Abstract

The effect of relative humidity on the backscattering of 0.694- and 10.6-μm radiation by aerosol particles in the lower troposphere is modeled. Two models of particle composition are considered: (1) all particles are composed of a uniform mixture of water-soluble material, dustlike material, and soot (uniform internal mixture) and (2) pure soot particles coexist with particles which are mixtures of water-soluble and dustlike materials (external mixture of soot). The amount of soot ranges from 1% to 20% of the volume of the aerosol. Changes in relative humidity have a greater effect on the backscattering coefficient, βπ, at 0.694 μm than at 10.6 μm. If soluble material accounts for 30% of the volume of mixed particles and if an urban type aerosol size distribution is assumed, an increase in relative humidity from 0% to 99% results in an increase in βπ at 0.694 μm ranging from a factor of 5.7 for an external mixture containing 20% soot by volume to a factor of 15.6 in the case of a uniform internal mixture containing 20% soot. At 10.6 μm the increase in βπ ranges from a factor of 2.1 to a factor of 2.8. The backscatter-to-extinction relation for 0.694-μm radiation propagating through a region of varying relative humidity is also investigated.

© 1984 Optical Society of America

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  1. M. J. Post, F. F. Hall, R. A. Richter, T. R. Lawrence, Appl. Opt. 21, 2442 (1982).
    [CrossRef] [PubMed]
  2. D. J. Hoffman, J. M. Rosen, J. Geophys. Res. 88, 3777 (1982).
    [CrossRef]
  3. G. K. Yue, G. S. Kent, U. O. Farrukh, A. Deepak, Appl. Opt. 22, 1671 (1983).
    [CrossRef] [PubMed]
  4. R. T. H. Collis, P. B. Russell, “Lidar Measurement of Particles and Gases by Elastic Backscattering and Differential Absorption,” in Topics in Applied Physics, Vol. 14 (Springer, Berlin, 1976).
    [CrossRef]
  5. E. J. McCartney, Optics of the Atmosphere (Wiley, New York, 1976).
  6. J. V. Dave, “Subroutines for Computing the Parameters of Electromagnetic Radiation Scattered by a Sphere,” IBM Palo Alto Scientific Center Report 320-3237 (1968).
  7. W. A. Hoppel, J. W. Fitzgerald, R. E. Larson, “Measurements of Atmospheric Aerosols: Experimental Methods and Results of Measurements Off the East Coast of the United States,” Naval Research Laboratory Report 8703 (1983).
  8. W. A. Hoppel, J. Aerosol Sci. 9, 41 (1978).
    [CrossRef]
  9. A. P. Waggoner, R. E. Weiss, N. A. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, Atmos. Environ. 15, 1891 (1981).
    [CrossRef]
  10. R. J. Countess, G. T. Wolff, S. H. Cadle, J. Air Pollut. Control Assoc. 30, 1194 (1980).
    [CrossRef]
  11. R. J. Countess, S. H. Cadle, P. J. Groblicki, G. T. Wolff, J. Air Pollut. Control Assoc. 31, 247 (1981).
    [CrossRef]
  12. T. P. Ackerman, O. B. Toon, Appl. Opt. 20, 3661 (1981).
    [CrossRef] [PubMed]
  13. I. N. Tang, W. T. Wong, H. R. Munkelwitz, Atmos. Environ. 15, 2463 (1981).
    [CrossRef]
  14. C. Sloane, Atmos. Environ. 17, 409 (1983).
    [CrossRef]
  15. J. W. Fitzgerald, W. A. Hoppel, M. A. Vietti, J. Atmos. Sci. 39, 1838 (1982).
    [CrossRef]
  16. D. J. Alofs, M. B. Trueblood, “The Correlation Between Size and Critical Supersaturation Exhibited by CCN in Missouri,” in Proceedings, Conference on Cloud Physics, Nov.1982, Chicago, Ill.
  17. G. Hänel, M. Lehmann, Contrib. Atmos. Phys. 54, 57 (1981).
  18. G. Hänel, Tellus 20, 371 (1968).
    [CrossRef]
  19. G. Hänel, “The Properties of Atmospheric Aerosol Particles as Functions of the Relative Humidity at Thermodynamic Equilibrium with the Surrounding Moist Air,” Adv. Geophys. 19, 73 (1976). (Academic Press, New York, 1976).
    [CrossRef]
  20. F. E. Volz, J. Geophys. Res. 77, 1017 (1972).
    [CrossRef]
  21. F. E. Volz, Appl. Opt. 12, 564 (1973).
    [CrossRef] [PubMed]
  22. E. P. Shettle, R. W. Fenn, “Models for the Aerosols of the Lower Atmosphere and the Effects of Humidity Variations on Their Optical Properties,” Air Force Geophysics Laboratory Report TR-79-0214 (1979).
  23. J. T. Twitty, J. A. Weinman, J. Appl. Meteorol. 10, 725 (1971).
    [CrossRef]
  24. G. M. Hale, M. R. Querry, Appl. Opt. 12, 555 (1973).
    [CrossRef] [PubMed]
  25. While the lognormal size distribution is usually given by an expression of the form (A/r) exp[−B ln2(r/rm)], it is noted by N. A. Fuchs, The Mechanics of Aerosols (Pergamon, New York, 1964), p. 13, that the various moments of a lognormal distribution are also lognormal. Thus, the distribution f(r) = A exp[−B ln2(r/rm)], which is obtained by multiplying the standard form by r, is also lognormal.
  26. J. D. Klett, Appl. Opt. 20, 211 (1981).
    [CrossRef] [PubMed]

