Abstract

The overlap function of a Raman channel for a lidar system is retrieved by nonlinear regression using an analytic description of the optical system and a simple model for the extinction profile, constrained by aerosol optical thickness. Considering simulated data, the scheme is successful even where the aerosol profile deviates significantly from the simple model assumed. Application to real data is found to reduce by a factor of 1.4–2.0 the root-mean-square difference between the attenuated backscatter coefficient as measured by the calibrated instrument and a commercial instrument.

© 2012 Optical Society of America

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  1. R. M. Measures, Lidar Remote Sensing: Fundamentals and Applications, 2nd ed. (Krieger, 1992).
  2. T. Fujii and T. Fukuchi, Laser Remote Sensing (Taylor and Francis, 2005).
  3. C. Weitkamp, Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, Springer Series in Optical Sciences (Springer, 2005).
  4. J. D. Klett, “Lidar inversion with variable backscatter extinction ratios,” Appl. Opt. 24, 1638–1643 (1985).
    [CrossRef]
  5. A. Ansmann, M. Riebesell, and C. Weitkamp, “Measurement of atmospheric aerosol extinction profiles with a Raman lidar,” Opt. Lett. 15, 746–748 (1990).
    [CrossRef]
  6. R. Velotta, B. Bartoli, R. Capobianco, L. Fiorani, and N. Spinelli, “Analysis of the receiver response in lidar measurements,” Appl. Opt. 37, 6999–7007 (1998).
    [CrossRef]
  7. I. Berezhnyy, “A combined diffraction and geometrical optics approach for lidar overlap function computation,” Opt. Lasers Eng. 47, 855–859 (2009).
    [CrossRef]
  8. T. Halldórsson and J. Langerholc, “Geometrical form factors for the lidar function,” Appl. Opt. 17, 240–244 (1978).
    [CrossRef]
  9. G. M. Ancellet, M. J. Kavaya, R. T. Menzies, and A. M. Brothers, “Lidar telescope overlap function and effects of misalignment for unstable resonator transmitter and coherent receiver,” Appl. Opt. 25, 2886–2890 (1986).
    [CrossRef]
  10. K. Stelmaszczyk, M. Dell’Aglio, S. Chudzynski, T. Stacewicz, and L. Woste, “Analytical function for lidar geometrical compression form-factor calculations,” Appl. Opt. 44, 1323–1331 (2005).
    [CrossRef]
  11. Y. Sasano, H. Shimizu, N. Takeuchi, and M. Okuda, “Geometrical form factor in the laser radar equation: an experimental determination,” Appl. Opt. 18, 3908–3910 (1979).
    [CrossRef]
  12. K. Tomine, C. Hirayama, K. Michimoto, and N. Takeuchi, “Experimental determination of the crossover function in the laser-radar equation for days with a light mist,” Appl. Opt. 28, 2194–2195 (1989).
    [CrossRef]
  13. J. L. Guerrero-Rascado, M. J. Costa, D. Bortoli, A. M. Silva, H. Lyamani, and L. Alados-Arboledas, “Infrared lidar overlap function: An experimental determination,” Opt. Express 18, 20350–20359 (2010).
    [CrossRef]
  14. U. Wandinger and A. Ansmann, “Experimental determination of the lidar overlap profile with Raman lidar,” Appl. Opt. 41, 511–514 (2002).
    [CrossRef]
  15. S. W. Dho, Y. J. Park, and H. J. Kong, “Experimental determination of a geometric form factor in a lidar equation for an inhomogeneous atmosphere,” Appl. Opt. 36, 6009–6010 (1997).
    [CrossRef]
  16. M. Adam, V. A. Kovalev, C. Wold, J. Newton, M. Pahlow, W. M. Hao, and M. B. Parlange, “Application of the Kano-Hamilton multiangle inversion method in clear atmospheres,” J. Atmos. Ocean. Technol. 24, 2014–2028 (2007).
    [CrossRef]
  17. G. Biavati, G. Di Donfrancesco, F. Cairo, and D. G. Feist, “Correction scheme for close-range lidar returns,” Appl. Opt. 50, 5872–5882 (2011).
    [CrossRef]
  18. C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice, Vol. 2 of Series on Atmospheric, Oceanic, and Planetary Physics, 2nd ed. (World Scientific, 2000).
  19. A. Gelb, Applied Optimal Estimation (Analytic Sciences Corporation, 1974).
  20. Q. S. He, C. C. Li, J. T. Mao, A. K. H. Lau, and D. A. Chu, “Analysis of aerosol vertical distribution and variability in Hong Kong,” J. Geophys. Res. Atmos. 113, D14211 (2008).
    [CrossRef]
  21. M. Wiegner, S. Emeis, V. Freudenthaler, B. Heese, W. Junkermann, C. Munkel, K. Schafer, M. Seefeldner, and S. Vogt, “Mixing layer height over Munich, Germany: variability and comparisons of different methodologies,” J. Geophys. Res. Atmos. 111, D13201 (2006).
    [CrossRef]
  22. R. Maurya, P. K. Dubey, B. C. Arya, and S. L. Jain, “Aerosol vertical profile measurements using micro pulse lidar at New Delhi, India,” presented at the International Symposium for the Advancement of Remote Sensing of the Boundary Layer, Guyancourt, France, 28–30June2010.
  23. D. G. Steyn, M. Baldi, and R. M. Hoff, “The detection of mixed layer depth and entrainment zone thickness from lidar backscatter profiles,” J. Atmos. Ocean. Technol. 16, 953–959 (1999).
    [CrossRef]
  24. S. Chib and E. Greenberg, “Understanding the Metropolis–Hastings algorithm,” Am. Stat. 49, 327–335 (1995).
  25. A. Bucholtz, “Rayleigh-scattering calculations for the terrestrial atmosphere,” Appl. Opt. 34, 2765–2773 (1995).
    [CrossRef]
  26. M. Kitchen, “Representativeness errors for radiosonde observations,” Q. J. R. Meteorol. Soc. 115, 673–700 (1989).
    [CrossRef]
  27. C. Marks and C. Rodgers, “A retrieval method for atmospheric composition from limb emission measurements,” J. Geophys. Res. Atmos. 98, 14939–14953 (1993).
    [CrossRef]
  28. P. Palmer, J. Barnett, J. Eyre, and S. Healy, “A nonlinear optimal, estimation inverse method for radio occultation measurements of temperature, humidity, and surface pressure,” J. Geophys. Res. Atmos. 105, 17513–17526 (2000).
    [CrossRef]
  29. W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
    [CrossRef]
  30. P. D. Watts, R. Bennartz, and F. Fell, “Retrieval of two-layer cloud properties from multispectral observations using optimal estimation,” J. Geophys. Res. Atmos. 116, D16203 (2011).
    [CrossRef]
  31. D. P. Donovan, J. A. Whiteway, and A. I. Carswell, “Correction for nonlinear photon-counting effects in lidar systems,” Appl. Opt. 32, 6742–6753 (1993).
    [CrossRef]

