Abstract

A novel aerosol lidar inversion method based on the use of multiple-scattering contributions measured by a multiple-field-of-view receiver is proposed. The method requires assumptions that restrict applications to aerosol particles large enough to give rise to measurable multiple scattering and depends on parameters that must be specified empirically but that have an uncertainty range of much less than the boundary value and the backscatter-to-extinction ratio of the conventional single-scattering inversion methods. The proposed method is applied to cloud measurements. The solutions obtained are the profiles of the scattering coefficient and the effective diameter of the cloud droplets. With mild assumptions on the form of the function, the full-size distribution is estimated at each range position from which the extinction coefficient at any visible and infrared wavelength and the liquid water content can be determined. Typical results on slant-path-integrated optical depth, vertical extinction profiles, and fluctuation statistics are compared with in situ data obtained in two field experiments. The inversion works well in all cases reported here, i.e., for water clouds at optical depths between ~0.1 and ~4.

© 1995 Optical Society of America

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References

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  1. J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
    [CrossRef] [PubMed]
  2. J. D. Klett, “Lidar inversion with variable backscatter/extinction ratios,” Appl. Opt. 24, 1638–1643 (1985).
    [CrossRef] [PubMed]
  3. G. J. Kunz, “Vertical atmospheric profiles measured with lidar,” Appl. Opt. 22, 1955–1957 (1983).
    [CrossRef] [PubMed]
  4. J. A. Ferguson, D. H. Stephens, “Algorithm for inverting lidar returns,” Appl. Opt. 22, 3673–3675 (1983).
    [CrossRef] [PubMed]
  5. F. G. Fernald, “Analysis of atmospheric lidar observations: some comments,” Appl. Opt. 23, 652–653 (1984).
    [CrossRef] [PubMed]
  6. J. M. Mulders, “Algorithm for inverting lidar returns: comment,” Appl. Opt. 23, 2855–2856 (1984).
    [CrossRef] [PubMed]
  7. G. J. Kunz, “Bipath method as a way to measure the spatial backscatter and extinction coefficients with lidar,” Appl. Opt. 26, 794–795 (1987).
    [CrossRef] [PubMed]
  8. H. G. Hughes, M. R. Paulson, “Double-ended lidar technique for aerosol studies,” Appl. Opt. 27, 2273–2278 (1988).
    [CrossRef] [PubMed]
  9. H. G. Hughes, J. A. Ferguson, D. H. Stephens, “Sensitivity of a lidar inversion algorithm to parameters relating atmospheric backscatter and extinction,” Appl. Opt. 24, 1609–1613 (1985).
    [CrossRef] [PubMed]
  10. L. R. Bissonnette, “Sensitivity analysis of lidar inversion algorithms,” Appl. Opt. 25, 2122–2125 (1986).
    [CrossRef] [PubMed]
  11. V. A. Kovalev, “Lidar measurements of the vertical aerosol extinction profiles with range-dependent backscatter-to-extinction ratios,” Appl. Opt. 32, 6053–6065 (1993).
    [CrossRef] [PubMed]
  12. M. Matsumoto, N. Takeuchi, “Effects of misestimated far-end boundary values on two common lidar inversion solutions,” Appl. Opt. 33, 6451–6456 (1994).
    [CrossRef] [PubMed]
  13. V. A. Kovalev, H. Moosmüller, “Distortion of particulate extinction profiles measured with lidar in a two-component atmosphere,” Appl. Opt. 33, 6499–6507 (1994).
    [CrossRef] [PubMed]
  14. L. R. Bissonnette, D. L. Hutt, “Multiple scattering lidar,” Appl. Opt. 29, 5045–5046 (1990).
    [CrossRef] [PubMed]
  15. L. R. Bissonnette, “Multiple scattering technique (MUST) lidar,” U.S. patent5,239,352 (24August1993).
  16. D. L. Hutt, L. R. Bissonnette, L. Durand, “Multiple field of view lidar returns from atmospheric aerosols,” Appl. Opt. 33, 2338–2348 (1994).
    [CrossRef] [PubMed]
  17. L. R. Bissonnette, “Multiscattering model for propagation of narrow light beams in aerosol media,” Appl. Opt. 27, 2478–2484 (1988).
    [CrossRef] [PubMed]
  18. L. R. Bissonnette, “Multiple scattering lidar equation,” submitted to Appl. Opt. (1995).
    [PubMed]
  19. D. Deirmendjian, “Far-infrared and submillimeter wave attenuation by clouds and rain,” J. Appl. Meteorol. 14, 1584–1593 (1975).
    [CrossRef]
  20. E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” AFGL TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).
  21. L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
    [CrossRef]
  22. G. J. Kunz, “Lidar observations during VAST92,” TNO report FEL-93-A242 (TNO Physics and Electronics Laboratory, The Hague, The Netherlands, 1994).

