Abstract

The differential absorption lidar (DIAL) technique generally assumes that atmospheric optical scattering is the same at the two laser wavelengths used in the DIAL measurement of a gas concentration profile. Errors can arise in this approach when the wavelengths are significantly separated, and there is a range dependence in the aerosol scattering distribution. This paper discusses the errors introduced by large DIAL wavelength separations and spatial inhomogeneity of aerosols in the atmosphere. A Bernoulli solution for determining the relative distribution of aerosol backscattering in the UV region is presented, and scattering ratio boundary values for these solutions are discussed. The results of this approach are used to derive a backscatter correction to the standard DIAL analysis method. It is shown that for the worst cases of severe range dependence in aerosol backscattering, the residual errors in the corrected DIAL O3 measurements were <10 ppbv for DIAL wavelengths at 286 and 300 nm.

© 1985 Optical Society of America

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References

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  1. R. M. Schotland, “Some Observations of the Vertical Profile of Water Vapor by Means of a Ground Based Optical Radar,” in Proceedings, Fourth Symposium on Remote Sensing of Environment, 12–14 Apr. 1966 (U. Michigan, Ann Arbor, 1966).
  2. R. L. Byer, M. Garbuny, “Pollutant Detection by Absorption Using Mie Scattering and Topographic Targets as Retroreflectors,” Appl. Opt. 12, 1496 (1973).
    [CrossRef] [PubMed]
  3. E. V. Browell, T. D. Wilkerson, T. J. McIlrath, “Water Vapor Differential Absorption Lidar Development and Evaluation,” Appl. Opt. 18, 3474 (1979).
    [CrossRef] [PubMed]
  4. E. V. Browell, “Lidar Measurements of Tropospheric Gases,” Opt. Eng. 21, 128 (1982).
    [CrossRef]
  5. E. V. Browell et al., “NASA Multipurpose Airborne DIAL System and Measurements of Ozone and Aerosol Profiles,” Appl. Opt. 22, 522 (1983).
    [CrossRef] [PubMed]
  6. M. L. Wright, E. K. Proctor, L. S. Gasiorek, E. M. Liston, “A Preliminary Study of Air Pollution by Active Remote Sensing,” NASA Contract Rep. 132724 (1975).
  7. E. E. Remsberg, L. L. Gordley, “Analysis of Differential Absorption Lidar from the Space Shuttle,” Appl. Opt. 17, 624 (1978).
    [CrossRef] [PubMed]
  8. E. V. Browell, Ed., “Shuttle Atmospheric Lidar Research Program—Final Report of Atmospheric Lidar Working Group,” NASA Spec. Publ. 433 (1979).
  9. R. T. Thompson, “Differential Absorption and Scattering Sensitivity Predictions,” NASA Contract. Rep. 2627 (1976).
  10. R. M. Schotland, “Errors in the Lidar Measurement of Atmospheric Gases by Differential Absorption,” J. Appl. Meteorol. 13, 71 (1974).
    [CrossRef]
  11. W. Hitschfeld, J. Bordan, “Errors Inherent in the Radar Measurement of Rainfall at Attenuating Wavelengths,” J. Meteorol. 11, 58 (1954).
    [CrossRef]
  12. F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of Aerosol Height Distribution by Lidar,” J. Appl. Meteorol. 11, 482 (1972).
    [CrossRef]
  13. E. V. Browell, S. T. Shipley, C. F. Butler, S. Ismail, “Airborne DIAL Measurements of Ozone and Aerosol Profiles in the 1980 PEPE/NEROS Field Experiment,” NASA Republ. in preparation (1985).
  14. L. Elterman, “UV, Visible, and IR Attenuation for Altitudes to 50 km, 1968,” AFCRL-68-0153 (1968).
  15. R. T. H. Collis, P. B. Russell, in Laser Monitoring of the Atmosphere, E. D. Hinkley, Ed. (Springer, New York, 1976), p. 117.
  16. G. L. Gregory, S. M. Beck, J. J. Mathis, “In Situ Correlative Measurements for the Ultraviolet Differential Absorption Lidar and the High Spectral Resolution Lidar Air Quality Remote Sensors: 1980 PEPE/NEROS Program,” NASA Tech. Memo. 83107 (1981).
  17. G. M. Murphy, Ordinary Differential Equations and Their Solutions (Van Nostrand, New York, 1960), p. 451.
  18. J. D. Klett, “Stable Analytical Inversion Solution for Processing Lidar Returns,” Appl. Opt. 20, 211 (1981).
    [CrossRef] [PubMed]
  19. U. S. Standard Model Atmosphere (GPO, Washington, D.C., 1976).
  20. E. P. Shettle, AFGL, Bedford, Mass. 01731; private communication.
  21. R. T. H. Collis, “Lidar: a New Atmospheric Probe,” Q. J. R. Meteorol. Soc. 92, 220 (1966).
    [CrossRef]
  22. R. G. Pinnick, J. M. Rosen, D. J. Hoffman, “Stratospheric Aerosol Measurements. III: Optical Model Calculations,” J. Atmos. Sci. 33, 304 (1976).
    [CrossRef]
  23. E. P. Shettle, R. W. Fenn, “Models of the Amospheric Aerosols and Their Optical Properties,” AGARD Conf. Proc. 183 (1976).

