Abstract

The backscatter and extinction of laboratory generated cloud and drizzle sized drops have been measured at CO2 laser wavelengths (predominately at λ = 10.591 μm). Measurements of volume backscatter coefficient σb and volume extinction coefficient σe for laboratory cloud of predominantly <20-μm radius droplets are dependent on the form of the size distribution in agreement with numerical prediction. For drops of ⪞20 μm at λ = 10.591 μm the relation between σe and σb has the appealingly simple size distribution independent form of σe/σb = 8π/G,

G=(n-1)2+k2(n+1)2+k2

is the asymptotic value of the backscatter gain, where n and k are the real and imaginary indices of refraction. The linear relation is in good agreement with extinction and backscatter measurements made on laboratory generated drizzle sized drops (r > 20 μm). This suggests that the extinction coefficient at CO2 laser wavelengths could be inferred from lidar backscatter return signals without requiring knowledge of the size distribution for drizzle and spherical precipitation sized water drops.

© 1986 Optical Society of America

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References

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  25. L. J. Battan, C. H. Reitan, Artificial Stimulation of Rain (Pergamon, New York, 1957), p. 184.

1985 (1)

1983 (1)

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).

1982 (1)

1981 (1)

1980 (1)

1979 (2)

R. G. Pinnick, H. J. Auvermann, “Response Characteristics of Knollenberg Light-Scattering Aerosol Counters,” J. Aerosol Sci. 10, 55 (1979).

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 Fogs,” J. Atmos. Sci. 36, 1577 (1979).

1978 (1)

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

1976 (1)

F. Tampieri, C. Tomasi, “Size Distribution Models of Fog and Cloud Droplets in Terms of the Modified Gamma Function,” Tellus 28, 333 (1976).

1975 (1)

D. Diermendjian, “Far-Infrared and Submillimetre Wave Attenuation by Clouds and Rain,” J. Appl. Meteorol. 14, 1584 (1975).

1973 (1)

1971 (1)

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

1970 (1)

1968 (1)

H. Vogt, “Visibility Measurement Using Backscattered Light,” J. Atmos. Sci. 25, 912 (1968).

1967 (1)

1965 (1)

1962 (1)

J. E. McDonald, “Large Sphere Limit of the Radar Back-scattering Coefficient,” Q. J. R. Meterol. Soc. 88, 183 (1962).

1958 (1)

1953 (1)

H. K. Weickmann, H. J. aufm Kampe, “Physical Properties of Cumulus Clouds,” J. Meteorol. 10, 204 (1953).

1952 (1)

H. J. aufm Kampe, H. K. Weickmann, “Trabert’s Formula and the Determination of the Water Content in Clouds,” J. Meteorol. 9, 167 (1952).

1948 (1)

M. Diem, “Messung der grose con wolken-elementen,” Meteorol. Rundsch. 9, 261 (1948).

aufm Kampe, H. J.

H. K. Weickmann, H. J. aufm Kampe, “Physical Properties of Cumulus Clouds,” J. Meteorol. 10, 204 (1953).

H. J. aufm Kampe, H. K. Weickmann, “Trabert’s Formula and the Determination of the Water Content in Clouds,” J. Meteorol. 9, 167 (1952).

Auvermann, H. J.

R. G. Pinnick, H. J. Auvermann, “Response Characteristics of Knollenberg Light-Scattering Aerosol Counters,” J. Aerosol Sci. 10, 55 (1979).

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 Fogs,” J. Atmos. Sci. 36, 1577 (1979).

Battan, L. J.

L. J. Battan, C. H. Reitan, Artificial Stimulation of Rain (Pergamon, New York, 1957), p. 184.

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).

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 Fogs,” J. Atmos. Sci. 36, 1577 (1979).

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

Curcio, J. A.

Derr, V. E.

Diem, M.

M. Diem, “Messung der grose con wolken-elementen,” Meteorol. Rundsch. 9, 261 (1948).

Diermendjian, D.

D. Diermendjian, “Far-Infrared and Submillimetre Wave Attenuation by Clouds and Rain,” J. Appl. Meteorol. 14, 1584 (1975).

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

Dubinsky, R. H.

Garland, J. A.

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

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).

Hale, G. M.

Hall, F. F.

