Abstract

A new inversion inhomogeneous atmosphere (IA) method that is more stable than Fernald’s method for two-component (molecule and aerosol) scattering analysis of polarized Mie lidar signals is proposed and examined. The backscattering coefficient and the extinction-to-backscattering ratio (EBR) can be calculated for specified regions at which the depolarization ratio is less than that of molecule without further assumptions. The inversion procedure can be extended to both inward stepwise and outward stepwise integration algorithms. Simulation results indicate that a higher precision was achieved with the IA method than with Fernald’s method in terms of error and random noise in estimating boundary value and EBR. Experimental results were also better with the IA method than with Fernald’s method.

© 2001 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. F. G. Fernald, “Analysis of atmospheric lidar observations: some comments,” Appl. Opt. 23, 652–653 (1984).
    [CrossRef] [PubMed]
  3. H. W. M. Salemink, P. Schotanus, J. B. Bergwerff, “Quantitative lidar at 532 nm for vertical extinction profiles and the effect of relative humidity,” Appl. Phys. B 34, 187–189 (1984).
    [CrossRef]
  4. 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]
  5. Y. Sasano, H. Nakane, “Quantitative analysis of RHI lidar data by an iterative adjustment of the boundary condition term in the lidar solution,” Appl. Opt. 26, 615–616 (1987).
    [CrossRef] [PubMed]
  6. H. G. Hughes, M. R. Paulson, “Double-ended lidar technique for aerosol studies,” Appl. Opt. 27, 2273–2278 (1988).
    [CrossRef] [PubMed]
  7. J. D. Klett, “Lidar inversion with variable backscatter/extinction ratios,” Appl. Opt. 24, 1638–1643 (1985).
    [CrossRef] [PubMed]
  8. Q. Jinhuan, “Sensitivity of lidar equation solution to boundary values and determination of the values,” Adv. Atmos. Sci. 2, 229–241 (1988).
    [CrossRef]
  9. Y. Sasano, H. Nakane, “Significance of the extinction/backscatter ratio and the boundary value term in the solution for the two-component lidar equation,” Appl. Opt. 23, 11–13 (1984).
    [CrossRef]
  10. A. Weber, S. P. S. Porto, L. E. Cheesman, J. J. Barrett, “High-resolution Raman spectroscopy of gases with cw-laser excitation,” J. Opt. Soc. Am. 57, 9–28 (1967).
    [CrossRef]
  11. E. W. Browell, S. Ismail, S. T. Shipley, “Ultraviolet DIAL measurements of O3 profiles in regions of spatially inhomogeneous aerosols,” Appl. Opt. 24, 2827–2836 (1985).
    [CrossRef] [PubMed]
  12. Y. Sasano, E. V. Browell, S. Ismail, “Error caused by using a constant extinction/backscattering ratio in the lidar solution,” Appl. Opt. 24, 3929–3932 (1985).
    [CrossRef] [PubMed]
  13. V. A. Kovalev, “Lidar measurement of the vertical aerosol extinction profiles with range-dependent backscatter-to-extinction ratios,” Appl. Opt. 32, 6053–6065 (1993).
    [CrossRef] [PubMed]
  14. S. A. Young, “Analysis of lidar backscatter profiles in optically thin clouds,” Appl. Opt. 34, 7019–7031 (1995).
    [CrossRef] [PubMed]
  15. G. P. Gobbi, G. Di Donfrancesco, A. Adriani, “Physical properties of stratospheric clouds during the Antarctic winter of 1995,” J. Geophys. Res. 103, 10859–10873 (1998).
    [CrossRef]
  16. G. P. Gobbi, “Polarization lidar returns from aerosols and thin clouds: a framework for the analysis,” Appl. Opt. 37, 5505–5508 (1998).
    [CrossRef]
  17. P. B. Russell, T. J. Swissler, M. P. McCormick, “Methodology for error analysis and simulation of lidar aerosol measurements,” Appl. Opt. 18, 3783–3797 (1979).
    [PubMed]
  18. R. M. Measures, Laser Remote Sensing (Wiley, New York, 1984), Chap. 6.

1998 (2)

G. P. Gobbi, G. Di Donfrancesco, A. Adriani, “Physical properties of stratospheric clouds during the Antarctic winter of 1995,” J. Geophys. Res. 103, 10859–10873 (1998).
[CrossRef]

G. P. Gobbi, “Polarization lidar returns from aerosols and thin clouds: a framework for the analysis,” Appl. Opt. 37, 5505–5508 (1998).
[CrossRef]

1995 (1)

1993 (1)

1988 (2)

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

Q. Jinhuan, “Sensitivity of lidar equation solution to boundary values and determination of the values,” Adv. Atmos. Sci. 2, 229–241 (1988).
[CrossRef]

1987 (1)

1985 (4)

1984 (3)

1981 (1)

1979 (1)

1967 (1)

A. Weber, S. P. S. Porto, L. E. Cheesman, J. J. Barrett, “High-resolution Raman spectroscopy of gases with cw-laser excitation,” J. Opt. Soc. Am. 57, 9–28 (1967).
[CrossRef]

Adriani, A.

