Abstract

The separation of the individual contributions of aerosols and gases to the total attenuation of radiation through the atmosphere has been the subject of much scientific investigation since remote sensing experiments first began. We describe a new scheme to account for the spectral variation of the aerosol extinction in the inversion of transmission data from occultation measurements. Because the spectral variation of the aerosol extinction is generally unknown, the inversion problem is underdetermined and cannot be solved without a reduction in the number of unknowns in the set of equations used to describe the attenuation at each wavelength. This reduction can be accomplished by a variety of methods, including use of a priori information, the parameterization of the aerosol spectral attenuation, and the specification of the form of the aerosol size distribution. We have developed and implemented a parameterization scheme based on existing empirical and modeled information about the microphysical properties of aerosols. This scheme employs the eigenvectors from an extensive set of simulations to parameterize the aerosol extinction coefficient for incorporation into the inversion algorithm. We examine the accuracy of our method using data sets containing over 24,000 extinction spectra and compare it with that of another scheme that is currently implemented in the Polar Ozone and Aerosol Measurement (POAM) satellite experiment. In simulations using 80 wavelengths in the UV-visible-near-IR spectral range of the Stratospheric Aerosol and Gas Experiment III (SAGE) instrument, we show that, for our optimal parameterization, errors below 1% are observed in 80% of cases, whereas only approximately 20% of all cases are as accurate as this in a quadratic parameterization employing the logarithm of the wavelength.

© 2003 Optical Society of America

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  42. For more detailed information on SAGE III, see http:/www.sage3.larc.nasa.gov/ .
  43. V. F. Turchin, V. P. Kozlov, M. S. Malkevich, “Applying the methods of mathematical statistics for solving ill-posed problems,” Uspekhi Fizicheskikh Nauk 102, 345–386 (1970) (in Russian).
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    [CrossRef]
  47. J. Anderson, C. Brogniez, L. Cazier, V. K. Saxena, J. Lenoble, M. P. McCormick, “Characterization of aerosols from simulated SAGE III measurements applying two retrieval techniques,” J. Geophys. Res. 105, 2013–2027 (2000).
    [CrossRef]
  48. These parameters can be found at the National Oceanic and Atmospheric Administration’s Surface Radiation Research Branch at http://www.srrb.noaa.gov/research/aerosol.html .
  49. W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
    [CrossRef]

2001 (1)

A. V. Polyakov, A. V. Vasil’ev, Yu. M. Timofeev, “Parameterization of the spectral dependence of the aerosol attenuation coefficient in problems of atmospheric occultation sounding from space,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 37, 599–609 (2001) (English translation).

2000 (2)

A. J. Stevermer, I. V. Petropavlovskikh, J. M. Rosen, J. J. DeLuisi, “Development of a global stratospheric aerosol climatology: optical properties and applications for UV,” J. Geophys. Res. 105, 22763–22776 (2000).
[CrossRef]

J. Anderson, C. Brogniez, L. Cazier, V. K. Saxena, J. Lenoble, M. P. McCormick, “Characterization of aerosols from simulated SAGE III measurements applying two retrieval techniques,” J. Geophys. Res. 105, 2013–2027 (2000).
[CrossRef]

1999 (2)

D. Fussen, C. Binger, “A volcanism dependent model for the extinction profile of stratospheric aerosols in the UV-visible range,” Geophys. Res. Lett. 26, 703–706 (1999).
[CrossRef]

A. V. Poberovskii, A. V. Polyakov, Yu. M. Timofeyev, A. E. Kovalev, V. M. Prokhorov, A. Z. Khrustalev, V. A. Panchenko, I. I. Mansurov, O. N. Volkov, “Ozone profile determination by occultation sounding from the Mir space station. 1. Instrumentation and data processing method. Examples of results,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 35, 282–290 (1999) (English translation).

1998 (3)

M. E. Hervig, T. Deshler, J. M. Russell, “Aerosol size distribution obtained from HALOE spectral extinction measurements,” J. Geophys. Res. 103, 1573–1583 (1998).
[CrossRef]

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
[CrossRef]

D. Fussen, “A critical analysis of the Stratospheric Aerosol and Gas Experiment II spectral inversion algorithm,” J. Geophys. Res. 103, 8455–8464 (1998).
[CrossRef]

1997 (4)

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

H. M. Steele, R. P. Turco, “Separation of aerosol and gas components in the Halogen Occultation Experiment and the Stratospheric Aerosol and Gas Experiment II extinction measurements: implications for SAGE II ozone concentration and trends,” J. Geophys. Res. 102, 19665–19681 (1997).
[CrossRef]

H. M. Steele, R. P. Turco, “Retrieval of aerosol size distributions from satellite extinction spectra using constrained linear inversion,” J. Geophys. Res. 102, D14, 16737–16747 (1997).
[CrossRef]

A. V. Vasilyev, L. S. Ivlev, “Empirical models and optical characteristics of aerosol ensembles of two-layer spherical particles,” Optika Atmosfery i Okena T. 10, 856–865 (1997) (in Russian).

1996 (2)

A. V. Vasilyev, L. S. Ivlev, “Universal algorithm for calculating the optical characteristic of two-layer spherical aerosol particles with homogeneous core and coat,” Optika Atmosfery i Okena T. 9, 1552–1561 (1996) (in Russian).

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

1995 (1)

M. E. Hervig, J. M. Russell, L. L. Gordley, J. Daniels, S. R. Drayson, J. H. Park, “Aerosol effects and corrections in the Halogen Occultation Experiment,” J. Geophys. Res. 100, 1067–1079 (1995).
[CrossRef]

1994 (1)

M. J. Newchurch, D. M. Cunnold, “Aerosol effects on Umkehr ozone profiles using Stratospheric Aerosol and Gas Experiment II measurements,” J. Geophys. Res. 99, 1383–1388 (1994).
[CrossRef]

1991 (2)

G. M. Grechko, N. F. Elansky, M. E. Plotkin, O. V. Postylyakov, “The Ozone and Aerosol Fine Structure Experiment: observing the fine structure of ozone and aerosol distribution in the atmosphere from the Salyut 7 orbiter,” J. Geophys. Res. 96, 18647–18653 (1991).
[CrossRef]

L. W. Thomason, “A diagnostic stratospheric aerosol size distribution inferred from SAGE II measurements,” J. Geophys. Res. 96, 22501–22508 (1991).
[CrossRef]

1990 (1)

M. S. Biryulina, V. V. Rozanov, “The parameterization of aerosol size distribution functions for forward and inverse problems of the atmosphere remote sensing,” Atmos. Opt. 3, 1087–1094 (1990) (in Russian).

