Abstract

The software code skypad.pack for retrieval of aerosol size distribution and optical thickness from data of direct and diffuse solar radiation is described; measurements are carried out with sky radiometers in the wavelength range 0.369–1.048 μm. The treatment of the radiative transfer problem concerning the optical quantities is mainly based on the IMS (improved multiple and single scattering) method, which uses the delta-M approximation for the truncation of the aerosol phase function and corrects the solution for the first- and second-order scattering. Both linear and nonlinear inversion methods can be used for retrieving the size distribution. Improved calibration methods for both direct and diffuse radiation, the data-analysis procedure, the results from the proposed code, and several connected problems are discussed. The results can be summarized as follows: (a) the skypad.pack code can retrieve the columnar aerosol features with accuracy and efficiency in several environmental situations, provided the input parameters are correctly given; (b) when data of both direct and diffuse solar radiation are used, the detectable radius interval for aerosol particles is approximately from 0.03 to 10 μm; (c) besides the retrieval of the aerosol features, the data-analysis procedure also permits the determination of average values for three input parameters (real and imaginary aerosol refractive index, ground albedo) from the optical data; (d) absolute calibrations for the sky radiometer are not needed, and calibrations for direct and diffuse radiation can be carried out with field data; (e) the nonlinear inversion gives satisfactory results in a larger radius interval, without the unrealistic humps that occur with the linear inversion, but the results strongly depend on the first-guess spectrum; (f) aerosol features retrieved from simulated data showed a better agreement with the given data for the linear inversion than for the nonlinear inversion.

© 1996 Optical Society of America

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1995

G. Dalu, R. Rao, A. Pompei, P. Boi, G. Tonna, B. Olivieri, “Aerosol optical properties retrieved from solar aureole measurements over Southern Sardinia,” J. Geophys. Res. 100, 864–871 (1995).
[CrossRef]

G. Tonna, T. Nakajima, R. Rao, “Aerosol features retrieved from solar aureole data: a simulation study concerning a turbid atmosphere,” Appl. Opt. 34, 4486–4499 (1995).
[CrossRef] [PubMed]

1994

M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994).
[CrossRef] [PubMed]

M. Shiobara, S. Asano, “Estimation of cirrus optical thickness from sun photometer measurements,” J. Appl. Meteorol. 33, 672–681 (1994).
[CrossRef]

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10341–10356 (1994).
[CrossRef]

1993

Y. J. Kaufman, “Aerosol optical thickness and atmospheric path radiance,” J. Geophys. Res. 98, 2677–2692 (1993).
[CrossRef]

1992

J. A. Reagan, K. J. Thome, B. M. Herman, “A simple instrument and technique for measuring columnar water vapor via near-IR differential solar transmission measurements,” IEEE Trans. Geosci. Remote Sensing 30, 825–831 (1992).
[CrossRef]

1991

M. Shiobara, T. Hayasaka, T. Nakajima, M. Tanaka, “Aerosol monitoring using a scanning spectral radiometer in Sendai, Japan,” J. Meteorol. Soc. Jpn. 69, 57–70 (1991).

K. Krishna Moorthy, P. R. Nair, B. V. Krishna Murthy, “Size distribution of coastal aerosols: effects of local sources and sinks,” J. Appl. Meteorol. 30, 844–852 (1991).
[CrossRef]

1990

M. Tanaka, T. Hayasada, T. Nakajima, “Airborne measurements of optical properties of tropospheric aerosols over an urban area,” J. Meteorol. Soc. Jpn. 68, 335–344 (1990).

T. Hayasaka, T. Nakajima, M. Tanaka, “The coarse particle aerosols in the free troposphere around Japan,” J. Geophys. Res. 95, 14,039–14,047 (1990).
[CrossRef]

1989

G. Zibordi, K. J. Voss, “Geometrical and spectral distribution of sky radiance: comparison between simulations and field measurements,” Remote Sensing Environ. 27, 343–358 (1989).
[CrossRef]

K. J. Voss, G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic ‘fisheye’ camera radiance distribution system,” J. Atmos. Ocean Technol. 6, 652–662 (1989).
[CrossRef]

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May, 1982 in Nagasaki—Part II, models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

H. Ogawa, M. Tanaka, T. Nakajima, “A simple expression for the additional sky radiance produced by polarization effects,” J. Meteorol. Soc. Jpn. 67, 877–888 (1989).