1983 (2)

1982 (3)

M. J. Post, F. F. Hall, R. A. Richter, T. R. Lawrence, Appl. Opt. 21, 2442 (1982).
[CrossRef] [PubMed]

J. W. Fitzgerald, W. A. Hoppel, M. A. Vietti, J. Atmos. Sci. 39, 1838 (1982).
[CrossRef]

D. J. Hoffman, J. M. Rosen, J. Geophys. Res. 88, 3777 (1982).
[CrossRef]

1981 (6)

A. P. Waggoner, R. E. Weiss, N. A. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, Atmos. Environ. 15, 1891 (1981).
[CrossRef]

J. D. Klett, Appl. Opt. 20, 211 (1981).
[CrossRef] [PubMed]

T. P. Ackerman, O. B. Toon, Appl. Opt. 20, 3661 (1981).
[CrossRef] [PubMed]

G. Hänel, M. Lehmann, Contrib. Atmos. Phys. 54, 57 (1981).

I. N. Tang, W. T. Wong, H. R. Munkelwitz, Atmos. Environ. 15, 2463 (1981).
[CrossRef]

R. J. Countess, S. H. Cadle, P. J. Groblicki, G. T. Wolff, J. Air Pollut. Control Assoc. 31, 247 (1981).
[CrossRef]

1980 (1)

R. J. Countess, G. T. Wolff, S. H. Cadle, J. Air Pollut. Control Assoc. 30, 1194 (1980).
[CrossRef]

1978 (1)

W. A. Hoppel, J. Aerosol Sci. 9, 41 (1978).
[CrossRef]

1976 (1)

G. Hänel, “The Properties of Atmospheric Aerosol Particles as Functions of the Relative Humidity at Thermodynamic Equilibrium with the Surrounding Moist Air,” Adv. Geophys. 19, 73 (1976). (Academic Press, New York, 1976).
[CrossRef]

1973 (2)

1972 (1)

F. E. Volz, J. Geophys. Res. 77, 1017 (1972).
[CrossRef]

1971 (1)

J. T. Twitty, J. A. Weinman, J. Appl. Meteorol. 10, 725 (1971).
[CrossRef]

1968 (1)

G. Hänel, Tellus 20, 371 (1968).
[CrossRef]

Ackerman, T. P.