2011 (2)

P. D. Watts, R. Bennartz, and F. Fell, “Retrieval of two-layer cloud properties from multispectral observations using optimal estimation,” J. Geophys. Res. Atmos. 116, D16203 (2011).
[CrossRef]

G. Biavati, G. Di Donfrancesco, F. Cairo, and D. G. Feist, “Correction scheme for close-range lidar returns,” Appl. Opt. 50, 5872–5882 (2011).
[CrossRef]

2010 (1)

2009 (1)

I. Berezhnyy, “A combined diffraction and geometrical optics approach for lidar overlap function computation,” Opt. Lasers Eng. 47, 855–859 (2009).
[CrossRef]

2008 (2)

Q. S. He, C. C. Li, J. T. Mao, A. K. H. Lau, and D. A. Chu, “Analysis of aerosol vertical distribution and variability in Hong Kong,” J. Geophys. Res. Atmos. 113, D14211 (2008).
[CrossRef]

W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
[CrossRef]

2007 (1)

M. Adam, V. A. Kovalev, C. Wold, J. Newton, M. Pahlow, W. M. Hao, and M. B. Parlange, “Application of the Kano-Hamilton multiangle inversion method in clear atmospheres,” J. Atmos. Ocean. Technol. 24, 2014–2028 (2007).
[CrossRef]

2006 (1)

M. Wiegner, S. Emeis, V. Freudenthaler, B. Heese, W. Junkermann, C. Munkel, K. Schafer, M. Seefeldner, and S. Vogt, “Mixing layer height over Munich, Germany: variability and comparisons of different methodologies,” J. Geophys. Res. Atmos. 111, D13201 (2006).
[CrossRef]

2005 (1)

2002 (1)

2000 (1)

P. Palmer, J. Barnett, J. Eyre, and S. Healy, “A nonlinear optimal, estimation inverse method for radio occultation measurements of temperature, humidity, and surface pressure,” J. Geophys. Res. Atmos. 105, 17513–17526 (2000).
[CrossRef]