A. Mugnai, W. J. Wiscombe, “Scattering from nonspherical Chebyshev particles. 3: variability in angular scattering patterns,” Appl. Opt. 28, 3061–3073 (1989).
[CrossRef] [PubMed]

1988

G. Hänel, “Single scattering albedo, asymmetry parameter, apparent refractive index, and apparent soot content of dry atmospheric particles,” Appl. Opt. 27, 2287–2295 (1988).
[CrossRef] [PubMed]

K. Arao, M. Tanaka, “Photometric and colorimetric properties of the solar aureole,” J. Meteorol. Soc. Jpn. 66, 167–177 (1988).

T. Nakajima, M. Tanaka, “Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation,” J. Quant. Spectrosc. Radiat. Transfer 40, 51–69 (1988).
[CrossRef]

D. Tanré, C. Devaux, M. Herman, R. Santer, “Radiative properties of desert aerosols by optical ground-based measurements at solar wavelengths,” J. Geophys. Res. 93, 14223–14231 (1988).
[CrossRef]

1986

1985

1984

1983

1982

1981

K. Stamnes, H. Dale, “A new look at the discrete ordinate method for radiative transfer calculations in anisotropically scattering atmospheres. II: intensity computations,” J. Atmos. Sci. 38, 2696–2706 (1981).
[CrossRef]

M. A. Box, A. Deepak, “An approximation to multiple scattering in the Earth’s atmosphere: almucantar radiance formulation,” J. Atmos. Sci. 38, 1037–1048 (1981).
[CrossRef]

1980

S. Asano, M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
[CrossRef] [PubMed]

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[CrossRef] [PubMed]

J. B. Pollack, J. N. Cuzzi, “Scattering by nonspherical particles of size comparable to a wavelength: a new semi-empirical theory and its application to tropospheric aerosols,” J. Atmos. Sci. 37, 868–881 (1980).
[CrossRef]

1979

M. D. King, B. M. Herman, “Determination of the ground albedo and the index of absorption of atmospheric particulates by remote sensing. Part I: theory,” J. Atmos. Sci. 36, 163–173 (1979).
[CrossRef]

M. D. King, “Determination of the ground albedo and the index of absorption of atmospheric particulates by remote sensing. Part II: application,” J. Atmos. Sci. 36, 1072–1083 (1979).
[CrossRef]

G. E. Shaw, “Inversion of optical scattering and spectral extinction measurements to recover aerosol size spectra,” Appl. Opt. 18, 988–993 (1979).
[CrossRef] [PubMed]

M. A. Box, A. Deepak, “Atmospheric scattering corrections to solar radiometry,” Appl. Opt. 18, 1941–1949 (1979).
[CrossRef] [PubMed]

1978

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]

M. A. Box, A. Deepak, “Single and multiple scattering contributions to circumsolar radiation,” Appl. Opt. 17, 3794–3797 (1978).
[CrossRef] [PubMed]

1977

W. J. Wiscombe, “The delta-M method: Rapid yet accurate radiative flux calculations for strongly asymmetric phase functions,” J. Atmos. Sci. 34, 1408–1422 (1977).
[CrossRef]

1976

G. E. Shaw, “Error analysis of multi-wavelength sun photometry,” Pure Appl. Geophys. 114, 1–14 (1976).
[CrossRef]

1975

J. A. Weinman, J. T. Twitty, S. R. Browning, B. M. Herman, “Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere,” J. Atmos. Sci. 32, 577–583 (1975).
[CrossRef]

1974

1971

M. Tanaka, “Radiative transfer in turbid atmospheres. II. Angular distribution of intensity of the solar radiation diffusely reflected and transmitted by turbid atmospheres,” J. Meteorol. Soc. Jpn. 49, 321–332 (1971).

1967

Arao, K.

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May, 1982 in Nagasaki—Part II, models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

K. Arao, M. Tanaka, “Photometric and colorimetric properties of the solar aureole,” J. Meteorol. Soc. Jpn. 66, 167–177 (1988).

K. Arao, M. Tanaka, “Dependence of the solar aureole upon the optical properties of aerosols and albedo of the ground surface,” J. Meteorol. Soc. Jpn. 64, 743–753 (1986).

Asano, S.

M. Shiobara, S. Asano, “Estimation of cirrus optical thickness from sun photometer measurements,” J. Appl. Meteorol. 33, 672–681 (1994).
[CrossRef]

S. Asano, M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
[CrossRef] [PubMed]

Boi, P.

G. Dalu, R. Rao, A. Pompei, P. Boi, G. Tonna, B. Olivieri, “Aerosol optical properties retrieved from solar aureole measurements over Southern Sardinia,” J. Geophys. Res. 100, 864–871 (1995).
[CrossRef]

Box, M. A.

