Abstract

This numerical study addresses the boundary value determination of the aerosol extinction coefficient from backscatter lidar measurements by use of the simultaneous evaluation of signals at 532 and 1064 nm. The basic equations are formulated for the most common case of a two-component atmosphere with variable aerosol extinction-to-backscatter ratios along the lidar line. The method proved to be quite stable for optically thick atmospheres even if the true profiles of the lidar ratios are not known exactly.

© 1998 Optical Society of America

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References

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  1. 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]
  2. G. J. Kunz, “Transmission as an input boundary value for an analytical solution of a single-scatter lidar equation,” Appl. Opt. 35, 3255–3260 (1996).
    [CrossRef] [PubMed]
  3. J. F. Potter, “Two-frequency lidar inversion technique,” Appl. Opt. 26, 1250–1256 (1987).
    [CrossRef] [PubMed]
  4. J. Ackermann, “Two-wavelength lidar inversion for a two-component atmosphere,” Appl. Opt. 36, 5134–5143 (1997).
    [CrossRef] [PubMed]
  5. J. D. Klett, “Lidar inversion with variable backscatter/extinction ratios,” Appl. Opt. 24, 1638–1643 (1985).
    [CrossRef] [PubMed]
  6. F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of aerosol height distribution by lidar,” J. Appl. Meteorol. 11, 482–489 (1972).
    [CrossRef]
  7. M. Kaestner, “Lidar inversion with variable backscatter/extinction ratios: comment,” Appl. Opt. 25, 833–835 (1986).
    [CrossRef] [PubMed]
  8. J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
    [CrossRef] [PubMed]
  9. P. B. Russell, T. J. Swissler, P. McCormick, “Methodology for error analysis and simulation of lidar aerosol measurements,” Appl. Opt. 18, 3783–3797 (1979).
    [PubMed]

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1972 (1)

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of aerosol height distribution by lidar,” J. Appl. Meteorol. 11, 482–489 (1972).
[CrossRef]

Ackermann, J.

Fernald, F. G.

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of aerosol height distribution by lidar,” J. Appl. Meteorol. 11, 482–489 (1972).
[CrossRef]

Herman, B. M.

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of aerosol height distribution by lidar,” J. Appl. Meteorol. 11, 482–489 (1972).
[CrossRef]

Kaestner, M.

Klett, J. D.

Kovalev, V. A.

Kunz, G. J.

McCormick, P.

Potter, J. F.

Reagan, J. A.

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of aerosol height distribution by lidar,” J. Appl. Meteorol. 11, 482–489 (1972).
[CrossRef]

Russell, P. B.

Swissler, T. J.

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Figures (8)

Fig. 1
Fig. 1

Flow chart of the different steps for boundary value determination of the aerosol extinction coefficient with a two-wavelength lidar inversion scheme. All the variables are explained in the text.

Fig. 2
Fig. 2

Input profiles of the aerosol and Rayleigh extinction coefficients at 532 nm, the lidar ratios at 532 and 1064 nm, and the values of k(R) for the optically thick (solid curves) and the optically thin (dashed curves) model atmosphere.

Fig. 3
Fig. 3

Range of variability of the lidar ratios at 532 nm used in this study. Cases A and B denote two different types of variation.

Fig. 4
Fig. 4

Calculated values of the boundary value of the extinction coefficient at 532 nm for two different variations of the assumed lidar ratios shown in Fig. 3. The symbols refer to the input lidar ratio profiles plotted in Fig. 3.

Fig. 5
Fig. 5

Influence of the boundary value misestimation on the retrieved extinction profiles for the lidar ratio profiles plotted in Fig. 3.

Fig. 6
Fig. 6

Input profile of k(R) (solid curves) and retrieved profiles (dotted and dashed curves) of k*(R) calculated with the lidar ratios plotted in Fig. 3 as input profiles for the inversion.

Fig. 7
Fig. 7

Contour plot of the dependence of α A,S *(R F ) on different combinations of range-independent lidar ratios at 532 and 1064 nm as input values. The shaded areas denote negative extinction coefficients and the dashed, dotted, and solid curves are the negative, zero, and positive percentage deviations from the true value of α A,S (R F ). The contour interval is 10%, and the upper and the lower parts refer to the results for the optically thin and the optically thick model atmosphere, respectively.

Fig. 8
Fig. 8

Influence of noise on the retrieved boundary value α A,S *(R F ) for the optically thick (upper part) and the optically thin (lower part) model atmosphere. Cases A and B refer to the lidar ratio profiles plotted in Fig. 3. The thick vertical lines mark the true boundary value α A,S (R F ).

Equations (18)

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L R = C β A R + β M R × exp - 2   0 R α A r + α M r d r .
T R = exp - 0 R   α A r d r ,
T M R = exp - 0 R   α M r d r ,
L R = C β A R + β M R T 2 R T M 2 R .
S A R = α A R β A R ,
T 2 R = exp 2   0 R   S A r β M r d r 1 - 2 C 0 R S A r L r T M 2 r × exp - 2   0 r   S A r β M r d r d r .
G r = exp - 2   0 r   S A r β M r d r
T 2 R G R = 1 - 2 C 0 R   S A r L r F r d r .
T 2 R F G R F - T 2 R 0 G R 0 = - 2 C R 0 R F   S A r L r F r d r .
α A R = - S A R β M R + S A R L R F R F R F - 1 L R F β A R F + β M R F - 1 + 2   R R F   S A r L r F r d rF R F - 1 .
α A R = - S A R β M R + S A R L R F R 2   R R F   S A r L r F r d r + 2   R 0 R F   S A r L r F r d r G R 0 G R F - 1 T A - 2 - 1 ,
T A 2 = T 2 R F T - 2 R 0 = exp - 2   R 0 R F   α A r d r .
α A , L R = k R α A , S R ,
L S R = C S α A , S R S A , S R - 1 + β M , S R × exp - 2   0 R α A , S r + α M , S r d r ,
L L R = C L k R α A , S R S A , L R - 1 + β M , L R × exp - 2   0 R k r α A , S r + α M , L r d r .
ln   A ij = ln c ij + k R j d ij c ji + k R i d ji + ln   B ij , A ij = L S R i L L R j L L R i L S R j × exp - 2   R i R j α M , S r - α M , L r + α A , S r d r , B ij = exp - 2   R i R j   k r α A , S r d r , c ij = β M , S R i β M , L R j + α A , S R i β M , L R j S A , S R i - 1 , d ij = α A , S R i α A , S R j S A , S R i - 1 S A , L R j - 1 + α A , S R j β M , S R i S A , L R j - 1 .
S A * R = ξ R S A R .
T A 2 < G R 0 2   R 0 R F   S A r L r F r d r β M R F T M 2 R F L R F + G R F .

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