard, “Estimations of atmospheric boundary layer fluxes and other turbulence parameters from Doppler lidar data” J. Geophys. Res. 97, 409–418 (1992).

W. L. Eberhard, R. E. Cupp, K. R. Healy, “Doppler lidar measurements of profiles of turbulence and momentum flux,” J. Atmos. Oceanic Technol. 6, 809–819 (1989).
[CrossRef]

Fitzjarrald, D.

J. W. Bilbro, C. DiMarzio, D. Fitzjarrald, S. Johnson, W. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 2952–2960 (1986).
[CrossRef]

Flamant, P. H.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing (Cambridge U. Press, London, 1987).

Frehlich, R. G.

R. G. Frehlich, S. Hannon, S. Henderson, “Coherent Doppler lidar measurements of winds in the weak signal regime,” Appl. Opt. 36, 3491–3499 (1997).
[CrossRef] [PubMed]

R. G. Frehlich, “Effects of wind turbulence on coherent Doppler lidar performance,” J. Atmos. Oceanic Technol. 14, 54–75 (1997).
[CrossRef]

R. G. Frehlich, “Simulation of coherent Doppler lidar performance in the weak signal regime,” J. Atmos. Oceanic Technol. 13, 646–658 (1996).
[CrossRef]

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

R. G. Frehlich, S. Hannon, S. Henderson, “Performance of a 2-µm coherent Doppler lidar for wind measurements,” J. Atmos. Oceanic Technol. 11, 1517–1528 (1994).
[CrossRef]

R. G. Frehlich, “Coherent Doppler lidar signal covariance including wind shear and wind turbulence,” Appl. Opt. 33, 6472–6481 (1994).
[CrossRef] [PubMed]

B. J. Rye, R. G. Frehlich, “Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscattered target,” Appl. Opt. 31, 2891–2899 (1992).
[CrossRef] [PubMed]

R. G. Frehlich, M. J. Kavaya, “Coherent laser radar performance for general atmospheric refractive turbulence,” Appl. Opt. 30, 5325–5352 (1991).
[CrossRef] [PubMed]

R. G. Frehlich, S. M. Hannon, S. W. Henderson, “Coherent Doppler lidar measurements of wind field statistics,” Boundary-Layer Meteorol. (to be published).

Gal-chen, T.

T. Gal-chen, M. Xu, W. L. Eberhard, “Estimations of atmospheric boundary layer fluxes and other turbulence parameters from Doppler lidar data” J. Geophys. Res. 97, 409–418 (1992).

Geist, J. M.

J. M. Geist, “Computer generation of correlated Gaussian random variables,” Proc. IEEE 67, 862–863 (1979).
[CrossRef]

Gultepe, I.

I. Gultepe, D. O.’C. Starr, A. J. Heymsfield, T. Uttal, T. P. Ackerman, D. L. Westphal, “Dynamical characteristics of cirrus clouds from aircraft and radar observations in micro and meso-γ scale,” J. Atmos. Sci. 52, 4060–4078 (1995).
[CrossRef]

Hale, C. P.

Hannon, S.

R. G. Frehlich, S. Hannon, S. Henderson, “Coherent Doppler lidar measurements of winds in the weak signal regime,” Appl. Opt. 36, 3491–3499 (1997).
[CrossRef] [PubMed]

R. G. Frehlich, S. Hannon, S. Henderson, “Performance of a 2-µm coherent Doppler lidar for wind measurements,” J. Atmos. Oceanic Technol. 11, 1517–1528 (1994).
[CrossRef]

Hannon, S. M.

S. M. Hannon, J. A. Thomson, “Aircraft wake vortex detection and measurement with pulsed solid-state coherent laser radar,” J. Mod. Opt. 41, 2175–2196 (1994).
[CrossRef]

S. W. Henderson, P. J. M. Suni, C. P. Hale, S. M. Hannon, J. R. Magee, D. L. Bruns, E. H. Yuen, “Coherent laser radar at 2 µm using solid-state lasers,” IEEE Trans. Geosci. Remote Sensing 31, 4–15 (1993).
[CrossRef]

R. G. Frehlich, S. M. Hannon, S. W. Henderson, “Coherent Doppler lidar measurements of wind field statistics,” Boundary-Layer Meteorol. (to be published).

Hardesty, R. M.

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. II. Correlogram accumulation,” IEEE Trans. Geosci. Remote Sensing 31, 28–35 (1993).
[CrossRef]

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

R. T. Menzies, R. M. Hardesty, “Coherent Doppler lidar for measurements of wind fields,” Proc. IEEE 77, 449–462 (1989).
[CrossRef]

Healy, K. R.

