Abstract

We present a methodology for objective and automated determination of the uncertainty in aerosol measurements made by lidar. The methodology is based on standard error-propagation procedures, a large data base on atmospheric behavior, and considerable experience in processing lidar data. It yields algebraic expressions for probable error as a function of the atmospheric, background lighting, and lidar parameters. This error includes contributions from (1) lidar signal; (2) molecular density; (3) atmospheric transmission; and (4) lidar calibration. The validity of the algebraic error expressions is tested by performing simulated measurements and analyses, in which random errors of appropriate size are injected at appropriate steps. As an example, the methodology is applied to a new airborne lidar system used for measurements of the stratospheric aerosol. It is shown that for stratospheric measurements below about 25 km, molecular density uncertainties are the dominant source of error for wavelengths shorter than about 1.1 μm during nonvolcanic conditions. Because the influence of molecular scattering (relative to particulate scattering) decreases with increasing wavelength, stratospheric measurements with a Nd:YAG lidar can thus be more accurate than those made with a ruby lidar, provided that a suitable detector is used.

© 1979 Optical Society of America

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References

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  1. G. Fiocco, G. Grams, J. Atmos. Sci. 21, 323 (1964).
    [CrossRef]
  2. B. G. Schuster, J. Geophys. Res. 75, 3123 (1970).
    [CrossRef]
  3. P. B. Russell, R. D. Hake, J. Atmos. Sci. 34, 163 (1977).
    [CrossRef]
  4. M. P. McCormick, T. J. Swissler, W. P. Chu, W. H. Fuller, J. Atmos. Sci. 35, 1296 (1978).
    [CrossRef]
  5. E. E. Uthe, Bull. Am. Meteorol. Soc. 53, 358 (1972).
  6. G. W. Grams, I. H. Blifford, D. A. Gillette, P. B. Russell, J. Appl. Meteorol. 13, 459 (1974).
    [CrossRef]
  7. R. T. H. Collis, P. B. Russell, in Laser Monitoring of the Atmosphere, E. D. Hinkley, Ed. (Springer, New York, 1976), p. 71.
    [CrossRef]
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    [CrossRef]
  9. G. B. Northam, J. M. Rosen, S. H. Melfi, T. J. Pepin, M. P. McCormick, D. J. Hofmann, W. H. Fuller, Appl. Opt. 13, 2416 (1974).
    [CrossRef]
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  15. M. F. Wu, Report ERT P-93 DOT-TST-74-4 (NTIS, Springfield, Va., 1973).
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    [CrossRef]
  18. W. Planet, J. Laver, NOAA-NESS; personal communication (1979).
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  20. K. A. Rah, R. Borys, G. E. Shaw, Nature 268, 713 (1977).
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  21. O. B. Toon, J. B. Pollack, J. Geophys. Res. 75, 7051 (1973).
    [CrossRef]
  22. J. M. Rosen, J. Appl. Meteorol. 18, 1044 (1971).
    [CrossRef]
  23. R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, J. Atmos. Sci. 36, 699 (1979).
    [CrossRef]
  24. P. Hamill, T. J. Swissler, R. P. Turco, O. B. Toon, Nature 278, 149 (1979).
    [CrossRef]
  25. T. H. Carlson, R. S. Caverly, J. Geophys. Res. 82, 3141 (1977).
    [CrossRef]
  26. E. M. Patterson, D. A. Gillette, B. H. Stockton, J. Geophys. Res. 82, 3153 (1977).
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  27. O. B. Toon, J. B. Pollack, B. N. Kahre, J. Geophys. Res. 81, 5733 (1976).
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  29. M. P. McCormick, P. Hamill, T. J. Pepin, W. P. Chu, T. J. Swissler, L. R. McMaster, Bull. Am. Meteorol. Soc.62, Sept. (1979) (In press).
  30. P. B. Russell, M. P. McCormick, L. R. McMaster, T. J. Pepin, W. P. Chu, T. J. Swissler, SAM II Ground Truth Plan, NASA TM 78747 (U.S. GPO, Washington, D.C., 1978).
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  34. W. H. Fuller, T. J. Swissler, M. P. McCormick, in Atmospheric Aerosols: Their Optical Properties and Effects, NASA CP-2004 (U.S. GPO, Washington, D.C., 1976), paper TUC2.
  35. P. B. Russell, W. Viezee, R. D. Hake, R. T. H. Collis, in Proceedings, Fourth Conference, Climatic Assessment Program, U.S. Department of Transportation Report DOT-TSC-OST-7-38-1976 (NTIS, Springfield, Va., 1976).
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1979 (3)