1989 (2)

Yu. M. Timofeyev, “Satellite methods of studying the gas content of atmosphere,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 25(5), 451–472 (1989) (English translation).

W. P. Chu, M. P. McCormick, J. Lenoble, C. Brogniez, P. Pruvost, “SAGE II inversion algorithm,” J. Geophys. Res. 94, 8339–8351 (1989).
[CrossRef]

1983 (1)

J. Lenoble, P. Pruvost, “Inference of the aerosol Angstrom coefficient from SAGE short-wavelength data,” J. Clim. Appl. Meteorol. 22, 1717–1725 (1983).
[CrossRef]

1981 (2)

H. M. Steele, P. Hamill, “Effects of temperature and humidity on the growth and optical properties of sulphuric acid-water droplets in the stratosphere,” J. Aerosol. Sci. 12, 517–528 (1981).
[CrossRef]

M. S. Biryulina, “The simulation of a priori ensemble of solutions of inverse problem and the stability of optimal designs of the ozone space experiment,” Meteorol. Hydrol. 4, 45–51 (1981) (in Russian).

1979 (2)

J. L. Gras, C. G. Michael, “Measurements of the stratospheric aerosol particle size distribution,” J. Appl. Meteorol. 18, 855–860 (1979).
[CrossRef]

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, “A one-dimensional model describing aerosol formation and evolution in the stratosphere,” J. Atmos. Sci. 36, 699–736 (1979).
[CrossRef]

1978 (1)

J. M. Rosen, D. J. Hofmann, S. P. Singh, “A steady state stratospheric aerosol model,” J. Atmos. Sci. 35, 1304–1313 (1978).
[CrossRef]

1976 (2)

R. G. Pinnick, J. M. Rosen, D. J. Hofmann, “Stratospheric aerosol measurements. 3. Optical model calculations,” J. Atmos. Sci. 33, 304–314 (1976).
[CrossRef]

O. B. Toon, J. B. Pollack, “A global average model of atmospheric aerosols for radiative transfer calculations,” J. Appl. Meteorol. 15, 225–246 (1976).
[CrossRef]

1975 (1)

1974 (1)

A. L. Lazrus, B. W. Gandrud, “Stratospheric sulfate aerosol,” J. Geophys. Res. 79, 3424–3431 (1974).
[CrossRef]

1970 (1)

V. F. Turchin, V. P. Kozlov, M. S. Malkevich, “Applying the methods of mathematical statistics for solving ill-posed problems,” Uspekhi Fizicheskikh Nauk 102, 345–386 (1970) (in Russian).
[CrossRef]

1963 (1)

S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
[CrossRef]

1960 (1)

A. M. Obukhov, “About statistically orthogonal expansions of empirical functions,” Izv. Akad. Nauk SSSR Ser. Geofiz. 3, 432–439 (1960) (in Russian).

Anderson, G. P.

G. P. Anderson, S. A. Clough, F. X. Kneizys, J. H. Chetwynd, E. P. Shettle, “AFGL atmospheric constituent profiles (0–120 km),” AFGL-TR-86-0110, No. 954 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1986).

Anderson, J.

J. Anderson, C. Brogniez, L. Cazier, V. K. Saxena, J. Lenoble, M. P. McCormick, “Characterization of aerosols from simulated SAGE III measurements applying two retrieval techniques,” J. Geophys. Res. 105, 2013–2027 (2000).
[CrossRef]

Andreev, S. D.

L. S. Ivlev, S. D. Andreev, Optical Properties of Atmospheric Aerosols (Leningrad, Leningrad State University, 1986) (in Russian).

Bevilacqua, R. M.

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

Binger, C.

D. Fussen, C. Binger, “A volcanism dependent model for the extinction profile of stratospheric aerosols in the UV-visible range,” Geophys. Res. Lett. 26, 703–706 (1999).
[CrossRef]

Biryulina, M. S.

M. S. Biryulina, V. V. Rozanov, “The parameterization of aerosol size distribution functions for forward and inverse problems of the atmosphere remote sensing,” Atmos. Opt. 3, 1087–1094 (1990) (in Russian).

M. S. Biryulina, “The simulation of a priori ensemble of solutions of inverse problem and the stability of optimal designs of the ozone space experiment,” Meteorol. Hydrol. 4, 45–51 (1981) (in Russian).

Brogniez, C.

J. Anderson, C. Brogniez, L. Cazier, V. K. Saxena, J. Lenoble, M. P. McCormick, “Characterization of aerosols from simulated SAGE III measurements applying two retrieval techniques,” J. Geophys. Res. 105, 2013–2027 (2000).
[CrossRef]

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

W. P. Chu, M. P. McCormick, J. Lenoble, C. Brogniez, P. Pruvost, “SAGE II inversion algorithm,” J. Geophys. Res. 94, 8339–8351 (1989).
[CrossRef]

Callan, M. T.

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
[CrossRef]

Cazier, L.

J. Anderson, C. Brogniez, L. Cazier, V. K. Saxena, J. Lenoble, M. P. McCormick, “Characterization of aerosols from simulated SAGE III measurements applying two retrieval techniques,” J. Geophys. Res. 105, 2013–2027 (2000).
[CrossRef]

Chassefiere, E.

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

Chen, D. T.

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

Chetwynd, J. H.

G. P. Anderson, S. A. Clough, F. X. Kneizys, J. H. Chetwynd, E. P. Shettle, “AFGL atmospheric constituent profiles (0–120 km),” AFGL-TR-86-0110, No. 954 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1986).

Chu, W. P.

W. P. Chu, M. P. McCormick, J. Lenoble, C. Brogniez, P. Pruvost, “SAGE II inversion algorithm,” J. Geophys. Res. 94, 8339–8351 (1989).
[CrossRef]

Clancy, R. T.

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
[CrossRef]

Claude, H.