W. L. Eberhard, R. E. Cupp, K. R. Healy, “Doppler lidar measurements of profiles of turbulence and momentum flux,” J. Atmos. Oceanic Technol. 6, 809–819 (1989).
[CrossRef]

Helstrom, C. W.

C. W. Helstrom, Statistical Theory of Signal Detection (McGraw-Hill, New York, 1968).

Henderson, S.

R. G. Frehlich, S. Hannon, S. Henderson, “Coherent Doppler lidar measurements of winds in the weak signal regime,” Appl. Opt. 36, 3491–3499 (1997).
[CrossRef] [PubMed]

R. G. Frehlich, S. Hannon, S. Henderson, “Performance of a 2-µm coherent Doppler lidar for wind measurements,” J. Atmos. Oceanic Technol. 11, 1517–1528 (1994).
[CrossRef]

Henderson, S. W.

S. W. Henderson, P. J. M. Suni, C. P. Hale, S. M. Hannon, J. R. Magee, D. L. Bruns, E. H. Yuen, “Coherent laser radar at 2 µm using solid-state lasers,” IEEE Trans. Geosci. Remote Sensing 31, 4–15 (1993).
[CrossRef]

S. W. Henderson, C. P. Hale, J. R. Magee, M. J. Kavaya, A. V. Huffaker, “Eye-safe coherent laser radar system at 2.1 µm using Tm,Ho:YAG lasers,” Opt. Lett. 16, 773–775 (1991).
[CrossRef] [PubMed]

M. J. Kavaya, S. W. Henderson, J. R. Magee, C. P. Hale, R. M. Huffaker, “Remote wind profiling with a solid-state Nd: YAG coherent lidar system,” Opt. Lett. 14, 776–778 (1989).
[CrossRef] [PubMed]

R. G. Frehlich, S. M. Hannon, S. W. Henderson, “Coherent Doppler lidar measurements of wind field statistics,” Boundary-Layer Meteorol. (to be published).

Heymsfield, A. J.

I. Gultepe, D. O.’C. Starr, A. J. Heymsfield, T. Uttal, T. P. Ackerman, D. L. Westphal, “Dynamical characteristics of cirrus clouds from aircraft and radar observations in micro and meso-γ scale,” J. Atmos. Sci. 52, 4060–4078 (1995).
[CrossRef]

Huffaker, A. V.

Huffaker, R. M.

Johnson, S.

J. W. Bilbro, C. DiMarzio, D. Fitzjarrald, S. Johnson, W. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 2952–2960 (1986).
[CrossRef]

Jones, W.

J. W. Bilbro, C. DiMarzio, D. Fitzjarrald, S. Johnson, W. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 2952–2960 (1986).
[CrossRef]

Kavaya, M. J.

Magee, J. R.

Menzies, R. T.

Post, M. J.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing (Cambridge U. Press, London, 1987).

Rye, B. J.

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

B. J. Rye, R. M. Hardesty, “Discrete spectral peak estimation in incoherent backscatter heterodyne lidar. II. Correlogram accumulation,” IEEE Trans. Geosci. Remote Sensing 31, 28–35 (1993).
[CrossRef]

B. J. Rye, R. G. Frehlich, “Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscattered target,” Appl. Opt. 31, 2891–2899 (1992).
[CrossRef] [PubMed]

B. J. Rye, “Spectral correlation of atmospheric lidar returns with range-dependent backscatter,” J. Opt. Soc. Am. A 7, 2199–2207 (1990).
[CrossRef]

Salamitou, P.

Sassen, K.

K. Sassen, “The polarization lidar technique for cloud research: a review and current assessment,” Bull. Am. Meteorol. Soc. 72, 1848–1866 (1991).
[CrossRef]

Schwiesow, R. L.

R. L. Schwiesow, M. P. Spowart, “The NCAR airborne infrared lidar system: status and applications,” J. Atmos. Oceanic Technol. 13, 4–15 (1996).
[CrossRef]

Spowart, M. P.

R. L. Schwiesow, M. P. Spowart, “The NCAR airborne infrared lidar system: status and applications,” J. Atmos. Oceanic Technol. 13, 4–15 (1996).
[CrossRef]

Starr, D. O.’C.

I. Gultepe, D. O.’C. Starr, A. J. Heymsfield, T. Uttal, T. P. Ackerman, D. L. Westphal, “Dynamical characteristics of cirrus clouds from aircraft and radar observations in micro and meso-γ scale,” J. Atmos. Sci. 52, 4060–4078 (1995).
[CrossRef]

Suni, P. J. M.