1999 (1)

D. G. Steyn, M. Baldi, and R. M. Hoff, “The detection of mixed layer depth and entrainment zone thickness from lidar backscatter profiles,” J. Atmos. Ocean. Technol. 16, 953–959 (1999).
[CrossRef]

1998 (1)

1997 (1)

1995 (2)

A. Bucholtz, “Rayleigh-scattering calculations for the terrestrial atmosphere,” Appl. Opt. 34, 2765–2773 (1995).
[CrossRef]

S. Chib and E. Greenberg, “Understanding the Metropolis–Hastings algorithm,” Am. Stat. 49, 327–335 (1995).

1993 (2)

C. Marks and C. Rodgers, “A retrieval method for atmospheric composition from limb emission measurements,” J. Geophys. Res. Atmos. 98, 14939–14953 (1993).
[CrossRef]

D. P. Donovan, J. A. Whiteway, and A. I. Carswell, “Correction for nonlinear photon-counting effects in lidar systems,” Appl. Opt. 32, 6742–6753 (1993).
[CrossRef]

1990 (1)

1989 (2)

1986 (1)

1985 (1)

1979 (1)

1978 (1)

Adam, M.

M. Adam, V. A. Kovalev, C. Wold, J. Newton, M. Pahlow, W. M. Hao, and M. B. Parlange, “Application of the Kano-Hamilton multiangle inversion method in clear atmospheres,” J. Atmos. Ocean. Technol. 24, 2014–2028 (2007).
[CrossRef]

Alados-Arboledas, L.

Ancellet, G. M.

Ansmann, A.

Arya, B. C.

R. Maurya, P. K. Dubey, B. C. Arya, and S. L. Jain, “Aerosol vertical profile measurements using micro pulse lidar at New Delhi, India,” presented at the International Symposium for the Advancement of Remote Sensing of the Boundary Layer, Guyancourt, France, 28–30June2010.

Baldi, M.

D. G. Steyn, M. Baldi, and R. M. Hoff, “The detection of mixed layer depth and entrainment zone thickness from lidar backscatter profiles,” J. Atmos. Ocean. Technol. 16, 953–959 (1999).
[CrossRef]

Barnett, J.

P. Palmer, J. Barnett, J. Eyre, and S. Healy, “A nonlinear optimal, estimation inverse method for radio occultation measurements of temperature, humidity, and surface pressure,” J. Geophys. Res. Atmos. 105, 17513–17526 (2000).
[CrossRef]

Bartoli, B.

Bennartz, R.

P. D. Watts, R. Bennartz, and F. Fell, “Retrieval of two-layer cloud properties from multispectral observations using optimal estimation,” J. Geophys. Res. Atmos. 116, D16203 (2011).
[CrossRef]

Berezhnyy, I.

I. Berezhnyy, “A combined diffraction and geometrical optics approach for lidar overlap function computation,” Opt. Lasers Eng. 47, 855–859 (2009).
[CrossRef]

Biavati, G.

Bortoli, D.

Brothers, A. M.

Bucholtz, A.

Cairo, F.

Capobianco, R.

Carswell, A. I.

Chib, S.

S. Chib and E. Greenberg, “Understanding the Metropolis–Hastings algorithm,” Am. Stat. 49, 327–335 (1995).

Chu, D. A.

Q. S. He, C. C. Li, J. T. Mao, A. K. H. Lau, and D. A. Chu, “Analysis of aerosol vertical distribution and variability in Hong Kong,” J. Geophys. Res. Atmos. 113, D14211 (2008).
[CrossRef]

Chudzynski, S.

Costa, M. J.

Dell’Aglio, M.

Dho, S. W.

Di Donfrancesco, G.

Donovan, D. P.

Dubey, P. K.

R. Maurya, P. K. Dubey, B. C. Arya, and S. L. Jain, “Aerosol vertical profile measurements using micro pulse lidar at New Delhi, India,” presented at the International Symposium for the Advancement of Remote Sensing of the Boundary Layer, Guyancourt, France, 28–30June2010.

Emeis, S.

M. Wiegner, S. Emeis, V. Freudenthaler, B. Heese, W. Junkermann, C. Munkel, K. Schafer, M. Seefeldner, and S. Vogt, “Mixing layer height over Munich, Germany: variability and comparisons of different methodologies,” J. Geophys. Res. Atmos. 111, D13201 (2006).
[CrossRef]

Eyre, J.

