Abstract

We describe a genetic method of deriving aerosol size distributions from multiwavelength extinction measurements. The genetic inversion searches for log-normal size distribution parameters whose calculated extinctions best fit the data. By repetitively applying the genetic inversion using different random number seeds, we are able to generate multiple solutions that fit the data equally well. When these solutions are similar, they lend confidence to an interpretation, whereas when they vary widely, they demonstrate nonuniqueness. In this way we show that, even in the case of a single log-normal distribution, many different distributions can fit the same set of extinction data unless the misfit is reduced below typical measurement error levels. In the case of a bimodal distribution, we find many dissimilar size distributions that fit the data to within 1% at six wavelengths. To recover the original bimodal distribution satisfactorily, we found that extinctions at ten wavelengths must be fitted to within 0.5%. Our results imply that many size distributions recovered from existing extinction measurements can be highly nonunique and should be treated with caution.

© 2001 Optical Society of America

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  1. D. Müller, U. Wandinger, A. Ansmann, “Microphysical particle parameters from extinction and backscatter data by inversion with regularization: theory,” Appl. Opt. 38, 2346–2357 (1999).
    [CrossRef]
  2. G. P. Box, K. M. Sealy, M. A. Box, “Inversion of Mie extinction measurements using analytic eigenfunction theory,” J. Atmos. Sci. 49, 2074–2081 (1989).
    [CrossRef]
  3. D. P. Donovan, A. I. Carswell, “Principal component analysis applied to multiwavelength lidar aerosol backscatter and extinction measurements,” Appl. Opt. 36, 9406–9424 (1997).
    [CrossRef]
  4. E. R. Westwater, A. Cohen, “Application of Backus–Gilbert inversion technique to determination of aerosol size distributions from optical scattering measurements,” Appl. Opt. 12, 1340–1348 (1973).
    [CrossRef] [PubMed]
  5. D. J. Carroll, “Chemical laser modeling with genetic algorithms,” AIAA J. 34, 338–346 (1996).
    [CrossRef]
  6. M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distributions obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
    [CrossRef]
  7. C. E. Junge, “The size distribution and aging of natural aerosols as determined from electrical and optical data on the atmosphere,” J. Meteorol. 12, 13–25 (1961).
    [CrossRef]
  8. O. Dubovik, M. D. King, “A flexible algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2000).
    [CrossRef]
  9. M. Kalos, P. Whitlock, Monte Carlo Methods (Wiley InterScience, New York, 1986).
    [CrossRef]
  10. M. Sambridge, “Geophysical inversion with a neighbourhood algorithm. I. Searching a parameter space,” Geophys. J. Int. 138, 479–494 (1999).
    [CrossRef]
  11. J. Besag, P. J. Green, D. Higdon, K. Mengersen, “Bayesian computation and stochastic systems,” Stat. Sci. 10, 3–66 (1995).
    [CrossRef]
  12. J. E. Gentile, Random Number Generation and Monte Carlo Methods (Springer-Verlag, New York, 1998).
    [CrossRef]
  13. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).
  14. J. H. Holland, Adaptation in Artificial and Natural Systems (University of Michigan, Ann Arbor, Mich., 1975).
  15. D. E. Goldberg, M. P. Samtani, “Engineering optimization via genetic algorithm,” in Proceedings of the Ninth Conference on Electronic Computation, American Society of Civil Engineers, Birmingham, Ala., 1986), pp. 471–482.
  16. S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
    [CrossRef] [PubMed]
  17. A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodel functions of continuous variables with the simulated annealing algorithm,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 13, 262–280 (1987).
    [CrossRef]
  18. K. T. Whitby, “The physical characteristics of sulfur aerosols,” Atmos. Environ. 12, 135–159 (1978).
    [CrossRef]
  19. P. K. Quinn, D. S. Covert, T. S. Bates, V. N. Kapustin, D. C. Ramsey-Bell, L. M. Melnnes, “Dimethylsulfide/cloud condensation nuclei/climate system: relevant size-resolved measurements of the chemical and physical properties of atmospheric aerosol particles,” J. Geophys. Res. 98, 10411–10427 (1993).
    [CrossRef]
  20. J. N. Porter, A. D. Clarke, “Aerosol size distribution models based on in situ measurements,” J. Geophys. Res. 102, 6035–6045 (1997).
    [CrossRef]
  21. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  22. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).
  23. M. J. Post, “A graphical technique for retrieving size distribution parameters from multiple measurements: visualization and error analysis,” J. Atmos. Oceanic Technol. 13, 865–873 (1996).
  24. B. R. Lienert, E. Berg, L. N. Frazer, “HYPOCENTER: an earthquake location method using centered, scaled and adaptively damped least squares,” Bull. Seismol. Soc. Am. 76, 771–783 (1986).
  25. M. J. Post, “Limitations of cloud droplet size distribution by Backus–Gilbert inversion of optical scattering data,” J. Opt. Soc. Am. 66, 483–486 (1976).
    [CrossRef]
  26. J. N. Porter, M. Miller, C. Pietras, C. Motell, “Ship-based sun photometer measurements using Microtops sun photometers,” J. Atmos. Oceanic Technol. 18, 765–774 (2001).
    [CrossRef]
  27. G. E. Shaw, “Sun photometry,” Bull. Am. Meteorol. Soc. 64, 4–11 (1983).
    [CrossRef]
  28. G. Backus, F. Gilbert, “The resolving power of gross earth data,” Geophys. J. R. Astron. Soc. 266, 169–205 (1969).
  29. D. D. Jackson, “Interpretation of inaccurate, insufficient and inconsistent data,” Geophys. J. R. Astron. Soc. 28, 97–109 (1972).
    [CrossRef]
  30. H. G. Jorge, J. A. Ogren, “Sensitivity of retrieved aerosol properties to assumptions in the inversion of spectral optical depths,” J. Atmos. Sci. 53, 3669–3683 (1996).
    [CrossRef]