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
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G. P. Anderson, S. A. Clough, F. X. Kneizys, J. H. Chetwynd, E. P. Shettle, “AFGL atmospheric constituent profiles (0–120 km),” AFGL-TR-86-0110, No. 954 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1986).

Cunnold, D. M.

M. J. Newchurch, D. M. Cunnold, “Aerosol effects on Umkehr ozone profiles using Stratospheric Aerosol and Gas Experiment II measurements,” J. Geophys. Res. 99, 1383–1388 (1994).
[CrossRef]

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G. A. d’Almeida, P. Koepke, E. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).

Dalaudier, F.

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

Daniels, J.

M. E. Hervig, J. M. Russell, L. L. Gordley, J. Daniels, S. R. Drayson, J. H. Park, “Aerosol effects and corrections in the Halogen Occultation Experiment,” J. Geophys. Res. 100, 1067–1079 (1995).
[CrossRef]

De Muer, D.

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
[CrossRef]

Debrestian, D. J.

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

DeLuisi, J. J.

A. J. Stevermer, I. V. Petropavlovskikh, J. M. Rosen, J. J. DeLuisi, “Development of a global stratospheric aerosol climatology: optical properties and applications for UV,” J. Geophys. Res. 105, 22763–22776 (2000).
[CrossRef]

Deniel, C.

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
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M. E. Hervig, T. Deshler, J. M. Russell, “Aerosol size distribution obtained from HALOE spectral extinction measurements,” J. Geophys. Res. 103, 1573–1583 (1998).
[CrossRef]

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M. E. Hervig, J. M. Russell, L. L. Gordley, J. Daniels, S. R. Drayson, J. H. Park, “Aerosol effects and corrections in the Halogen Occultation Experiment,” J. Geophys. Res. 100, 1067–1079 (1995).
[CrossRef]

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G. M. Grechko, N. F. Elansky, M. E. Plotkin, O. V. Postylyakov, “The Ozone and Aerosol Fine Structure Experiment: observing the fine structure of ozone and aerosol distribution in the atmosphere from the Salyut 7 orbiter,” J. Geophys. Res. 96, 18647–18653 (1991).
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W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
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W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

Gordley, L. L.

M. E. Hervig, J. M. Russell, L. L. Gordley, J. Daniels, S. R. Drayson, J. H. Park, “Aerosol effects and corrections in the Halogen Occultation Experiment,” J. Geophys. Res. 100, 1067–1079 (1995).
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J. L. Gras, C. G. Michael, “Measurements of the stratospheric aerosol particle size distribution,” J. Appl. Meteorol. 18, 855–860 (1979).
[CrossRef]

Grechko, G. M.

G. M. Grechko, N. F. Elansky, M. E. Plotkin, O. V. Postylyakov, “The Ozone and Aerosol Fine Structure Experiment: observing the fine structure of ozone and aerosol distribution in the atmosphere from the Salyut 7 orbiter,” J. Geophys. Res. 96, 18647–18653 (1991).
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Hekryach, F. E.

I. T. Goronovski, Yu. P. Nazarenko, F. E. Hekryach, Short Chemical Handbook (Naukova Dumka, Kiev, Russia, 1974) (in Russian).

Hervig, M. E.

M. E. Hervig, T. Deshler, J. M. Russell, “Aerosol size distribution obtained from HALOE spectral extinction measurements,” J. Geophys. Res. 103, 1573–1583 (1998).
[CrossRef]

M. E. Hervig, J. M. Russell, L. L. Gordley, J. Daniels, S. R. Drayson, J. H. Park, “Aerosol effects and corrections in the Halogen Occultation Experiment,” J. Geophys. Res. 100, 1067–1079 (1995).
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J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

Horanyi, M.

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
[CrossRef]

Hornstein, J. S.

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
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A. V. Vasilyev, L. S. Ivlev, “Empirical models and optical characteristics of aerosol ensembles of two-layer spherical particles,” Optika Atmosfery i Okena T. 10, 856–865 (1997) (in Russian).

A. V. Vasilyev, L. S. Ivlev, “Universal algorithm for calculating the optical characteristic of two-layer spherical aerosol particles with homogeneous core and coat,” Optika Atmosfery i Okena T. 9, 1552–1561 (1996) (in Russian).

L. S. Ivlev, S. D. Andreev, Optical Properties of Atmospheric Aerosols (Leningrad, Leningrad State University, 1986) (in Russian).

Johnson, B. J.

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
[CrossRef]

Khrustalev, A. Z.

A. V. Poberovskii, A. V. Polyakov, Yu. M. Timofeyev, A. E. Kovalev, V. M. Prokhorov, A. Z. Khrustalev, V. A. Panchenko, I. I. Mansurov, O. N. Volkov, “Ozone profile determination by occultation sounding from the Mir space station. 1. Instrumentation and data processing method. Examples of results,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 35, 282–290 (1999) (English translation).

Kiang, C. S.

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, “A one-dimensional model describing aerosol formation and evolution in the stratosphere,” J. Atmos. Sci. 36, 699–736 (1979).
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Kneizys, F. X.

G. P. Anderson, S. A. Clough, F. X. Kneizys, J. H. Chetwynd, E. P. Shettle, “AFGL atmospheric constituent profiles (0–120 km),” AFGL-TR-86-0110, No. 954 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1986).

Koehler, U.

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
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Koepke, P.

G. A. d’Almeida, P. Koepke, E. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).

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K. Ya. Kondratyev, Actinometry (Gidrometeoizdat, Leningrad, 1965).

Kovalev, A. E.

A. V. Poberovskii, A. V. Polyakov, Yu. M. Timofeyev, A. E. Kovalev, V. M. Prokhorov, A. Z. Khrustalev, V. A. Panchenko, I. I. Mansurov, O. N. Volkov, “Ozone profile determination by occultation sounding from the Mir space station. 1. Instrumentation and data processing method. Examples of results,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 35, 282–290 (1999) (English translation).

Kozlov, V. P.

V. F. Turchin, V. P. Kozlov, M. S. Malkevich, “Applying the methods of mathematical statistics for solving ill-posed problems,” Uspekhi Fizicheskikh Nauk 102, 345–386 (1970) (in Russian).
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G. M. Krekov, S. G. Zvenigorodski, Optical Model of Middle Atmosphere (Nauka, Novosibirsk, Russia, 1990) (in Russian).