F. F. Hall, “Atmospheric Infrared Backscatter: Summary of Present Knowledge and Recommendations for Future Work,” NOAA Tech. Memo. ERL WPL-110, Wave Propagation Laboratory, Boulder, CO 80303 (1983).

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).

Howell, H. B.

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).

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 Fogs,” J. Atmos. Sci. 36, 1577 (1979).

Klett, J. D.

Knestrick, G. L.

Kruger, C. H.

Long, R. K.

McDonald, J. E.

J. E. McDonald, “Large Sphere Limit of the Radar Back-scattering Coefficient,” Q. J. R. Meterol. Soc. 88, 183 (1962).

Mudd, H. T.

Murray, E. R.

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).

R. G. Pinnick, H. J. Auvermann, “Response Characteristics of Knollenberg Light-Scattering Aerosol Counters,” J. Aerosol Sci. 10, 55 (1979).

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 Fogs,” J. Atmos. Sci. 36, 1577 (1979).

Querry, M. R.

Reitan, C. H.

L. J. Battan, C. H. Reitan, Artificial Stimulation of Rain (Pergamon, New York, 1957), p. 184.

Rensch, D. B.

Tampieri, F.

F. Tampieri, C. Tomasi, “Size Distribution Models of Fog and Cloud Droplets in Terms of the Modified Gamma Function,” Tellus 28, 333 (1976).

Tomasi, C.

F. Tampieri, C. Tomasi, “Size Distribution Models of Fog and Cloud Droplets in Terms of the Modified Gamma Function,” Tellus 28, 333 (1976).

Twomey, S.

van de Hulst, H. C.

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

Vogt, H.

H. Vogt, “Visibility Measurement Using Backscattered Light,” J. Atmos. Sci. 25, 912 (1968).

von Essen, K. J.

Weickmann, H. K.

H. K. Weickmann, H. J. aufm Kampe, “Physical Properties of Cumulus Clouds,” J. Meteorol. 10, 204 (1953).

H. J. aufm Kampe, H. K. Weickmann, “Trabert’s Formula and the Determination of the Water Content in Clouds,” J. Meteorol. 9, 167 (1952).

Appl. Opt. (8)

J. Aerosol Sci. (1)

R. G. Pinnick, H. J. Auvermann, “Response Characteristics of Knollenberg Light-Scattering Aerosol Counters,” J. Aerosol Sci. 10, 55 (1979).

J. Appl. Meteorol. (1)

D. Diermendjian, “Far-Infrared and Submillimetre Wave Attenuation by Clouds and Rain,” J. Appl. Meteorol. 14, 1584 (1975).

J. Atmos. Sci. (3)

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

H. Vogt, “Visibility Measurement Using Backscattered Light,” J. Atmos. Sci. 25, 912 (1968).

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 Fogs,” J. Atmos. Sci. 36, 1577 (1979).

J. Geophys. Res. (1)

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).

J. Meteorol. (2)

H. J. aufm Kampe, H. K. Weickmann, “Trabert’s Formula and the Determination of the Water Content in Clouds,” J. Meteorol. 9, 167 (1952).

H. K. Weickmann, H. J. aufm Kampe, “Physical Properties of Cumulus Clouds,” J. Meteorol. 10, 204 (1953).

J. Opt. Soc. Am. (1)

Meteorol. Rundsch. (1)

M. Diem, “Messung der grose con wolken-elementen,” Meteorol. Rundsch. 9, 261 (1948).

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).

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

J. E. McDonald, “Large Sphere Limit of the Radar Back-scattering Coefficient,” Q. J. R. Meterol. Soc. 88, 183 (1962).

Tellus (1)

F. Tampieri, C. Tomasi, “Size Distribution Models of Fog and Cloud Droplets in Terms of the Modified Gamma Function,” Tellus 28, 333 (1976).

Other (4)

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

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

F. F. Hall, “Atmospheric Infrared Backscatter: Summary of Present Knowledge and Recommendations for Future Work,” NOAA Tech. Memo. ERL WPL-110, Wave Propagation Laboratory, Boulder, CO 80303 (1983).

L. J. Battan, C. H. Reitan, Artificial Stimulation of Rain (Pergamon, New York, 1957), p. 184.

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Figures (8)

Fig. 1
Fig. 1

Efficiency factor for extinction Qe vs droplet size parameter x for water at wavelength λ = 10.591 μm (index of refraction m = 1.179–0.0718i). The efficiency factor is approximated by a straight line Qe = cx for xxm.