P. Palmer, J. Barnett, J. Eyre, and S. Healy, “A nonlinear optimal, estimation inverse method for radio occultation measurements of temperature, humidity, and surface pressure,” J. Geophys. Res. Atmos. 105, 17513–17526 (2000).
[CrossRef]

Feist, D. G.

Fell, F.

P. D. Watts, R. Bennartz, and F. Fell, “Retrieval of two-layer cloud properties from multispectral observations using optimal estimation,” J. Geophys. Res. Atmos. 116, D16203 (2011).
[CrossRef]

Fiorani, L.

Freudenthaler, V.

M. Wiegner, S. Emeis, V. Freudenthaler, B. Heese, W. Junkermann, C. Munkel, K. Schafer, M. Seefeldner, and S. Vogt, “Mixing layer height over Munich, Germany: variability and comparisons of different methodologies,” J. Geophys. Res. Atmos. 111, D13201 (2006).
[CrossRef]

Fujii, T.

T. Fujii and T. Fukuchi, Laser Remote Sensing (Taylor and Francis, 2005).

Fukuchi, T.

T. Fujii and T. Fukuchi, Laser Remote Sensing (Taylor and Francis, 2005).

Gelb, A.

A. Gelb, Applied Optimal Estimation (Analytic Sciences Corporation, 1974).

Greenberg, E.

S. Chib and E. Greenberg, “Understanding the Metropolis–Hastings algorithm,” Am. Stat. 49, 327–335 (1995).

Guerrero-Rascado, J. L.

Halldórsson, T.

Hao, W. M.

M. Adam, V. A. Kovalev, C. Wold, J. Newton, M. Pahlow, W. M. Hao, and M. B. Parlange, “Application of the Kano-Hamilton multiangle inversion method in clear atmospheres,” J. Atmos. Ocean. Technol. 24, 2014–2028 (2007).
[CrossRef]

He, Q. S.

Q. S. He, C. C. Li, J. T. Mao, A. K. H. Lau, and D. A. Chu, “Analysis of aerosol vertical distribution and variability in Hong Kong,” J. Geophys. Res. Atmos. 113, D14211 (2008).
[CrossRef]

Healy, S.

P. Palmer, J. Barnett, J. Eyre, and S. Healy, “A nonlinear optimal, estimation inverse method for radio occultation measurements of temperature, humidity, and surface pressure,” J. Geophys. Res. Atmos. 105, 17513–17526 (2000).
[CrossRef]

Heese, B.

M. Wiegner, S. Emeis, V. Freudenthaler, B. Heese, W. Junkermann, C. Munkel, K. Schafer, M. Seefeldner, and S. Vogt, “Mixing layer height over Munich, Germany: variability and comparisons of different methodologies,” J. Geophys. Res. Atmos. 111, D13201 (2006).
[CrossRef]

Hirayama, C.

Hoff, R. M.

D. G. Steyn, M. Baldi, and R. M. Hoff, “The detection of mixed layer depth and entrainment zone thickness from lidar backscatter profiles,” J. Atmos. Ocean. Technol. 16, 953–959 (1999).
[CrossRef]

Jain, S. L.

R. Maurya, P. K. Dubey, B. C. Arya, and S. L. Jain, “Aerosol vertical profile measurements using micro pulse lidar at New Delhi, India,” presented at the International Symposium for the Advancement of Remote Sensing of the Boundary Layer, Guyancourt, France, 28–30June2010.

Junkermann, W.

M. Wiegner, S. Emeis, V. Freudenthaler, B. Heese, W. Junkermann, C. Munkel, K. Schafer, M. Seefeldner, and S. Vogt, “Mixing layer height over Munich, Germany: variability and comparisons of different methodologies,” J. Geophys. Res. Atmos. 111, D13201 (2006).
[CrossRef]

Kavaya, M. J.

Kitchen, M.

M. Kitchen, “Representativeness errors for radiosonde observations,” Q. J. R. Meteorol. Soc. 115, 673–700 (1989).
[CrossRef]

Klett, J. D.

Kong, H. J.

Kovalev, V. A.

M. Adam, V. A. Kovalev, C. Wold, J. Newton, M. Pahlow, W. M. Hao, and M. B. Parlange, “Application of the Kano-Hamilton multiangle inversion method in clear atmospheres,” J. Atmos. Ocean. Technol. 24, 2014–2028 (2007).
[CrossRef]

Langerholc, J.

Lau, A. K. H.