2001

J. N. Porter, M. Miller, C. Pietras, C. Motell, “Ship-based sun photometer measurements using Microtops sun photometers,” J. Atmos. Oceanic Technol. 18, 765–774 (2001).
[CrossRef]

2000

O. Dubovik, M. D. King, “A flexible algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2000).
[CrossRef]

1999

M. Sambridge, “Geophysical inversion with a neighbourhood algorithm. I. Searching a parameter space,” Geophys. J. Int. 138, 479–494 (1999).
[CrossRef]

D. Müller, U. Wandinger, A. Ansmann, “Microphysical particle parameters from extinction and backscatter data by inversion with regularization: theory,” Appl. Opt. 38, 2346–2357 (1999).
[CrossRef]

1997

D. P. Donovan, A. I. Carswell, “Principal component analysis applied to multiwavelength lidar aerosol backscatter and extinction measurements,” Appl. Opt. 36, 9406–9424 (1997).
[CrossRef]

J. N. Porter, A. D. Clarke, “Aerosol size distribution models based on in situ measurements,” J. Geophys. Res. 102, 6035–6045 (1997).
[CrossRef]

1996

M. J. Post, “A graphical technique for retrieving size distribution parameters from multiple measurements: visualization and error analysis,” J. Atmos. Oceanic Technol. 13, 865–873 (1996).