M. A. Box, A. Deepak, “An approximation to multiple scattering in the Earth’s atmosphere: almucantar radiance formulation,” J. Atmos. Sci. 38, 1037–1048 (1981).
[CrossRef]

M. A. Box, A. Deepak, “Atmospheric scattering corrections to solar radiometry,” Appl. Opt. 18, 1941–1949 (1979).
[CrossRef] [PubMed]

M. A. Box, A. Deepak, “Single and multiple scattering contributions to circumsolar radiation,” Appl. Opt. 17, 3794–3797 (1978).
[CrossRef] [PubMed]

M. A. Box, G. Viera, “Information content of aerosol remote sensing experiments: scattering versus extinction,” in Proceedings of the International Radiation Symposium 1988, J. Lenoble, J. F. Geleyn, eds. (Deepak, Hampton, Va., 1989), p. 579.

Browning, S. R.

J. A. Weinman, J. T. Twitty, S. R. Browning, B. M. Herman, “Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere,” J. Atmos. Sci. 32, 577–583 (1975).
[CrossRef]

Buiss, J. P.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buiss, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, “Multiband authomatic sun and sky scanning radiometer system for measurement of aerosol,” Remote Sensing Environ. (to be published).

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]

Cabot, F.

F. Cabot, G. Dedieu, P. M. Maisongrande, “Surface albedo from space over Hapex Sahel sites,” in Proceedings of the 6th AVHRR Data Users’ Meeting (European Organization for the Exploitation of Meteorological Satellites, Darmstadt, Germany, 1993), p. 51.

Caroli, E.

C. Tomasi, E. Caroli, V. Vitale, “Study of the relationship between Ångström’s wavelength exponent and Junge particle size distribution exponent,” J. Climate Appl. Meteorol. 22, 1707–1716 (1983).
[CrossRef]

Cesari, G.

Cuzzi, J. N.

J. B. Pollack, J. N. Cuzzi, “Scattering by nonspherical particles of size comparable to a wavelength: a new semi-empirical theory and its application to tropospheric aerosols,” J. Atmos. Sci. 37, 868–881 (1980).
[CrossRef]

Dale, H.

K. Stamnes, H. Dale, “A new look at the discrete ordinate method for radiative transfer calculations in anisotropically scattering atmospheres. II: intensity computations,” J. Atmos. Sci. 38, 2696–2706 (1981).
[CrossRef]

Dalu, G.

G. Dalu, R. Rao, A. Pompei, P. Boi, G. Tonna, B. Olivieri, “Aerosol optical properties retrieved from solar aureole measurements over Southern Sardinia,” J. Geophys. Res. 100, 864–871 (1995).
[CrossRef]

Dedieu, G.

F. Cabot, G. Dedieu, P. M. Maisongrande, “Surface albedo from space over Hapex Sahel sites,” in Proceedings of the 6th AVHRR Data Users’ Meeting (European Organization for the Exploitation of Meteorological Satellites, Darmstadt, Germany, 1993), p. 51.

Deepak, A.

Devaux, C.

D. Tanré, C. Devaux, M. Herman, R. Santer, “Radiative properties of desert aerosols by optical ground-based measurements at solar wavelengths,” J. Geophys. Res. 93, 14223–14231 (1988).
[CrossRef]

Eck, T. F.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buiss, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, “Multiband authomatic sun and sky scanning radiometer system for measurement of aerosol,” Remote Sensing Environ. (to be published).

Fenn, R. W.

E. P. Shettle, R. W. Fenn, “Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties,” AFGL Rep. TR-79-0214 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1979), p. 94.

Fraser, R. S.

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10341–10356 (1994).
[CrossRef]

Ganor, E.

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10341–10356 (1994).
[CrossRef]

Gitelson, A.

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10341–10356 (1994).
[CrossRef]

Y. J. Kaufman, B. N. Holben, L. Remer, A. Gitelson, A. Karnieli, T. Nakajima, “Measurements of the ambient aerosol backscattering fraction,” in Abstracts of the Fourth International Aerosol Conference, UCLA (University of California, Los Angeles, Calif., 1994).

Guzzi, R.

Hänel, G.

Hashida, G.

T. Nakajima, T. Hayasaka, A. Higurashi, G. Hashida, N. Moharram-Nejad, Y. Najafi, H. Valavi, “ Aerosol optical properties in the Iranian region obtained by ground-based solar radiation measurements in the Summer of 1991,” J. Appl. Meteorol. (to be published).

Hayasada, T.

M. Tanaka, T. Hayasada, T. Nakajima, “Airborne measurements of optical properties of tropospheric aerosols over an urban area,” J. Meteorol. Soc. Jpn. 68, 335–344 (1990).

Hayasaka, T.