1983 (1)

1982 (1)

E. V. Browell, “Lidar Measurements of Tropospheric Gases,” Opt. Eng. 21, 128 (1982).
[CrossRef]

1981 (1)

1979 (1)

1978 (1)

1976 (1)

R. G. Pinnick, J. M. Rosen, D. J. Hoffman, “Stratospheric Aerosol Measurements. III: Optical Model Calculations,” J. Atmos. Sci. 33, 304 (1976).
[CrossRef]

1974 (1)

R. M. Schotland, “Errors in the Lidar Measurement of Atmospheric Gases by Differential Absorption,” J. Appl. Meteorol. 13, 71 (1974).
[CrossRef]

1973 (1)

1972 (1)

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of Aerosol Height Distribution by Lidar,” J. Appl. Meteorol. 11, 482 (1972).
[CrossRef]

1966 (1)

R. T. H. Collis, “Lidar: a New Atmospheric Probe,” Q. J. R. Meteorol. Soc. 92, 220 (1966).
[CrossRef]

1954 (1)

W. Hitschfeld, J. Bordan, “Errors Inherent in the Radar Measurement of Rainfall at Attenuating Wavelengths,” J. Meteorol. 11, 58 (1954).
[CrossRef]

Beck, S. M.

G. L. Gregory, S. M. Beck, J. J. Mathis, “In Situ Correlative Measurements for the Ultraviolet Differential Absorption Lidar and the High Spectral Resolution Lidar Air Quality Remote Sensors: 1980 PEPE/NEROS Program,” NASA Tech. Memo. 83107 (1981).

Bordan, J.

W. Hitschfeld, J. Bordan, “Errors Inherent in the Radar Measurement of Rainfall at Attenuating Wavelengths,” J. Meteorol. 11, 58 (1954).
[CrossRef]

Browell, E. V.

E. V. Browell et al., “NASA Multipurpose Airborne DIAL System and Measurements of Ozone and Aerosol Profiles,” Appl. Opt. 22, 522 (1983).
[CrossRef] [PubMed]

E. V. Browell, “Lidar Measurements of Tropospheric Gases,” Opt. Eng. 21, 128 (1982).
[CrossRef]

E. V. Browell, T. D. Wilkerson, T. J. McIlrath, “Water Vapor Differential Absorption Lidar Development and Evaluation,” Appl. Opt. 18, 3474 (1979).
[CrossRef] [PubMed]

E. V. Browell, S. T. Shipley, C. F. Butler, S. Ismail, “Airborne DIAL Measurements of Ozone and Aerosol Profiles in the 1980 PEPE/NEROS Field Experiment,” NASA Republ. in preparation (1985).

Butler, C. F.

E. V. Browell, S. T. Shipley, C. F. Butler, S. Ismail, “Airborne DIAL Measurements of Ozone and Aerosol Profiles in the 1980 PEPE/NEROS Field Experiment,” NASA Republ. in preparation (1985).