Ahlquist, N. A.

A. P. Waggoner, R. E. Weiss, N. A. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, Atmos. Environ. 15, 1891 (1981).
[CrossRef]

Alofs, D. J.

D. J. Alofs, M. B. Trueblood, “The Correlation Between Size and Critical Supersaturation Exhibited by CCN in Missouri,” in Proceedings, Conference on Cloud Physics, Nov.1982, Chicago, Ill.

Cadle, S. H.

R. J. Countess, S. H. Cadle, P. J. Groblicki, G. T. Wolff, J. Air Pollut. Control Assoc. 31, 247 (1981).
[CrossRef]

R. J. Countess, G. T. Wolff, S. H. Cadle, J. Air Pollut. Control Assoc. 30, 1194 (1980).
[CrossRef]

Charlson, R. J.

A. P. Waggoner, R. E. Weiss, N. A. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, Atmos. Environ. 15, 1891 (1981).
[CrossRef]

Collis, R. T. H.

R. T. H. Collis, P. B. Russell, “Lidar Measurement of Particles and Gases by Elastic Backscattering and Differential Absorption,” in Topics in Applied Physics, Vol. 14 (Springer, Berlin, 1976).
[CrossRef]

Countess, R. J.

R. J. Countess, S. H. Cadle, P. J. Groblicki, G. T. Wolff, J. Air Pollut. Control Assoc. 31, 247 (1981).
[CrossRef]

R. J. Countess, G. T. Wolff, S. H. Cadle, J. Air Pollut. Control Assoc. 30, 1194 (1980).
[CrossRef]

Covert, D. S.

A. P. Waggoner, R. E. Weiss, N. A. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, Atmos. Environ. 15, 1891 (1981).
[CrossRef]

Dave, J. V.

J. V. Dave, “Subroutines for Computing the Parameters of Electromagnetic Radiation Scattered by a Sphere,” IBM Palo Alto Scientific Center Report 320-3237 (1968).

Deepak, A.

Farrukh, U. O.

Fenn, R. W.

E. P. Shettle, R. W. Fenn, “Models for the Aerosols of the Lower Atmosphere and the Effects of Humidity Variations on Their Optical Properties,” Air Force Geophysics Laboratory Report TR-79-0214 (1979).

Fitzgerald, J. W.

J. W. Fitzgerald, W. A. Hoppel, M. A. Vietti, J. Atmos. Sci. 39, 1838 (1982).
[CrossRef]

W. A. Hoppel, J. W. Fitzgerald, R. E. Larson, “Measurements of Atmospheric Aerosols: Experimental Methods and Results of Measurements Off the East Coast of the United States,” Naval Research Laboratory Report 8703 (1983).

Fuchs, N. A.

While the lognormal size distribution is usually given by an expression of the form (A/r) exp[−B ln2(r/rm)], it is noted by N. A. Fuchs, The Mechanics of Aerosols (Pergamon, New York, 1964), p. 13, that the various moments of a lognormal distribution are also lognormal. Thus, the distribution f(r) = A exp[−B ln2(r/rm)], which is obtained by multiplying the standard form by r, is also lognormal.

Groblicki, P. J.

R. J. Countess, S. H. Cadle, P. J. Groblicki, G. T. Wolff, J. Air Pollut. Control Assoc. 31, 247 (1981).
[CrossRef]

Hale, G. M.

Hall, F. F.

Hänel, G.

G. Hänel, M. Lehmann, Contrib. Atmos. Phys. 54, 57 (1981).

G. Hänel, “The Properties of Atmospheric Aerosol Particles as Functions of the Relative Humidity at Thermodynamic Equilibrium with the Surrounding Moist Air,” Adv. Geophys. 19, 73 (1976). (Academic Press, New York, 1976).
[CrossRef]

G. Hänel, Tellus 20, 371 (1968).
[CrossRef]

Hoffman, D. J.