1995

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

1994

1993

1990

1988

1987

1986

1985

1984

1983

1981

1975

D. Deirmendjian, “Far-infrared and submillimeter wave attenuation by clouds and rain,” J. Appl. Meteorol. 14, 1584–1593 (1975).
[CrossRef]

Benayahu, Y.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Bissonnette, L. R.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

D. L. Hutt, L. R. Bissonnette, L. Durand, “Multiple field of view lidar returns from atmospheric aerosols,” Appl. Opt. 33, 2338–2348 (1994).
[CrossRef] [PubMed]

L. R. Bissonnette, D. L. Hutt, “Multiple scattering lidar,” Appl. Opt. 29, 5045–5046 (1990).
[CrossRef] [PubMed]

L. R. Bissonnette, “Multiscattering model for propagation of narrow light beams in aerosol media,” Appl. Opt. 27, 2478–2484 (1988).
[CrossRef] [PubMed]

L. R. Bissonnette, “Sensitivity analysis of lidar inversion algorithms,” Appl. Opt. 25, 2122–2125 (1986).
[CrossRef] [PubMed]

L. R. Bissonnette, “Multiple scattering lidar equation,” submitted to Appl. Opt. (1995).
[PubMed]

L. R. Bissonnette, “Multiple scattering technique (MUST) lidar,” U.S. patent5,239,352 (24August1993).

Bruscaglioni, P.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Cohen, A.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Deirmendjian, D.

D. Deirmendjian, “Far-infrared and submillimeter wave attenuation by clouds and rain,” J. Appl. Meteorol. 14, 1584–1593 (1975).
[CrossRef]

Durand, L.

Egert, S.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Fenn, R. W.

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” AFGL TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

Ferguson, J. A.

Fernald, F. G.

Flesia, C.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Hughes, H. G.

Hutt, D. L.

Ismaelli, A.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Katsev, I. L.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Kleiman, M.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Klett, J. D.

Kovalev, V. A.

Kunz, G. J.

Matsumoto, M.

Moosmüller, H.

Mulders, J. M.

Noormohammadian, M.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Oppel, U. G.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Paulson, M. R.

Polonsky, I. N.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Schwendimann, P.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Shettle, E. P.

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” AFGL TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

Starkov, A. V.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Stephens, D. H.

Takeuchi, N.

Winker, D. M.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Zaccanti, G.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Zege, E. P.

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

Appl. Opt.

J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
[CrossRef] [PubMed]

F. G. Fernald, “Analysis of atmospheric lidar observations: some comments,” Appl. Opt. 23, 652–653 (1984).
[CrossRef] [PubMed]

H. G. Hughes, J. A. Ferguson, D. H. Stephens, “Sensitivity of a lidar inversion algorithm to parameters relating atmospheric backscatter and extinction,” Appl. Opt. 24, 1609–1613 (1985).
[CrossRef] [PubMed]

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

L. R. Bissonnette, “Sensitivity analysis of lidar inversion algorithms,” Appl. Opt. 25, 2122–2125 (1986).
[CrossRef] [PubMed]

G. J. Kunz, “Bipath method as a way to measure the spatial backscatter and extinction coefficients with lidar,” Appl. Opt. 26, 794–795 (1987).
[CrossRef] [PubMed]