P. B. Russell, J. M. Livingston, E. E. Uthe, J. Atmos. Sci. 36, 1587 (1979).
[CrossRef]

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, J. Atmos. Sci. 36, 699 (1979).
[CrossRef]

P. Hamill, T. J. Swissler, R. P. Turco, O. B. Toon, Nature 278, 149 (1979).
[CrossRef]

1978 (1)

M. P. McCormick, T. J. Swissler, W. P. Chu, W. H. Fuller, J. Atmos. Sci. 35, 1296 (1978).
[CrossRef]

1977 (4)

P. B. Russell, R. D. Hake, J. Atmos. Sci. 34, 163 (1977).
[CrossRef]

T. H. Carlson, R. S. Caverly, J. Geophys. Res. 82, 3141 (1977).
[CrossRef]

E. M. Patterson, D. A. Gillette, B. H. Stockton, J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

K. A. Rah, R. Borys, G. E. Shaw, Nature 268, 713 (1977).
[CrossRef]

1976 (2)

P. B. Russell, W. Viezee, R. D. Hake, R. T. H. Collis, Q. J. R. Meteorol. Soc. 102, 275 (1976).
[CrossRef]

O. B. Toon, J. B. Pollack, B. N. Kahre, J. Geophys. Res. 81, 5733 (1976).
[CrossRef]

1975 (2)

D. J. Hofmann, J. M. Rosen, T. J. Pepin, R. G. Pinnick, J. Atmos. Sci. 32, 1446 (1975).
[CrossRef]

J. M. Rosen, D. J. Hofmann, J. Laby, J. Atmos. Sci. 32, 1457 (1975).
[CrossRef]

1974 (2)

1973 (3)

R. W. Lenhard, Bull. Am. Meteorol. Soc. 54, 691 (1973).

L. R. Hoxit, R. H. Henry, J. Atmos. Sci. 30, 922 (1973).
[CrossRef]

O. B. Toon, J. B. Pollack, J. Geophys. Res. 75, 7051 (1973).
[CrossRef]

1972 (1)

E. E. Uthe, Bull. Am. Meteorol. Soc. 53, 358 (1972).

1971 (1)

J. M. Rosen, J. Appl. Meteorol. 18, 1044 (1971).
[CrossRef]

1970 (1)

B. G. Schuster, J. Geophys. Res. 75, 3123 (1970).
[CrossRef]

1964 (1)

G. Fiocco, G. Grams, J. Atmos. Sci. 21, 323 (1964).
[CrossRef]

Beers, Y.

Y. Beers, Introduction to the Theory of Error (Addison-Wesley, Reading, Mass., 1953).

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Blifford, I. H.

G. W. Grams, I. H. Blifford, D. A. Gillette, P. B. Russell, J. Appl. Meteorol. 13, 459 (1974).
[CrossRef]

Borys, R.

K. A. Rah, R. Borys, G. E. Shaw, Nature 268, 713 (1977).
[CrossRef]

Carlson, T. H.

T. H. Carlson, R. S. Caverly, J. Geophys. Res. 82, 3141 (1977).
[CrossRef]

Caverly, R. S.

T. H. Carlson, R. S. Caverly, J. Geophys. Res. 82, 3141 (1977).
[CrossRef]

Cerni, T. A.

T. J. Pepin, T. A. Cerni, High-Latitude Model Atmospheres for Application to the SAM II Experiment, SAGE Experiment, and Associated Ground Truth Measurements, Report APP-20, Department of Physics and Astronomy, University of Wyoming, Laramie 80207 (1978).

Chu, W. P.

M. P. McCormick, T. J. Swissler, W. P. Chu, W. H. Fuller, J. Atmos. Sci. 35, 1296 (1978).
[CrossRef]

M. P. McCormick, P. Hamill, T. J. Pepin, W. P. Chu, T. J. Swissler, L. R. McMaster, Bull. Am. Meteorol. Soc.62, Sept. (1979) (In press).

P. B. Russell, M. P. McCormick, L. R. McMaster, T. J. Pepin, W. P. Chu, T. J. Swissler, SAM II Ground Truth Plan, NASA TM 78747 (U.S. GPO, Washington, D.C., 1978).

Collis, R. T. H.