Q. S. He, C. C. Li, J. T. Mao, A. K. H. Lau, and D. A. Chu, “Analysis of aerosol vertical distribution and variability in Hong Kong,” J. Geophys. Res. Atmos. 113, D14211 (2008).
[CrossRef]

Li, C. C.

Q. S. He, C. C. Li, J. T. Mao, A. K. H. Lau, and D. A. Chu, “Analysis of aerosol vertical distribution and variability in Hong Kong,” J. Geophys. Res. Atmos. 113, D14211 (2008).
[CrossRef]

Li, W.

W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
[CrossRef]

Lyamani, H.

Mao, J. T.

Q. S. He, C. C. Li, J. T. Mao, A. K. H. Lau, and D. A. Chu, “Analysis of aerosol vertical distribution and variability in Hong Kong,” J. Geophys. Res. Atmos. 113, D14211 (2008).
[CrossRef]

Marks, C.

C. Marks and C. Rodgers, “A retrieval method for atmospheric composition from limb emission measurements,” J. Geophys. Res. Atmos. 98, 14939–14953 (1993).
[CrossRef]

Maurya, R.

R. Maurya, P. K. Dubey, B. C. Arya, and S. L. Jain, “Aerosol vertical profile measurements using micro pulse lidar at New Delhi, India,” presented at the International Symposium for the Advancement of Remote Sensing of the Boundary Layer, Guyancourt, France, 28–30June2010.

Measures, R. M.

R. M. Measures, Lidar Remote Sensing: Fundamentals and Applications, 2nd ed. (Krieger, 1992).

Menzies, R. T.

Michimoto, K.

Munkel, C.

M. Wiegner, S. Emeis, V. Freudenthaler, B. Heese, W. Junkermann, C. Munkel, K. Schafer, M. Seefeldner, and S. Vogt, “Mixing layer height over Munich, Germany: variability and comparisons of different methodologies,” J. Geophys. Res. Atmos. 111, D13201 (2006).
[CrossRef]

Newton, J.

M. Adam, V. A. Kovalev, C. Wold, J. Newton, M. Pahlow, W. M. Hao, and M. B. Parlange, “Application of the Kano-Hamilton multiangle inversion method in clear atmospheres,” J. Atmos. Ocean. Technol. 24, 2014–2028 (2007).
[CrossRef]

Okuda, M.

Pahlow, M.

M. Adam, V. A. Kovalev, C. Wold, J. Newton, M. Pahlow, W. M. Hao, and M. B. Parlange, “Application of the Kano-Hamilton multiangle inversion method in clear atmospheres,” J. Atmos. Ocean. Technol. 24, 2014–2028 (2007).
[CrossRef]

Palmer, P.

P. Palmer, J. Barnett, J. Eyre, and S. Healy, “A nonlinear optimal, estimation inverse method for radio occultation measurements of temperature, humidity, and surface pressure,” J. Geophys. Res. Atmos. 105, 17513–17526 (2000).
[CrossRef]

Park, Y. J.

Parlange, M. B.

M. Adam, V. A. Kovalev, C. Wold, J. Newton, M. Pahlow, W. M. Hao, and M. B. Parlange, “Application of the Kano-Hamilton multiangle inversion method in clear atmospheres,” J. Atmos. Ocean. Technol. 24, 2014–2028 (2007).
[CrossRef]

Riebesell, M.

Rodgers, C.

C. Marks and C. Rodgers, “A retrieval method for atmospheric composition from limb emission measurements,” J. Geophys. Res. Atmos. 98, 14939–14953 (1993).
[CrossRef]

Rodgers, C. D.

C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice, Vol. 2 of Series on Atmospheric, Oceanic, and Planetary Physics, 2nd ed. (World Scientific, 2000).

Sasano, Y.

Schafer, K.

M. Wiegner, S. Emeis, V. Freudenthaler, B. Heese, W. Junkermann, C. Munkel, K. Schafer, M. Seefeldner, and S. Vogt, “Mixing layer height over Munich, Germany: variability and comparisons of different methodologies,” J. Geophys. Res. Atmos. 111, D13201 (2006).
[CrossRef]

Seefeldner, M.

M. Wiegner, S. Emeis, V. Freudenthaler, B. Heese, W. Junkermann, C. Munkel, K. Schafer, M. Seefeldner, and S. Vogt, “Mixing layer height over Munich, Germany: variability and comparisons of different methodologies,” J. Geophys. Res. Atmos. 111, D13201 (2006).
[CrossRef]

Shimizu, H.

Silva, A. M.

Spinelli, N.

