Abstract

The extinction and backscattering of 514-nm laser radiation in polydisperse water droplet clouds have been studied in the laboratory. Three cloud size distributions with modal diameters of 0.02, 5, and 12 μm have been investigated. The relationships between the cloud optical parameters (attenuation coefficient σ and volume backscattering coefficient βπ) and the cloud water content C have been measured for each size distribution. It has been found that a linear relationship exists between σ and C and between βπ and C for cloud water content values up to 3 g/m3. The linear relationships obtained, however, have slopes which depend on the droplet size distribution. For a given water content both σ and βπ increase as the modal diameter decreases. The measured data are compared with existing theoretical analyses and discussed in terms of their application to lidar measurements of atmospheric clouds. It is concluded that the empirical information obtained can serve as a basis for quantitative lidar measurements.

© 1985 Optical Society of America

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References

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  1. A. I. Carswell, “Lidar Measurements of the Atmosphere,” Can. J. Phys. 61, 378 (1983).
    [CrossRef]
  2. R. M. Measures, Laser Remote Sensing Fundamentals and Applicants (Wiley, New York, 1983).
  3. V. E. Zuev, Laser Beams in the Atmosphere (Plenum, New York, 1982).
    [CrossRef]
  4. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  5. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).
  6. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).
  7. L. W. Carrier, G. A. Cato, K. J. van Essen, “The Backscattering and Extinction of Visible and Infrared Radiation by Selected Major Cloud Models,” Appl. Opt. 6, 1209 (1967).
    [CrossRef] [PubMed]
  8. B. J. Brinkworth, “Calculation of Attenuation and Backscattering in Cloud and Fog,” Atmos. Environ. 5, 605 (1971).
    [CrossRef]
  9. R. C. Anderson, E. V. Browell, “First- and Second-Order Backscattering from Clouds Illuminated by Finite Beams,” Appl. Opt. 11, 1345 (1972).
    [CrossRef] [PubMed]
  10. R. G. Pinnick, S. G. Jennings, P. Chylek, H. J. Auvermann, “Verification of a Linear Relation Between IR Extinction, Absorption, and Liquid Water Content of Fog,” J. Atmos. Sci. 36, 1577 (1979).
    [CrossRef]
  11. R. G. Pinnick, S. G. Jennings, P. Chylek, “Relationships Between Extinction, Absorption, Backscattering and Mass Content of Sulphuric Acid Aerosols,” J. Geophys. Res. 85, 4059 (1980).
    [CrossRef]
  12. R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, “Backscatter and Extinction in Water Clouds,” Report ASL-TR-0097, Atmos. Sci. Lab., White Sands Missile Range, N.M. (1981).
  13. R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and Extinction in Water Clouds,” J. Geophys. Res. 88, 6787 (1983).
    [CrossRef]
  14. J. S. Ryan, S. R. Pal, A. I. Carswell, “Laser Backscattering from Dense Water-Droplet Clouds,” J. Opt. Soc. Am. 69, 60 (1979).
    [CrossRef]
  15. J. A. Garland, “Some Fog Droplet Size Distributions Obtained by an Impaction Method,” Q. J. R. Meteorol. Soc. 97, 483 (1971).
    [CrossRef]
  16. P. Chylek, “Extinction and Liquid Water Content of Fogs and Clouds,” J. Atmos. Sci. 35, 296 (1978).
  17. E. Uthe, “Particle Size Evaluations using Multiwavelength Extinction Measurements,” Appl. Opt. 21, 454 (1982).
    [CrossRef] [PubMed]
  18. M. A. Kolosov, A. V. Sokolov, L. V. Fedorova, R. A. Shirley, “The Relation Between the Coefficient of Attenuation of Laser Radiation Intensity and the Water Content of Artificial Mists,” Atmos. Oceanic Phys. 5, 6 (1969).
  19. D. Bruce, C. W. Bruce, Y. P. Yee, L. Cahenzli, H. Burket, “Experimentally Determined Relationship Between Extinction Coefficients and Liquid Water Content,” Appl. Opt. 19, 3355 (1980).
    [CrossRef] [PubMed]
  20. A. W. Gertler, R. L. Steele, “Experimental Verification of the Linear Relationship Between IR Extinction and Liquid Water Content of Clouds,” J. Appl. Meteorol. 19, 1314 (1980).
    [CrossRef]
  21. V. E. Derr, “Estimation of Extinction Coefficient of Clouds from Multiwavelength Lidar Backscatter Measurements,” Appl. Opt. 19, 2310 (1980).
    [CrossRef] [PubMed]

1983 (2)