P. B. Russell, W. Viezee, R. D. Hake, R. T. H. Collis, Q. J. R. Meteorol. Soc. 102, 275 (1976).
[CrossRef]

R. T. H. Collis, P. B. Russell, in Laser Monitoring of the Atmosphere, E. D. Hinkley, Ed. (Springer, New York, 1976), p. 71.
[CrossRef]

P. B. Russell, W. Viezee, R. D. Hake, R. T. H. Collis, in Proceedings, Fourth Conference, Climatic Assessment Program, U.S. Department of Transportation Report DOT-TSC-OST-7-38-1976 (NTIS, Springfield, Va., 1976).

Edwards, H. B.

M. P. McCormick, H. B. Edwards, L. E. Mauldin, L. R. McMaster, in Atmospheric Aerosols: Their Optical Properties and Effects, NASA CP-2004 (U.S. GPO, Washington, D.C., 1976), paper TUB2.

Fiocco, G.

G. Fiocco, G. Grams, J. Atmos. Sci. 21, 323 (1964).
[CrossRef]

Fuller, W. H.

M. P. McCormick, T. J. Swissler, W. P. Chu, W. H. Fuller, J. Atmos. Sci. 35, 1296 (1978).
[CrossRef]

G. B. Northam, J. M. Rosen, S. H. Melfi, T. J. Pepin, M. P. McCormick, D. J. Hofmann, W. H. Fuller, Appl. Opt. 13, 2416 (1974).
[CrossRef]

W. H. Fuller, T. J. Swissler, M. P. McCormick, in Atmospheric Aerosols: Their Optical Properties and Effects, NASA CP-2004 (U.S. GPO, Washington, D.C., 1976), paper TUC2.

Gillette, D. A.

E. M. Patterson, D. A. Gillette, B. H. Stockton, J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

G. W. Grams, I. H. Blifford, D. A. Gillette, P. B. Russell, J. Appl. Meteorol. 13, 459 (1974).
[CrossRef]

Grams, G.

G. Fiocco, G. Grams, J. Atmos. Sci. 21, 323 (1964).
[CrossRef]

Grams, G. W.

G. W. Grams, I. H. Blifford, D. A. Gillette, P. B. Russell, J. Appl. Meteorol. 13, 459 (1974).
[CrossRef]

Hake, R. D.

P. B. Russell, R. D. Hake, J. Atmos. Sci. 34, 163 (1977).
[CrossRef]

P. B. Russell, W. Viezee, R. D. Hake, R. T. H. Collis, Q. J. R. Meteorol. Soc. 102, 275 (1976).
[CrossRef]

P. B. Russell, W. Viezee, R. D. Hake, R. T. H. Collis, in Proceedings, Fourth Conference, Climatic Assessment Program, U.S. Department of Transportation Report DOT-TSC-OST-7-38-1976 (NTIS, Springfield, Va., 1976).

Hamill, P.

P. Hamill, T. J. Swissler, R. P. Turco, O. B. Toon, Nature 278, 149 (1979).
[CrossRef]

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, J. Atmos. Sci. 36, 699 (1979).
[CrossRef]

M. P. McCormick, P. Hamill, T. J. Pepin, W. P. Chu, T. J. Swissler, L. R. McMaster, Bull. Am. Meteorol. Soc.62, Sept. (1979) (In press).

Henry, R. H.

L. R. Hoxit, R. H. Henry, J. Atmos. Sci. 30, 922 (1973).
[CrossRef]

Hoel, P. G.

P. G. Hoel, Introduction to Mathematical Statistics (Wiley, New York, 1971).

Hofmann, D. J.

D. J. Hofmann, J. M. Rosen, T. J. Pepin, R. G. Pinnick, J. Atmos. Sci. 32, 1446 (1975).
[CrossRef]

J. M. Rosen, D. J. Hofmann, J. Laby, J. Atmos. Sci. 32, 1457 (1975).
[CrossRef]

G. B. Northam, J. M. Rosen, S. H. Melfi, T. J. Pepin, M. P. McCormick, D. J. Hofmann, W. H. Fuller, Appl. Opt. 13, 2416 (1974).
[CrossRef]

Hoxit, L. R.

L. R. Hoxit, R. H. Henry, J. Atmos. Sci. 30, 922 (1973).
[CrossRef]

Kahre, B. N.

O. B. Toon, J. B. Pollack, B. N. Kahre, J. Geophys. Res. 81, 5733 (1976).
[CrossRef]

Kiang, C. S.