D. J. Carroll, “Chemical laser modeling with genetic algorithms,” AIAA J. 34, 338–346 (1996).
[CrossRef]

H. G. Jorge, J. A. Ogren, “Sensitivity of retrieved aerosol properties to assumptions in the inversion of spectral optical depths,” J. Atmos. Sci. 53, 3669–3683 (1996).
[CrossRef]

1995

J. Besag, P. J. Green, D. Higdon, K. Mengersen, “Bayesian computation and stochastic systems,” Stat. Sci. 10, 3–66 (1995).
[CrossRef]

1993

P. K. Quinn, D. S. Covert, T. S. Bates, V. N. Kapustin, D. C. Ramsey-Bell, L. M. Melnnes, “Dimethylsulfide/cloud condensation nuclei/climate system: relevant size-resolved measurements of the chemical and physical properties of atmospheric aerosol particles,” J. Geophys. Res. 98, 10411–10427 (1993).
[CrossRef]

1989

G. P. Box, K. M. Sealy, M. A. Box, “Inversion of Mie extinction measurements using analytic eigenfunction theory,” J. Atmos. Sci. 49, 2074–2081 (1989).
[CrossRef]

1987

A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodel functions of continuous variables with the simulated annealing algorithm,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

1986

B. R. Lienert, E. Berg, L. N. Frazer, “HYPOCENTER: an earthquake location method using centered, scaled and adaptively damped least squares,” Bull. Seismol. Soc. Am. 76, 771–783 (1986).

1983

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

G. E. Shaw, “Sun photometry,” Bull. Am. Meteorol. Soc. 64, 4–11 (1983).
[CrossRef]

1978

K. T. Whitby, “The physical characteristics of sulfur aerosols,” Atmos. Environ. 12, 135–159 (1978).
[CrossRef]

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distributions obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[CrossRef]

1976

1973

1972

D. D. Jackson, “Interpretation of inaccurate, insufficient and inconsistent data,” Geophys. J. R. Astron. Soc. 28, 97–109 (1972).
[CrossRef]

1969

G. Backus, F. Gilbert, “The resolving power of gross earth data,” Geophys. J. R. Astron. Soc. 266, 169–205 (1969).

1961

C. E. Junge, “The size distribution and aging of natural aerosols as determined from electrical and optical data on the atmosphere,” J. Meteorol. 12, 13–25 (1961).
[CrossRef]

Ansmann, A.

Backus, G.

G. Backus, F. Gilbert, “The resolving power of gross earth data,” Geophys. J. R. Astron. Soc. 266, 169–205 (1969).

Bates, T. S.

P. K. Quinn, D. S. Covert, T. S. Bates, V. N. Kapustin, D. C. Ramsey-Bell, L. M. Melnnes, “Dimethylsulfide/cloud condensation nuclei/climate system: relevant size-resolved measurements of the chemical and physical properties of atmospheric aerosol particles,” J. Geophys. Res. 98, 10411–10427 (1993).
[CrossRef]

Berg, E.

B. R. Lienert, E. Berg, L. N. Frazer, “HYPOCENTER: an earthquake location method using centered, scaled and adaptively damped least squares,” Bull. Seismol. Soc. Am. 76, 771–783 (1986).

Besag, J.

J. Besag, P. J. Green, D. Higdon, K. Mengersen, “Bayesian computation and stochastic systems,” Stat. Sci. 10, 3–66 (1995).
[CrossRef]

Bohren, C. F.

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

Box, G. P.

G. P. Box, K. M. Sealy, M. A. Box, “Inversion of Mie extinction measurements using analytic eigenfunction theory,” J. Atmos. Sci. 49, 2074–2081 (1989).
[CrossRef]

Box, M. A.

G. P. Box, K. M. Sealy, M. A. Box, “Inversion of Mie extinction measurements using analytic eigenfunction theory,” J. Atmos. Sci. 49, 2074–2081 (1989).
[CrossRef]

Byrne, D. M.

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distributions obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[CrossRef]

Carroll, D. J.

D. J. Carroll, “Chemical laser modeling with genetic algorithms,” AIAA J. 34, 338–346 (1996).
[CrossRef]

Carswell, A. I.

Clarke, A. D.

J. N. Porter, A. D. Clarke, “Aerosol size distribution models based on in situ measurements,” J. Geophys. Res. 102, 6035–6045 (1997).
[CrossRef]

Cohen, A.

Corana, A.

