Abstract

Using light scattering matrix elements measured by a polar nephelometer, a procedure for estimating the characteristics of atmospheric particulates was developed. A theoretical library data set of scattering matrices derived from Mie theory was tabulated for a range of values of the size parameter and refractive index typical of atmospheric particles. Integration over the size parameter yielded the scattering matrix elements for a variety of hypothesized particulate size distributions. A least squares curve fitting technique was used to find a best fit for the experimental measurements. This was used as a first guess for a nonlinear iterative inversion of the size distributions. A real index of 1.50 and an imaginary index of −0.005 are representative of the smoothed inversion results for the near ground level atmospheric aerosol in Tucson.

© 1980 Optical Society of America

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1980

M. Z. Hansen, W. H. Evans, Appl. Opt. 19, 3389 (1980).
[CrossRef] [PubMed]

J. D. Spinhirne, J. A. Reagan, B. M. Herman, J. Appl. Meteorol. 19, 426 (1980).
[CrossRef]

J. A. Reagan, D. M. Byrne, M. D. King, J. D. Spinhirne, B. M. Herman, J. Geophys. Res. 85, 1591 (1980).
[CrossRef]

1979

M. D. King, J. Atmos. Sci. 36, 1072 (1979).
[CrossRef]

1978

C. Acquista, Appl. Opt. 17, 3851 (1978).
[CrossRef] [PubMed]

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, J. Atmos. Sci. 35, 2153 (1978).
[CrossRef]

1976

1975

S. Twomey, J. Comput. Phys. 18, 188 (1975).
[CrossRef]

1974

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

J. D. Lindberg, L. S. Laude, Appl. Opt. 13, 1923 (1974).
[CrossRef] [PubMed]

1973

1971

B. M. Herman, S. R. Browning, J. A. Reagan, J. Atmos. Sci. 28, 763 (1971).
[CrossRef]

1969

1968

1966

S. Twomey, Mon. Weather Rev. 94, 363 (1966).
[CrossRef]

1963

S. Twomey, J. Assoc. Comput. Mach. 10, 97 (1963).
[CrossRef]

1962

D. L. Phillips, J. Assoc. Comput. Mach. 9, 84 (1962).
[CrossRef]

Acquista, C.

Blifford, I. H.

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

Browning, S. R.

B. M. Herman, S. R. Browning, J. A. Reagan, J. Atmos. Sci. 28, 763 (1971).
[CrossRef]

Byrne, D. M.

J. A. Reagan, D. M. Byrne, M. D. King, J. D. Spinhirne, B. M. Herman, J. Geophys. Res. 85, 1591 (1980).
[CrossRef]

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, J. Atmos. Sci. 35, 2153 (1978).
[CrossRef]

D. M. Byrne, Ph.D. Dissertation, U. Arizona (1978).

Carroll, D. E.

Chahine, M. T.

Chylek, P.

P. Chylek, G. W. Grams, R. G. Pinnick, Science 193, 480 (1976).
[CrossRef]

Cohen, A.

Dave, J. V.

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

Evans, W. H.

Gillette, D. A.

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

Grams, G. W.

P. Chylek, G. W. Grams, R. G. Pinnick, Science 193, 480 (1976).
[CrossRef]

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

Hansen, M. Z.

Herman, B. M.

J. D. Spinhirne, J. A. Reagan, B. M. Herman, J. Appl. Meteorol. 19, 426 (1980).
[CrossRef]

J. A. Reagan, D. M. Byrne, M. D. King, J. D. Spinhirne, B. M. Herman, J. Geophys. Res. 85, 1591 (1980).
[CrossRef]

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, J. Atmos. Sci. 35, 2153 (1978).
[CrossRef]

B. M. Herman, S. R. Browning, J. A. Reagan, J. Atmos. Sci. 28, 763 (1971).
[CrossRef]

Hofmann, D. J.

King, M. D.

J. A. Reagan, D. M. Byrne, M. D. King, J. D. Spinhirne, B. M. Herman, J. Geophys. Res. 85, 1591 (1980).
[CrossRef]

M. D. King, J. Atmos. Sci. 36, 1072 (1979).
[CrossRef]

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, J. Atmos. Sci. 35, 2153 (1978).
[CrossRef]

Laude, L. S.

Lindberg, J. D.

Phillips, D. L.

D. L. Phillips, J. Assoc. Comput. Mach. 9, 84 (1962).
[CrossRef]

Pinnick, R. G.

Post, M. J.

Reagan, J. A.

J. D. Spinhirne, J. A. Reagan, B. M. Herman, J. Appl. Meteorol. 19, 426 (1980).
[CrossRef]

J. A. Reagan, D. M. Byrne, M. D. King, J. D. Spinhirne, B. M. Herman, J. Geophys. Res. 85, 1591 (1980).
[CrossRef]

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, J. Atmos. Sci. 35, 2153 (1978).
[CrossRef]

B. M. Herman, S. R. Browning, J. A. Reagan, J. Atmos. Sci. 28, 763 (1971).
[CrossRef]

Russell, P. B.