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, J. Atmos. Sci. 36, 699 (1979).
[CrossRef]

Laby, J.

J. M. Rosen, D. J. Hofmann, J. Laby, J. Atmos. Sci. 32, 1457 (1975).
[CrossRef]

Laver, J.

W. Planet, J. Laver, NOAA-NESS; personal communication (1979).

Lenhard, R. W.

R. W. Lenhard, Bull. Am. Meteorol. Soc. 54, 691 (1973).

Livingston, J. M.

P. B. Russell, J. M. Livingston, E. E. Uthe, J. Atmos. Sci. 36, 1587 (1979).
[CrossRef]

P. B. Russell, J. M. Livingston, for submission to Appl. Opt.00, 0000 (1979).

Mauldin, L. E.

M. P. McCormick, H. B. Edwards, L. E. Mauldin, L. R. McMaster, in Atmospheric Aerosols: Their Optical Properties and Effects, NASA CP-2004 (U.S. GPO, Washington, D.C., 1976), paper TUB2.

McCormick, M. P.

M. P. McCormick, T. J. Swissler, W. P. Chu, W. H. Fuller, J. Atmos. Sci. 35, 1296 (1978).
[CrossRef]

G. B. Northam, J. M. Rosen, S. H. Melfi, T. J. Pepin, M. P. McCormick, D. J. Hofmann, W. H. Fuller, Appl. Opt. 13, 2416 (1974).
[CrossRef]

M. P. McCormick, H. B. Edwards, L. E. Mauldin, L. R. McMaster, in Atmospheric Aerosols: Their Optical Properties and Effects, NASA CP-2004 (U.S. GPO, Washington, D.C., 1976), paper TUB2.

P. B. Russell, M. P. McCormick, L. R. McMaster, T. J. Pepin, W. P. Chu, T. J. Swissler, SAM II Ground Truth Plan, NASA TM 78747 (U.S. GPO, Washington, D.C., 1978).

M. P. McCormick, P. Hamill, T. J. Pepin, W. P. Chu, T. J. Swissler, L. R. McMaster, Bull. Am. Meteorol. Soc.62, Sept. (1979) (In press).

W. H. Fuller, T. J. Swissler, M. P. McCormick, in Atmospheric Aerosols: Their Optical Properties and Effects, NASA CP-2004 (U.S. GPO, Washington, D.C., 1976), paper TUC2.

McMaster, L. R.

P. B. Russell, M. P. McCormick, L. R. McMaster, T. J. Pepin, W. P. Chu, T. J. Swissler, SAM II Ground Truth Plan, NASA TM 78747 (U.S. GPO, Washington, D.C., 1978).

M. P. McCormick, P. Hamill, T. J. Pepin, W. P. Chu, T. J. Swissler, L. R. McMaster, Bull. Am. Meteorol. Soc.62, Sept. (1979) (In press).

M. P. McCormick, H. B. Edwards, L. E. Mauldin, L. R. McMaster, in Atmospheric Aerosols: Their Optical Properties and Effects, NASA CP-2004 (U.S. GPO, Washington, D.C., 1976), paper TUB2.

Melfi, S. H.

Northam, G. B.

Patterson, E. M.

E. M. Patterson, D. A. Gillette, B. H. Stockton, J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

Pepin, T. J.

D. J. Hofmann, J. M. Rosen, T. J. Pepin, R. G. Pinnick, J. Atmos. Sci. 32, 1446 (1975).
[CrossRef]

G. B. Northam, J. M. Rosen, S. H. Melfi, T. J. Pepin, M. P. McCormick, D. J. Hofmann, W. H. Fuller, Appl. Opt. 13, 2416 (1974).
[CrossRef]

P. B. Russell, M. P. McCormick, L. R. McMaster, T. J. Pepin, W. P. Chu, T. J. Swissler, SAM II Ground Truth Plan, NASA TM 78747 (U.S. GPO, Washington, D.C., 1978).

M. P. McCormick, P. Hamill, T. J. Pepin, W. P. Chu, T. J. Swissler, L. R. McMaster, Bull. Am. Meteorol. Soc.62, Sept. (1979) (In press).

T. J. Pepin, T. A. Cerni, High-Latitude Model Atmospheres for Application to the SAM II Experiment, SAGE Experiment, and Associated Ground Truth Measurements, Report APP-20, Department of Physics and Astronomy, University of Wyoming, Laramie 80207 (1978).