Byer, R. L.

Collis, R. T. H.

R. T. H. Collis, “Lidar: a New Atmospheric Probe,” Q. J. R. Meteorol. Soc. 92, 220 (1966).
[CrossRef]

R. T. H. Collis, P. B. Russell, in Laser Monitoring of the Atmosphere, E. D. Hinkley, Ed. (Springer, New York, 1976), p. 117.

Elterman, L.

L. Elterman, “UV, Visible, and IR Attenuation for Altitudes to 50 km, 1968,” AFCRL-68-0153 (1968).

Fenn, R. W.

E. P. Shettle, R. W. Fenn, “Models of the Amospheric Aerosols and Their Optical Properties,” AGARD Conf. Proc. 183 (1976).

Fernald, F. G.

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of Aerosol Height Distribution by Lidar,” J. Appl. Meteorol. 11, 482 (1972).
[CrossRef]

Garbuny, M.

Gasiorek, L. S.

M. L. Wright, E. K. Proctor, L. S. Gasiorek, E. M. Liston, “A Preliminary Study of Air Pollution by Active Remote Sensing,” NASA Contract Rep. 132724 (1975).

Gordley, L. L.

Gregory, G. L.

G. L. Gregory, S. M. Beck, J. J. Mathis, “In Situ Correlative Measurements for the Ultraviolet Differential Absorption Lidar and the High Spectral Resolution Lidar Air Quality Remote Sensors: 1980 PEPE/NEROS Program,” NASA Tech. Memo. 83107 (1981).

Herman, B. M.

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of Aerosol Height Distribution by Lidar,” J. Appl. Meteorol. 11, 482 (1972).
[CrossRef]

Hitschfeld, W.

W. Hitschfeld, J. Bordan, “Errors Inherent in the Radar Measurement of Rainfall at Attenuating Wavelengths,” J. Meteorol. 11, 58 (1954).
[CrossRef]

Hoffman, D. J.

R. G. Pinnick, J. M. Rosen, D. J. Hoffman, “Stratospheric Aerosol Measurements. III: Optical Model Calculations,” J. Atmos. Sci. 33, 304 (1976).
[CrossRef]

Ismail, S.

E. V. Browell, S. T. Shipley, C. F. Butler, S. Ismail, “Airborne DIAL Measurements of Ozone and Aerosol Profiles in the 1980 PEPE/NEROS Field Experiment,” NASA Republ. in preparation (1985).

Klett, J. D.

Liston, E. M.

M. L. Wright, E. K. Proctor, L. S. Gasiorek, E. M. Liston, “A Preliminary Study of Air Pollution by Active Remote Sensing,” NASA Contract Rep. 132724 (1975).

Mathis, J. J.

G. L. Gregory, S. M. Beck, J. J. Mathis, “In Situ Correlative Measurements for the Ultraviolet Differential Absorption Lidar and the High Spectral Resolution Lidar Air Quality Remote Sensors: 1980 PEPE/NEROS Program,” NASA Tech. Memo. 83107 (1981).

McIlrath, T. J.

Murphy, G. M.

G. M. Murphy, Ordinary Differential Equations and Their Solutions (Van Nostrand, New York, 1960), p. 451.

Pinnick, R. G.

R. G. Pinnick, J. M. Rosen, D. J. Hoffman, “Stratospheric Aerosol Measurements. III: Optical Model Calculations,” J. Atmos. Sci. 33, 304 (1976).
[CrossRef]

Proctor, E. K.

M. L. Wright, E. K. Proctor, L. S. Gasiorek, E. M. Liston, “A Preliminary Study of Air Pollution by Active Remote Sensing,” NASA Contract Rep. 132724 (1975).

Reagan, J. A.

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of Aerosol Height Distribution by Lidar,” J. Appl. Meteorol. 11, 482 (1972).
[CrossRef]

Remsberg, E. E.

Rosen, J. M.