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

Spinhirne, J. D.

J. A. Reagan, D. M. Byrne, M. D. King, J. D. Spinhirne, B. M. Herman, J. Geophys. Res. 85, 1591 (1980).
[CrossRef]

J. D. Spinhirne, J. A. Reagan, B. M. Herman, J. Appl. Meteorol. 19, 426 (1980).
[CrossRef]

Tanaka, M.

Twomey, S.

S. Twomey, J. Atmos. Sci. 33, 1073 (1976).
[CrossRef]

S. Twomey, J. Comput. Phys. 18, 188 (1975).
[CrossRef]

S. Twomey, Mon. Weather Rev. 94, 363 (1966).
[CrossRef]

S. Twomey, J. Assoc. Comput. Mach. 10, 97 (1963).
[CrossRef]

Westwater, E. R.

Yamamoto, G.

Appl. Opt.

J. Appl. Meteorol.

J. D. Spinhirne, J. A. Reagan, B. M. Herman, J. Appl. Meteorol. 19, 426 (1980).
[CrossRef]

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

J. Assoc. Comput. Mach.

D. L. Phillips, J. Assoc. Comput. Mach. 9, 84 (1962).
[CrossRef]

S. Twomey, J. Assoc. Comput. Mach. 10, 97 (1963).
[CrossRef]

J. Atmos. Sci.

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, J. Atmos. Sci. 35, 2153 (1978).
[CrossRef]

B. M. Herman, S. R. Browning, J. A. Reagan, J. Atmos. Sci. 28, 763 (1971).
[CrossRef]

M. D. King, J. Atmos. Sci. 36, 1072 (1979).
[CrossRef]

S. Twomey, J. Atmos. Sci. 33, 1073 (1976).
[CrossRef]

J. Comput. Phys.

S. Twomey, J. Comput. Phys. 18, 188 (1975).
[CrossRef]

J. Geophys. Res.

J. A. Reagan, D. M. Byrne, M. D. King, J. D. Spinhirne, B. M. Herman, J. Geophys. Res. 85, 1591 (1980).
[CrossRef]

J. Opt. Soc. Am.

Mon. Weather Rev.

S. Twomey, Mon. Weather Rev. 94, 363 (1966).
[CrossRef]

Science

P. Chylek, G. W. Grams, R. G. Pinnick, Science 193, 480 (1976).
[CrossRef]

Other

D. M. Byrne, Ph.D. Dissertation, U. Arizona (1978).

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

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Figures (22)

Fig. 1
Fig. 1

Junge size distribution curves.

Fig. 2
Fig. 2

Two-slope size distribution curves.

Fig. 3
Fig. 3

Scattering element M2 integrated over Junge size distributions.

Fig. 4
Fig. 4

Scattering element S21 integrated over a Junge size distribution for two particle size ranges.

Fig. 5
Fig. 5

Scattering element M2 integrated over a Junge size distribution for two particle size ranges.

Fig. 6
Fig. 6

Weighted scattering element M2 for single particles

Fig. 7
Fig. 7

Weighted scattering element M1 for single particles.

Fig. 8
Fig. 8

Scattering element M1 for single particles.

Fig. 9
Fig. 9

Scattering element M2 for single particles.

Fig. 10
Fig. 10

Power spectrum of M2.

Fig. 11
Fig. 11

Power spectrum of D21.

Fig. 12
Fig. 12

Convergence of iterative inversion for theoretical data with no error.

Fig. 13
Fig. 13

Theoretical size distribution inversions for various mass loading initial guesses.

Fig. 14
Fig. 14

Theoretical size distribution inversions for various Junge slope initial guesses.

Fig. 15
Fig. 15

Convergence of iterative inversion for theoretical data with 11% error.

Fig. 16
Fig. 16

M2 scattering matrix element.

Fig. 17
Fig. 17

S21 scattering matrix element.

Fig. 18
Fig. 18

Size distribution inversions for the 9 March experimental data.

Fig. 19
Fig. 19

Convergence of iterative inversion for experimental data with various mass loading initial guesses.

Fig. 20
Fig. 20

Size distribution inversions for the 4 March experimental data.

Fig. 21
Fig. 21

Size distribution inversions for the 10 March experimental data.

Fig. 22
Fig. 22

Average of inverted size distributions.

Equations (6)

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d N d r = C r ( ν + 1 ) ,
d N d r = C [ 1 + ( r / r B ) ν 2 ] [ 1 + ( r / r A ) ν 1 ] ,
H = i ( b i ξ d i ) 2 ,
f ( r ) = [ 1 + [ g ( s ) f 0 ( r ) k ( r , s ) d r 1 ] k ( r , s ) k ( s ) max ] f 0 ( r ) ,
f ( r ) = ( 1 + M R ) f 0 ( r ) ,
M = [ g ( s ) f 0 ( r ) k ( r , s ) d r 1 ] k ( r , s ) k ( s ) max .

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