Pinnick, R. G.

D. J. Hofmann, J. M. Rosen, T. J. Pepin, R. G. Pinnick, J. Atmos. Sci. 32, 1446 (1975).
[CrossRef]

Planet, W.

W. Planet, J. Laver, NOAA-NESS; personal communication (1979).

Pollack, J. B.

O. B. Toon, J. B. Pollack, B. N. Kahre, J. Geophys. Res. 81, 5733 (1976).
[CrossRef]

O. B. Toon, J. B. Pollack, J. Geophys. Res. 75, 7051 (1973).
[CrossRef]

Rah, K. A.

K. A. Rah, R. Borys, G. E. Shaw, Nature 268, 713 (1977).
[CrossRef]

Rosen, J. M.

J. M. Rosen, D. J. Hofmann, J. Laby, J. Atmos. Sci. 32, 1457 (1975).
[CrossRef]

D. J. Hofmann, J. M. Rosen, T. J. Pepin, R. G. Pinnick, J. Atmos. Sci. 32, 1446 (1975).
[CrossRef]

G. B. Northam, J. M. Rosen, S. H. Melfi, T. J. Pepin, M. P. McCormick, D. J. Hofmann, W. H. Fuller, Appl. Opt. 13, 2416 (1974).
[CrossRef]

J. M. Rosen, J. Appl. Meteorol. 18, 1044 (1971).
[CrossRef]

Russell, P. B.

P. B. Russell, J. M. Livingston, E. E. Uthe, J. Atmos. Sci. 36, 1587 (1979).
[CrossRef]

P. B. Russell, R. D. Hake, J. Atmos. Sci. 34, 163 (1977).
[CrossRef]

P. B. Russell, W. Viezee, R. D. Hake, R. T. H. Collis, Q. J. R. Meteorol. Soc. 102, 275 (1976).
[CrossRef]

G. W. Grams, I. H. Blifford, D. A. Gillette, P. B. Russell, J. Appl. Meteorol. 13, 459 (1974).
[CrossRef]

R. T. H. Collis, P. B. Russell, in Laser Monitoring of the Atmosphere, E. D. Hinkley, Ed. (Springer, New York, 1976), p. 71.
[CrossRef]

P. B. Russell, J. M. Livingston, for submission to Appl. Opt.00, 0000 (1979).

P. B. Russell, M. P. McCormick, L. R. McMaster, T. J. Pepin, W. P. Chu, T. J. Swissler, SAM II Ground Truth Plan, NASA TM 78747 (U.S. GPO, Washington, D.C., 1978).

P. B. Russell, W. Viezee, R. D. Hake, R. T. H. Collis, in Proceedings, Fourth Conference, Climatic Assessment Program, U.S. Department of Transportation Report DOT-TSC-OST-7-38-1976 (NTIS, Springfield, Va., 1976).

Schuster, B. G.

B. G. Schuster, J. Geophys. Res. 75, 3123 (1970).
[CrossRef]

Shaw, G. E.

K. A. Rah, R. Borys, G. E. Shaw, Nature 268, 713 (1977).
[CrossRef]

Stockton, B. H.

E. M. Patterson, D. A. Gillette, B. H. Stockton, J. Geophys. Res. 82, 3153 (1977).
[CrossRef]

Swissler, T. J.

P. Hamill, T. J. Swissler, R. P. Turco, O. B. Toon, Nature 278, 149 (1979).
[CrossRef]

M. P. McCormick, T. J. Swissler, W. P. Chu, W. H. Fuller, J. Atmos. Sci. 35, 1296 (1978).
[CrossRef]

M. P. McCormick, P. Hamill, T. J. Pepin, W. P. Chu, T. J. Swissler, L. R. McMaster, Bull. Am. Meteorol. Soc.62, Sept. (1979) (In press).

W. H. Fuller, T. J. Swissler, M. P. McCormick, in Atmospheric Aerosols: Their Optical Properties and Effects, NASA CP-2004 (U.S. GPO, Washington, D.C., 1976), paper TUC2.

P. B. Russell, M. P. McCormick, L. R. McMaster, T. J. Pepin, W. P. Chu, T. J. Swissler, SAM II Ground Truth Plan, NASA TM 78747 (U.S. GPO, Washington, D.C., 1978).

Toon, O. B.

