Abstract

The relation between the accumulated single scattering factor and the layer accumulated depolarization ratio appears to be independent of the geometry of the measurements and contains information on the optical depth and thus on the extinction coefficient. A simple equation is developed to retrieve the extinction coefficient from the total integrated signal and the integrated depolarization ratio measurements. The results compare well with Klett and Weinman lidar inversion techniques. The results from the measurements of the integrated depolarization ratio can be used to set the far end initial extinction coefficient value required for Klett and Weinman lidar inversion or can be used directly.

© 2010 Optical Society of America

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References

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  1. Y. Hu, Z. Liu, D. Winker, M. Vaughan, V. Noel, L. Bissonnette, G. Roy, and M. McGill, “Simple relation between lidar multiple scattering and depolarization for water clouds,” Opt. Lett. 31, 1809-1811 (2006).
    [CrossRef] [PubMed]
  2. Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24-28 July 2006, pp. 19-22.
  3. Y. Hu, M. Vaughan, Z. Liu, B. Lin, P. Yang, D. Flittner, B. Hunt, R. Kuehn, J. Huang, D. Wu, S. Rodier, K. Powell, C. Trepte, and D. Winker, “The depolarization-attenuated backscatter relation: CALIPSO lidar measurements vs. theory,” Opt. Express 15, 5327-5332 (2007).
    [CrossRef] [PubMed]
  4. X. Cao, G. Roy, N. Roy, and R. Bernier, “Comparison of the relationships between lidar integrated backscattered light and accumulated depolarization ratios for linear and circular polarization for water droplets, fog-oil and dust,” Appl. Opt. 48, 4130-4141 (2009).
    [CrossRef] [PubMed]
  5. G. G. Gimmestad, “Reexamination of depolarization in lidar measurements,” Appl. Opt. 47, 3795-3802 (2008).
    [CrossRef] [PubMed]
  6. J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211-220 (1981).
    [CrossRef] [PubMed]
  7. J. A. Weinman, “Derivation of atmospheric extinction profiles and wind speed over the ocean from a satellite-borne lidar,” Appl. Opt. 27, 3994-4001 (1988).
    [CrossRef] [PubMed]
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    [CrossRef]
  9. G. Roy and N. Roy, “Relation between circular and linear depolarization ratios under multiple scattering conditions,” Appl. Opt. 47, 6563-6579 (2008).
    [CrossRef] [PubMed]
  10. C. M. R. Platt, “Remote sounding of high clouds. I: Calculation of visible and infrared optical properties from lidar and radiometer measurements,” J. Appl. Meteor. 18, 1130-1143 (1979).
    [CrossRef]

2009

2008

2007

2006

1988

1981

1979

C. M. R. Platt, “Remote sounding of high clouds. I: Calculation of visible and infrared optical properties from lidar and radiometer measurements,” J. Appl. Meteor. 18, 1130-1143 (1979).
[CrossRef]

1973

C. M. R. Platt, “Lidar and radiometric observations of cirrus clouds,” J. Atmos. Sci. 30, 1191-1204 (1973).
[CrossRef]

Bernier, R.

Bissonnette, L.

Y. Hu, Z. Liu, D. Winker, M. Vaughan, V. Noel, L. Bissonnette, G. Roy, and M. McGill, “Simple relation between lidar multiple scattering and depolarization for water clouds,” Opt. Lett. 31, 1809-1811 (2006).
[CrossRef] [PubMed]

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24-28 July 2006, pp. 19-22.

Cao, X.

Flittner, D.

Gimmestad, G. G.

Hu, Y.

Huang, J.

Hunt, B.

Klett, J. D.

Kuehn, R.

Lin, B.

Liu, Z.

McGill, M.

Y. Hu, Z. Liu, D. Winker, M. Vaughan, V. Noel, L. Bissonnette, G. Roy, and M. McGill, “Simple relation between lidar multiple scattering and depolarization for water clouds,” Opt. Lett. 31, 1809-1811 (2006).
[CrossRef] [PubMed]

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24-28 July 2006, pp. 19-22.

Noel, V.

Y. Hu, Z. Liu, D. Winker, M. Vaughan, V. Noel, L. Bissonnette, G. Roy, and M. McGill, “Simple relation between lidar multiple scattering and depolarization for water clouds,” Opt. Lett. 31, 1809-1811 (2006).
[CrossRef] [PubMed]

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24-28 July 2006, pp. 19-22.

Platt, C. M. R.

C. M. R. Platt, “Remote sounding of high clouds. I: Calculation of visible and infrared optical properties from lidar and radiometer measurements,” J. Appl. Meteor. 18, 1130-1143 (1979).
[CrossRef]

C. M. R. Platt, “Lidar and radiometric observations of cirrus clouds,” J. Atmos. Sci. 30, 1191-1204 (1973).
[CrossRef]

Powell, K.

Rodier, S.

Roy, G.

Roy, N.

Trepte, C.

Trepte, C. R.