D. J. Hoffman, J. M. Rosen, J. Geophys. Res. 88, 3777 (1982).
[CrossRef]

Hoppel, W. A.

J. W. Fitzgerald, W. A. Hoppel, M. A. Vietti, J. Atmos. Sci. 39, 1838 (1982).
[CrossRef]

W. A. Hoppel, J. Aerosol Sci. 9, 41 (1978).
[CrossRef]

W. A. Hoppel, J. W. Fitzgerald, R. E. Larson, “Measurements of Atmospheric Aerosols: Experimental Methods and Results of Measurements Off the East Coast of the United States,” Naval Research Laboratory Report 8703 (1983).

Kent, G. S.

Klett, J. D.

Larson, R. E.

W. A. Hoppel, J. W. Fitzgerald, R. E. Larson, “Measurements of Atmospheric Aerosols: Experimental Methods and Results of Measurements Off the East Coast of the United States,” Naval Research Laboratory Report 8703 (1983).

Lawrence, T. R.

Lehmann, M.

G. Hänel, M. Lehmann, Contrib. Atmos. Phys. 54, 57 (1981).

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere (Wiley, New York, 1976).

Munkelwitz, H. R.

I. N. Tang, W. T. Wong, H. R. Munkelwitz, Atmos. Environ. 15, 2463 (1981).
[CrossRef]

Post, M. J.

Querry, M. R.

Richter, R. A.

Rosen, J. M.

D. J. Hoffman, J. M. Rosen, J. Geophys. Res. 88, 3777 (1982).
[CrossRef]

Russell, P. B.

R. T. H. Collis, P. B. Russell, “Lidar Measurement of Particles and Gases by Elastic Backscattering and Differential Absorption,” in Topics in Applied Physics, Vol. 14 (Springer, Berlin, 1976).
[CrossRef]

Shettle, E. P.

E. P. Shettle, R. W. Fenn, “Models for the Aerosols of the Lower Atmosphere and the Effects of Humidity Variations on Their Optical Properties,” Air Force Geophysics Laboratory Report TR-79-0214 (1979).

Sloane, C.

C. Sloane, Atmos. Environ. 17, 409 (1983).
[CrossRef]

Tang, I. N.

I. N. Tang, W. T. Wong, H. R. Munkelwitz, Atmos. Environ. 15, 2463 (1981).
[CrossRef]

Toon, O. B.

Trueblood, M. B.

D. J. Alofs, M. B. Trueblood, “The Correlation Between Size and Critical Supersaturation Exhibited by CCN in Missouri,” in Proceedings, Conference on Cloud Physics, Nov.1982, Chicago, Ill.

Twitty, J. T.

J. T. Twitty, J. A. Weinman, J. Appl. Meteorol. 10, 725 (1971).
[CrossRef]

Vietti, M. A.

J. W. Fitzgerald, W. A. Hoppel, M. A. Vietti, J. Atmos. Sci. 39, 1838 (1982).
[CrossRef]

Volz, F. E.

F. E. Volz, Appl. Opt. 12, 564 (1973).
[CrossRef] [PubMed]

F. E. Volz, J. Geophys. Res. 77, 1017 (1972).
[CrossRef]

Waggoner, A. P.

A. P. Waggoner, R. E. Weiss, N. A. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, Atmos. Environ. 15, 1891 (1981).
[CrossRef]

Weinman, J. A.

J. T. Twitty, J. A. Weinman, J. Appl. Meteorol. 10, 725 (1971).
[CrossRef]

Weiss, R. E.

A. P. Waggoner, R. E. Weiss, N. A. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, Atmos. Environ. 15, 1891 (1981).
[CrossRef]

Will, S.

A. P. Waggoner, R. E. Weiss, N. A. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, Atmos. Environ. 15, 1891 (1981).
[CrossRef]

Wolff, G. T.

