Abstract

A method of analytical differentiation is developed for processing differential absorption lidar (DIAL) data. The method is based on simple analytical transformation of the DIAL on and off signal ratio. The derivatives consequently are found for either individual data points or local zones of the measurement range. The method makes possible the separation of local zones of interest and the separate investigation of these. The smoothing level is established by the selected value of the exponent in a transformation formula rather than by the selection of the resolution range. The method does not require the calculation of local signal increments. This reduces significantly the high-frequency noise in the measured concentration. The method is general and can be used for different experimental data, including inelastic (Raman) lidar data. The processing technique is practical and does not require a determination of the solution for a large set of algebraic equations. It is based on the simple repetition of the same type of calculations with different constants. The method can easily be implemented for practical computations.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. M. Measures, Laser remote sensing (Wiley, New York, 1984).
  2. E. V. 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]
  3. V. E. Zuev, Yu. S. Makushkin, V. N. Marichev, A. A. Mitsel, V. V. Zuev, “Lidar differential absorbing and scattering technique: theory,” Appl. Opt. 22, 3733–3741 (1983).
    [CrossRef] [PubMed]
  4. A. Ansmann, M. Riebesell, C. Weitkamp, “Measurement of atmospheric aerosol extinction profiles with a Raman lidar,” Opt. Lett. 15, 746–748 (1990).
    [CrossRef] [PubMed]
  5. G. Beyerle, S. McDermid, “Altitude range resolution of differential absorption lidar ozone profiles,” Appl. Opt. 38, 924–927 (1999).
    [CrossRef]
  6. Numerical Recipes. The Art of Scientific Computing (Cambridge U. Press, Cambridge, England, 1986).
  7. C. R. Wylie, L. C. Barrett, Advanced Engineering Mathematics (McGraw-Hill, New York, 1982).
  8. B. P. Ivanenko, I. E. Naats, “Integral-equation method for interpreting laser-sounding data on atmospheric gas components using differential absorption,” Opt. Lett. 6, 305–307 (1981).
    [CrossRef] [PubMed]
  9. A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Wiley, New York, 1977).
  10. J. Pelon, G. Megie, “Ozone monitoring in the troposphere and lower stratosphere: evaluation and operation of a ground-based lidar station,” J. Geophys. Res. 87, 4947–4955 (1982).
    [CrossRef]
  11. I. S. McDermid, S. M. Godin, L. O. Lindqvist, “Ground-based laser DIAL system for long-term measurements of stratospheric ozone,” Appl. Opt. 29, 3603–3612 (1990).
    [CrossRef] [PubMed]
  12. D. N. Whiteman, “Application of statistical methods to the determination of slope in lidar data,” Appl. Opt. 38, 3360–3369 (1999).
    [CrossRef]
  13. S. Godin, A. I. Carswell, D. P. Donovan, H. Claude, W. Steinbrecht, I. S. McDermid, T. I. McGee, M. R. Gross, N. Nakane, D. P. J. Swart, H. B. Bergwerff, O. Uchino, P. Gathen, R. Neuber, “Ozone differential absorption lidar algorithm intercomparison,” Appl. Opt. 38, 6225–6236 (1999).
    [CrossRef]
  14. V. A. Kovalev, J. L. McElroy, “Differential absorption lidar measurement of vertical ozone profiles in the troposphere that contains aerosol layers with strong backscattering gradients: a simplified version,” Appl. Opt. 33, 8393–8401 (1994).
    [CrossRef] [PubMed]
  15. W. Viezee, E. E. Uthe, R. T. H. Collis, “Lidar observations of airfield approach conditions: an exploratory study,” J. Appl. Meteorol. 8, 274–283 (1969).
    [CrossRef]
  16. J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
    [CrossRef] [PubMed]

1999 (3)

1994 (1)

1990 (2)

1985 (1)

1983 (1)

1982 (1)

J. Pelon, G. Megie, “Ozone monitoring in the troposphere and lower stratosphere: evaluation and operation of a ground-based lidar station,” J. Geophys. Res. 87, 4947–4955 (1982).
[CrossRef]

1981 (2)

1969 (1)

W. Viezee, E. E. Uthe, R. T. H. Collis, “Lidar observations of airfield approach conditions: an exploratory study,” J. Appl. Meteorol. 8, 274–283 (1969).
[CrossRef]

Ansmann, A.