Spurr, R.

W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
[CrossRef]

Stacewicz, T.

Stamnes, J.

W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
[CrossRef]

Stamnes, K.

W. Li, K. Stamnes, R. Spurr, and J. Stamnes, “Simultaneous retrieval of aerosol and ocean properties by optimal estimation: SeaWiFS case studies for the Santa Barbara Channel,” Int. J. Remote Sens. 29, 5689–5698 (2008).
[CrossRef]

Stelmaszczyk, K.

Steyn, D. G.

D. G. Steyn, M. Baldi, and R. M. Hoff, “The detection of mixed layer depth and entrainment zone thickness from lidar backscatter profiles,” J. Atmos. Ocean. Technol. 16, 953–959 (1999).
[CrossRef]

Takeuchi, N.

Tomine, K.

Velotta, R.

Vogt, S.

M. Wiegner, S. Emeis, V. Freudenthaler, B. Heese, W. Junkermann, C. Munkel, K. Schafer, M. Seefeldner, and S. Vogt, “Mixing layer height over Munich, Germany: variability and comparisons of different methodologies,” J. Geophys. Res. Atmos. 111, D13201 (2006).
[CrossRef]

Wandinger, U.

Watts, P. D.

P. D. Watts, R. Bennartz, and F. Fell, “Retrieval of two-layer cloud properties from multispectral observations using optimal estimation,” J. Geophys. Res. Atmos. 116, D16203 (2011).
[CrossRef]

Weitkamp, C.

A. Ansmann, M. Riebesell, and C. Weitkamp, “Measurement of atmospheric aerosol extinction profiles with a Raman lidar,” Opt. Lett. 15, 746–748 (1990).
[CrossRef]

C. Weitkamp, Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, Springer Series in Optical Sciences (Springer, 2005).

Whiteway, J. A.

Wiegner, M.

M. Wiegner, S. Emeis, V. Freudenthaler, B. Heese, W. Junkermann, C. Munkel, K. Schafer, M. Seefeldner, and S. Vogt, “Mixing layer height over Munich, Germany: variability and comparisons of different methodologies,” J. Geophys. Res. Atmos. 111, D13201 (2006).
[CrossRef]

Wold, C.

M. Adam, V. A. Kovalev, C. Wold, J. Newton, M. Pahlow, W. M. Hao, and M. B. Parlange, “Application of the Kano-Hamilton multiangle inversion method in clear atmospheres,” J. Atmos. Ocean. Technol. 24, 2014–2028 (2007).
[CrossRef]

Woste, L.

Am. Stat. (1)

S. Chib and E. Greenberg, “Understanding the Metropolis–Hastings algorithm,” Am. Stat. 49, 327–335 (1995).

Appl. Opt. (12)

G. Biavati, G. Di Donfrancesco, F. Cairo, and D. G. Feist, “Correction scheme for close-range lidar returns,” Appl. Opt. 50, 5872–5882 (2011).
[CrossRef]

T. Halldórsson and J. Langerholc, “Geometrical form factors for the lidar function,” Appl. Opt. 17, 240–244 (1978).
[CrossRef]

Y. Sasano, H. Shimizu, N. Takeuchi, and M. Okuda, “Geometrical form factor in the laser radar equation: an experimental determination,” Appl. Opt. 18, 3908–3910 (1979).
[CrossRef]

J. D. Klett, “Lidar inversion with variable backscatter extinction ratios,” Appl. Opt. 24, 1638–1643 (1985).
[CrossRef]

G. M. Ancellet, M. J. Kavaya, R. T. Menzies, and A. M. Brothers, “Lidar telescope overlap function and effects of misalignment for unstable resonator transmitter and coherent receiver,” Appl. Opt. 25, 2886–2890 (1986).
[CrossRef]

D. P. Donovan, J. A. Whiteway, and A. I. Carswell, “Correction for nonlinear photon-counting effects in lidar systems,” Appl. Opt. 32, 6742–6753 (1993).
[CrossRef]

S. W. Dho, Y. J. Park, and H. J. Kong, “Experimental determination of a geometric form factor in a lidar equation for an inhomogeneous atmosphere,” Appl. Opt. 36, 6009–6010 (1997).
[CrossRef]

A. Bucholtz, “Rayleigh-scattering calculations for the terrestrial atmosphere,” Appl. Opt. 34, 2765–2773 (1995).
[CrossRef]

R. Velotta, B. Bartoli, R. Capobianco, L. Fiorani, and N. Spinelli, “Analysis of the receiver response in lidar measurements,” Appl. Opt. 37, 6999–7007 (1998).
[CrossRef]