A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodel functions of continuous variables with the simulated annealing algorithm,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Covert, D. S.

P. K. Quinn, D. S. Covert, T. S. Bates, V. N. Kapustin, D. C. Ramsey-Bell, L. M. Melnnes, “Dimethylsulfide/cloud condensation nuclei/climate system: relevant size-resolved measurements of the chemical and physical properties of atmospheric aerosol particles,” J. Geophys. Res. 98, 10411–10427 (1993).
[CrossRef]

Deirmendjian, D.

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

Donovan, D. P.

Dubovik, O.

O. Dubovik, M. D. King, “A flexible algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2000).
[CrossRef]

Frazer, L. N.

B. R. Lienert, E. Berg, L. N. Frazer, “HYPOCENTER: an earthquake location method using centered, scaled and adaptively damped least squares,” Bull. Seismol. Soc. Am. 76, 771–783 (1986).

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Gentile, J. E.

J. E. Gentile, Random Number Generation and Monte Carlo Methods (Springer-Verlag, New York, 1998).
[CrossRef]

Gilbert, F.

G. Backus, F. Gilbert, “The resolving power of gross earth data,” Geophys. J. R. Astron. Soc. 266, 169–205 (1969).

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

D. E. Goldberg, M. P. Samtani, “Engineering optimization via genetic algorithm,” in Proceedings of the Ninth Conference on Electronic Computation, American Society of Civil Engineers, Birmingham, Ala., 1986), pp. 471–482.

Green, P. J.

J. Besag, P. J. Green, D. Higdon, K. Mengersen, “Bayesian computation and stochastic systems,” Stat. Sci. 10, 3–66 (1995).
[CrossRef]

Herman, B. M.

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distributions obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[CrossRef]

Higdon, D.

J. Besag, P. J. Green, D. Higdon, K. Mengersen, “Bayesian computation and stochastic systems,” Stat. Sci. 10, 3–66 (1995).
[CrossRef]

Holland, J. H.

J. H. Holland, Adaptation in Artificial and Natural Systems (University of Michigan, Ann Arbor, Mich., 1975).

Huffman, D. R.

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

Jackson, D. D.

D. D. Jackson, “Interpretation of inaccurate, insufficient and inconsistent data,” Geophys. J. R. Astron. Soc. 28, 97–109 (1972).
[CrossRef]

Jorge, H. G.

H. G. Jorge, J. A. Ogren, “Sensitivity of retrieved aerosol properties to assumptions in the inversion of spectral optical depths,” J. Atmos. Sci. 53, 3669–3683 (1996).
[CrossRef]

Junge, C. E.

C. E. Junge, “The size distribution and aging of natural aerosols as determined from electrical and optical data on the atmosphere,” J. Meteorol. 12, 13–25 (1961).
[CrossRef]

Kalos, M.

M. Kalos, P. Whitlock, Monte Carlo Methods (Wiley InterScience, New York, 1986).
[CrossRef]

Kapustin, V. N.

P. K. Quinn, D. S. Covert, T. S. Bates, V. N. Kapustin, D. C. Ramsey-Bell, L. M. Melnnes, “Dimethylsulfide/cloud condensation nuclei/climate system: relevant size-resolved measurements of the chemical and physical properties of atmospheric aerosol particles,” J. Geophys. Res. 98, 10411–10427 (1993).
[CrossRef]

King, M. D.

O. Dubovik, M. D. King, “A flexible algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2000).
[CrossRef]

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distributions obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Lienert, B. R.

B. R. Lienert, E. Berg, L. N. Frazer, “HYPOCENTER: an earthquake location method using centered, scaled and adaptively damped least squares,” Bull. Seismol. Soc. Am. 76, 771–783 (1986).

Marchesi, M.

A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodel functions of continuous variables with the simulated annealing algorithm,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Martini, C.

A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodel functions of continuous variables with the simulated annealing algorithm,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Melnnes, L. M.