M. Shiobara, T. Hayasaka, T. Nakajima, M. Tanaka, “Aerosol monitoring using a scanning spectral radiometer in Sendai, Japan,” J. Meteorol. Soc. Jpn. 69, 57–70 (1991).

T. Hayasaka, T. Nakajima, M. Tanaka, “The coarse particle aerosols in the free troposphere around Japan,” J. Geophys. Res. 95, 14,039–14,047 (1990).
[CrossRef]

T. Nakajima, M. Tanaka, T. Hayasaka, Y. Miyake, Y. Nakanishi, K. Sasamoto, “Airborne measurements of the optical stratification of aerosols in turbid atmospheres,” Appl. Opt. 25, 4374–4381 (1986).
[CrossRef] [PubMed]

T. Nakajima, T. Hayasaka, A. Higurashi, G. Hashida, N. Moharram-Nejad, Y. Najafi, H. Valavi, “ Aerosol optical properties in the Iranian region obtained by ground-based solar radiation measurements in the Summer of 1991,” J. Appl. Meteorol. (to be published).

Heintzenberg, J.

Herman, B. M.

J. A. Reagan, K. J. Thome, B. M. Herman, “A simple instrument and technique for measuring columnar water vapor via near-IR differential solar transmission measurements,” IEEE Trans. Geosci. Remote Sensing 30, 825–831 (1992).
[CrossRef]

M. D. King, B. M. Herman, “Determination of the ground albedo and the index of absorption of atmospheric particulates by remote sensing. Part I: theory,” J. Atmos. Sci. 36, 163–173 (1979).
[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. A. Weinman, J. T. Twitty, S. R. Browning, B. M. Herman, “Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere,” J. Atmos. Sci. 32, 577–583 (1975).
[CrossRef]

Herman, M.

D. Tanré, C. Devaux, M. Herman, R. Santer, “Radiative properties of desert aerosols by optical ground-based measurements at solar wavelengths,” J. Geophys. Res. 93, 14223–14231 (1988).
[CrossRef]

Higurashi, A.

T. Nakajima, T. Hayasaka, A. Higurashi, G. Hashida, N. Moharram-Nejad, Y. Najafi, H. Valavi, “ Aerosol optical properties in the Iranian region obtained by ground-based solar radiation measurements in the Summer of 1991,” J. Appl. Meteorol. (to be published).

Hitzenberger, R.

Holben, B. N.

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10341–10356 (1994).
[CrossRef]

Y. J. Kaufman, B. N. Holben, L. Remer, A. Gitelson, A. Karnieli, T. Nakajima, “Measurements of the ambient aerosol backscattering fraction,” in Abstracts of the Fourth International Aerosol Conference, UCLA (University of California, Los Angeles, Calif., 1994).

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buiss, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, “Multiband authomatic sun and sky scanning radiometer system for measurement of aerosol,” Remote Sensing Environ. (to be published).

Howell, H. B.

Karnieli, A.

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10341–10356 (1994).
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Y. J. Kaufman, B. N. Holben, L. Remer, A. Gitelson, A. Karnieli, T. Nakajima, “Measurements of the ambient aerosol backscattering fraction,” in Abstracts of the Fourth International Aerosol Conference, UCLA (University of California, Los Angeles, Calif., 1994).

Kaufman, Y. J.

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10341–10356 (1994).
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Y. J. Kaufman, B. N. Holben, L. Remer, A. Gitelson, A. Karnieli, T. Nakajima, “Measurements of the ambient aerosol backscattering fraction,” in Abstracts of the Fourth International Aerosol Conference, UCLA (University of California, Los Angeles, Calif., 1994).

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M. D. King, B. M. Herman, “Determination of the ground albedo and the index of absorption of atmospheric particulates by remote sensing. Part I: theory,” J. Atmos. Sci. 36, 163–173 (1979).
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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).
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H. Kremser, P. Koepke, H. Quenzel, “Aerosol optical thickness from direct solar radiation improved Langley method applied to measured data,” in Proceedings of the International Radiation Symposium 1984: Current Problems in Atmospheric Radiation, G. Fiocco, ed. (Deepak, Hampton, Va., 1984), p. 46.

Kremser, H.

H. Kremser, P. Koepke, H. Quenzel, “Aerosol optical thickness from direct solar radiation improved Langley method applied to measured data,” in Proceedings of the International Radiation Symposium 1984: Current Problems in Atmospheric Radiation, G. Fiocco, ed. (Deepak, Hampton, Va., 1984), p. 46.

Krishna Moorthy, K.