Kremer, R.

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

Kriebel, D. L.

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
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Krigman, S. S.

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
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A. L. Lazrus, B. W. Gandrud, “Stratospheric sulfate aerosol,” J. Geophys. Res. 79, 3424–3431 (1974).
[CrossRef]

Lenoble, J.

J. Anderson, C. Brogniez, L. Cazier, V. K. Saxena, J. Lenoble, M. P. McCormick, “Characterization of aerosols from simulated SAGE III measurements applying two retrieval techniques,” J. Geophys. Res. 105, 2013–2027 (2000).
[CrossRef]

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
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W. P. Chu, M. P. McCormick, J. Lenoble, C. Brogniez, P. Pruvost, “SAGE II inversion algorithm,” J. Geophys. Res. 94, 8339–8351 (1989).
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J. Lenoble, P. Pruvost, “Inference of the aerosol Angstrom coefficient from SAGE short-wavelength data,” J. Clim. Appl. Meteorol. 22, 1717–1725 (1983).
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Lucke, R. L.

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

Lumpe, J. D.

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

Malkevich, M. S.

V. F. Turchin, V. P. Kozlov, M. S. Malkevich, “Applying the methods of mathematical statistics for solving ill-posed problems,” Uspekhi Fizicheskikh Nauk 102, 345–386 (1970) (in Russian).
[CrossRef]

Mansurov, I. I.

A. V. Poberovskii, A. V. Polyakov, Yu. M. Timofeyev, A. E. Kovalev, V. M. Prokhorov, A. Z. Khrustalev, V. A. Panchenko, I. I. Mansurov, O. N. Volkov, “Ozone profile determination by occultation sounding from the Mir space station. 1. Instrumentation and data processing method. Examples of results,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 35, 282–290 (1999) (English translation).

McCormick, M. P.

J. Anderson, C. Brogniez, L. Cazier, V. K. Saxena, J. Lenoble, M. P. McCormick, “Characterization of aerosols from simulated SAGE III measurements applying two retrieval techniques,” J. Geophys. Res. 105, 2013–2027 (2000).
[CrossRef]

W. P. Chu, M. P. McCormick, J. Lenoble, C. Brogniez, P. Pruvost, “SAGE II inversion algorithm,” J. Geophys. Res. 94, 8339–8351 (1989).
[CrossRef]

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J. L. Gras, C. G. Michael, “Measurements of the stratospheric aerosol particle size distribution,” J. Appl. Meteorol. 18, 855–860 (1979).
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Mikhailov, G. A.

S. M. Ermakov, G. A. Mikhailov, Course of Statistical Simulation (Nauka, Moscow, 1976) (in Russian).

Nazarenko, Yu. P.

I. T. Goronovski, Yu. P. Nazarenko, F. E. Hekryach, Short Chemical Handbook (Naukova Dumka, Kiev, Russia, 1974) (in Russian).

Newchurch, M. J.

M. J. Newchurch, D. M. Cunnold, “Aerosol effects on Umkehr ozone profiles using Stratospheric Aerosol and Gas Experiment II measurements,” J. Geophys. Res. 99, 1383–1388 (1994).
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A. M. Obukhov, “About statistically orthogonal expansions of empirical functions,” Izv. Akad. Nauk SSSR Ser. Geofiz. 3, 432–439 (1960) (in Russian).

Olivera, J. J.

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

Olivero, J. J.

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

Oltmans, S. J.

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
[CrossRef]

Palmer, K. F.

Panchenko, V. A.

A. V. Poberovskii, A. V. Polyakov, Yu. M. Timofeyev, A. E. Kovalev, V. M. Prokhorov, A. Z. Khrustalev, V. A. Panchenko, I. I. Mansurov, O. N. Volkov, “Ozone profile determination by occultation sounding from the Mir space station. 1. Instrumentation and data processing method. Examples of results,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 35, 282–290 (1999) (English translation).

Park, J. H.

M. E. Hervig, J. M. Russell, L. L. Gordley, J. Daniels, S. R. Drayson, J. H. Park, “Aerosol effects and corrections in the Halogen Occultation Experiment,” J. Geophys. Res. 100, 1067–1079 (1995).
[CrossRef]

Petropavlovskikh, I. V.

A. J. Stevermer, I. V. Petropavlovskikh, J. M. Rosen, J. J. DeLuisi, “Development of a global stratospheric aerosol climatology: optical properties and applications for UV,” J. Geophys. Res. 105, 22763–22776 (2000).
[CrossRef]

Pinnick, R. G.

R. G. Pinnick, J. M. Rosen, D. J. Hofmann, “Stratospheric aerosol measurements. 3. Optical model calculations,” J. Atmos. Sci. 33, 304–314 (1976).
[CrossRef]

Plotkin, M. E.

G. M. Grechko, N. F. Elansky, M. E. Plotkin, O. V. Postylyakov, “The Ozone and Aerosol Fine Structure Experiment: observing the fine structure of ozone and aerosol distribution in the atmosphere from the Salyut 7 orbiter,” J. Geophys. Res. 96, 18647–18653 (1991).
[CrossRef]

Poberovskii, A. V.

A. V. Poberovskii, A. V. Polyakov, Yu. M. Timofeyev, A. E. Kovalev, V. M. Prokhorov, A. Z. Khrustalev, V. A. Panchenko, I. I. Mansurov, O. N. Volkov, “Ozone profile determination by occultation sounding from the Mir space station. 1. Instrumentation and data processing method. Examples of results,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 35, 282–290 (1999) (English translation).

Pollack, J. B.

O. B. Toon, J. B. Pollack, “A global average model of atmospheric aerosols for radiative transfer calculations,” J. Appl. Meteorol. 15, 225–246 (1976).
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Polyakov, A. V.

A. V. Polyakov, A. V. Vasil’ev, Yu. M. Timofeev, “Parameterization of the spectral dependence of the aerosol attenuation coefficient in problems of atmospheric occultation sounding from space,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 37, 599–609 (2001) (English translation).