P. K. Quinn, D. S. Covert, T. S. Bates, V. N. Kapustin, D. C. Ramsey-Bell, L. M. Melnnes, “Dimethylsulfide/cloud condensation nuclei/climate system: relevant size-resolved measurements of the chemical and physical properties of atmospheric aerosol particles,” J. Geophys. Res. 98, 10411–10427 (1993).
[CrossRef]

Mengersen, K.

J. Besag, P. J. Green, D. Higdon, K. Mengersen, “Bayesian computation and stochastic systems,” Stat. Sci. 10, 3–66 (1995).
[CrossRef]

Miller, M.

J. N. Porter, M. Miller, C. Pietras, C. Motell, “Ship-based sun photometer measurements using Microtops sun photometers,” J. Atmos. Oceanic Technol. 18, 765–774 (2001).
[CrossRef]

Motell, C.

J. N. Porter, M. Miller, C. Pietras, C. Motell, “Ship-based sun photometer measurements using Microtops sun photometers,” J. Atmos. Oceanic Technol. 18, 765–774 (2001).
[CrossRef]

Müller, D.

Ogren, J. A.

H. G. Jorge, J. A. Ogren, “Sensitivity of retrieved aerosol properties to assumptions in the inversion of spectral optical depths,” J. Atmos. Sci. 53, 3669–3683 (1996).
[CrossRef]

Pietras, C.

J. N. Porter, M. Miller, C. Pietras, C. Motell, “Ship-based sun photometer measurements using Microtops sun photometers,” J. Atmos. Oceanic Technol. 18, 765–774 (2001).
[CrossRef]

Porter, J. N.

J. N. Porter, M. Miller, C. Pietras, C. Motell, “Ship-based sun photometer measurements using Microtops sun photometers,” J. Atmos. Oceanic Technol. 18, 765–774 (2001).
[CrossRef]

J. N. Porter, A. D. Clarke, “Aerosol size distribution models based on in situ measurements,” J. Geophys. Res. 102, 6035–6045 (1997).
[CrossRef]

Post, M. J.

M. J. Post, “A graphical technique for retrieving size distribution parameters from multiple measurements: visualization and error analysis,” J. Atmos. Oceanic Technol. 13, 865–873 (1996).

M. J. Post, “Limitations of cloud droplet size distribution by Backus–Gilbert inversion of optical scattering data,” J. Opt. Soc. Am. 66, 483–486 (1976).
[CrossRef]

Quinn, P. K.

P. K. Quinn, D. S. Covert, T. S. Bates, V. N. Kapustin, D. C. Ramsey-Bell, L. M. Melnnes, “Dimethylsulfide/cloud condensation nuclei/climate system: relevant size-resolved measurements of the chemical and physical properties of atmospheric aerosol particles,” J. Geophys. Res. 98, 10411–10427 (1993).
[CrossRef]

Ramsey-Bell, D. C.

P. K. Quinn, D. S. Covert, T. S. Bates, V. N. Kapustin, D. C. Ramsey-Bell, L. M. Melnnes, “Dimethylsulfide/cloud condensation nuclei/climate system: relevant size-resolved measurements of the chemical and physical properties of atmospheric aerosol particles,” J. Geophys. Res. 98, 10411–10427 (1993).
[CrossRef]

Reagan, J. A.

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distributions obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[CrossRef]

Ridella, S.

A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodel functions of continuous variables with the simulated annealing algorithm,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

Sambridge, M.

M. Sambridge, “Geophysical inversion with a neighbourhood algorithm. I. Searching a parameter space,” Geophys. J. Int. 138, 479–494 (1999).
[CrossRef]

Samtani, M. P.

D. E. Goldberg, M. P. Samtani, “Engineering optimization via genetic algorithm,” in Proceedings of the Ninth Conference on Electronic Computation, American Society of Civil Engineers, Birmingham, Ala., 1986), pp. 471–482.