H. G. Hughes, M. R. Paulson, “Double-ended lidar technique for aerosol studies,” Appl. Opt. 27, 2273–2278 (1988).
[CrossRef] [PubMed]

L. R. Bissonnette, “Multiscattering model for propagation of narrow light beams in aerosol media,” Appl. Opt. 27, 2478–2484 (1988).
[CrossRef] [PubMed]

V. A. Kovalev, “Lidar measurements of the vertical aerosol extinction profiles with range-dependent backscatter-to-extinction ratios,” Appl. Opt. 32, 6053–6065 (1993).
[CrossRef] [PubMed]

D. L. Hutt, L. R. Bissonnette, L. Durand, “Multiple field of view lidar returns from atmospheric aerosols,” Appl. Opt. 33, 2338–2348 (1994).
[CrossRef] [PubMed]

M. Matsumoto, N. Takeuchi, “Effects of misestimated far-end boundary values on two common lidar inversion solutions,” Appl. Opt. 33, 6451–6456 (1994).
[CrossRef] [PubMed]

V. A. Kovalev, H. Moosmüller, “Distortion of particulate extinction profiles measured with lidar in a two-component atmosphere,” Appl. Opt. 33, 6499–6507 (1994).
[CrossRef] [PubMed]

G. J. Kunz, “Vertical atmospheric profiles measured with lidar,” Appl. Opt. 22, 1955–1957 (1983).
[CrossRef] [PubMed]

J. A. Ferguson, D. H. Stephens, “Algorithm for inverting lidar returns,” Appl. Opt. 22, 3673–3675 (1983).
[CrossRef] [PubMed]

J. M. Mulders, “Algorithm for inverting lidar returns: comment,” Appl. Opt. 23, 2855–2856 (1984).
[CrossRef] [PubMed]

L. R. Bissonnette, D. L. Hutt, “Multiple scattering lidar,” Appl. Opt. 29, 5045–5046 (1990).
[CrossRef] [PubMed]

Appl. Phys. B

L. R. Bissonnette, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, A. Cohen, Y. Benayahu, M. Kleiman, S. Egert, C. Flesia, P. Schwendimann, A. V. Starkov, M. Noormohammadian, U. G. Oppel, D. M. Winker, E. P. Zege, I. L. Katsev, I. N. Polonsky, “LIDAR multiple scattering from clouds,” Appl. Phys. B 60, 355–362 (1995).
[CrossRef]

J. Appl. Meteorol.

D. Deirmendjian, “Far-infrared and submillimeter wave attenuation by clouds and rain,” J. Appl. Meteorol. 14, 1584–1593 (1975).
[CrossRef]

Other

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” AFGL TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979).

G. J. Kunz, “Lidar observations during VAST92,” TNO report FEL-93-A242 (TNO Physics and Electronics Laboratory, The Hague, The Netherlands, 1994).

L. R. Bissonnette, “Multiple scattering technique (MUST) lidar,” U.S. patent5,239,352 (24August1993).

L. R. Bissonnette, “Multiple scattering lidar equation,” submitted to Appl. Opt. (1995).
[PubMed]

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Figures (14)

Fig. 1
Fig. 1

Plots of the raw MFOV lidar signals recorded at 1010 on 13 October 1992. Det 1, 0–1.98 mrad; Det 2, 2.30–6.39 mrad; Det 3, 6.70–12.77 mrad half-angle (Det, detector).

Fig. 2
Fig. 2

Plots of (a) the scattering coefficient α s and (b) the effective droplet radius d/2, calculated with the proposed multiple-scattering inversion method for the lidar recordings of Fig. 1.

Fig. 3
Fig. 3

Comparison of time plots of transmissometer- (filled circles) and lidar-derived (open squares) 1.06-μm optical depth through the cloud layer of 13 October 1992.

Fig. 4
Fig. 4

Comparison of time plots of transmissometer- (filled circles) and lidar-derived (open squares) 10.6-μm optical depth through the cloud layer of 13 October 1992.