A. V. Poberovskii, A. V. Polyakov, Yu. M. Timofeyev, A. E. Kovalev, V. M. Prokhorov, A. Z. Khrustalev, V. A. Panchenko, I. I. Mansurov, O. N. Volkov, “Ozone profile determination by occultation sounding from the Mir space station. 1. Instrumentation and data processing method. Examples of results,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 35, 282–290 (1999) (English translation).

Postylyakov, O. V.

G. M. Grechko, N. F. Elansky, M. E. Plotkin, O. V. Postylyakov, “The Ozone and Aerosol Fine Structure Experiment: observing the fine structure of ozone and aerosol distribution in the atmosphere from the Salyut 7 orbiter,” J. Geophys. Res. 96, 18647–18653 (1991).
[CrossRef]

Prokhorov, V. M.

A. V. Poberovskii, A. V. Polyakov, Yu. M. Timofeyev, A. E. Kovalev, V. M. Prokhorov, A. Z. Khrustalev, V. A. Panchenko, I. I. Mansurov, O. N. Volkov, “Ozone profile determination by occultation sounding from the Mir space station. 1. Instrumentation and data processing method. Examples of results,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 35, 282–290 (1999) (English translation).

Pruvost, P.

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

W. P. Chu, M. P. McCormick, J. Lenoble, C. Brogniez, P. Pruvost, “SAGE II inversion algorithm,” J. Geophys. Res. 94, 8339–8351 (1989).
[CrossRef]

J. Lenoble, P. Pruvost, “Inference of the aerosol Angstrom coefficient from SAGE short-wavelength data,” J. Clim. Appl. Meteorol. 22, 1717–1725 (1983).
[CrossRef]

Ramananahérisoa, R.

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

Randall, C. E.

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
[CrossRef]

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

Rodgers, C. D.

C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice (World Scientific, Singapore, 2000).

Rosen, J. M.

A. J. Stevermer, I. V. Petropavlovskikh, J. M. Rosen, J. J. DeLuisi, “Development of a global stratospheric aerosol climatology: optical properties and applications for UV,” J. Geophys. Res. 105, 22763–22776 (2000).
[CrossRef]

J. M. Rosen, D. J. Hofmann, S. P. Singh, “A steady state stratospheric aerosol model,” J. Atmos. Sci. 35, 1304–1313 (1978).
[CrossRef]

R. G. Pinnick, J. M. Rosen, D. J. Hofmann, “Stratospheric aerosol measurements. 3. Optical model calculations,” J. Atmos. Sci. 33, 304–314 (1976).
[CrossRef]

Rozanov, V. V.

M. S. Biryulina, V. V. Rozanov, “The parameterization of aerosol size distribution functions for forward and inverse problems of the atmosphere remote sensing,” Atmos. Opt. 3, 1087–1094 (1990) (in Russian).

Rusch, D. W.

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
[CrossRef]

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

Russell, J. M.

M. E. Hervig, T. Deshler, J. M. Russell, “Aerosol size distribution obtained from HALOE spectral extinction measurements,” J. Geophys. Res. 103, 1573–1583 (1998).
[CrossRef]

M. E. Hervig, J. M. Russell, L. L. Gordley, J. Daniels, S. R. Drayson, J. H. Park, “Aerosol effects and corrections in the Halogen Occultation Experiment,” J. Geophys. Res. 100, 1067–1079 (1995).
[CrossRef]

Saxena, V. K.

J. Anderson, C. Brogniez, L. Cazier, V. K. Saxena, J. Lenoble, M. P. McCormick, “Characterization of aerosols from simulated SAGE III measurements applying two retrieval techniques,” J. Geophys. Res. 105, 2013–2027 (2000).
[CrossRef]

Shettle, E.

G. A. d’Almeida, P. Koepke, E. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).

Shettle, E. P.

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

E. P. Shettle, U.S. Naval Research Laboratory Washington, D.C. (personal communication, 2000).

G. P. Anderson, S. A. Clough, F. X. Kneizys, J. H. Chetwynd, E. P. Shettle, “AFGL atmospheric constituent profiles (0–120 km),” AFGL-TR-86-0110, No. 954 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1986).

Singh, S. P.

J. M. Rosen, D. J. Hofmann, S. P. Singh, “A steady state stratospheric aerosol model,” J. Atmos. Sci. 35, 1304–1313 (1978).
[CrossRef]

Solomon, S. C.

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
[CrossRef]

Steele, H. M.

H. M. Steele, R. P. Turco, “Separation of aerosol and gas components in the Halogen Occultation Experiment and the Stratospheric Aerosol and Gas Experiment II extinction measurements: implications for SAGE II ozone concentration and trends,” J. Geophys. Res. 102, 19665–19681 (1997).
[CrossRef]

H. M. Steele, R. P. Turco, “Retrieval of aerosol size distributions from satellite extinction spectra using constrained linear inversion,” J. Geophys. Res. 102, D14, 16737–16747 (1997).
[CrossRef]

H. M. Steele, P. Hamill, “Effects of temperature and humidity on the growth and optical properties of sulphuric acid-water droplets in the stratosphere,” J. Aerosol. Sci. 12, 517–528 (1981).
[CrossRef]

Stevermer, A. J.

A. J. Stevermer, I. V. Petropavlovskikh, J. M. Rosen, J. J. DeLuisi, “Development of a global stratospheric aerosol climatology: optical properties and applications for UV,” J. Geophys. Res. 105, 22763–22776 (2000).
[CrossRef]

Thomason, L. W.

L. W. Thomason, “A diagnostic stratospheric aerosol size distribution inferred from SAGE II measurements,” J. Geophys. Res. 96, 22501–22508 (1991).
[CrossRef]

Timofeev, Yu. M.

A. V. Polyakov, A. V. Vasil’ev, Yu. M. Timofeev, “Parameterization of the spectral dependence of the aerosol attenuation coefficient in problems of atmospheric occultation sounding from space,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 37, 599–609 (2001) (English translation).

Timofeyev, Yu. M.

A. V. Poberovskii, A. V. Polyakov, Yu. M. Timofeyev, A. E. Kovalev, V. M. Prokhorov, A. Z. Khrustalev, V. A. Panchenko, I. I. Mansurov, O. N. Volkov, “Ozone profile determination by occultation sounding from the Mir space station. 1. Instrumentation and data processing method. Examples of results,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 35, 282–290 (1999) (English translation).