A. I. Carswell, “Lidar Measurements of the Atmosphere,” Can. J. Phys. 61, 378 (1983).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and Extinction in Water Clouds,” J. Geophys. Res. 88, 6787 (1983).
[CrossRef]

1982 (1)

1980 (4)

D. Bruce, C. W. Bruce, Y. P. Yee, L. Cahenzli, H. Burket, “Experimentally Determined Relationship Between Extinction Coefficients and Liquid Water Content,” Appl. Opt. 19, 3355 (1980).
[CrossRef] [PubMed]

A. W. Gertler, R. L. Steele, “Experimental Verification of the Linear Relationship Between IR Extinction and Liquid Water Content of Clouds,” J. Appl. Meteorol. 19, 1314 (1980).
[CrossRef]

V. E. Derr, “Estimation of Extinction Coefficient of Clouds from Multiwavelength Lidar Backscatter Measurements,” Appl. Opt. 19, 2310 (1980).
[CrossRef] [PubMed]

R. G. Pinnick, S. G. Jennings, P. Chylek, “Relationships Between Extinction, Absorption, Backscattering and Mass Content of Sulphuric Acid Aerosols,” J. Geophys. Res. 85, 4059 (1980).
[CrossRef]

1979 (2)

R. G. Pinnick, S. G. Jennings, P. Chylek, H. J. Auvermann, “Verification of a Linear Relation Between IR Extinction, Absorption, and Liquid Water Content of Fog,” J. Atmos. Sci. 36, 1577 (1979).
[CrossRef]

J. S. Ryan, S. R. Pal, A. I. Carswell, “Laser Backscattering from Dense Water-Droplet Clouds,” J. Opt. Soc. Am. 69, 60 (1979).
[CrossRef]

1978 (1)

P. Chylek, “Extinction and Liquid Water Content of Fogs and Clouds,” J. Atmos. Sci. 35, 296 (1978).

1972 (1)

1971 (2)

B. J. Brinkworth, “Calculation of Attenuation and Backscattering in Cloud and Fog,” Atmos. Environ. 5, 605 (1971).
[CrossRef]

J. A. Garland, “Some Fog Droplet Size Distributions Obtained by an Impaction Method,” Q. J. R. Meteorol. Soc. 97, 483 (1971).
[CrossRef]

1969 (1)

M. A. Kolosov, A. V. Sokolov, L. V. Fedorova, R. A. Shirley, “The Relation Between the Coefficient of Attenuation of Laser Radiation Intensity and the Water Content of Artificial Mists,” Atmos. Oceanic Phys. 5, 6 (1969).

1967 (1)

Anderson, R. C.

Auvermann, H. J.

R. G. Pinnick, S. G. Jennings, P. Chylek, H. J. Auvermann, “Verification of a Linear Relation Between IR Extinction, Absorption, and Liquid Water Content of Fog,” J. Atmos. Sci. 36, 1577 (1979).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

Brinkworth, B. J.

B. J. Brinkworth, “Calculation of Attenuation and Backscattering in Cloud and Fog,” Atmos. Environ. 5, 605 (1971).
[CrossRef]

Browell, E. V.

Bruce, C. W.

Bruce, D.

Burket, H.

Cahenzli, L.

Carrier, L. W.

Carswell, A. I.

Cato, G. A.

Chylek, P.

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and Extinction in Water Clouds,” J. Geophys. Res. 88, 6787 (1983).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, “Relationships Between Extinction, Absorption, Backscattering and Mass Content of Sulphuric Acid Aerosols,” J. Geophys. Res. 85, 4059 (1980).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, H. J. Auvermann, “Verification of a Linear Relation Between IR Extinction, Absorption, and Liquid Water Content of Fog,” J. Atmos. Sci. 36, 1577 (1979).
[CrossRef]

P. Chylek, “Extinction and Liquid Water Content of Fogs and Clouds,” J. Atmos. Sci. 35, 296 (1978).

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, “Backscatter and Extinction in Water Clouds,” Report ASL-TR-0097, Atmos. Sci. Lab., White Sands Missile Range, N.M. (1981).

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

Derr, V. E.

Fedorova, L. V.

M. A. Kolosov, A. V. Sokolov, L. V. Fedorova, R. A. Shirley, “The Relation Between the Coefficient of Attenuation of Laser Radiation Intensity and the Water Content of Artificial Mists,” Atmos. Oceanic Phys. 5, 6 (1969).

Garland, J. A.

J. A. Garland, “Some Fog Droplet Size Distributions Obtained by an Impaction Method,” Q. J. R. Meteorol. Soc. 97, 483 (1971).
[CrossRef]

Gertler, A. W.