P. Hamill, T. J. Swissler, R. P. Turco, O. B. Toon, Nature 278, 149 (1979).
[CrossRef]

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, J. Atmos. Sci. 36, 699 (1979).
[CrossRef]

O. B. Toon, J. B. Pollack, B. N. Kahre, J. Geophys. Res. 81, 5733 (1976).
[CrossRef]

O. B. Toon, J. B. Pollack, J. Geophys. Res. 75, 7051 (1973).
[CrossRef]

Turco, R. P.

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, J. Atmos. Sci. 36, 699 (1979).
[CrossRef]

P. Hamill, T. J. Swissler, R. P. Turco, O. B. Toon, Nature 278, 149 (1979).
[CrossRef]

Uthe, E. E.

P. B. Russell, J. M. Livingston, E. E. Uthe, J. Atmos. Sci. 36, 1587 (1979).
[CrossRef]

E. E. Uthe, Bull. Am. Meteorol. Soc. 53, 358 (1972).

Viezee, W.

P. B. Russell, W. Viezee, R. D. Hake, R. T. H. Collis, Q. J. R. Meteorol. Soc. 102, 275 (1976).
[CrossRef]

P. B. Russell, W. Viezee, R. D. Hake, R. T. H. Collis, in Proceedings, Fourth Conference, Climatic Assessment Program, U.S. Department of Transportation Report DOT-TSC-OST-7-38-1976 (NTIS, Springfield, Va., 1976).

Whitten, R. C.

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, J. Atmos. Sci. 36, 699 (1979).
[CrossRef]

Wu, M. F.

M. F. Wu, Report ERT P-93 DOT-TST-74-4 (NTIS, Springfield, Va., 1973).

Appl. Opt. (1)

Bull. Am. Meteorol. Soc. (2)

E. E. Uthe, Bull. Am. Meteorol. Soc. 53, 358 (1972).

R. W. Lenhard, Bull. Am. Meteorol. Soc. 54, 691 (1973).

J. Appl. Meteorol. (2)

G. W. Grams, I. H. Blifford, D. A. Gillette, P. B. Russell, J. Appl. Meteorol. 13, 459 (1974).
[CrossRef]

J. M. Rosen, J. Appl. Meteorol. 18, 1044 (1971).
[CrossRef]

J. Atmos. Sci. (8)

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, J. Atmos. Sci. 36, 699 (1979).
[CrossRef]

D. J. Hofmann, J. M. Rosen, T. J. Pepin, R. G. Pinnick, J. Atmos. Sci. 32, 1446 (1975).
[CrossRef]

L. R. Hoxit, R. H. Henry, J. Atmos. Sci. 30, 922 (1973).
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Figures (8)

Fig. 1
Fig. 1

Simulation procedure for evaluating lidar measurement errors. Circles symbolize random number generators that inject simulated errors into derived quantities at appropriate steps of the computation. Numbers in parentheses indicate equations in the text.

Fig. 2
Fig. 2

Molecular density, particulate extinction, and ozone concentration profiles for the B-10 model atmosphere (arctic nonvolcanic conditions).

Fig. 3
Fig. 3

Ruby and Nd scattering ratio profiles for the B-10 model atmosphere (arctic nonvolcanic conditions).

Fig. 4
Fig. 4

Expected lidar-measurement error bars for ruby and Nd scattering ratios with the B-10 model atmosphere (arctic nonvolcanic conditions). Error calculation assumes the lidar parameters of Table II, lidar-flight altitude of 4 km, sun on the horizon, and integration for 1 min.

Fig. 5
Fig. 5

Expected lidar-measurement error bars for ruby and Nd particulate backscattering coefficients with the B-10 model atmosphere (arctic nonvolcanic conditions). Error calculations are as described in Fig. 1. Dots show simulated measurements with all four sources of random error included as a check on the error-bar computation. Systematic underestimations in the simulated measurements are discussed in the text.

Fig. 6
Fig. 6

Height dependence of expected uncertainty in lidar-measured particulate backscattering for the B-10 (arctic nonvolcanic) model atmosphere showing contributions by source. Assumed parameters are as in Fig. 5.

Fig. 7
Fig. 7

Lidar-measurement uncertainties and simulated measurements for P-10 (tropical nonvolcanic) model atmosphere: (a) model scattering ratios, simulated measurements (dots), and expected error bars; (b) model backscattering coefficients, simulated measurements (dots), and expected error bars; (c) and (d) relative uncertainty in particulate backscattering showing contributions by source.

