Abstract

We have designed an airborne spectrometer system for the simultaneous measurement of the direct sun irradiance and the aureole radiance in two different solid angles. The high-resolution spectral radiation measurements are used to derive vertical profiles of aerosol optical properties. Combined measurements in two solid angles provide better information about the aerosol type without additional and elaborate measuring geometries. It is even possible to discriminate between absorbing and nonabsorbing aerosol types. Furthermore, they allow to apply additional calibration methods and simplify the detection of contaminated data (e.g., by thin cirrus clouds). For the characterization of the detected aerosol type a new index is introduced that is the slope of the aerosol phase function in the forward scattering region. The instrumentation is a flexible modular setup, which has already been successfully applied in airborne and ground-based field campaigns. We describe the setup as well as the calibration of the instrument. In addition, example vertical profiles of aerosol optical properties—including the aureole measurements—are shown and discussed.

© 2007 Optical Society of America

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  3. A. Keil and J. M. Haywood, "Solar radiative forcing by biomass burning aerosol particles during SAFARI 2000: a case study based on measured aerosol and cloud properties," J. Geophys. Res. 108, 8467, doi: (2003).
    [CrossRef]
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  5. B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  20. Data can be accessed from the website of the World Ozone and Ultraviolet Radiation Data Centre, http://es-ee.tor.ec.gc.ca/e/ozone/ozoneworld.htm.
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  22. J. Nieke, B. Pflug, and G. Zimmermann, "An aureole-corrected Langley-plot method developed for the calibration of HiRES grating spectrometers," J. Atmos. Sol.-Terr. Phys. 61, 739-722 (1999).
    [CrossRef]
  23. T. Ruhtz and J. Fischer, "Calibration of FUBISS (Free University Berlins Integrated Spectrographic System)," in Proceedings of the Fourth International Airborne Remote Sensing Conference and Exhibition, Vol. II-1 (ERIM International, 1999), Vol. II-1.
  24. R. R. Draxler and G. D. Rolph, "HYSPLIT (HYbrid Single-Particle Lagrangian Integrated Trajectory) Model," NOAA Air Resources Laboratory, 2003, http://www.arl.noaa.gov/ready/hysplit4.html.
  25. Data can be accessed from the website of the Tropospheric Emission Monitoring Internet Service, http://www.temis.nl.

2005 (2)

J. Redemann, B. Schmid, J. A. Eilers, R. Kahn, R. C. Levy, P. B. Russell, J. M. Livingston, P. V. Hobbs, W. L. Smith, and B. N. Holben, "Suborbital measurements of spectral aerosol optical depth and its variability at subsatellite grid scales in support of CLAMS 2001," J. Atmos. Sci. 62, 993-1007 (2005).
[CrossRef]

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

2004 (1)

2003 (1)

A. Keil and J. M. Haywood, "Solar radiative forcing by biomass burning aerosol particles during SAFARI 2000: a case study based on measured aerosol and cloud properties," J. Geophys. Res. 108, 8467, doi: (2003).
[CrossRef]

2002 (2)

Y. J. Kaufman, D. Tanre, and O. Boucher, "A satellite view of aerosols in the climate system," Nature (London) 419, 215-223 (2002).
[CrossRef] [PubMed]

K. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, 2002), Vol. 84.
[CrossRef]

2001 (1)

V. Ramanathan, P. J. Crutzen, J. T. Kiehl, and D. Rosenfeld, "Aerosols, climate and the hydrological cycle," Science 294, 2119-2124 (2001).
[CrossRef] [PubMed]

2000 (1)

O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements," J. Geophys. Res. 105, 673-696 (2000).
[CrossRef]

1999 (3)

B. Bodhaine, N. Wood, E. Dutton, and J. Slusser, "On Rayleigh optical depth calculations," J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
[CrossRef]

J. Nieke, B. Pflug, and G. Zimmermann, "An aureole-corrected Langley-plot method developed for the calibration of HiRES grating spectrometers," J. Atmos. Sol.-Terr. Phys. 61, 739-722 (1999).
[CrossRef]

T. Ruhtz and J. Fischer, "Calibration of FUBISS (Free University Berlins Integrated Spectrographic System)," in Proceedings of the Fourth International Airborne Remote Sensing Conference and Exhibition, Vol. II-1 (ERIM International, 1999), Vol. II-1.