U. Wandinger and A. Ansmann, “Experimental determination of the lidar overlap profile with Raman lidar,” Appl. Opt. 41, 511–514 (2002).
[CrossRef]

K. Stelmaszczyk, M. Dell’Aglio, S. Chudzynski, T. Stacewicz, and L. Woste, “Analytical function for lidar geometrical compression form-factor calculations,” Appl. Opt. 44, 1323–1331 (2005).
[CrossRef]

K. Tomine, C. Hirayama, K. Michimoto, and N. Takeuchi, “Experimental determination of the crossover function in the laser-radar equation for days with a light mist,” Appl. Opt. 28, 2194–2195 (1989).
[CrossRef]

Int. J. Remote Sens. (1)

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Figures (9)

Fig. 1.
Fig. 1.

Aerosol extinction profiles used for simulating data. All have χ=0.4 at 355 nm. (a) Unperturbed model profile, where extinction is constant to 640 m and decreases exponentially above that with a scale height of 38 m. (b) Addition of a Gaussian peak at 500 m (dashed) or sinusoidal variations from 230–590 m (dotted). (c) Addition of normally distributed multiplicative noise (short dashes) or a linear decrease in extinction (dotted–dashed) over 1.3 km.

Fig. 2.
Fig. 2.

Schematic of the optimal estimation algorithm.

Fig. 3.
Fig. 3.

Raman lidar profiles, y, simulated for four representative alignments of the RACHEL system (Table 2). Models 1–4 are marked with diamonds, triangles, squares, or exes, respectively, where only points with an SNR greater than 2 are shown. Plotted in black over each is the forward modeled profile, F(x,b), resulting from a retrieval on these data.

Fig. 4.
Fig. 4.

Retrieved calibration function CraA(r) from simulated data of Fig. 3, with errors derived from Eq. (15). The profile used to simulate these data are plotted with the symbols from the previous figure.

Fig. 5.
Fig. 5.

As Fig. 4, but for profiles simulated with a perturbation to their extinction profile, as introduced in Fig. 1. The degeneracy of the model states is evident from the very similar profiles, despite differing parameter values (Table 2).

Fig. 6.
Fig. 6.

As Fig. 4, but for data simulated using features not included in the forward model. Curves marked with characters used a Gaussian beam profile and the red solid curve perturbed the overlap function (unperturbed function as dotted curve). Discrepancies are concentrated in the region below 2 km, where the overlap of the beam and FOV is incomplete, such that beam shape is potentially important.

Fig. 7.
Fig. 7.

Analysis of 8 April 2010, when RACHEL was reasonably well aligned. (a) Retrieved calibration function with errors. Plotted as points is an arithmetic inversion of the measurement, Eq. (8), with the a priori extinction profile. Measurements beyond the reasonably linear range of the detectors are not plotted and were not used in the retrieval. (b) Attenuated backscatter coefficient at 355 nm for the retrieved aerosol profile (black), the elastic profile corrected with the retrieved overlap function (diamonds), and as reported independently by an EZ lidar at the same site (red). A lidar ratio of 15 was chosen to give consistency between the three signals above 6 km.

Fig. 8.
Fig. 8.

As Fig. 7, but for 10 April, when RACHEL was significantly misaligned. In addition, the results for three different initial conditions are presented (Table 3), conditions 1–3 plotted in black, orange, and green, respectively. Measurements with an SNR of less than 2 are not plotted and were not used in the retrieval. A lidar ratio of 50 was used. Note the greater error introduced by the reduced SNR of the data at 2 km compared to Fig. 7.

Fig. 9.
Fig. 9.

Effect of Ro on retrieval of 8 April 2010. The calibration function presented in Fig. 7 is shown in black, with the functions retrieved with a ±5mm perturbation of Ro in orange and green, respectively. Retrieval with Ro=0, shown in blue and red, shows the effect of further reducing RT to maintain a constant effective telescope area.