R. G. Pinnick, J. M. Rosen, D. J. Hoffman, “Stratospheric Aerosol Measurements. III: Optical Model Calculations,” J. Atmos. Sci. 33, 304 (1976).
[CrossRef]

Russell, P. B.

R. T. H. Collis, P. B. Russell, in Laser Monitoring of the Atmosphere, E. D. Hinkley, Ed. (Springer, New York, 1976), p. 117.

Schotland, R. M.

R. M. Schotland, “Errors in the Lidar Measurement of Atmospheric Gases by Differential Absorption,” J. Appl. Meteorol. 13, 71 (1974).
[CrossRef]

R. M. Schotland, “Some Observations of the Vertical Profile of Water Vapor by Means of a Ground Based Optical Radar,” in Proceedings, Fourth Symposium on Remote Sensing of Environment, 12–14 Apr. 1966 (U. Michigan, Ann Arbor, 1966).

Shettle, E. P.

E. P. Shettle, AFGL, Bedford, Mass. 01731; private communication.

E. P. Shettle, R. W. Fenn, “Models of the Amospheric Aerosols and Their Optical Properties,” AGARD Conf. Proc. 183 (1976).

Shipley, S. T.

E. V. Browell, S. T. Shipley, C. F. Butler, S. Ismail, “Airborne DIAL Measurements of Ozone and Aerosol Profiles in the 1980 PEPE/NEROS Field Experiment,” NASA Republ. in preparation (1985).

Thompson, R. T.

R. T. Thompson, “Differential Absorption and Scattering Sensitivity Predictions,” NASA Contract. Rep. 2627 (1976).

Wilkerson, T. D.

Wright, M. L.

M. L. Wright, E. K. Proctor, L. S. Gasiorek, E. M. Liston, “A Preliminary Study of Air Pollution by Active Remote Sensing,” NASA Contract Rep. 132724 (1975).

Appl. Opt. (5)

J. Appl. Meteorol. (2)

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of Aerosol Height Distribution by Lidar,” J. Appl. Meteorol. 11, 482 (1972).
[CrossRef]

R. M. Schotland, “Errors in the Lidar Measurement of Atmospheric Gases by Differential Absorption,” J. Appl. Meteorol. 13, 71 (1974).
[CrossRef]

J. Atmos. Sci. (1)

R. G. Pinnick, J. M. Rosen, D. J. Hoffman, “Stratospheric Aerosol Measurements. III: Optical Model Calculations,” J. Atmos. Sci. 33, 304 (1976).
[CrossRef]

J. Meteorol. (1)

W. Hitschfeld, J. Bordan, “Errors Inherent in the Radar Measurement of Rainfall at Attenuating Wavelengths,” J. Meteorol. 11, 58 (1954).
[CrossRef]

Opt. Eng. (1)

E. V. Browell, “Lidar Measurements of Tropospheric Gases,” Opt. Eng. 21, 128 (1982).
[CrossRef]

Q. J. R. Meteorol. Soc. (1)

R. T. H. Collis, “Lidar: a New Atmospheric Probe,” Q. J. R. Meteorol. Soc. 92, 220 (1966).
[CrossRef]

Other (12)

R. M. Schotland, “Some Observations of the Vertical Profile of Water Vapor by Means of a Ground Based Optical Radar,” in Proceedings, Fourth Symposium on Remote Sensing of Environment, 12–14 Apr. 1966 (U. Michigan, Ann Arbor, 1966).

U. S. Standard Model Atmosphere (GPO, Washington, D.C., 1976).

E. P. Shettle, AFGL, Bedford, Mass. 01731; private communication.

E. V. Browell, S. T. Shipley, C. F. Butler, S. Ismail, “Airborne DIAL Measurements of Ozone and Aerosol Profiles in the 1980 PEPE/NEROS Field Experiment,” NASA Republ. in preparation (1985).

L. Elterman, “UV, Visible, and IR Attenuation for Altitudes to 50 km, 1968,” AFCRL-68-0153 (1968).

R. T. H. Collis, P. B. Russell, in Laser Monitoring of the Atmosphere, E. D. Hinkley, Ed. (Springer, New York, 1976), p. 117.