K. Krishna Moorthy, P. R. Nair, B. V. Krishna Murthy, “Size distribution of coastal aerosols: effects of local sources and sinks,” J. Appl. Meteorol. 30, 844–852 (1991).
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Krishna Murthy, B. V.

K. Krishna Moorthy, P. R. Nair, B. V. Krishna Murthy, “Size distribution of coastal aerosols: effects of local sources and sinks,” J. Appl. Meteorol. 30, 844–852 (1991).
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Mattoo, S.

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10341–10356 (1994).
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Miller, J. R.

Mishchenko, M. I.

Miyake, Y.

Moharram-Nejad, N.

T. Nakajima, T. Hayasaka, A. Higurashi, G. Hashida, N. Moharram-Nejad, Y. Najafi, H. Valavi, “ Aerosol optical properties in the Iranian region obtained by ground-based solar radiation measurements in the Summer of 1991,” J. Appl. Meteorol. (to be published).

Mugnai, A.

Nair, P. R.

K. Krishna Moorthy, P. R. Nair, B. V. Krishna Murthy, “Size distribution of coastal aerosols: effects of local sources and sinks,” J. Appl. Meteorol. 30, 844–852 (1991).
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T. Nakajima, T. Hayasaka, A. Higurashi, G. Hashida, N. Moharram-Nejad, Y. Najafi, H. Valavi, “ Aerosol optical properties in the Iranian region obtained by ground-based solar radiation measurements in the Summer of 1991,” J. Appl. Meteorol. (to be published).

Nakajima, T.

G. Tonna, T. Nakajima, R. Rao, “Aerosol features retrieved from solar aureole data: a simulation study concerning a turbid atmosphere,” Appl. Opt. 34, 4486–4499 (1995).
[CrossRef] [PubMed]

Y. J. Kaufman, A. Gitelson, A. Karnieli, E. Ganor, R. S. Fraser, T. Nakajima, S. Mattoo, B. N. Holben, “Size distribution and scattering phase function of aerosol particles retrieved from sky brightness measurements,” J. Geophys. Res. 99, 10341–10356 (1994).
[CrossRef]

M. Shiobara, T. Hayasaka, T. Nakajima, M. Tanaka, “Aerosol monitoring using a scanning spectral radiometer in Sendai, Japan,” J. Meteorol. Soc. Jpn. 69, 57–70 (1991).

T. Hayasaka, T. Nakajima, M. Tanaka, “The coarse particle aerosols in the free troposphere around Japan,” J. Geophys. Res. 95, 14,039–14,047 (1990).
[CrossRef]

M. Tanaka, T. Hayasada, T. Nakajima, “Airborne measurements of optical properties of tropospheric aerosols over an urban area,” J. Meteorol. Soc. Jpn. 68, 335–344 (1990).

H. Ogawa, M. Tanaka, T. Nakajima, “A simple expression for the additional sky radiance produced by polarization effects,” J. Meteorol. Soc. Jpn. 67, 877–888 (1989).

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May, 1982 in Nagasaki—Part II, models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

T. Nakajima, M. Tanaka, “Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation,” J. Quant. Spectrosc. Radiat. Transfer 40, 51–69 (1988).
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T. Nakajima, M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 35, 13–21 (1986).
[CrossRef]

M. Tanaka, T. Nakajima, M. Shiobara, “Calibration of a sunphotometer by simultaneous measurements of direct-solar and circumsolar radiations,” Appl. Opt. 25, 1170–1176 (1986).
[CrossRef] [PubMed]

T. Nakajima, M. Tanaka, T. Hayasaka, Y. Miyake, Y. Nakanishi, K. Sasamoto, “Airborne measurements of the optical stratification of aerosols in turbid atmospheres,” Appl. Opt. 25, 4374–4381 (1986).
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T. Nakajima, M. Tanaka, T. Yamauchi, “Retrieval of the optical properties of aerosols from aureole and extinction data,” Appl. Opt. 22, 2951–2959 (1983).
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M. Tanaka, T. Nakajima, T. Takamura, “Simultaneous determination of complex refractive index and size distribution of airborne and water-suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60, 1259–1272 (1982).

Y. J. Kaufman, B. N. Holben, L. Remer, A. Gitelson, A. Karnieli, T. Nakajima, “Measurements of the ambient aerosol backscattering fraction,” in Abstracts of the Fourth International Aerosol Conference, UCLA (University of California, Los Angeles, Calif., 1994).

T. Nakajima, T. Hayasaka, A. Higurashi, G. Hashida, N. Moharram-Nejad, Y. Najafi, H. Valavi, “ Aerosol optical properties in the Iranian region obtained by ground-based solar radiation measurements in the Summer of 1991,” J. Appl. Meteorol. (to be published).