R. J. Countess, S. H. Cadle, P. J. Groblicki, G. T. Wolff, J. Air Pollut. Control Assoc. 31, 247 (1981).
[CrossRef]

R. J. Countess, G. T. Wolff, S. H. Cadle, J. Air Pollut. Control Assoc. 30, 1194 (1980).
[CrossRef]

Wong, W. T.

I. N. Tang, W. T. Wong, H. R. Munkelwitz, Atmos. Environ. 15, 2463 (1981).
[CrossRef]

Yue, G. K.

Adv. Geophys. (1)

G. Hänel, “The Properties of Atmospheric Aerosol Particles as Functions of the Relative Humidity at Thermodynamic Equilibrium with the Surrounding Moist Air,” Adv. Geophys. 19, 73 (1976). (Academic Press, New York, 1976).
[CrossRef]

Appl. Opt. (6)

Atmos. Environ. (3)

A. P. Waggoner, R. E. Weiss, N. A. Ahlquist, D. S. Covert, S. Will, R. J. Charlson, Atmos. Environ. 15, 1891 (1981).
[CrossRef]

I. N. Tang, W. T. Wong, H. R. Munkelwitz, Atmos. Environ. 15, 2463 (1981).
[CrossRef]

C. Sloane, Atmos. Environ. 17, 409 (1983).
[CrossRef]

Contrib. Atmos. Phys. (1)

G. Hänel, M. Lehmann, Contrib. Atmos. Phys. 54, 57 (1981).

J. Aerosol Sci. (1)

W. A. Hoppel, J. Aerosol Sci. 9, 41 (1978).
[CrossRef]

J. Air Pollut. Control Assoc. (2)

R. J. Countess, G. T. Wolff, S. H. Cadle, J. Air Pollut. Control Assoc. 30, 1194 (1980).
[CrossRef]

R. J. Countess, S. H. Cadle, P. J. Groblicki, G. T. Wolff, J. Air Pollut. Control Assoc. 31, 247 (1981).
[CrossRef]

J. Appl. Meteorol. (1)

J. T. Twitty, J. A. Weinman, J. Appl. Meteorol. 10, 725 (1971).
[CrossRef]

J. Atmos. Sci. (1)

J. W. Fitzgerald, W. A. Hoppel, M. A. Vietti, J. Atmos. Sci. 39, 1838 (1982).
[CrossRef]

J. Geophys. Res. (2)

F. E. Volz, J. Geophys. Res. 77, 1017 (1972).
[CrossRef]

D. J. Hoffman, J. M. Rosen, J. Geophys. Res. 88, 3777 (1982).
[CrossRef]

Tellus (1)

G. Hänel, Tellus 20, 371 (1968).
[CrossRef]

Other (7)

E. P. Shettle, R. W. Fenn, “Models for the Aerosols of the Lower Atmosphere and the Effects of Humidity Variations on Their Optical Properties,” Air Force Geophysics Laboratory Report TR-79-0214 (1979).

D. J. Alofs, M. B. Trueblood, “The Correlation Between Size and Critical Supersaturation Exhibited by CCN in Missouri,” in Proceedings, Conference on Cloud Physics, Nov.1982, Chicago, Ill.

R. T. H. Collis, P. B. Russell, “Lidar Measurement of Particles and Gases by Elastic Backscattering and Differential Absorption,” in Topics in Applied Physics, Vol. 14 (Springer, Berlin, 1976).
[CrossRef]

E. J. McCartney, Optics of the Atmosphere (Wiley, New York, 1976).

J. V. Dave, “Subroutines for Computing the Parameters of Electromagnetic Radiation Scattered by a Sphere,” IBM Palo Alto Scientific Center Report 320-3237 (1968).

W. A. Hoppel, J. W. Fitzgerald, R. E. Larson, “Measurements of Atmospheric Aerosols: Experimental Methods and Results of Measurements Off the East Coast of the United States,” Naval Research Laboratory Report 8703 (1983).