G. L. Gregory, S. M. Beck, J. J. Mathis, “In Situ Correlative Measurements for the Ultraviolet Differential Absorption Lidar and the High Spectral Resolution Lidar Air Quality Remote Sensors: 1980 PEPE/NEROS Program,” NASA Tech. Memo. 83107 (1981).

G. M. Murphy, Ordinary Differential Equations and Their Solutions (Van Nostrand, New York, 1960), p. 451.

M. L. Wright, E. K. Proctor, L. S. Gasiorek, E. M. Liston, “A Preliminary Study of Air Pollution by Active Remote Sensing,” NASA Contract Rep. 132724 (1975).

E. V. Browell, Ed., “Shuttle Atmospheric Lidar Research Program—Final Report of Atmospheric Lidar Working Group,” NASA Spec. Publ. 433 (1979).

R. T. Thompson, “Differential Absorption and Scattering Sensitivity Predictions,” NASA Contract. Rep. 2627 (1976).

E. P. Shettle, R. W. Fenn, “Models of the Amospheric Aerosols and Their Optical Properties,” AGARD Conf. Proc. 183 (1976).

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Figures (14)

Fig. 1
Fig. 1

Backscatter correction in the DIAL measurement of ozone at the top of the mixed layer due to the change in wavelength dependence of atmospheric scattering. The correction is shown as a function of the aerosol to molecular scattering ratio within the mixed layer. The atmosphere above the mixed layer is assumed free of aerosols.

Fig. 2
Fig. 2

Comparison of uncorrected DIAL O3 profile and in situ measurement of O3 made in spiral at a location along the Electra flight track. A DIAL vertical resolution of 210 m and a 300-shot average (20-m horizontal resolution per shot) were used in these calculations. The Electra altitude for DIAL measurements was 3361-m MSL. Also plotted is the difference between the in situ and DIAL O3 measurements (ΔO3).

Fig. 3
Fig. 3

Sensitivity of Bernoulli solution for ξ(R) to assumed boundary values of ξ(Rmax) at 460-m altitude. Also plotted are values of ξ derived from the slope solution for extinction coefficient determination over the altitude ranges indicated by the vertical bars. A value of Pπ = 0.028 sr−1 was assumed in above calculations.

Fig. 4
Fig. 4

Sensitivity of ξ(R) determination to assumption of phase function value. A value of ξ(460 m) = 2.0 was assumed in these calculations.

Fig. 5
Fig. 5

Plots of ξ(R) and range corrected signals are shown for λon and λoff. ξoff(R) was derived assuming ξ(460 m) = 2.0 and Pπ = 0.028 sr−1, and ξon(β) was calculated from ξoff(R) assuming δ = 1.0.

Fig. 6
Fig. 6

Sensitivity of backscatter correction profile to values of (a) Pπ, (b) δ, and (c) ξ(Rmax).

Fig. 7
Fig. 7

Variation of DIAL O3 profile resulting from application of backscatter correction using various values of Pπ.

Fig. 8
Fig. 8

Comparison of corrected DIAL O3 profile [assuming Pπ = 0.028 sr−1, ξ(Rmax) = 2.0, and δ = 1.0] to in situ measurement of O3 concentrations on 7 Aug. 1980. A DIAL vertical resolution of 210 m and a 300-shot average were used in these calculations. Electra altitude for DIAL measurements was 3361-m MSL.

Fig. 9
Fig. 9

Comparison of DIAL and in situ O3 profiles on 24 July 1980. The Electra altitude for DIAL measurements was 3305-m MSL, and the DIAL resolution was the same as in Fig. 8.

Fig. 10
Fig. 10

Comparison of DIAL and in situ O3 profile on 31 July 1980. The Electra altitude for DIAL measurements was 4235-m MSL, and the DIAL resolution was the same as in Fig. 8.

Fig. 11
Fig. 11

Variation in DIAL O3 profile with smoothing interval size. A range cell of 210 m was used with both smoothing intervals.

Fig. 12
Fig. 12

Comparison of O3 profiles with smoothing of raw data and smoothing of the ratio of λon and λoff lidar returns. The range cell was 210 m in both cases.