Nakanishi, Y.

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May, 1982 in Nagasaki—Part II, models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

T. Nakajima, M. Tanaka, T. Hayasaka, Y. Miyake, Y. Nakanishi, K. Sasamoto, “Airborne measurements of the optical stratification of aerosols in turbid atmospheres,” Appl. Opt. 25, 4374–4381 (1986).
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Ogawa, H.

H. Ogawa, M. Tanaka, T. Nakajima, “A simple expression for the additional sky radiance produced by polarization effects,” J. Meteorol. Soc. Jpn. 67, 877–888 (1989).

Olivieri, B.

G. Dalu, R. Rao, A. Pompei, P. Boi, G. Tonna, B. Olivieri, “Aerosol optical properties retrieved from solar aureole measurements over Southern Sardinia,” J. Geophys. Res. 100, 864–871 (1995).
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G. Dalu, R. Rao, A. Pompei, P. Boi, G. Tonna, B. Olivieri, “Aerosol optical properties retrieved from solar aureole measurements over Southern Sardinia,” J. Geophys. Res. 100, 864–871 (1995).
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Rao, R.

G. Dalu, R. Rao, A. Pompei, P. Boi, G. Tonna, B. Olivieri, “Aerosol optical properties retrieved from solar aureole measurements over Southern Sardinia,” J. Geophys. Res. 100, 864–871 (1995).
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G. Tonna, T. Nakajima, R. Rao, “Aerosol features retrieved from solar aureole data: a simulation study concerning a turbid atmosphere,” Appl. Opt. 34, 4486–4499 (1995).
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Reagan, J. A.

J. A. Reagan, K. J. Thome, B. M. Herman, “A simple instrument and technique for measuring columnar water vapor via near-IR differential solar transmission measurements,” IEEE Trans. Geosci. Remote Sensing 30, 825–831 (1992).
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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]

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buiss, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, “Multiband authomatic sun and sky scanning radiometer system for measurement of aerosol,” Remote Sensing Environ. (to be published).

Remer, L.

Y. J. Kaufman, B. N. Holben, L. Remer, A. Gitelson, A. Karnieli, T. Nakajima, “Measurements of the ambient aerosol backscattering fraction,” in Abstracts of the Fourth International Aerosol Conference, UCLA (University of California, Los Angeles, Calif., 1994).

Rizzi, R.

Santer, R.

D. Tanré, C. Devaux, M. Herman, R. Santer, “Radiative properties of desert aerosols by optical ground-based measurements at solar wavelengths,” J. Geophys. Res. 93, 14223–14231 (1988).
[CrossRef]

Sasamoto, K.

Sato, M.

Sentimenti, M.

Setzer, A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buiss, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, “Multiband authomatic sun and sky scanning radiometer system for measurement of aerosol,” Remote Sensing Environ. (to be published).

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Shettle, E. P.

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M. Shiobara, S. Asano, “Estimation of cirrus optical thickness from sun photometer measurements,” J. Appl. Meteorol. 33, 672–681 (1994).
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M. Shiobara, T. Hayasaka, T. Nakajima, M. Tanaka, “Aerosol monitoring using a scanning spectral radiometer in Sendai, Japan,” J. Meteorol. Soc. Jpn. 69, 57–70 (1991).

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May, 1982 in Nagasaki—Part II, models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

M. Tanaka, T. Nakajima, M. Shiobara, “Calibration of a sunphotometer by simultaneous measurements of direct-solar and circumsolar radiations,” Appl. Opt. 25, 1170–1176 (1986).
[CrossRef] [PubMed]

Slutsker, I.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buiss, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, “Multiband authomatic sun and sky scanning radiometer system for measurement of aerosol,” Remote Sensing Environ. (to be published).

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M. Tanaka, T. Nakajima, T. Takamura, “Simultaneous determination of complex refractive index and size distribution of airborne and water-suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60, 1259–1272 (1982).

Tanaka, M.

M. Shiobara, T. Hayasaka, T. Nakajima, M. Tanaka, “Aerosol monitoring using a scanning spectral radiometer in Sendai, Japan,” J. Meteorol. Soc. Jpn. 69, 57–70 (1991).

M. Tanaka, T. Hayasada, T. Nakajima, “Airborne measurements of optical properties of tropospheric aerosols over an urban area,” J. Meteorol. Soc. Jpn. 68, 335–344 (1990).