G. P. Gobbi, G. Di Donfrancesco, A. Adriani, “Physical properties of stratospheric clouds during the Antarctic winter of 1995,” J. Geophys. Res. 103, 10859–10873 (1998).
[CrossRef]

Barrett, J. J.

A. Weber, S. P. S. Porto, L. E. Cheesman, J. J. Barrett, “High-resolution Raman spectroscopy of gases with cw-laser excitation,” J. Opt. Soc. Am. 57, 9–28 (1967).
[CrossRef]

Bergwerff, J. B.

H. W. M. Salemink, P. Schotanus, J. B. Bergwerff, “Quantitative lidar at 532 nm for vertical extinction profiles and the effect of relative humidity,” Appl. Phys. B 34, 187–189 (1984).
[CrossRef]

Browell, E. V.

Browell, E. W.

Cheesman, L. E.

A. Weber, S. P. S. Porto, L. E. Cheesman, J. J. Barrett, “High-resolution Raman spectroscopy of gases with cw-laser excitation,” J. Opt. Soc. Am. 57, 9–28 (1967).
[CrossRef]

Di Donfrancesco, G.

G. P. Gobbi, G. Di Donfrancesco, A. Adriani, “Physical properties of stratospheric clouds during the Antarctic winter of 1995,” J. Geophys. Res. 103, 10859–10873 (1998).
[CrossRef]

Ferguson, J. A.

Fernald, F. G.

Gobbi, G. P.

G. P. Gobbi, G. Di Donfrancesco, A. Adriani, “Physical properties of stratospheric clouds during the Antarctic winter of 1995,” J. Geophys. Res. 103, 10859–10873 (1998).
[CrossRef]

G. P. Gobbi, “Polarization lidar returns from aerosols and thin clouds: a framework for the analysis,” Appl. Opt. 37, 5505–5508 (1998).
[CrossRef]

Hughes, H. G.

Ismail, S.

Jinhuan, Q.

Q. Jinhuan, “Sensitivity of lidar equation solution to boundary values and determination of the values,” Adv. Atmos. Sci. 2, 229–241 (1988).
[CrossRef]

Klett, J. D.

Kovalev, V. A.

McCormick, M. P.

Measures, R. M.

R. M. Measures, Laser Remote Sensing (Wiley, New York, 1984), Chap. 6.

Nakane, H.

Paulson, M. R.

Porto, S. P. S.

A. Weber, S. P. S. Porto, L. E. Cheesman, J. J. Barrett, “High-resolution Raman spectroscopy of gases with cw-laser excitation,” J. Opt. Soc. Am. 57, 9–28 (1967).
[CrossRef]

Russell, P. B.

Salemink, H. W. M.

H. W. M. Salemink, P. Schotanus, J. B. Bergwerff, “Quantitative lidar at 532 nm for vertical extinction profiles and the effect of relative humidity,” Appl. Phys. B 34, 187–189 (1984).
[CrossRef]

Sasano, Y.

Schotanus, P.

H. W. M. Salemink, P. Schotanus, J. B. Bergwerff, “Quantitative lidar at 532 nm for vertical extinction profiles and the effect of relative humidity,” Appl. Phys. B 34, 187–189 (1984).
[CrossRef]

Shipley, S. T.

Stephens, D. H.

Swissler, T. J.

Weber, A.

A. Weber, S. P. S. Porto, L. E. Cheesman, J. J. Barrett, “High-resolution Raman spectroscopy of gases with cw-laser excitation,” J. Opt. Soc. Am. 57, 9–28 (1967).
[CrossRef]

Young, S. A.

Adv. Atmos. Sci. (1)

Q. Jinhuan, “Sensitivity of lidar equation solution to boundary values and determination of the values,” Adv. Atmos. Sci. 2, 229–241 (1988).
[CrossRef]

Appl. Opt. (13)

Y. Sasano, H. Nakane, “Significance of the extinction/backscatter ratio and the boundary value term in the solution for the two-component lidar equation,” Appl. Opt. 23, 11–13 (1984).
[CrossRef]

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]

Y. Sasano, H. Nakane, “Quantitative analysis of RHI lidar data by an iterative adjustment of the boundary condition term in the lidar solution,” Appl. Opt. 26, 615–616 (1987).
[CrossRef] [PubMed]

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

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

E. W. Browell, S. Ismail, S. T. Shipley, “Ultraviolet DIAL measurements of O3 profiles in regions of spatially inhomogeneous aerosols,” Appl. Opt. 24, 2827–2836 (1985).
[CrossRef] [PubMed]

Y. Sasano, E. V. Browell, S. Ismail, “Error caused by using a constant extinction/backscattering ratio in the lidar solution,” Appl. Opt. 24, 3929–3932 (1985).
[CrossRef] [PubMed]

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

S. A. Young, “Analysis of lidar backscatter profiles in optically thin clouds,” Appl. Opt. 34, 7019–7031 (1995).
[CrossRef] [PubMed]