S. W. Henderson, P. J. M. Suni, C. P. Hale, S. M. Hannon, J. R. Magee, D. L. Bruns, E. H. Yuen, “Coherent laser radar at 2 µm using solid-state lasers,” IEEE Trans. Geosci. Remote Sensing 31, 4–15 (1993).
[CrossRef]

Targ, R.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing (Cambridge U. Press, London, 1987).

Thomson, J. A.

S. M. Hannon, J. A. Thomson, “Aircraft wake vortex detection and measurement with pulsed solid-state coherent laser radar,” J. Mod. Opt. 41, 2175–2196 (1994).
[CrossRef]

Tratt, D. M.

Uttal, T.

I. Gultepe, D. O.’C. Starr, A. J. Heymsfield, T. Uttal, T. P. Ackerman, D. L. Westphal, “Dynamical characteristics of cirrus clouds from aircraft and radar observations in micro and meso-γ scale,” J. Atmos. Sci. 52, 4060–4078 (1995).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes, The Art of Scientific Computing (Cambridge U. Press, London, 1987).

Westphal, D. L.

I. Gultepe, D. O.’C. Starr, A. J. Heymsfield, T. Uttal, T. P. Ackerman, D. L. Westphal, “Dynamical characteristics of cirrus clouds from aircraft and radar observations in micro and meso-γ scale,” J. Atmos. Sci. 52, 4060–4078 (1995).
[CrossRef]

Xu, M.

T. Gal-chen, M. Xu, W. L. Eberhard, “Estimations of atmospheric boundary layer fluxes and other turbulence parameters from Doppler lidar data” J. Geophys. Res. 97, 409–418 (1992).

Yadlowsky, M. J.

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

Yuen, E. H.

S. W. Henderson, P. J. M. Suni, C. P. Hale, S. M. Hannon, J. R. Magee, D. L. Bruns, E. H. Yuen, “Coherent laser radar at 2 µm using solid-state lasers,” IEEE Trans. Geosci. Remote Sensing 31, 4–15 (1993).
[CrossRef]

Zrnic, D. S.

D. S. Zrnic, “Estimation of spectral moments of weather echoes,” IEEE Trans. Geosci. Electron. GE-17, 113–128 (1979).
[CrossRef]

Appl. Opt. (10)

J. W. Bilbro, C. DiMarzio, D. Fitzjarrald, S. Johnson, W. Jones, “Airborne Doppler lidar measurements,” Appl. Opt. 25, 2952–2960 (1986).
[CrossRef]

M. J. Post, R. E. Cupp, “Optimizing a pulsed Doppler lidar,” Appl. Opt. 29, 4145–4158 (1990).
[CrossRef] [PubMed]

R. Targ, M. J. Kavaya, R. M. Huffaker, R. L. Bowles, “Coherent lidar airborne wind shear sensor: performance evaluation,” Appl. Opt. 30, 2013–2026 (1991).
[CrossRef] [PubMed]

R. G. Frehlich, S. Hannon, S. Henderson, “Coherent Doppler lidar measurements of winds in the weak signal regime,” Appl. Opt. 36, 3491–3499 (1997).
[CrossRef] [PubMed]

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Figures (11)

Fig. 1
Fig. 1

Examples of typical velocity and system response profiles. The two pulse weighting function locations correspond to the first and last data points of the range gate.

Fig. 2
Fig. 2

Examples of several columns of both the model covariance matrix R and the estimates of the covariance matrix RD for Φ = 100, Ω = 0.3, MR = 32, and N = 5. The models and estimates are shown as the solid and dashed curves, respectively.

Fig. 3
Fig. 3

Slices of the 3D MSE estimator error surface for Θ = 100, Ω = 0.3, MR = 32, and N = 5. The estimates near the global minimum are (z0)/vs, α̂, and δ̂. The free-velocity model parameters are the same as the simulated data, or v(z0)/vs = 0.5, α = 5.0, δ = 0.0, and ∊ = 0.2.

Fig. 4
Fig. 4

PDF’s for the 1D and 3D MSE estimators for a high-resolution configuration. The PDF’s are based on 20,000 estimates.

Fig. 5
Fig. 5

Normalized estimator error g/wv and normalized bias ΔVb/wv versus the normalized velocity at the center of the range gate v(z0)/vs or case 0 in Table 2.

Fig. 6
Fig. 6

Normalized estimator error gυ and normalized bias ΔVbυ versus the system response gradient ∊ = b(z0p/2 or case 1 in Table 2.

Fig. 7
Fig. 7

Normalized estimator error g/wv and normalized bias ΔVb/wv versus the linear velocity gradient α or case 2 in Table 2.