Fig. 5
Fig. 5

Scatter plot of lidar-derived versus transmissometer-derived optical depths for the cloud layer of 13 October 1992; the solid circles are for 1.06 μm, and the open squares are for 10.6 μm.

Fig. 6
Fig. 6

Comparison of lidar-derived (filled squares) profiles of cloud extinction coefficients at (a) 0.55 μm and (b) 10.6 μm with point-sensor measurements (open squares) made from cable car, 13 October 1992, 0935–0950.

Fig. 7
Fig. 7

Comparison of histograms of (a) visible and (b) 10.6-μm extinction coefficients derived from the lidar (crosshatched bars) and the cable car sensors (filled bars), 13 October 1992, 0935–0950 at 885–895 m for lidar, and 0942–0947 at 948 m for cable car.

Fig. 8
Fig. 8

Comparison of lidar-derived (filled squares) profiles of cloud extinction coefficients at (a) 0.55 μm and (b) 10.6 μm with point-sensor measurements (open squares) made from cable car, 10 October 1992, 1540–1545.

Fig. 9
Fig. 9

Comparison of lidar-derived (filled squares) profiles of cloud extinction coefficients at (a) 0.55 μm, (b) 10.6 μm, and (c) of the liquid water content with profiles calculated from aircraft particle spectrometer data (open squares), 25 August 1993, 0724–0727 for both aircraft and lidar data.

Fig. 10
Fig. 10

Comparison of lidar-derived (filled squares) profiles of cloud extinction coefficients at (a) 0.55 μm, (b) 10.6 μm, and (c) of the liquid water content with profiles calculated from aircraft particle spectrometer data (open squares), 25 August 1993, 0818–0820 for both aircraft and lidar data.

Fig. 11
Fig. 11

Comparison of lidar-derived (filled squares) profiles of cloud extinction coefficients at (a) 0.55 μm, (b) 10.6 μm, and (c) of the liquid water content with profiles calculated from aircraft particle spectrometer data (open squares), 2 September 1993, 1130–1133 for both aircraft and lidar data.

Fig. 12
Fig. 12

Comparison of histograms of the (a) 0.55-μm, (b) 10.6-μm extinction coefficients and (c) of the liquid water content derived from the aircraft sensors (filled bars) and the lidar solutions (crosshatched bars), 2 September 1993, 1130–1133 at 590–605 m for aircraft, 1130–1133 at 600–615 m for lidar.

Fig. 13
Fig. 13

Comparison of lidar-derived (filled squares) profiles of cloud extinction coefficients at (a) 0.55 μm, (b) 10.6 μm, and (c) of the liquid water content with profiles calculated from aircraft particle spectrometer data (open squares), 2 September 1993, 1144–1145 for both aircraft and lidar data.

Fig. 14
Fig. 14

Comparison of the multiple-scattering solution (solid curve) with far end single-scattering solutions (dashed curves) for the lidar recordings of Fig. 1.

Tables (3)

Tables Icon

Table 1 MFOV Lidar Source

Tables Icon

Table 2 MFOV Lidar Receiver

Tables Icon

Table 3 MFOV Lidar Signal Processing

Equations (36)