A. W. Gertler, R. L. Steele, “Experimental Verification of the Linear Relationship Between IR Extinction and Liquid Water Content of Clouds,” J. Appl. Meteorol. 19, 1314 (1980).
[CrossRef]

Grandy, W. T.

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and Extinction in Water Clouds,” J. Geophys. Res. 88, 6787 (1983).
[CrossRef]

Ham, C.

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and Extinction in Water Clouds,” J. Geophys. Res. 88, 6787 (1983).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, “Backscatter and Extinction in Water Clouds,” Report ASL-TR-0097, Atmos. Sci. Lab., White Sands Missile Range, N.M. (1981).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

Jennings, S. G.

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and Extinction in Water Clouds,” J. Geophys. Res. 88, 6787 (1983).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, “Relationships Between Extinction, Absorption, Backscattering and Mass Content of Sulphuric Acid Aerosols,” J. Geophys. Res. 85, 4059 (1980).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, H. J. Auvermann, “Verification of a Linear Relation Between IR Extinction, Absorption, and Liquid Water Content of Fog,” J. Atmos. Sci. 36, 1577 (1979).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, “Backscatter and Extinction in Water Clouds,” Report ASL-TR-0097, Atmos. Sci. Lab., White Sands Missile Range, N.M. (1981).

Kolosov, M. A.

M. A. Kolosov, A. V. Sokolov, L. V. Fedorova, R. A. Shirley, “The Relation Between the Coefficient of Attenuation of Laser Radiation Intensity and the Water Content of Artificial Mists,” Atmos. Oceanic Phys. 5, 6 (1969).

Measures, R. M.

R. M. Measures, Laser Remote Sensing Fundamentals and Applicants (Wiley, New York, 1983).

Pal, S. R.

Pinnick, R. G.

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and Extinction in Water Clouds,” J. Geophys. Res. 88, 6787 (1983).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, “Relationships Between Extinction, Absorption, Backscattering and Mass Content of Sulphuric Acid Aerosols,” J. Geophys. Res. 85, 4059 (1980).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, H. J. Auvermann, “Verification of a Linear Relation Between IR Extinction, Absorption, and Liquid Water Content of Fog,” J. Atmos. Sci. 36, 1577 (1979).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, “Backscatter and Extinction in Water Clouds,” Report ASL-TR-0097, Atmos. Sci. Lab., White Sands Missile Range, N.M. (1981).

Ryan, J. S.

Shirley, R. A.

M. A. Kolosov, A. V. Sokolov, L. V. Fedorova, R. A. Shirley, “The Relation Between the Coefficient of Attenuation of Laser Radiation Intensity and the Water Content of Artificial Mists,” Atmos. Oceanic Phys. 5, 6 (1969).

Sokolov, A. V.

M. A. Kolosov, A. V. Sokolov, L. V. Fedorova, R. A. Shirley, “The Relation Between the Coefficient of Attenuation of Laser Radiation Intensity and the Water Content of Artificial Mists,” Atmos. Oceanic Phys. 5, 6 (1969).

Steele, R. L.

A. W. Gertler, R. L. Steele, “Experimental Verification of the Linear Relationship Between IR Extinction and Liquid Water Content of Clouds,” J. Appl. Meteorol. 19, 1314 (1980).
[CrossRef]

Uthe, E.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

van Essen, K. J.

Yee, Y. P.

Zuev, V. E.

V. E. Zuev, Laser Beams in the Atmosphere (Plenum, New York, 1982).
[CrossRef]

Appl. Opt. (5)

Atmos. Environ. (1)

B. J. Brinkworth, “Calculation of Attenuation and Backscattering in Cloud and Fog,” Atmos. Environ. 5, 605 (1971).
[CrossRef]

Atmos. Oceanic Phys. (1)

M. A. Kolosov, A. V. Sokolov, L. V. Fedorova, R. A. Shirley, “The Relation Between the Coefficient of Attenuation of Laser Radiation Intensity and the Water Content of Artificial Mists,” Atmos. Oceanic Phys. 5, 6 (1969).