Arsenin, V. Y.

A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Wiley, New York, 1977).

Barrett, L. C.

C. R. Wylie, L. C. Barrett, Advanced Engineering Mathematics (McGraw-Hill, New York, 1982).

Bergwerff, H. B.

Beyerle, G.

Browell, E. V.

Carswell, A. I.

Claude, H.

Collis, R. T. H.

W. Viezee, E. E. Uthe, R. T. H. Collis, “Lidar observations of airfield approach conditions: an exploratory study,” J. Appl. Meteorol. 8, 274–283 (1969).
[CrossRef]

Donovan, D. P.

Gathen, P.

Godin, S.

Godin, S. M.

Gross, M. R.

Ismail, S.

Ivanenko, B. P.

Klett, J. D.

Kovalev, V. A.

Lindqvist, L. O.

Makushkin, Yu. S.

Marichev, V. N.

McDermid, I. S.

McDermid, S.

McElroy, J. L.

McGee, T. I.

Measures, R. M.

R. M. Measures, Laser remote sensing (Wiley, New York, 1984).

Megie, G.

J. Pelon, G. Megie, “Ozone monitoring in the troposphere and lower stratosphere: evaluation and operation of a ground-based lidar station,” J. Geophys. Res. 87, 4947–4955 (1982).
[CrossRef]

Mitsel, A. A.

Naats, I. E.

Nakane, N.

Neuber, R.

Pelon, J.

J. Pelon, G. Megie, “Ozone monitoring in the troposphere and lower stratosphere: evaluation and operation of a ground-based lidar station,” J. Geophys. Res. 87, 4947–4955 (1982).
[CrossRef]

Riebesell, M.

Shipley, S. T.

Steinbrecht, W.

Swart, D. P. J.

Tikhonov, A. N.

A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Wiley, New York, 1977).

Uchino, O.

Uthe, E. E.

W. Viezee, E. E. Uthe, R. T. H. Collis, “Lidar observations of airfield approach conditions: an exploratory study,” J. Appl. Meteorol. 8, 274–283 (1969).
[CrossRef]

Viezee, W.

W. Viezee, E. E. Uthe, R. T. H. Collis, “Lidar observations of airfield approach conditions: an exploratory study,” J. Appl. Meteorol. 8, 274–283 (1969).
[CrossRef]

Weitkamp, C.

Whiteman, D. N.

Wylie, C. R.

C. R. Wylie, L. C. Barrett, Advanced Engineering Mathematics (McGraw-Hill, New York, 1982).

Zuev, V. E.

Zuev, V. V.

Appl. Opt. (8)

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

V. E. Zuev, Yu. S. Makushkin, V. N. Marichev, A. A. Mitsel, V. V. Zuev, “Lidar differential absorbing and scattering technique: theory,” Appl. Opt. 22, 3733–3741 (1983).
[CrossRef] [PubMed]

E. V. 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]

I. S. McDermid, S. M. Godin, L. O. Lindqvist, “Ground-based laser DIAL system for long-term measurements of stratospheric ozone,” Appl. Opt. 29, 3603–3612 (1990).
[CrossRef] [PubMed]

V. A. Kovalev, J. L. McElroy, “Differential absorption lidar measurement of vertical ozone profiles in the troposphere that contains aerosol layers with strong backscattering gradients: a simplified version,” Appl. Opt. 33, 8393–8401 (1994).
[CrossRef] [PubMed]

D. N. Whiteman, “Application of statistical methods to the determination of slope in lidar data,” Appl. Opt. 38, 3360–3369 (1999).
[CrossRef]