Fig. 2
Fig. 2

(a) Mie calculations of the backscatter gain G(m,x) vs size parameter x for water droplets at wavelength λ = 10.591 μm (index of refraction m = 1.179–0.0718i). (b) Curve fit to the Mie gain G(x,m) = g(λ)x2/3 exp (−x/3); Eq. (5) is shown.

Fig. 3
Fig. 3

Mie calculation of the extinction-to-backscatter ratio for water droplets vs droplet radius at wavelength λ = 10.591 μm (index of refraction m = 1.179–0.0718i).

Fig. 4
Fig. 4

Schematic diagram of the experimental arrangement.

Fig. 5
Fig. 5

Averaged laboratory cloud size distribution histogram from the Hankscraft spinning disk generators. The measured size distribution has been fitted with a gamma function [Eq. (7)] with parameters α = 3, b = 0.75. Larger drop size categories indicated by —●— were measured using a modified two-stage impactor.20

Fig. 6
Fig. 6

(a) Size distribution histogram of water drops produced by a pair of atomizing fine spray nozzles;(b) sample of the drop spectrum produced by the pair of spray nozzles; (c) size distribution histogram of water drops produced by a Micromax spinning disk atomizer; (d) photograph of a sample of the drop spectrum produced by the Micromax spinning disk atomizer. The channel numbers are given in Table III.

Fig. 7
Fig. 7

Measured values of backscatter and extinction coefficient for laboratory water cloud at wavelength λ = 10.591 μm. Hankscraft spinning disk steady-state cloud values, ●; Hankscraft spinning disk decay cloud values, ○; Hankscraft spinning disk combined with ultrasonic nebulizer steady-state values, ▲; Hankscraft spinning disk combined with ultrasonic nebulizer decay values, △. Measurements made at λ = 10.247 μm: Hankscraft spinning disk steady-state values, ■; Hankscraft spinning disk decay values, □. Two solid lines representing extinction-to-backscatter ratios of 300 to 600 sr are also shown.

Fig. 8
Fig. 8

Measured values of backscatter and extinction coefficient for larger sized water drops at wavelength λ = 10.591 μm. Steady-state measurements, ●; decay measurements, ○. All measurements were made with drops produced by atomizer spray nozzles except for those using a rotary spinning disk device indicated by ▲. The solid line represents the asymtotic ratio of extinction to backscatter, Eq. (11).

Tables (3)

Tables Icon

Table I Extinction-to-Backscatter Ratio Values of λ = 10.591 μm for Water Drops Having a Modified Gamma Size Distribution form Characterized by Parameters α and b

Tables Icon

Table II Calculated Extinction to Backscatter Ratios at λ = 10.591 μm for Selected Cloud Size Distributions

Tables Icon

Table III Key to Channel Numbers

Equations (13)

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G = ( n - 1 ) 2 + k 2 ( n + 1 ) 2 + k 2
I = I 0 exp ( - σ e L ) ,
σ e = π r 2 Q e n ( r ) d r ,
σ b = 1 4 π π r 2 G n ( r ) d r ,
Q e ( m , x ) = c ( λ ) x .
G ( m , x ) = g ( λ ) x 2 / 3 exp ( - x / 3 ) ,
σ e σ b = 4 π c k 1 / 3 g · r 3 n ( r ) d r r 8 / 3 exp ( - k r / 3 ) n ( r ) d r ,
n ( r ) = a r α exp ( - b r )
σ e σ b = 4 π c k 1 / 3 g r α + 3 exp ( - b r ) d r r α + 8 / 3 exp [ - ( b + k 3 ) r ] d r ,
σ e σ b = 4 π c k 1 / 3 g · ( b + k / 3 ) α + 11 / 3 b α + 4 · 3 α + 3 ( α + 3 ) ( α + 2 ) ( α + 1 ) α Γ ( α ) [ 2.5.8 ( 3 α + 8 ) ] Γ ( 2 / 3 ) ,
R = ( n - 1 ) 2 + k 2 ( n + 1 ) 2 + k 2 ,
σ e σ b = 4 π Q e G = 3.21 × 10 3 sr .
I B = b b + L I s σ b A ( b + l ) 2 exp ( - 2 σ e l ) d l ,

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