Abstract

The volume extinction coefficients at 1.03 μm, 3.70 μm, and 10.38 μm, normalized to that at 0.50-μm wavelength, are calculated as a function of the shape parameters of the modified gamma size distribution using parameter ranges appropriate for haze and fog droplet polydispersions. Based on the sensitivity of the normalized volume extinction coefficients on the shape parameters, different procedures are proposed for utilizing the extinction features in giving form to the size distribution corresponding to the various evolutionary stages of the water droplet population. Such a methodology presents applicability in the field of fog forecast.

© 1976 Optical Society of America

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References

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  1. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 75–119.
  2. J. A. Garland, Quart. J. R. Meteorol. Soc. 97, 483 (1971).
  3. R. Pilie, W. Eadie, E. Mack, C. Rogers, W. Kocmond, NASA Contractor Rep. CR-2078 (Washington, D.C., 1972).
  4. V. E. Zuev, Atmospheric Transparency in the Visible and the Infrared (Israel Program for Scientific Translations, Jerusalem, 1970), pp. 81–125.
  5. L. M. Levin, Izv. Akad. Nauk SSSR, Ser. Geofiz. 10, 1211 (1958).
  6. D. Deirmendjian, Appl. Opt. 3, 187 (1964).
  7. F. Tampieri, C. Tomasi, Tellus 28, 1976.
  8. H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 174–183.
  9. D. Deirmendjian, Quart. J. R. Meteorol. Soc. 86, 371 (1960).
  10. W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).
  11. G. Hänel, Beitr. Phys. Atmos. 44, 137 (1971).
  12. F. E. Volz, Appl. Opt. 11, 755 (1972).
  13. R. Penndorf, J. Opt. Soc. Am. 47, 176 (1957).
  14. C. Tomasi, R. Guzzi, O. Vittori, J. Atmos. Sci. 31, 255 (1974).
  15. R. S. Fraser, J. Appl. Meteorol. 14, 1187 (1975).
  16. A. Arnulf, J. Bricard, E. Cure, C. Veret, J. Opt. Soc. Am. 47, 491 (1957).
  17. R. G. Eldridge, J. Atmos. Sci. 23, 605 (1966).

1976 (1)

F. Tampieri, C. Tomasi, Tellus 28, 1976.

1975 (1)

R. S. Fraser, J. Appl. Meteorol. 14, 1187 (1975).

1974 (1)

C. Tomasi, R. Guzzi, O. Vittori, J. Atmos. Sci. 31, 255 (1974).

1972 (1)

1971 (2)

G. Hänel, Beitr. Phys. Atmos. 44, 137 (1971).

J. A. Garland, Quart. J. R. Meteorol. Soc. 97, 483 (1971).

1968 (1)

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).

1966 (1)

R. G. Eldridge, J. Atmos. Sci. 23, 605 (1966).

1964 (1)

1960 (1)

D. Deirmendjian, Quart. J. R. Meteorol. Soc. 86, 371 (1960).

1958 (1)

L. M. Levin, Izv. Akad. Nauk SSSR, Ser. Geofiz. 10, 1211 (1958).

1957 (2)

Arnulf, A.

Bricard, J.

Cure, E.

Deirmendjian, D.

D. Deirmendjian, Appl. Opt. 3, 187 (1964).

D. Deirmendjian, Quart. J. R. Meteorol. Soc. 86, 371 (1960).

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 75–119.

Eadie, W.

R. Pilie, W. Eadie, E. Mack, C. Rogers, W. Kocmond, NASA Contractor Rep. CR-2078 (Washington, D.C., 1972).

Eldridge, R. G.

R. G. Eldridge, J. Atmos. Sci. 23, 605 (1966).

Fraser, R. S.

R. S. Fraser, J. Appl. Meteorol. 14, 1187 (1975).

Garland, J. A.

J. A. Garland, Quart. J. R. Meteorol. Soc. 97, 483 (1971).

Guzzi, R.

C. Tomasi, R. Guzzi, O. Vittori, J. Atmos. Sci. 31, 255 (1974).

Hänel, G.

G. Hänel, Beitr. Phys. Atmos. 44, 137 (1971).

Irvine, W. M.

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).

Kocmond, W.

R. Pilie, W. Eadie, E. Mack, C. Rogers, W. Kocmond, NASA Contractor Rep. CR-2078 (Washington, D.C., 1972).

Levin, L. M.

L. M. Levin, Izv. Akad. Nauk SSSR, Ser. Geofiz. 10, 1211 (1958).

Mack, E.

R. Pilie, W. Eadie, E. Mack, C. Rogers, W. Kocmond, NASA Contractor Rep. CR-2078 (Washington, D.C., 1972).

Penndorf, R.

Pilie, R.

R. Pilie, W. Eadie, E. Mack, C. Rogers, W. Kocmond, NASA Contractor Rep. CR-2078 (Washington, D.C., 1972).

Pollack, J. B.