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

P ss ( z ) = P 0 c t 2 A z 2 β ( z ) exp [ - 2 0 z α ( z ) d z ] ,
p ( z , ϕ ) A 2 π d 2 ( z ) λ 2 exp [ - A 1 2 π 2 d 2 ( z ) λ 2 ϕ 2 ] ,
P ( z , θ ) = P ss ( z ) [ F 0 ( z ) + F 1 ( z ) θ + F 2 ( z ) θ 2 + ] ,
F 0 ( z ) = 1 - 4 A 2 A 1 δ 1 K π x y ,
F 1 ( z ) = 4 A 2 A 1 δ 1 π x y ,
F 2 ( z ) = - 4 A 2 C δ 1 x y 2 + 4 A 2 A 1 2 δ 1 D 3 ( e τ - 1 ) + D 2 ( e τ - 1 ) + D 1 δ 2 e τ ( e τ - 1 ) + D 0 δ 2 e τ .
x = α s ( z ) z ,
y = π d ( z ) λ .
D 0 ( z ) = z ¯ z exp [ - τ ( z ) ] { 1 - exp [ - τ s ( z ) + τ s ( z ) ] } θ ms 2 ( z , z ) α s ( z ) d z ,
D 1 ( z ) = z ¯ z exp [ - τ ( z ) ] { 1 - exp [ - τ s ( z ) + τ s ( z ) ] } [ θ p 2 ( z ) + θ ms 2 ( z , z ) ] α s ( z ) d z ,
D 2 ( z ) = 1 / [ θ p 2 ( z ) + θ 0 2 ] ,
D 3 ( z ) = x ( z ) C θ p 2 ( z ) ,
θ ms 2 ( z , z ) = θ 0 2 z 2 z 2 + γ A 1 z 2 z z { exp [ τ s ( z ) - τ s ( z ) ] - 1 } y ( z ) [ τ s ( z ) - τ s ( z ) ] × ( z - z ) d z ,
θ p 2 ( z ) = 1 A 1 2 y 2 ( z ¯ ) + z ¯ z α s ( z ) d z A 1 2 y 2 ( z ) { 1 - exp [ - τ ( z ) ] } ,
C = z / ( z - z ¯ ) ,
K = θ 0 π [ 1 - 2 π tan - 1 ( C A 1 y θ 0 ) ] ,
τ ( z ) = 0 z α d z
τ s ( z ) = 0 z α s d z
P m ( z , θ ) C 0 ( z ) + C 1 ( z ) θ + C 2 ( z ) θ 2 .
y ( z ) = π C A 1 { - C 2 C 1 + C 0 C 1 ( 1 + K C 1 / C 0 ) [ D 0 δ 2 e τ + D 1 δ 2 e τ ( e τ - 1 ) + D 2 ( e τ - 1 ) + 4 A 2 A 1 2 δ 1 D 3 ( e τ - 1 ) ] } ,
x ( z ) = A 1 4 A 2 δ 1 C 1 C 0 1 π ( 1 + K C 1 / C 0 ) 1 y ( z ) .
d N d r = N 0 r u exp ( - v r ) ,
u = { 1.163 + 3.715 v 0.65 for v 1.5 6.0 for v > 1.5 .
d 2 = r 3 r 2 = 0 r 3 d N / d r d r 0 r 2 d N / d r d r .
d 2 = ( u + 3 ) v .
α s = 0 d N d r π r 2 Q s ( λ , r ) d r ,
α s = π N 0 0 r u + 2 Q s ( λ , r ) exp ( - v r ) d r .
α e ( λ ) = α s Q e ¯ ( λ , d ) Q s ¯ ( λ l , d ) ,
W = 2 3 ρ w α s d Q s ¯ ( λ l , d ) ,
Q e ¯ ( λ , d ) = 0 r u + 2 exp ( - v r ) Q e ( λ , r ) d r 0 r u + 2 exp ( - v r ) d r ,
Q s ¯ ( λ l , d ) = 0 r u + 2 exp ( - v r ) Q s ( λ l , r ) d r 0 r u + 2 exp ( - v r ) d r ,
Δ α e α e ( 0.55 μ m ) Δ α e α e ( 1.06 μ m ) Δ α s α s ,
Δ α e α e ( 10.6 μ m ) Δ W W Δ α s α s + Δ d d .
Δ α e α e ( 0.55 μ m ) Δ α e α e ( 1.06 μ m ) 2 | Δ ( C 1 / C 0 ) ( C 1 / C 0 ) | + | Δ ( C 2 / C 1 ) ( C 2 / C 1 ) | ,
Δ α e α e ( 10.6 μ m ) Δ W W | Δ ( C 1 / C 0 ) ( C 1 / C 0 ) | + | Δ ( C 2 / C 1 ) ( C 2 / C 1 ) | .
α ( z ) = S ( z ) S ( z f ) α - 1 ( z f ) + 2 z z f S ( z ) d z ,

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