T. Hayasaka, T. Nakajima, M. Tanaka, “The coarse particle aerosols in the free troposphere around Japan,” J. Geophys. Res. 95, 14,039–14,047 (1990).
[CrossRef]

T. Nakajima, M. Tanaka, M. Yamano, M. Shiobara, K. Arao, Y. Nakanishi, “Aerosol optical characteristics in the yellow sand events observed in May, 1982 in Nagasaki—Part II, models,” J. Meteorol. Soc. Jpn. 67, 279–291 (1989).

H. Ogawa, M. Tanaka, T. Nakajima, “A simple expression for the additional sky radiance produced by polarization effects,” J. Meteorol. Soc. Jpn. 67, 877–888 (1989).

K. Arao, M. Tanaka, “Photometric and colorimetric properties of the solar aureole,” J. Meteorol. Soc. Jpn. 66, 167–177 (1988).

T. Nakajima, M. Tanaka, “Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation,” J. Quant. Spectrosc. Radiat. Transfer 40, 51–69 (1988).
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K. Arao, M. Tanaka, “Dependence of the solar aureole upon the optical properties of aerosols and albedo of the ground surface,” J. Meteorol. Soc. Jpn. 64, 743–753 (1986).

T. Nakajima, M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 35, 13–21 (1986).
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T. Nakajima, M. Tanaka, T. Hayasaka, Y. Miyake, Y. Nakanishi, K. Sasamoto, “Airborne measurements of the optical stratification of aerosols in turbid atmospheres,” Appl. Opt. 25, 4374–4381 (1986).
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T. Nakajima, M. Tanaka, T. Yamauchi, “Retrieval of the optical properties of aerosols from aureole and extinction data,” Appl. Opt. 22, 2951–2959 (1983).
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M. Tanaka, T. Nakajima, T. Takamura, “Simultaneous determination of complex refractive index and size distribution of airborne and water-suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60, 1259–1272 (1982).

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B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buiss, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, “Multiband authomatic sun and sky scanning radiometer system for measurement of aerosol,” Remote Sensing Environ. (to be published).

Thomalla, E.

Thome, K. J.

J. A. Reagan, K. J. Thome, B. M. Herman, “A simple instrument and technique for measuring columnar water vapor via near-IR differential solar transmission measurements,” IEEE Trans. Geosci. Remote Sensing 30, 825–831 (1992).
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Tonna, G.

G. Dalu, R. Rao, A. Pompei, P. Boi, G. Tonna, B. Olivieri, “Aerosol optical properties retrieved from solar aureole measurements over Southern Sardinia,” J. Geophys. Res. 100, 864–871 (1995).
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G. Tonna, T. Nakajima, R. Rao, “Aerosol features retrieved from solar aureole data: a simulation study concerning a turbid atmosphere,” Appl. Opt. 34, 4486–4499 (1995).
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Travis, L. D.

Twitty, J. T.

J. A. Weinman, J. T. Twitty, S. R. Browning, B. M. Herman, “Derivation of phase functions from multiply scattered sunlight transmitted through a hazy atmosphere,” J. Atmos. Sci. 32, 577–583 (1975).
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Valavi, H.

T. Nakajima, T. Hayasaka, A. Higurashi, G. Hashida, N. Moharram-Nejad, Y. Najafi, H. Valavi, “ Aerosol optical properties in the Iranian region obtained by ground-based solar radiation measurements in the Summer of 1991,” J. Appl. Meteorol. (to be published).

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[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Example of dependence of R on Θ, at λ = 0.369, 0.500, and 1.048 μm, and of τ A on λ; on the left-hand side the dotted curves are the SS approximation to R. Data are from a simulation carried out with the skyrad.pack code, concerning the almucantar geometry and the following parameters: θ0 = 30°, τ A (0.5 μm) = 0.2, ground albedo A = 0.20, and aerosol refractive index m ˜ = 1.5–0.01i. The aerosol size distribution was taken from Shettle and Fenn11; the radius interval is from 0.05 to 20 μm.

Fig. 2
Fig. 2

Flow chart of the redml program for inverting data of direct and diffuse solar radiation.

Fig. 3
Fig. 3

Aerosol volume size distributions retrieved with a linear and a nonlinear inversion scheme from the ratios R of Fig. 1 (mode INDM = 2), within the 3° ≤ Θ ≤ 30° interval; at the bottom there is the relative difference between given and retrieved spectra. The inversion was carried out with the skyrad.pack code, assuming a radius interval from 0.05 to 20 μm.

Fig. 4
Fig. 4

Aerosol volume size distributions retrieved with the skyrad.pack code, for modes INDM = 0 and INDM = 2, and the linear inversion method; at the bottom there is the relative difference between given and retrieved spectra. Data are from Fig. 1, with R within the 3° ≤ Θ ≤ 30° interval; a radius interval from 0.05 to 20 μm was assumed.