Yu. M. Timofeyev, “Satellite methods of studying the gas content of atmosphere,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 25(5), 451–472 (1989) (English translation).

Toon, O. B.

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, “A one-dimensional model describing aerosol formation and evolution in the stratosphere,” J. Atmos. Sci. 36, 699–736 (1979).
[CrossRef]

O. B. Toon, J. B. Pollack, “A global average model of atmospheric aerosols for radiative transfer calculations,” J. Appl. Meteorol. 15, 225–246 (1976).
[CrossRef]

Turchin, V. F.

V. F. Turchin, V. P. Kozlov, M. S. Malkevich, “Applying the methods of mathematical statistics for solving ill-posed problems,” Uspekhi Fizicheskikh Nauk 102, 345–386 (1970) (in Russian).
[CrossRef]

Turco, R. P.

H. M. Steele, R. P. Turco, “Separation of aerosol and gas components in the Halogen Occultation Experiment and the Stratospheric Aerosol and Gas Experiment II extinction measurements: implications for SAGE II ozone concentration and trends,” J. Geophys. Res. 102, 19665–19681 (1997).
[CrossRef]

H. M. Steele, R. P. Turco, “Retrieval of aerosol size distributions from satellite extinction spectra using constrained linear inversion,” J. Geophys. Res. 102, D14, 16737–16747 (1997).
[CrossRef]

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, “A one-dimensional model describing aerosol formation and evolution in the stratosphere,” J. Atmos. Sci. 36, 699–736 (1979).
[CrossRef]

Twomey, S.

S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
[CrossRef]

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977).

Vasil’ev, A. V.

A. V. Polyakov, A. V. Vasil’ev, Yu. M. Timofeev, “Parameterization of the spectral dependence of the aerosol attenuation coefficient in problems of atmospheric occultation sounding from space,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 37, 599–609 (2001) (English translation).

Vasilyev, A. V.

A. V. Vasilyev, L. S. Ivlev, “Empirical models and optical characteristics of aerosol ensembles of two-layer spherical particles,” Optika Atmosfery i Okena T. 10, 856–865 (1997) (in Russian).

A. V. Vasilyev, L. S. Ivlev, “Universal algorithm for calculating the optical characteristic of two-layer spherical aerosol particles with homogeneous core and coat,” Optika Atmosfery i Okena T. 9, 1552–1561 (1996) (in Russian).

A. V. Vasilyev, “Universal algorithm for calculating the optical characteristics of homogeneous spherical aerosol particles. I. Single particles.” Vestnik S-Peterburgskogo Universiteta, Series 4: Physics and Chemistry, 4, 3–11 (1996) (in Russian).

A. V. Vasilyev, “Universal algorithm for calculating the optical characteristics of homogeneous spherical aerosol particles. II. Ensembles of particles. Vestnik S-Peterburgskogo Universiteta, Series 4: Physics and Chemistry1, 14–24 (1997) (in Russian).

Volkov, O. N.

A. V. Poberovskii, A. V. Polyakov, Yu. M. Timofeyev, A. E. Kovalev, V. M. Prokhorov, A. Z. Khrustalev, V. A. Panchenko, I. I. Mansurov, O. N. Volkov, “Ozone profile determination by occultation sounding from the Mir space station. 1. Instrumentation and data processing method. Examples of results,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 35, 282–290 (1999) (English translation).

Whitten, R. C.

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, “A one-dimensional model describing aerosol formation and evolution in the stratosphere,” J. Atmos. Sci. 36, 699–736 (1979).
[CrossRef]

Williams, D.

Zuev, V. E.

V. E. Zuev, G. M. Krekov, Current Problems of Atmospheric Optics, Vol. 2 of Optical Models of the Atmosphere (Gidrometeoizdat, Leningrad, 1986) (in Russian).

Zvenigorodski, S. G.

G. M. Krekov, S. G. Zvenigorodski, Optical Model of Middle Atmosphere (Nauka, Novosibirsk, Russia, 1990) (in Russian).

Appl. Opt. (1)

Atmos. Opt. (1)

M. S. Biryulina, V. V. Rozanov, “The parameterization of aerosol size distribution functions for forward and inverse problems of the atmosphere remote sensing,” Atmos. Opt. 3, 1087–1094 (1990) (in Russian).

Geophys. Res. Lett. (1)

D. Fussen, C. Binger, “A volcanism dependent model for the extinction profile of stratospheric aerosols in the UV-visible range,” Geophys. Res. Lett. 26, 703–706 (1999).
[CrossRef]

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

A. M. Obukhov, “About statistically orthogonal expansions of empirical functions,” Izv. Akad. Nauk SSSR Ser. Geofiz. 3, 432–439 (1960) (in Russian).

Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. (3)

A. V. Polyakov, A. V. Vasil’ev, Yu. M. Timofeev, “Parameterization of the spectral dependence of the aerosol attenuation coefficient in problems of atmospheric occultation sounding from space,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 37, 599–609 (2001) (English translation).

A. V. Poberovskii, A. V. Polyakov, Yu. M. Timofeyev, A. E. Kovalev, V. M. Prokhorov, A. Z. Khrustalev, V. A. Panchenko, I. I. Mansurov, O. N. Volkov, “Ozone profile determination by occultation sounding from the Mir space station. 1. Instrumentation and data processing method. Examples of results,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 35, 282–290 (1999) (English translation).

Yu. M. Timofeyev, “Satellite methods of studying the gas content of atmosphere,” Izv. Ross. Akad. Nauk Atmos. Oceanic Phys. 25(5), 451–472 (1989) (English translation).