Fig. 8
Fig. 8

Lidar-measurement uncertainties and simulated measurements for the ASTP (mid-latitude moderate volcanic) model atmosphere: (a) model scattering ratios and expected error bars; (b) model backscattering coefficients, simulated measurements (dots), and expected error bars; (c) and (d) relative uncertainty in particulate backscattering showing contributions by source.

Tables (3)

Tables Icon

Table I Expected Value of Rmin(λ), and its Probable Error, for Nonvolcanic Conditions and Various Latitude Bands

Tables Icon

Table II Parameters of Airborne Lidar Used for Simulations

Tables Icon

Table III Assumed Sizes of Error Sources in Lidar Data Analysis

Equations (51)

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N S ( λ , z ) = Δ z E ( λ ) A r T o ( λ ) T d ( λ ) ( z - z L ) 2 ( λ h c ) F ( λ , z ) exp [ - 2 z L z σ e ( λ , z ) d z ] ,
N S ( λ , z ) = [ K ( λ ) / ( z - z L ) 2 ] Q 2 ( λ , z L , z ) F ( λ , z ) ,
K ( λ ) = E ( λ ) A r T o ( λ ) T d ( λ ) ( λ Δ z / h c ) , Q 2 ( λ , z L , z ) = exp [ - 2 z L z σ e ( λ , z ) d z ] .
R ( λ , z ) F ( λ , z ) F M ( λ , z ) = F M ( λ , z ) + F A ( λ , z ) F M ( λ , z ) .
R ( λ , z ) = ( z - z L ) 2 N S ( λ , z ) K ( λ ) Q 2 ( λ , z L , z ) F M ( λ , z ) .
K ( λ ) = ( z * - z L ) 2 N S ( λ , z * ) R min ( λ ) Q 2 ( λ , z L , z * ) F M ( λ , z * ) .
R ( λ , z ) = ( z - z L ) 2 ( z * - z L ) 2 N S ( λ , z ) N S ( λ , z * ) Q 2 ( λ , z L , z * ) Q 2 ( λ , z L , z ) F M ( λ , z * ) F M ( λ , z ) R min ( λ ) .
F A ( λ , z ) = [ R ( λ , z ) - 1 ] F M ( λ , z ) .
F A ( λ , z ) = [ ( z - z L ) 2 ( z * - z L ) 2 N S ( λ , z ) N S ( λ , z * ) Q 2 ( λ , z L , z * ) Q 2 ( λ , z L , z ) F M ( λ , z * ) F M ( λ , z ) R min ( λ ) - 1 ] × F M ( λ , z ) .
F A ( λ , z ) = h ( z - z L , z * - z L ) s ( λ , z , z * ) q ( λ , z , z * ) F M ( λ , z * ) R min ( λ ) - F M ( λ , z ) ,
h ( z - z L , z * - z L ) ( z - z L ) 2 ( z * - z L ) 2 ,
s ( λ , z , z * ) N S ( λ , z ) N S ( λ , z * ) ,
q ( λ , z , z * ) Q 2 ( λ , z L , z * ) Q 2 ( λ , z L , z ) = exp [ - 2 z z * σ e ( λ , z ) d z ] .
( δ χ ) 2 = ( δ u ) 2 ( χ u ) 2 + ( δ v ) 2 ( χ u ) 2 + 2 C u v 2 ( χ u ) ( χ v ) + ,
C u v 2 = lim n 1 n Σ [ ( u i - u ¯ ) ( v i - v ¯ ) ] ,
( δ F A ) 2 = ( δ s ) 2 ( F A s ) 2 + ( δ q ) 2 ( F A q ) 2 + ( δ R min ) 2 ( F A R min ) 2 + ( δ F M * ) 2 ( F A F M * ) 2 + ( δ F M ) 2 ( F A F M ) 2 + 2 C F F * 2 ( F A F M * ) ( F A F M ) ,
F M * F M ( λ , z * ) .