Sealy, K. M.

G. P. Box, K. M. Sealy, M. A. Box, “Inversion of Mie extinction measurements using analytic eigenfunction theory,” J. Atmos. Sci. 49, 2074–2081 (1989).
[CrossRef]

Shaw, G. E.

G. E. Shaw, “Sun photometry,” Bull. Am. Meteorol. Soc. 64, 4–11 (1983).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Wandinger, U.

Westwater, E. R.

Whitby, K. T.

K. T. Whitby, “The physical characteristics of sulfur aerosols,” Atmos. Environ. 12, 135–159 (1978).
[CrossRef]

Whitlock, P.

M. Kalos, P. Whitlock, Monte Carlo Methods (Wiley InterScience, New York, 1986).
[CrossRef]

ACM (Assoc. Comput. Mach.) Trans. Math. Software

A. Corana, M. Marchesi, C. Martini, S. Ridella, “Minimizing multimodel functions of continuous variables with the simulated annealing algorithm,” ACM (Assoc. Comput. Mach.) Trans. Math. Software 13, 262–280 (1987).
[CrossRef]

AIAA J.

D. J. Carroll, “Chemical laser modeling with genetic algorithms,” AIAA J. 34, 338–346 (1996).
[CrossRef]

Appl. Opt.

Atmos. Environ.

K. T. Whitby, “The physical characteristics of sulfur aerosols,” Atmos. Environ. 12, 135–159 (1978).
[CrossRef]

Bull. Am. Meteorol. Soc.

G. E. Shaw, “Sun photometry,” Bull. Am. Meteorol. Soc. 64, 4–11 (1983).
[CrossRef]

Bull. Seismol. Soc. Am.

B. R. Lienert, E. Berg, L. N. Frazer, “HYPOCENTER: an earthquake location method using centered, scaled and adaptively damped least squares,” Bull. Seismol. Soc. Am. 76, 771–783 (1986).

Geophys. J. Int.

M. Sambridge, “Geophysical inversion with a neighbourhood algorithm. I. Searching a parameter space,” Geophys. J. Int. 138, 479–494 (1999).
[CrossRef]

Geophys. J. R. Astron. Soc.

G. Backus, F. Gilbert, “The resolving power of gross earth data,” Geophys. J. R. Astron. Soc. 266, 169–205 (1969).

D. D. Jackson, “Interpretation of inaccurate, insufficient and inconsistent data,” Geophys. J. R. Astron. Soc. 28, 97–109 (1972).
[CrossRef]

J. Atmos. Oceanic Technol.

M. J. Post, “A graphical technique for retrieving size distribution parameters from multiple measurements: visualization and error analysis,” J. Atmos. Oceanic Technol. 13, 865–873 (1996).

J. N. Porter, M. Miller, C. Pietras, C. Motell, “Ship-based sun photometer measurements using Microtops sun photometers,” J. Atmos. Oceanic Technol. 18, 765–774 (2001).
[CrossRef]

J. Atmos. Sci.

H. G. Jorge, J. A. Ogren, “Sensitivity of retrieved aerosol properties to assumptions in the inversion of spectral optical depths,” J. Atmos. Sci. 53, 3669–3683 (1996).
[CrossRef]

G. P. Box, K. M. Sealy, M. A. Box, “Inversion of Mie extinction measurements using analytic eigenfunction theory,” J. Atmos. Sci. 49, 2074–2081 (1989).
[CrossRef]

M. D. King, D. M. Byrne, B. M. Herman, J. A. Reagan, “Aerosol size distributions obtained by inversion of spectral optical depth measurements,” J. Atmos. Sci. 35, 2153–2167 (1978).
[CrossRef]

J. Geophys. Res.

O. Dubovik, M. D. King, “A flexible algorithm for retrieval of aerosol optical properties from sun and sky radiance measurements,” J. Geophys. Res. 105, 20673–20696 (2000).
[CrossRef]