Can. J. Phys. (1)

A. I. Carswell, “Lidar Measurements of the Atmosphere,” Can. J. Phys. 61, 378 (1983).
[CrossRef]

J. Appl. Meteorol. (1)

A. W. Gertler, R. L. Steele, “Experimental Verification of the Linear Relationship Between IR Extinction and Liquid Water Content of Clouds,” J. Appl. Meteorol. 19, 1314 (1980).
[CrossRef]

J. Atmos. Sci. (2)

R. G. Pinnick, S. G. Jennings, P. Chylek, H. J. Auvermann, “Verification of a Linear Relation Between IR Extinction, Absorption, and Liquid Water Content of Fog,” J. Atmos. Sci. 36, 1577 (1979).
[CrossRef]

P. Chylek, “Extinction and Liquid Water Content of Fogs and Clouds,” J. Atmos. Sci. 35, 296 (1978).

J. Geophys. Res. (2)

R. G. Pinnick, S. G. Jennings, P. Chylek, “Relationships Between Extinction, Absorption, Backscattering and Mass Content of Sulphuric Acid Aerosols,” J. Geophys. Res. 85, 4059 (1980).
[CrossRef]

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, W. T. Grandy, “Backscatter and Extinction in Water Clouds,” J. Geophys. Res. 88, 6787 (1983).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. A. Garland, “Some Fog Droplet Size Distributions Obtained by an Impaction Method,” Q. J. R. Meteorol. Soc. 97, 483 (1971).
[CrossRef]

Other (6)

R. G. Pinnick, S. G. Jennings, P. Chylek, C. Ham, “Backscatter and Extinction in Water Clouds,” Report ASL-TR-0097, Atmos. Sci. Lab., White Sands Missile Range, N.M. (1981).

R. M. Measures, Laser Remote Sensing Fundamentals and Applicants (Wiley, New York, 1983).

V. E. Zuev, Laser Beams in the Atmosphere (Plenum, New York, 1982).
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).

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Figures (15)

Fig. 1
Fig. 1

Schematic diagram of the experimental system: C, laser beam chopper; F, mixing fans; H, humidity sensor; I, cascade impactor; M, mass sampling system; L, large particle generator; N, ultrasonic nabulizer; R, flow regulator; S, submicron particle generator.

Fig. 2
Fig. 2

S size distribution.

Fig. 3
Fig. 3

M size distribution.

Fig. 4
Fig. 4

L size distribution.

Fig. 5
Fig. 5

Measured extinction coefficient vs mass concentration for M size distributions. The best fit line σ = 0.6C + 0.08 is also shown.

Fig. 6
Fig. 6

Best fit lines for extinction coefficient vs mass concentration for all three size distributions.

Fig. 7
Fig. 7

Dependence, of extinction-to-mass ratio k on droplet radius. The points M, L are obtained by using the measured k values from Fig. 6 along with the measured modal radii of the M and L distributions. The line is the theoretical prediction using Eq. (6).

Fig. 8
Fig. 8

Measured cloud reflectance vs extinction coefficient for the M size distributions at a field of view of 6 mrad.

Fig. 9
Fig. 9

Summary of cloud reflectance measurements for the three different drop size distributions.

Fig. 10
Fig. 10

Relationship between cloud reflectance and modal droplet diameter for various concentrations as taken from Fig. 9.

Fig. 11
Fig. 11

Relationship between the extinction coefficient and backscatter coefficient for the M size distribution. Also shown is a linear fit to the data.

Fig. 12
Fig. 12

Measured extinction-to-backscatter relation for the S distribution.

Fig. 13
Fig. 13

Measured extinction-to-backscatter relation for the L distribution.

Fig. 14
Fig. 14

Measured extinction-to-backscatter relation for the M size distribution when using a larger field of view (12 mrad) in the backscatter receiver. Compare with Fig. 11.

Fig. 15
Fig. 15

Relationship between βπ and C determined by combining the data of Fig. 4 with the data of Figs. 1113.

Tables (1)

Tables Icon

Table I Comparison of the Measured Modal Radius with the Effective Droplet Radius re Determined from the Measured Values of σ/C

Equations (15)

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P = P 0 exp ( σ z ) .
σ = r 1 r 2 π r 2 QN ( r ) dr .
σ = 2 π r 1 r 2 r 2 N ( r ) dr .
C = 4 π 3 δ r 1 r 2 r 3 N ( r ) dr ,
C = 2 σ 3 δ r 3 N ( r ) dr r 2 N ( r ) dr .
C = ( 2 δ r e σ ) / 3 or σ = 3 C / ( 2 δ r e ) .
σ = 2 π s λ r 3 N ( r ) dr .
C = 2 δ λ 3 π s σ .
P d = A P 0 β π exp ( 2 σ R 1 ) R 1 R 2 exp ( 2 σ R ) R 2 dR ,
β π = β P π / 4 π ,
β π = P d P 0 A exp ( 2 σ R 1 ) K .
σ M = 0.6 C + 0.08 ,
σ L = 0.2 C + 0.04 ,
σ S = 10.8 C + 0.10 .
ρ = ( π P d P 0 ) ( R 1 2 A )

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