J. Aerosol. Sci. (1)

H. M. Steele, P. Hamill, “Effects of temperature and humidity on the growth and optical properties of sulphuric acid-water droplets in the stratosphere,” J. Aerosol. Sci. 12, 517–528 (1981).
[CrossRef]

J. Appl. Meteorol. (2)

O. B. Toon, J. B. Pollack, “A global average model of atmospheric aerosols for radiative transfer calculations,” J. Appl. Meteorol. 15, 225–246 (1976).
[CrossRef]

J. L. Gras, C. G. Michael, “Measurements of the stratospheric aerosol particle size distribution,” J. Appl. Meteorol. 18, 855–860 (1979).
[CrossRef]

J. Assoc. Comput. Mach. (1)

S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
[CrossRef]

J. Atmos. Sci. (3)

R. G. Pinnick, J. M. Rosen, D. J. Hofmann, “Stratospheric aerosol measurements. 3. Optical model calculations,” J. Atmos. Sci. 33, 304–314 (1976).
[CrossRef]

R. P. Turco, P. Hamill, O. B. Toon, R. C. Whitten, C. S. Kiang, “A one-dimensional model describing aerosol formation and evolution in the stratosphere,” J. Atmos. Sci. 36, 699–736 (1979).
[CrossRef]

J. M. Rosen, D. J. Hofmann, S. P. Singh, “A steady state stratospheric aerosol model,” J. Atmos. Sci. 35, 1304–1313 (1978).
[CrossRef]

J. Clim. Appl. Meteorol. (1)

J. Lenoble, P. Pruvost, “Inference of the aerosol Angstrom coefficient from SAGE short-wavelength data,” J. Clim. Appl. Meteorol. 22, 1717–1725 (1983).
[CrossRef]

J. Geophys. Res. (15)

G. M. Grechko, N. F. Elansky, M. E. Plotkin, O. V. Postylyakov, “The Ozone and Aerosol Fine Structure Experiment: observing the fine structure of ozone and aerosol distribution in the atmosphere from the Salyut 7 orbiter,” J. Geophys. Res. 96, 18647–18653 (1991).
[CrossRef]

M. J. Newchurch, D. M. Cunnold, “Aerosol effects on Umkehr ozone profiles using Stratospheric Aerosol and Gas Experiment II measurements,” J. Geophys. Res. 99, 1383–1388 (1994).
[CrossRef]

H. M. Steele, R. P. Turco, “Separation of aerosol and gas components in the Halogen Occultation Experiment and the Stratospheric Aerosol and Gas Experiment II extinction measurements: implications for SAGE II ozone concentration and trends,” J. Geophys. Res. 102, 19665–19681 (1997).
[CrossRef]

D. W. Rusch, C. E. Randall, M. T. Callan, M. Horanyi, R. T. Clancy, S. C. Solomon, S. J. Oltmans, B. J. Johnson, U. Koehler, H. Claude, D. De Muer, “A new inversion for Stratospheric Aerosol and Gas Experiment II data,” J. Geophys. Res. 103, 8465–8475 (1998).
[CrossRef]

D. Fussen, “A critical analysis of the Stratospheric Aerosol and Gas Experiment II spectral inversion algorithm,” J. Geophys. Res. 103, 8455–8464 (1998).
[CrossRef]

M. E. Hervig, J. M. Russell, L. L. Gordley, J. Daniels, S. R. Drayson, J. H. Park, “Aerosol effects and corrections in the Halogen Occultation Experiment,” J. Geophys. Res. 100, 1067–1079 (1995).
[CrossRef]

M. E. Hervig, T. Deshler, J. M. Russell, “Aerosol size distribution obtained from HALOE spectral extinction measurements,” J. Geophys. Res. 103, 1573–1583 (1998).
[CrossRef]

J. D. Lumpe, R. M. Bevilacqua, K. W. Hoppel, S. S. Krigman, D. L. Kriebel, D. J. Debrestian, C. E. Randall, D. W. Rusch, C. Brogniez, R. Ramananahérisoa, E. P. Shettle, J. J. Olivera, J. Lenoble, P. Pruvost, “POAM II retrieval algorithm and error analysis,” J. Geophys. Res. 102, 23593–23614 (1997).
[CrossRef]

W. P. Chu, M. P. McCormick, J. Lenoble, C. Brogniez, P. Pruvost, “SAGE II inversion algorithm,” J. Geophys. Res. 94, 8339–8351 (1989).
[CrossRef]

L. W. Thomason, “A diagnostic stratospheric aerosol size distribution inferred from SAGE II measurements,” J. Geophys. Res. 96, 22501–22508 (1991).
[CrossRef]

H. M. Steele, R. P. Turco, “Retrieval of aerosol size distributions from satellite extinction spectra using constrained linear inversion,” J. Geophys. Res. 102, D14, 16737–16747 (1997).
[CrossRef]

A. L. Lazrus, B. W. Gandrud, “Stratospheric sulfate aerosol,” J. Geophys. Res. 79, 3424–3431 (1974).
[CrossRef]

W. Glaccum, R. L. Lucke, R. M. Bevilacqua, E. P. Shettle, J. S. Hornstein, D. T. Chen, J. D. Lumpe, S. S. Krigman, D. J. Debrestian, M. D. Fromm, F. Dalaudier, E. Chassefiere, C. Deniel, C. E. Randall, D. W. Rusch, J. J. Olivero, C. Brogniez, J. Lenoble, R. Kremer, “The polar ozone and aerosol measurement instrument,” J. Geophys. Res. 101, 14479–14487 (1996).
[CrossRef]

A. J. Stevermer, I. V. Petropavlovskikh, J. M. Rosen, J. J. DeLuisi, “Development of a global stratospheric aerosol climatology: optical properties and applications for UV,” J. Geophys. Res. 105, 22763–22776 (2000).
[CrossRef]

J. Anderson, C. Brogniez, L. Cazier, V. K. Saxena, J. Lenoble, M. P. McCormick, “Characterization of aerosols from simulated SAGE III measurements applying two retrieval techniques,” J. Geophys. Res. 105, 2013–2027 (2000).
[CrossRef]

Meteorol. Hydrol. (1)

M. S. Biryulina, “The simulation of a priori ensemble of solutions of inverse problem and the stability of optimal designs of the ozone space experiment,” Meteorol. Hydrol. 4, 45–51 (1981) (in Russian).

Optika Atmosfery i Okena T. (2)

A. V. Vasilyev, L. S. Ivlev, “Universal algorithm for calculating the optical characteristic of two-layer spherical aerosol particles with homogeneous core and coat,” Optika Atmosfery i Okena T. 9, 1552–1561 (1996) (in Russian).