P. K. Quinn, D. S. Covert, T. S. Bates, V. N. Kapustin, D. C. Ramsey-Bell, L. M. Melnnes, “Dimethylsulfide/cloud condensation nuclei/climate system: relevant size-resolved measurements of the chemical and physical properties of atmospheric aerosol particles,” J. Geophys. Res. 98, 10411–10427 (1993).
[CrossRef]

J. N. Porter, A. D. Clarke, “Aerosol size distribution models based on in situ measurements,” J. Geophys. Res. 102, 6035–6045 (1997).
[CrossRef]

J. Meteorol.

C. E. Junge, “The size distribution and aging of natural aerosols as determined from electrical and optical data on the atmosphere,” J. Meteorol. 12, 13–25 (1961).
[CrossRef]

J. Opt. Soc. Am.

Science

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Stat. Sci.

J. Besag, P. J. Green, D. Higdon, K. Mengersen, “Bayesian computation and stochastic systems,” Stat. Sci. 10, 3–66 (1995).
[CrossRef]

Other

J. E. Gentile, Random Number Generation and Monte Carlo Methods (Springer-Verlag, New York, 1998).
[CrossRef]

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

J. H. Holland, Adaptation in Artificial and Natural Systems (University of Michigan, Ann Arbor, Mich., 1975).

D. E. Goldberg, M. P. Samtani, “Engineering optimization via genetic algorithm,” in Proceedings of the Ninth Conference on Electronic Computation, American Society of Civil Engineers, Birmingham, Ala., 1986), pp. 471–482.

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

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

M. Kalos, P. Whitlock, Monte Carlo Methods (Wiley InterScience, New York, 1986).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Size distribution model (heavy solid curve) and four models (light curves) obtained by genetic inversions of the extinctions predicted by Mie theory at four wavelengths for this model. Units for the size distribution concentrations are area per unit volume (m-1).

Fig. 2
Fig. 2

Extinctions calculated for the models shown in Fig. 1. The filled circles are the input data used for the genetic inversions. The rms extinction misfits are all < = 1 × 10-5 m-1.

Fig. 3
Fig. 3

Size distribution models obtained with the same data as those in Fig. 1, but with the rms extinction misfit reduced to 2 × 10-6 m-1.

Fig. 4
Fig. 4

Changes in fitness with generation for different population sizes obtained with genetic inversion of the data in Fig. 2.

Fig. 5
Fig. 5

Bimodal size distribution models (light curves) obtained by genetic inversion of synthetic data at six wavelengths generated with the heavy solid curve model.

Fig. 6
Fig. 6

Extinctions calculated with the models in Fig. 5. The filled squares are the input data used for the genetic inversions.

Fig. 7
Fig. 7

Size distribution models (light curves) obtained by genetic inversions of synthetic data generated with the heavy solid curve model at ten wavelengths from 0.26 to 1.54 µm. The rms data misfits for these models are all <5 × 10-7 m-1.

Fig. 8
Fig. 8

Measured sunphotometer optical thicknesses converted to extinction assuming a 2-km-thick aerosol layer (filled squares). The curves are theoretical extinctions for the models in Fig. 9.

Fig. 9
Fig. 9

Unimodal size distribution models obtained by repeated genetic inversion of the extinction data in Fig. 8. The data misfits are all <5 × 10-6 m-1. HOTS, Hawaii Ocean Time-series.

Fig. 10
Fig. 10

Unimodal size distribution models obtained by repeated genetic inversion of the extinction data in Fig. 8. The data misfits are all <2.5 × 10-6 m-1.

Tables (1)

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Table 1 Settings Used in the Genetic Inversion Algorithm

Equations (4)

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dNdD=AD-ν*+1,
dNd loge D=i=13Ni2πloge σi× exp-loge D-logeD¯i22loge σi2,
αaλ, m=0QσD, λ, mdNDdDdD,
F=σdi=0N Δdi2/N1/2

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