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24-28 July 2006, pp. 19-22.

Vaughan, M.

Vaughan, M. A.

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24-28 July 2006, pp. 19-22.

Weinman, J. A.

Winker, D.

Winker, D. M.

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24-28 July 2006, pp. 19-22.

Wu, D.

Yang, P.

Appl. Opt.

J. Appl. Meteor.

C. M. R. Platt, “Remote sounding of high clouds. I: Calculation of visible and infrared optical properties from lidar and radiometer measurements,” J. Appl. Meteor. 18, 1130-1143 (1979).
[CrossRef]

J. Atmos. Sci.

C. M. R. Platt, “Lidar and radiometric observations of cirrus clouds,” J. Atmos. Sci. 30, 1191-1204 (1973).
[CrossRef]

Opt. Express

Opt. Lett.

Other

Y. Hu, M. A. Vaughan, D. M. Winker, Z. Liu, V. Noel, L. Bissonnette, G. Roy, M. McGill, and C. R. Trepte, “A simple multiple scattering-depolarization relation of water clouds and its potential applications,” presented at the 23rd International Laser Radar Conference, Nara, Japan, 24-28 July 2006, pp. 19-22.

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Figures (7)

Fig. 1
Fig. 1

Calculated extinction coefficients from LAD and Klett lidar as a function of the extinction coefficient calculated using Weinman lidar inversion. The start extinction value for Klett inversion used the LAD estimation at the cloud end.

Fig. 2
Fig. 2

Range corrected parallel polarization lidar signal as a function of distance for five FOVs.

Fig. 3
Fig. 3

Range corrected perpendicular polarization lidar signal as a function of distance for five FOVs.

Fig. 4
Fig. 4

Range corrected single scattering signals, I s ( z ) , superimpose well for five different FOVs. The difference is attributed to cloud fluctuation between the different measurements.

Fig. 5
Fig. 5

Calculated extinction coefficients obtained using the LAD lidar inversion as a function of distance for all the FOVs considered. For larger penetration depths, solutions do not exist for all FOVs.

Fig. 6
Fig. 6

Comparison of the retrieved extinction coefficients for LAD, Klett, and Weinman lidar inversion methods.

Fig. 7
Fig. 7

Comparison of the retrieved extinction coefficients for LAD inversion technique for five different values of Ck.

Equations (16)

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P ( z ) = C z 2 β ( z ) exp [ 2 0 z σ ( z ) d z ] ,
I s ( z ) = 0 z P ( z ) z 2 d z = 0 z C k σ ( z ) exp ( 2 0 z σ ( z ) d z ) d z .
I s ( z ) = C k 2 ( 1 T 2 ) .
A s ( θ ) I s ( z ) I T ( z , θ ) = ( 1 δ acc _ lin ( z , θ ) ) 2 ( 1 + δ acc _ lin ( z , θ ) ) 2 = 1 ( 1 + δ acc _ cir ( z , θ ) ) 2 ,
δ acc ( z , θ ) = z a z P T ( z , θ ) z ' 2 d z z a z P / / T ( z , θ ) z ' 2 d z ,
I T ( z , θ ) = z a z ( P / / T ( z , θ ) + P T ( z , θ ) ) z 2 d z .
T 2 ( z ) = C k 2 A s ( θ ) I T ( z , θ ) .
T 2 ( z 1 ) = exp ( 2 0 z 1 σ ( z ) d z ) ,
T 2 ( z 2 ) = exp ( 2 0 z 2 σ ( z ) d z ) = exp ( 2 0 z 1 σ ( z ) d z 2 z 1 z 1 + Δ z σ ( z ) d z ) .
ln ( T 2 ( z 1 ) ) ln ( T 2 ( z 2 ) ) = 2 σ ( z ¯ ) ( z 2 z 1 ) .
σ ( z ¯ ) = 1 2 ( z 2 z 1 ) ln [ C k 2 A s ( θ , z 1 ) I T ( z 1 , θ ) C k 2 A s ( θ , z 2 ) I T ( z 2 , θ ) ] .
C k = 2 A s ( z , θ ) I T ( z , θ ) 1 T 2 ( z ) .
σ ( z ) Klett = [ S ( z ) / S ( z g ) ] σ 1 ( z g ) + 2 k z z g ( S ( z ) / S ( z g ) ) d z ,
σ ( z ) Weiman = [ S ( z ) ] [ 1 exp ( 2 τ ) ] 2 { z z g [ S ( z ) ] d z + exp ( 2 τ ) z 0 z [ S ( z ) ] d z } .
T 2 ( z 1 , z 2 ) = ( d I s ( z = z 2 ) / d z ) ( d I s ( z = z 1 ) / d z ) .
C k = 2 A s ( z 2 , θ ) I T ( z 2 , θ ) 2 T 2 ( z 1 , z 2 ) A s ( z 1 , θ ) I T ( z 1 , θ ) 1 T 2 ( z 1 , z 2 ) .

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