A. V. Vasilyev, L. S. Ivlev, “Empirical models and optical characteristics of aerosol ensembles of two-layer spherical particles,” Optika Atmosfery i Okena T. 10, 856–865 (1997) (in Russian).

Uspekhi Fizicheskikh Nauk (1)

V. F. Turchin, V. P. Kozlov, M. S. Malkevich, “Applying the methods of mathematical statistics for solving ill-posed problems,” Uspekhi Fizicheskikh Nauk 102, 345–386 (1970) (in Russian).
[CrossRef]

Other (15)

C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice (World Scientific, Singapore, 2000).

For more detailed information on SAGE III, see http:/www.sage3.larc.nasa.gov/ .

G. P. Anderson, S. A. Clough, F. X. Kneizys, J. H. Chetwynd, E. P. Shettle, “AFGL atmospheric constituent profiles (0–120 km),” AFGL-TR-86-0110, No. 954 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1986).

These parameters can be found at the National Oceanic and Atmospheric Administration’s Surface Radiation Research Branch at http://www.srrb.noaa.gov/research/aerosol.html .

I. T. Goronovski, Yu. P. Nazarenko, F. E. Hekryach, Short Chemical Handbook (Naukova Dumka, Kiev, Russia, 1974) (in Russian).

A. V. Vasilyev, “Universal algorithm for calculating the optical characteristics of homogeneous spherical aerosol particles. I. Single particles.” Vestnik S-Peterburgskogo Universiteta, Series 4: Physics and Chemistry, 4, 3–11 (1996) (in Russian).

A. V. Vasilyev, “Universal algorithm for calculating the optical characteristics of homogeneous spherical aerosol particles. II. Ensembles of particles. Vestnik S-Peterburgskogo Universiteta, Series 4: Physics and Chemistry1, 14–24 (1997) (in Russian).

S. M. Ermakov, G. A. Mikhailov, Course of Statistical Simulation (Nauka, Moscow, 1976) (in Russian).

V. E. Zuev, G. M. Krekov, Current Problems of Atmospheric Optics, Vol. 2 of Optical Models of the Atmosphere (Gidrometeoizdat, Leningrad, 1986) (in Russian).

E. P. Shettle, U.S. Naval Research Laboratory Washington, D.C. (personal communication, 2000).

L. S. Ivlev, S. D. Andreev, Optical Properties of Atmospheric Aerosols (Leningrad, Leningrad State University, 1986) (in Russian).

G. A. d’Almeida, P. Koepke, E. Shettle, Atmospheric Aerosols: Global Climatology and Radiative Characteristics (Deepak, Hampton, Va., 1991).

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977).

G. M. Krekov, S. G. Zvenigorodski, Optical Model of Middle Atmosphere (Nauka, Novosibirsk, Russia, 1990) (in Russian).

K. Ya. Kondratyev, Actinometry (Gidrometeoizdat, Leningrad, 1965).

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Figures (7)

Fig. 1
Fig. 1

First seven eigenvectors derived from the logarithm of the extinction spectra comprising the main data set.

Fig. 2
Fig. 2

(a) Spectral dependence of the relative error in the parameterization for different numbers of eigenvectors used in the approximation for one example simulation (simulation 24 at an altitude of 48 km). (b) The spectral dependence of the relative error in the parameterization for different numbers of eigenvectors used in the approximation for one example simulation (simulation 2 at an altitude of 17 km).

Fig. 3
Fig. 3

Spectral dependence of the rms relative error for the main data set that is due to the logarithmic parameterization for different numbers of eigenvectors used in the approximation.

Fig. 4
Fig. 4

Spectral dependence of the aerosol extinction for the main and independent data sets. The vertical bars show the rms deviation for each data set.

Fig. 5
Fig. 5

Spectral dependence of the aerosol extinction for the three worst-case approximations for each of the parameterizations. The curves are labeled with the simulation number, altitude, and rms error.

Fig. 6
Fig. 6

Example of a spectrum and its approximation by the optimal eigenanalysis method for a case in which the approximation error is large. Note the abrupt change in slope of the spectrum at 0.6 μm.

Fig. 7
Fig. 7

Example of a spectrum and its approximation by the quadratic method for a case in which the approximation error is large. Note the changes in slope of the spectrum between 0.4 and 0.6 μm.

Tables (4)

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Table 1 Some of the Parameters Employed to Model the Aerosols and the Standard Deviation in Them

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Table 2 Eigenvalues of the Covariance Matrices Kβ and Kβ L

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Table 3 Dependence of the Absolute and Relative rms Errors of the Aerosol Extinction Approximation on the Number of Approximation Parameters

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Table 4 Statistical Characteristics of the Errors of Parameterizationsa

Equations (20)

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Pλ, S=Iλ, SI0λ,
Pλ, S=exp-Si=1,Ng ρizsKiλ, Tzs,×pzs+βaλ, zs+βRλ, zsds.
βazλ=j0 πr2Qjmj, r, λfjrdr.
fr=N exp-ln2r/rg/2 ln2 σr2πln σ,
ln βaλ, z=μ0z+μ1zln λ+μ2zln λ2,
βaλ5=i=1,4 αiβaλi,
mλ=i=1N pimiλi=1N pi.
fr=Nrbrgb+1ln σ2πexpln2 σ2b+12×exp-ln2r/rg2 ln2 σ.
covXzi, zj=σXziσXzjexp-|zi-zj|/rC,
r/rc=1+CQ1/3,
β˜¯λi=Eβ˜λi1500149s=1,500j=1,49 β˜s,jλi,
ln¯ β˜λi=Eln β˜λi1500149s=1,500j=1,49ln β˜s,jλi.
Kβ=kβi,ji=1,mj=1,n, n=80, the number of wavelengths)
kβi,j1500×49-1s=1,500r=1,49β˜s,rλi-β˜¯λi×β˜s,rλj-β˜¯λj.
kβi,jL1500×49-1s=1,500r=1,49ln β˜s,rλi-ln¯ β˜λi×ln β˜s,rλj-ln¯ β˜λj.
β˜λiβ˜¯λi+p=1,n apfpλi,
ln β˜λiln¯ β˜λi+p=1,n apLfpLλi.
ap=i=180 β˜λifpλi,
apL=i=180ln β˜λifpLλi.
dm=α=1,m eαα=1,n eα,

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