While the lognormal size distribution is usually given by an expression of the form (A/r) exp[−B ln2(r/rm)], it is noted by N. A. Fuchs, The Mechanics of Aerosols (Pergamon, New York, 1964), p. 13, that the various moments of a lognormal distribution are also lognormal. Thus, the distribution f(r) = A exp[−B ln2(r/rm)], which is obtained by multiplying the standard form by r, is also lognormal.

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Figures (7)

Fig. 1
Fig. 1

Dry aerosol size distribution models used in the calculations.

Fig. 2
Fig. 2

Particle growth factor r/r0 as a function of relative humidity for two values of the volume fraction of water-soluble material Vws/V0.

Fig. 3
Fig. 3

Volume backscattering coefficient as a function of relative humidity for a wavelength of 0.694 πm. Solid curves are for uniform internal mixtures of soot, water-soluble material, and dustlike material (models A, B, and C in Table II). Dashed curves are for external mixtures of soot and nonsoot particles. Nonsoot particles are uniform mixtures of 30% water-soluble and 70% dustlike materials. The symbols indicate the volume fraction of soot in the aerosol as identified in the key. Particle size distribution 1 in Fig. 1 is used.

Fig. 4
Fig. 4

As in Fig. 3 except for a wavelength of 10.6 μm.

Fig. 5
Fig. 5

Volume backscattering coefficient as a function of relative humidity for the case of a uniform internal mixture containing 10% soot by volume, showing the effect of a change in the dry size distribution and in the volume fraction of water-soluble material Vws/V0. Curve 1 is for size distribution 1 (Fig. 1) and Vws/V0 = 0.65, curve 2 for size distribution 1 and Vws/V0 = 0.30, and curve 3 for size distribution 2 and Vws/V0 = 0.3. λ = 0.694 μm.

Fig. 6
Fig. 6

As in Fig. 5 except for a wavelength of 10.6 μm.

Fig. 7
Fig. 7

Relationship between the volume backscattering and volume extinction coefficients at 0.694 μm for a path of varying relative humidity. Particles are composed of a uniform internal mixture of soot, water-soluble material, and dustlike material. Curves 1, 2, and 3 are, respectively, for aerosol models A, B, and C in Table II. Size distribution 1 in Fig. 1 is assumed.

Tables (2)

Tables Icon

Table I Index of Refraction of Aerosol Components for 0.694- and 10.6-μm Radiation

Tables Icon

Table II Models of Uniformly Mixed Aerosols Used in the Computations

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

β π = 0 σ π ( r , λ , m ) f ( r ) d r ,
σ π = λ 2 4 π 2 · i 1 ( 180 ° , r , m , λ ) + i 2 ( 180 ° , r , m , λ ) 2 ,
β π = 0 π r 2 Q π f ( r ) d r .
Q π = 1 π α 2 i 1 + i 2 2 ,
β e = 0 π r 2 Q e f ( r ) d r ,
f 0 ( r ) = d N d r = { 92 r - 2.2 , 0.015 μ m r 0.15 μ m , 2.5 r - 4.1 , 0.15 μ m r 5.0 μ m , 14.4 r - 5.0 , r > 5.0 μ m .
f 0 ( r ) = d N d r = 1.02 × 10 5 exp [ - 1.93 l n 2 ( 0.038 / r ) ] + 3.8 exp [ - 1.68 l n 2 ( 0.454 / r ) ] .
n 0 = i n i V i V 0 ,             κ 0 = i κ i V i V 0 ,
n = n w + ( n 0 - n w ) ( r r 0 ) - 3 , κ = κ w + ( κ 0 - κ w ) ( r r 0 ) - 3 ,
f 0 ( r ) d r = f ( F r ) F d r , or f ( r ) = 1 F f 0 ( r / F ) ,
β π = c β e k .

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