( δ F A ) 2 = ( δ s ) 2 ( R F M s ) 2 + ( δ q ) 2 ( R F M q ) 2 + ( δ R min ) 2 ( R F M R min ) 2 + ( δ F M * ) 2 ( R F M F M * ) 2 + ( δ F M ) 2 - 2 C F F * 2 ( R F M F M * ) ,
( δ F A F A ) 2 = ( F M F A ) 2 { [ ( δ s s ) 2 + ( δ q q ) 2 + ( δ R min R min ) 2 + ( δ F M * F M * ) 2 - 2 C F F * 2 R F M F M * ] R 2 + ( δ F M F M ) 2 } .
( δ R R ) 2 = ( δ s s ) 2 + ( δ q q ) 2 + ( δ F M F M ) 2 + ( δ F M * F M * ) - 2 C F F * 2 F M F M * + ( δ R min R min ) 2 .
( δ s s ) 2 = { ( δ N S N S ) 2 + ( δ N S * N S * ) 2 , z z * , 0 , z = z * ,
δ N S N S = ( N S + N B + N I ) 1 / 2 N S ,
q ( λ , z , z * ) = exp [ - 2 τ A ( λ , z , z * ) - 2 τ M ( λ , z , z * ) - 2 τ 3 ( λ , z , z * ) ] ,
( δ q q ) 2 = 4 { [ δ τ A ( λ , z , z * ) ] 2 + [ δ τ M ( λ , z , z * ) ] 2 + [ δ τ 3 ( λ , z , z * ) ] 2 } .
δ τ 3 ( λ , z , z ) = 0.2 τ 3 ( λ , z , z ) .
δ τ A ( z , z ) = 0.5 τ A ( z , z ) ,
δ τ M ( z , z ) = 0.1 τ M ( z , z ) .
δ F M ( λ , z ) F M ( λ , z ) 0.01 ( density measured ) ,
δ F M ( λ , z ) F M ( λ , z ) 0.03 ( density modeled or interpolated ) .
C F F * 2 = lim n 1 n Σ [ F M , i ( λ , z * ) - F ¯ M ( λ , z * ) ] 2 ,
C F F * 2 = { ( δ F M * ) 2 [ 1 - ( z - z * Δ z D ) 2 ] , z - z * Δ z D , 0 , z - z * Δ z D ,
( δ F A * F A * ) 2 = ( F M * F A * ) { [ 0 + 0 + ( δ R min R min ) 2 + ( δ F M * F M * ) 2 - 2 R min ( δ F M * F M * ) 2 ] R min 2 + ( δ F M * F M * ) 2 } ,
( δ F A * F A * ) 2 = ( δ R min R min - 1 ) 2 + ( 1 R min - 1 ) 2 ( δ F M * F M * ) 2 ( R min 2 - 2 R min + 1 ) = ( δ R min R min - 1 ) 2 + ( δ F M * F M * ) 2 .
x ^ = x + .
x ^ i - σ i x ^ m + σ m
( Σ x i w i ) / ( Σ w i ) ,
w i 1 / σ i 2 .
( Σ x i w i ) / ( Σ w i ) ,
w i P ( x ^ i - x ^ m x i x m ) .
P ( x ^ i - x ^ m x i x m ) = k 0 P ( x ^ i - x ^ m x i = x m - h ) d h ,
P ( x ^ i - x ^ m x i = x m - h ) = P ( x ^ i - x ^ m + h x i = x m ) .
P ( x ^ i - x ^ m + h x i = x m ) = f [ ( x ^ i - x ^ m + h ) / ( σ i 2 + σ m 2 ) 1 / 2 ] ,
f ( y ) = 1 ( 2 π ) 1 / 2 exp ( - y 2 / 2 ) ,
y ( x ^ i - x ^ m + h ) / σ .
P ( x ^ i - x ^ m x i x m ) = k σ ( x ^ i - x ^ m ) / σ f ( y ) d y .
w i = E [ ( x ^ i - x ^ m ) / σ ] ,
x ^ i = R ^ ( λ , z i ) = ( z i - z L ) 2 N ^ S ( λ , z i ) K ( λ ) Q ^ 2 ( λ , z i ) F ^ M ( λ , z i ) .
σ i = δ x ^ i = x ^ i { [ δ N S ( λ , z i ) N S ( λ , z i ) ] 2 + [ δ Q 2 ( λ , z i ) Q 2 ( λ , z i ) ] 2 + [ δ F M ( λ , z i ) F M ( λ , z i ) ] 2 } 1 / 2 .
D ^ ( Z j ) = D ( Z j ) + D ( Z j ) .
τ ^ ( z far ) = τ ( z far ) + τ ( z far ) ,
τ ^ ( z ) = τ ( z ) + τ ( z ) - τ ( z L ) τ ( z far ) - τ ( z L ) τ ( z far ) .

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