Fig. 8
Fig. 8

Normalized estimator error g/wv and normalized bias ΔVb/wv versus the linear velocity gradient α for system response gradient ∊ = 0.1 or case 3 in Table 2.

Fig. 9
Fig. 9

Normalized estimator error g/wv and normalized bias ΔVb/wv versus the linear velocity gradient α for system response gradient ∊ = 0.2 or case 4 in Table 2.

Fig. 10
Fig. 10

Normalized estimator error g/wv and normalized bias ΔVb/wv versus the parabolic velocity gradient δ or case 5 in Table 2.

Fig. 11
Fig. 11

Normalized estimator error g/wv and normalized bias ΔVb/wv versus the number of data points per estimate with N = 5. Lidar parameters for real data are Ω = 0.3 and Φ = 100.

Tables (2)

Tables Icon

Table 1 Examples of Typical Linear and Parabolic Sheara

Tables Icon

Table 2 Atmospheric Parameters Evaluated in This Paper

Equations (69)

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ALt=JL1/2texp2πi t=0tfCtdt,
-ALt2dt=- JLtdt=1.
Poutt=ALt2UL,
zt=st+nt.
Rt1, t2=zt1zt2*,
Rt1, t2=RSt1, t2+RNt1, t2,
SNRt=s2tn2t=RSt, t,
RSt1, t2=ULηQhνB×0HzALt1-2zcAL*t2-2zc×exp2πit1-t2Δf×exp-4πλit1-t2υzdz,
Hz=KzβzCz,
Cz=ARz2TTηHz,
RSt1, t2=SNR exp2πifmτ-ALtAL*t-τdt,
fm=2vλ.
Poutt=P0 exp-t2/σ2,
Δr=cσln 2.
z=ct2.
Tobs=tend-tstart,
z0=zend-zstart2.
Δp=c2Tobs
w=18πσ,
wv=λw2.
υz=vz0+gz0z-z0+hz0z-z02,
Hz=Hz01+bz0z-z0,
RSμ, τ=SNRz01+iττR1+γ1+iττRμ-t0σ-iττ1×exp2πifmτ-2μ-t0σ1+iττR×iττWS+τ2τRτc×exp-τ2τA2-τ21+i ττRτ12-iμ-t02σ21+iττRττR,
fm=Δf-2υz0λ
τA=2σ
τc=1πϕσ
τWS=λ2πrPgz0
rP=cσ2
τR=λπc2σ2hz0
μ=t1+t22
1τT2=1τ12+1τA2,
1τ1=1τc+1τWS,
γ=Hz0+rp-Hz0Hz0=bz0rP
t0=z0c2.
Φ=PRηHTobs,
Ω=wTobs=Tobs8πσ0.1874ΔpΔr.
Rk,l=zkzl*=RSkTS, lTs+δk-l,
μ-t0σ=2πΩMk+l-M-1,
ττ1=ττWS=k-l2Mα,
ττR=k-lπΩMδ,
ττA=2πk-lΩM,
γ=2πΩ,
α=ΔVLwv,
ΔVL=vz0+Δp/2-vz0=gz0Δp2
δ=ΔVPwv,
ΔVP=vz0+Δp/2-vz0=hz0Δp22
=Hz0+Δp/2-Hz0Hz0=bz0Δp2
Φ=SNRz0×M.
vz0vs=fmfN,
fN=1TS
vs=λfN2.
τAτWS=α2πΩ=cπσ22gz0λ=12ΔVLrpwv>1,
2πifmτWS-2iμ-t0/σ-τWS2/τA2-12πifmτWS-τWS2/τA2-1,
μ-t0σ12.
Ω<2π.
wvl=wv1+α24π2Ω21/2=wv2+ΔVL24π2Ω21/2,
τAτR=δ2π2Ω2=πc2σ32hz0λ=22ΔVPrpwv>1,
2πifmτR-iμ-t02/σ21+i-τR2/τA22πifmτR-τR2/τA2,
μ-t0σ12.
Ω<π.
wvp=wv1+δ22π2Ω21/2=wv2+ΔVP22π2Ω21/2,
Rˆk,l=1Ni=1Nzk,izl,i*,
σRˆk,l2Θ=1NRk,kΘRl,lΘ+Rk,lΘ2.
e2=1MR2k=1MRl=1MRRˆk,l-Rk,lΘˆ2σRˆk,lΘˆ2.
Hˆz0=2hvBηQcSNR¯,
SNR¯=1Mk=0M-1Rˆk,k-1
SDRˆk,l=Rk,kΘRl,lΘN1/2.
ΔVbwv=-δ2,
ΔVbwv=-δ4,

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