G. Beyerle, S. McDermid, “Altitude range resolution of differential absorption lidar ozone profiles,” Appl. Opt. 38, 924–927 (1999).
[CrossRef]

S. Godin, A. I. Carswell, D. P. Donovan, H. Claude, W. Steinbrecht, I. S. McDermid, T. I. McGee, M. R. Gross, N. Nakane, D. P. J. Swart, H. B. Bergwerff, O. Uchino, P. Gathen, R. Neuber, “Ozone differential absorption lidar algorithm intercomparison,” Appl. Opt. 38, 6225–6236 (1999).
[CrossRef]

J. Appl. Meteorol. (1)

W. Viezee, E. E. Uthe, R. T. H. Collis, “Lidar observations of airfield approach conditions: an exploratory study,” J. Appl. Meteorol. 8, 274–283 (1969).
[CrossRef]

J. Geophys. Res. (1)

J. Pelon, G. Megie, “Ozone monitoring in the troposphere and lower stratosphere: evaluation and operation of a ground-based lidar station,” J. Geophys. Res. 87, 4947–4955 (1982).
[CrossRef]

Opt. Lett. (2)

Other (4)

Numerical Recipes. The Art of Scientific Computing (Cambridge U. Press, Cambridge, England, 1986).

C. R. Wylie, L. C. Barrett, Advanced Engineering Mathematics (McGraw-Hill, New York, 1982).

R. M. Measures, Laser remote sensing (Wiley, New York, 1984).

A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Wiley, New York, 1977).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Simulated function K(r) (solid line) and function K*(r, C) obtained with Eq. (8) (bold line).

Fig. 2
Fig. 2

(a) Model profile (solid line) and that obtained with Eq. (8) (bold line) for the noise-corrupted data, where a = 0.02. (b) Same as in (a) but with a = 0.06.

Fig. 3
Fig. 3

Differential optical depth, τ(r 0, r), calculated for the model profile (solid curve) and that for the same profile when signals are corrupted with noise (bold line).

Fig. 4
Fig. 4

Difference Δτ between τ(r 0, r) and τ*(r 0, r) obtained for different K b *. Cuves 1, 2, and 3 are calculated with K b * = 0.10, 0.32, and 0.70 km-1, respectively.

Fig. 5
Fig. 5

(a) Difference Δτ between τ(r 1, r) and τ*(r 1, r) obtained with K b * = 0.53 km-1. (b) The difference Δτ between τ(r 2, r) and τ*(r 2, r) obtained with K b * = 0.07 km-1.

Fig. 6
Fig. 6

Resulting minimized Δτ for the total measurement range.

Fig. 7
Fig. 7

Model profile K(r) (solid line) and the restored profile found with the minimization procedure (bold line).

Fig. 8
Fig. 8

Model profile K(r) (solid line) and the profile retrieved with the conventional regression procedure using 11-point running mean (bold line).

Equations (17)

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

PonrPoffr=ConCoffβΠ,onrβΠ,offrexp-2 r0r Krdr,
Kr=Konr-Koffr,
Tr=PonrPonr1/2=A exp-τr0, r,
τr0, r=r0r Kxdx,
A=Ponr0Ponr01/2.
Tr=TrA=exp-τr0, r.
Tr=CK*r, Ca exp-r0r K*r, Cdr,
K*r, C=Tr1/aC1/a-1ar0rTr1/adr.
τr0, r=τ*r0, r-aln C1/a+ln K*r, C,
τ*r0, r=r0r K*xdx.
τr0, r=τ*r0, r-a lnK*r, CK*r0, C.
Kr=K*r, C-addrlnK*r, C.
KrK*r, C.
ddrlnK*ri, C0,
K*r, Kb*=Tr1/aTrb1/aKb*+1arrbTr1/adr.
C1/a=Trb1/aKb*+1ar0rbTr1/adr.
Δτ=τ*r0, r-τr0, r=a lnK*r, Kb*K*r0, Kb*.

Metrics