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).

Rogers, C.

R. Pilie, W. Eadie, E. Mack, C. Rogers, W. Kocmond, NASA Contractor Rep. CR-2078 (Washington, D.C., 1972).

Tampieri, F.

F. Tampieri, C. Tomasi, Tellus 28, 1976.

Tomasi, C.

F. Tampieri, C. Tomasi, Tellus 28, 1976.

C. Tomasi, R. Guzzi, O. Vittori, J. Atmos. Sci. 31, 255 (1974).

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 174–183.

Veret, C.

Vittori, O.

C. Tomasi, R. Guzzi, O. Vittori, J. Atmos. Sci. 31, 255 (1974).

Volz, F. E.

Zuev, V. E.

V. E. Zuev, Atmospheric Transparency in the Visible and the Infrared (Israel Program for Scientific Translations, Jerusalem, 1970), pp. 81–125.

Appl. Opt. (2)

Beitr. Phys. Atmos. (1)

G. Hänel, Beitr. Phys. Atmos. 44, 137 (1971).

Icarus (1)

W. M. Irvine, J. B. Pollack, Icarus 8, 324 (1968).

Izv. Akad. Nauk SSSR, Ser. Geofiz. (1)

L. M. Levin, Izv. Akad. Nauk SSSR, Ser. Geofiz. 10, 1211 (1958).

J. Appl. Meteorol. (1)

R. S. Fraser, J. Appl. Meteorol. 14, 1187 (1975).

J. Atmos. Sci. (2)

R. G. Eldridge, J. Atmos. Sci. 23, 605 (1966).

C. Tomasi, R. Guzzi, O. Vittori, J. Atmos. Sci. 31, 255 (1974).

J. Opt. Soc. Am. (2)

Quart. J. R. Meteorol. Soc. (2)

D. Deirmendjian, Quart. J. R. Meteorol. Soc. 86, 371 (1960).

J. A. Garland, Quart. J. R. Meteorol. Soc. 97, 483 (1971).

Tellus (1)

F. Tampieri, C. Tomasi, Tellus 28, 1976.

Other (4)

H. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), pp. 174–183.

R. Pilie, W. Eadie, E. Mack, C. Rogers, W. Kocmond, NASA Contractor Rep. CR-2078 (Washington, D.C., 1972).

V. E. Zuev, Atmospheric Transparency in the Visible and the Infrared (Israel Program for Scientific Translations, Jerusalem, 1970), pp. 81–125.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), pp. 75–119.

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Figures (11)

Fig. 1
Fig. 1

Histograms of the shape parameters α, γ, and rc of the modified gamma function derived from size spectra of water droplets for haze and ground fog.

Fig. 2
Fig. 2

As in Fig. 1 for radiation and valley fog.

Fig. 3
Fig. 3

As in Fig. 1 for advection and arctic marine fog.

Fig. 4
Fig. 4

Theoretical ratio TN = β(1.03 μm)/β(0.50 μm) vs the mode radius rc of the modified gamma function for α = 2. The isopleths are drawn for the following values of the shape parameter γ: 0.25, 0.35, 0.50, 0.75, 1.00, 1.50, 2.00, 4.00, and 6.00.

Fig. 5
Fig. 5

As in Fig. 4 for the theoretical ratio TM = β(3.70 μm)/β(0.50 μm).

Fig. 6
Fig. 6

As in Fig. 4 for the theoretical ratio TF = β(10.38 μm)/β(0.50 μm).

Fig. 7
Fig. 7

Theoretical ratio FN = β(1.03 μm)/β(0.50 μm) vs the mode radius rc of the modified gamma function for α = 5. The isopleths are drawn for the following values of the shape parameter γ: 0.25, 0.35, 0.50, 0.75, 1.00, 1.50, 2.00, 4.00, and 6.00.

Fig. 8
Fig. 8

As in Fig. 7 for the theoretical ratio FM = β(3.70 μm)/β(0.50 μm).

Fig. 9
Fig. 9

As in Fig. 7 for the theoretical ratio FF = β(10.38 μm)/β(0.50 μm).

Fig. 10
Fig. 10

On the left side the suggested procedure (1) is applied to the empirical data given by Arnulf et al.16 for the case “haze 11:30” for deriving the best-fit set of modified gamma parameters. On the right the suggested procedure (2) is applied to the empirical data given by Arnulf et al.16 for the “stable fog” called G by Eldridge.17

Fig. 11
Fig. 11

Water droplet size distribution curves drawn for a unit total concentration corresponding to the best-fit solutions found in Fig. 10.

Equations (3)

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n ( r ) = a r α exp ( - α r r c ) , 0 r < ,
n ( r ) = a r α exp [ - α γ ( r r c ) γ ] , 0 r < ,
β ( λ ) = 10 - 3 π 0 n ( r ) r 2 K [ r , λ , m w ( λ ) ] d r ,

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