Fig. 5
Fig. 5

Method solar disk scanning for the determination of the solid view angle of the sky radiometer. Behavior of the response function versus r, from measurements concerning aureolemeter Model Pom-01 L (Prede); λ = 0.500 μm.

Fig. 6
Fig. 6

Left-hand side shows the improved Langley plot; optical thicknesses were derived from R data (INDM = 2), with input parameters m = 1.4, k = 0.01, A = 0.1. The right-hand side shows the normal Langley plot. Experimental data were taken in the center of the Mediterranean Sea, Cagliari, Sardinia, and elaborated with the skyrad.pack code.

Fig. 7
Fig. 7

Aerosol volume distributions derived with the skyrad.pack code from sky measurements by Sun/sky radiometers during the SCAR-A experiment; data are averaged every 5 or 10 measurements. For radius r < 0.3 μm, accumulation mode; 0.3 < r < 0.8 μm, stratospheric aerosol mode; 0.8 < r < 2.5 μm, maritime salt particles mode; r > 2.5 μm, coarse particles mode.

Fig. 8
Fig. 8

Dependence of R(Θ) on m (top), k (middle), and A (bottom). Data are from numerical computations carried out with the skyrad.pack code and refer to an aerosol volume radius distribution by Shettle and Fenn.11

Fig. 9
Fig. 9

Comparison between optical thickness [τ(dir)] derived from Sun photometric data with improved Langley plots and [τ(diff)] derived from diffuse light data; results from all the six standard wavelengths were put together. Experimental data are as in Fig. 6, elaborated with the skyrad.pack code.

Equations (19)

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F = F 0 exp ( - m 0 τ ) ,
E ( θ 0 , ϕ ) E ( Θ ) = F m 0 Δ Ω [ ω τ P ( Θ ) + q ( Θ ) ] ,
R ( Θ ) E ( Θ ) F m o Δ Ω = ω τ P ( Θ ) + q ( Θ ) β ( Θ ) + q ( Θ ) ,
τ A ( λ ) = r m r M π r 2 Q ext ( x , m ˜ ) n ( r ) d r ,
β A ( Θ ) = λ 2 2 π r m r M [ i 1 ( Θ , x , m ˜ ) + i 2 ( Θ , x , m ˜ ) ] n ( r ) d r ,
τ A ( λ ) = ( 2 π / λ ) r m r M K ext ( x , m ˜ ) v ( r ) d ln r , β A ( Θ ) = ( 2 π / λ ) r m r M K ( Θ , x , m ˜ ) v ( r ) d ln r ,
K ext ( x ) = ( 3 4 ) Q ext ( x ) x ,             K ( Θ , x , m ˜ ) = ( 3 2 ) i 1 + i 2 x 3 .
V = V 0 exp ( - m 0 τ ) ,             R ( Θ ) V E ( Θ ) V m 0 Δ Ω = β ( Θ ) + q ( Θ ) .
u 1 ( τ , Ω ) = F 0 μ exp ( - τ / μ ) 0 τ d t ω P ( Ω · Ω 0 ) × exp [ ( 1 / μ - 1 / μ 0 ) t ] ,
u ^ ( τ , Ω ) = - ( 1 - f ω ) ω ^ 2 [ 2 P ^ ( Ω · Ω 0 ) - P ^ 2 ( Ω · Ω 0 ) ] × h ( τ , μ , μ 0 * , μ 0 * ) ,
P ^ 2 ( x ) = 1 4 π n = 0 M ( 2 n + 1 ) g ¯ n 2 P n ( x ) , ω ^ = f ω / ( 1 - f ω ) ,             μ 0 * = μ 0 / ( 1 - f ω ) , h ( τ , μ , μ , μ 0 ) = exp ( - τ / μ ) μ μ 0 τ d t exp [ ( 1 μ - 1 μ ) t ] × 0 t d t exp [ ( 1 μ - 1 μ 0 ) t ] .
β ( n + 1 ) ( Θ ) = [ R meas ( Θ ) / R ( n ) ( Θ ) ] β ( n ) ( Θ ) ;
v ( m + 1 ) ( r i ) = v ( m ) ( r i ) j = 1 N M ( 1 + j m K j i * ) ,             ( i = 1 , , N S ) ,
g = A v ( n ) + ,
v = ( A T A + γ H ) - 1 A T g ,
Δ Ω = E / c L ¯ ,
Δ Ω = π E / r c F .
Δ Ω = Δ A E ( x , y ) d x d y / E ( 0 , 0 ) Δ A f ( x , y ) d x d y ,
d τ τ = 1 m 0 τ d V 0 V 0 ,

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