G. P. Gobbi, “Polarization lidar returns from aerosols and thin clouds: a framework for the analysis,” Appl. Opt. 37, 5505–5508 (1998).
[CrossRef]

P. B. Russell, T. J. Swissler, M. P. McCormick, “Methodology for error analysis and simulation of lidar aerosol measurements,” Appl. Opt. 18, 3783–3797 (1979).
[PubMed]

Appl. Phys. B (1)

H. W. M. Salemink, P. Schotanus, J. B. Bergwerff, “Quantitative lidar at 532 nm for vertical extinction profiles and the effect of relative humidity,” Appl. Phys. B 34, 187–189 (1984).
[CrossRef]

J. Geophys. Res. (1)

G. P. Gobbi, G. Di Donfrancesco, A. Adriani, “Physical properties of stratospheric clouds during the Antarctic winter of 1995,” J. Geophys. Res. 103, 10859–10873 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

A. Weber, S. P. S. Porto, L. E. Cheesman, J. J. Barrett, “High-resolution Raman spectroscopy of gases with cw-laser excitation,” J. Opt. Soc. Am. 57, 9–28 (1967).
[CrossRef]

Other (1)

R. M. Measures, Laser Remote Sensing (Wiley, New York, 1984), Chap. 6.

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Figures (6)

Fig. 1
Fig. 1

Simulated results of backscattering coefficients assuming incorrect EBR and correct BV. Curve 1 shows the model βa profile in all figures. Curve 2 and curve 3 in (a) and (b) stand for the βa profile retrieved by the IA method with +20% and -20% error in the estimate of EBR at each layer except for molecule layers and liquid regions. Curve 2 and curve 3 in (c) and (d) show the βa profiles retrieved by Fernald’s method with S=50 and S=30 for all ranges, which leads to very large errors compared with the IA method. Positions of the boundary for each layer are drawn only in the model profile of Fig. 1. It is the same for Figs. 2 and 3.

Fig. 2
Fig. 2

Simulated results of backscattering coefficients assuming incorrect BV and correct EBR. Curve 1 shows the model βa profile in all figures. Curve 2 and curve 3 in (a) and (b) stand for the βa profile retrieved by the IA method with +20% and -20% error in the estimate of BV except for molecule layers and liquid regions. EBR is correct in each layer. Curve 2 and curve 3 in (c) and (d) stand for the βa profile retrieved by Fernald’s method with S=50 for all ranges but including +20% and -20% error in the estimate of BV.

Fig. 3
Fig. 3

Simulated results of backscattering coefficients with random noise. Curve 1 shows the model βa profile in all figures. The SNR that we used to simulate the model signal with noise is shown only as curve 3 in (a). It is the same for all of Fig. 3. Curve 2 and curve 3 in (a) and (b) stand for the βa profiles with noise retrieved by the IA method. Curve 2 and curve 3 in (c) and (d) stand for the βa profile with noise retrieved by Fernald’s method with S=50 for all ranges.

Fig. 4
Fig. 4

Vertical profiles of the range normalized on April 28, 1998 at three different times. 

Fig. 5
Fig. 5

Vertical profiles of the depolarization ratio on April 28, 1998 at three different times. Dashed lines stand for the positions of the boundary.

Fig. 6
Fig. 6

Vertical profiles of backscattering coefficients on April 28, 1998. Curve 1 and curve 3 stand for the derived backscattering coefficients from Fig. 4 with the inward stepwise and the outward stepwise integration algorithm of the IA method, respectively. Curve 2 stand for the derived backscattering coefficient from Fig. 4 with the inward stepwise integration algorithm of Fernald’s method.

Equations (11)

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P(Z)=ECZ-2[βa(Z)+βm(Z)]×exp-2z0Z[σa(z)+σm(z)]dz,
βa(Z)=N(Z)exp[-2(Sa(Z)-Sm)ZsZβ(z)dz]N(Zs)βa(Zs)+βm(Zs)-2Sa(Z)ZsZN(z)exp[-2(Sa(Z)-Sm)ZsZβ(z)dz]dz-βm(Z),
δ(Z)=P(Z)/P(Z)=βa(Z)+βm(Z)βa(Z)+βm(Z),
βa(Z)=βa(Z)+βa(Z).
βa(Z)=βm(Z)/δ(Z)-βm(Z).
Sa(I-1)
=N(I-1)exp[H(I-I, I)]βa(I-1)+βm(I-1)-N(I)βa(I)+βm(I){N(I)+N(I-1)exp[H(I-1, I)]}ΔZ,
H(1-1, I)=[Sa(I)-Sm][βm(I-1)+βm(I)]ΔZ.
Sa(I+1)
=N(I)βa(I)+βm(I)-N(I+1)exp[-H(I, I+1)]βa(I+1)+βm(I+1){N(I)+N(I+1)exp[-H(I, I+1)]}ΔZ,
H(I, I+1)=(Sa(I)-Sm)[βm(I)+βm(I+1)]ΔZ.

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