Tables (3)

Tables Icon

Table 1. RACHEL System Specification

Tables Icon

Table 2. State Vectors Used in Section 3a

Tables Icon

Table 3. State Vectors Used in Section 4a

Equations (39)

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πRT2A(r)=[γν(r)w(r)]2{SH[ν(r)γRT,r]SH[ν(r)γRo,r]},
SH(b,r)=1πμ=0w(r)+d(r)A[Rprfγ,b;μ]dA[μ,w(r);d(r)],
γ=1+Δf,
ν(r)=|γΔrf2|,
w(r)=RL+ϕLr,
d(r)=(δ+ϕr)2+(ϕr)2,
Eel(r)=E0Celr2Ael(r)[βm(λL,r)+βa(λL,r)]×exp[20rαm(λL,r)+αa(λL,r)dr],
Era(r)=E0Crar2Ara(r)NX(r)×exp[0rαm(λL,r)+αa(λL,r)+αm(λX,r)+αa(λX,r)dr],
αa(λ,z)={α0,zz0;α0exp[z0zH],z>z0.
0zαa(λL,r)dr={χH+z0z,z<z0;χH+z0[z0+H(1expz0zH)],zz0.
y=F(x,b)+ε,
2lnP(x|y)=[yF(x,b)]TSε1[yF(x,b)]+[xxa]TSa1[xxa]+c,
KT(x^)Sε1[yF(x^,b)]+Sa1[x^xa]=0,
xi+1=xi+[(1+Γi)Sa1+KiTSϵ1Ki]1{KiTSϵ1[yF(xi,b)]Sa1(xixa)}
Sx=(KTSε1K+Sa1)1.
C=CraA(r),
SC=KSx(K)T,
Gy[fF(x^,b)],
β*(r)=Eel(r)r2CelE0A(r)exp[20rαm(λL,r)dr]
[βm(λL,r)+βa(λL,r)]exp[20rαa(λL,r)dr]
ρ=Rprfγ.
SH(b,z)=1πμ=0w+dA(ρ,b;μ)dA[μ,w;d],
A(R1,R2;μ)={0,μR1+R2;πmin[R12,R22],μ|R1R2|;A(R1,R2;μ)otherwise,
A(R1,R2;μ)=R12cos1(μ2+R12R222μR1)+R22cos1(μ2+R22R122μR2)12ϒ(R1,R2;μ),
ϒ(R1,R2;μ)=[(R1+R2)2μ2][μ2(R1R2)2].
dA(R1,R2;μ)={ϒ(R1,R2;μ)dμμ,|R1R2|μR1+R2;0,otherwise.
SH(b,z,w+d|ρb|)=πw2min[ρ2,b2].
SH(b,z)=w2A[ρ,b;w+d]+1π|ρb|ΛA[μ,w;d]ϒ(ρ,b;μ)dμμ,
SH(b,z,|ρb|>w+d)=0.
κH(b,z)=Γwdμϒ(ρ,b;μ)dμ+wdΛA[μ,w;d]ϒ(ρ,b;μ)dμπμ.
SH(b,z)=w2A[ρ,b;w+d]+|ρb|ρ+bμϒ(ρ,b;μ)dμ
=πρ2b2.
κH(b,z)=|ρb|ΛA[μ,w;d]ϒ(ρ,b;μ)dμπμ
=min[ρ2,b2]A(|ρb|,w;d)
+2π|ρb|ρ+bμcos1(d2+μ2w22dμ)A(ρ,b;μ)dμ.
κH(b,z)=dwΛA[μ,w;d]ϒ(ρ,b;μ)dμπμ.
κH(b,z)=(wd)2ρ2b24ϒ(ρ,b;wd)+2ρ2b2tan1(wd)2(ρb)2(ρ+b)2(wd)2+wdΛA[μ,w;d]ϒ(ρ,b;μ)dμπμ
=B+wdΛA[μ,w;d]ϒ(ρ,b;μ)dμπμ.
SH(b,r)={0,ρ+bdw;πw2min[ρ2,b2],w+d|ρb|;πρ2b2,ρ+bwd;|ρb|ρ+bϒ(ρ,b;μ)A(μ,w;d)dμπμ,ρ+bw+dand|wd||ρb|;dwρ+bϒ(ρ,b;μ)A(μ,w;d)dμπμ,ρ+bw+dand|ρb|<dw;B+wdρ+bϒ(ρ,b;μ)A(μ,w;d)dμπμ,ρ+bw+dand|ρb|<wd;w2A(ρ,b;w+d)+|ρb|w+dϒ(ρ,b;μ)A(μ,w;d)dμπμ,w+d<ρ+band|wd||ρb|;w2A(ρ,b;w+d)+dww+dϒ(ρ,b;μ)A(μ,w;d)dμπμ,w+d<ρ+band|ρb|<dw;w2A(ρ,b;w+d)+B+wdw+dϒ(ρ,b;μ)A(μ,w;d)dμπμ,w+d<ρ+band|ρb|<wd.

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