Fig. 13
Fig. 13

Comparion of O3 profiles with different smoothing intervals of the ratio profile. A range cell of 210 m was used in both cases.

Fig. 14
Fig. 14

Plot of range corrected lidar return at λoff for 7 Aug. 1980. Average slopes for clean and aerosol laden regions are indicated, and these lines are projected to ranges where aerosol scattering ratios are estimated.

Tables (2)

Tables Icon

Table I Ozone DIAL Parameters

Tables Icon

Table II Determination of δ from Lidar Observations at 300 and 600 nm

Equations (19)

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P λ ( R ) R 2 = γ λ B λ ( R ) exp { 2 0 R [ β λ ( r ) + N O 3 ( r ) σ O 3 ] d r } ,
N ¯ O 3 ( R 1 , R 2 ) = 1 2 ( R 2 R 1 ) Δ σ O 3 ln [ P on ( R 1 ) P off ( R 2 ) P off ( R 1 ) P on ( R 2 ) ] [ M ] 1 2 ( R 2 R 1 ) Δ σ O 3 ln [ B on ( R 1 ) B off ( R 2 ) B off ( R 1 ) B on ( R 2 ) ] [ B ] 1 Δ σ O 3 ( β on β off ) , [ E ]
[ E ] Δ λ Δ σ O 3 λ off ( α β aer , off + 4 β mol , off ) ,
S λ ( R ) = P aer , π , λ ( R ) 4 π · β aer ( R ) 3 8 π · β mol ( R ) S λ 0 ( R ) ( λ λ 0 ) 4 δ ,
( λ on λ off ) 4 δ 1 ( 4 δ ) Δλ λ off ,
[ B ] ( 4 δ ) 2 ( R 2 R 1 ) Δ σ O · Δλ λ off · [ S off ( R 1 ) 1 + S off ( R 1 ) S off ( R 2 ) 1 + S off ( R 2 ) ] .
μ ( R ) = P ( R ) R 2 P ( R 0 ) R 0 2 = B ( R ) B ( R 0 ) exp { 2 R 0 R [ β ( r ) + N O 3 ( r ) σ O ] d r } .
B ( R ) B ( R 0 ) = B mol ( R ) [ 1 + S ( R ) ] B mol ( R 0 ) [ 1 + S ( R ) ] , and
B ( R ) B ( R 0 ) = ρ ( R ) ξ ( R ) ρ ( R 0 ) ξ ( R 0 ) ,
μ ( R ) = ρ ( R ) ρ ( R 0 ) · ξ ( R ) ξ ( R 0 ) . · exp { 2 R 0 R [ β mol ( r ) + β aer + N O 3 ( r ) σ O 3 ] d r } .
μ * ( R ) = μ ( R ) ρ ( R 0 ) ρ ( R ) exp [ + 2 R 0 R β mol ( r ) d r ] .
μ * ( R ) = ξ ( R ) ξ ( R 0 ) · exp [ 2 R 0 R β aer ( r ) d r ] .
d ξ d R = 2 g ( R ) ξ 2 + ξ d d R { ln [ μ * ( R ) 2 g ( R ) ] } ,
g ( R ) = ( 3 / 8 π ) β mol ( R ) P π ( R )
ξ ( R ) = μ * ( R ) exp [ 2 R 0 R g ( r ) d r ] C ( R 0 ) 2 R 0 R { g ( r ) μ * ( R ) · exp [ 2 R 0 r g ( r ) d r ] } d r ,
P 1 R 2 = γ ( 1 + S 1 ) ρ ( R ) exp [ 2 0 R β 1 ( r ) d r ] for 0 R R 1 ,
P 2 R 2 = γ ( 1 + S 2 ) ρ ( R ) exp [ 2 0 R 1 β 1 ( r ) d r 2 R 1 R β 2 ( r ) d r ] for R 1 R R 2 .
P 1 R 2 P 2 R 2 = 1 + S 1 1 + S 2 .
P 1 R 2 P 2 R 2 1 1 + S 2 .

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