1998 (2)

M. Hess, P. Koepke, and I. Schult, "Optical properties of aerosols and clouds: the software package OPAC," Bull. Am. Meteorol. Soc. 79, 831-844 (1998).
[CrossRef]

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

1995 (1)

1989 (1)

1986 (1)

1983 (2)

T. Nakajima, M. Tanaka, and T. Yamauchi, "Retrieval of the optical properties of aerosols from aureole and extinction data," Appl. Opt. 22, 2951-2959 (1983).
[CrossRef] [PubMed]

L. W. Thomason, B. M. Herman, and J. A. Reagan, "The effect of atmospheric attenuators with structured vertical distributions on air mass determinations and Langley plot analyses," J. Atmos. Sci. 40, 1851-1854 (1983).
[CrossRef]

1980 (1)

1978 (1)

M. King and D. Byrne, "A method for interfering total ozone content from the spectral variation of total optical depth obtained with a solar radiometer," J. Atmos. Sci. 33, 2242-2251 (1978).
[CrossRef]

1964 (1)

K. Bullrich, "Scattered radiation in the atmosphere and the natural aerosol," Adv. Geophys. 10, 99-256 (1964).
[CrossRef]

Asseng, H.

Avery, M. A.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Bevilacqua, R. M.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Bittner, M.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Bodhaine, B.

B. Bodhaine, N. Wood, E. Dutton, and J. Slusser, "On Rayleigh optical depth calculations," J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
[CrossRef]

Boucher, O.

Y. J. Kaufman, D. Tanre, and O. Boucher, "A satellite view of aerosols in the climate system," Nature (London) 419, 215-223 (2002).
[CrossRef] [PubMed]

Browell, E. V.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Buis, J.

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Bullrich, K.

K. Bullrich, "Scattered radiation in the atmosphere and the natural aerosol," Adv. Geophys. 10, 99-256 (1964).
[CrossRef]

Byrne, D.

M. King and D. Byrne, "A method for interfering total ozone content from the spectral variation of total optical depth obtained with a solar radiometer," J. Atmos. Sci. 33, 2242-2251 (1978).
[CrossRef]

Crutzen, P. J.

V. Ramanathan, P. J. Crutzen, J. T. Kiehl, and D. Rosenfeld, "Aerosols, climate and the hydrological cycle," Science 294, 2119-2124 (2001).
[CrossRef] [PubMed]

Draxler, R. R.

R. R. Draxler and G. D. Rolph, "HYSPLIT (HYbrid Single-Particle Lagrangian Integrated Trajectory) Model," NOAA Air Resources Laboratory, 2003, http://www.arl.noaa.gov/ready/hysplit4.html.

Dubovik, O.

O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements," J. Geophys. Res. 105, 673-696 (2000).
[CrossRef]

Dutton, E.

B. Bodhaine, N. Wood, E. Dutton, and J. Slusser, "On Rayleigh optical depth calculations," J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
[CrossRef]

Eck, T.

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Eilers, J. A.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

J. Redemann, B. Schmid, J. A. Eilers, R. Kahn, R. C. Levy, P. B. Russell, J. M. Livingston, P. V. Hobbs, W. L. Smith, and B. N. Holben, "Suborbital measurements of spectral aerosol optical depth and its variability at subsatellite grid scales in support of CLAMS 2001," J. Atmos. Sci. 62, 993-1007 (2005).
[CrossRef]

Erbertseder, T.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Fischer, J.

H. Asseng, T. Ruhtz, and J. Fischer, "Sun and aureole spectrometer for airborne measurements to derive aerosol optical properties," Appl. Opt. 43, 2146-2155 (2004).
[CrossRef] [PubMed]

T. Ruhtz and J. Fischer, "Calibration of FUBISS (Free University Berlins Integrated Spectrographic System)," in Proceedings of the Fourth International Airborne Remote Sensing Conference and Exhibition, Vol. II-1 (ERIM International, 1999), Vol. II-1.

Haywood, J. M.

A. Keil and J. M. Haywood, "Solar radiative forcing by biomass burning aerosol particles during SAFARI 2000: a case study based on measured aerosol and cloud properties," J. Geophys. Res. 108, 8467, doi: (2003).
[CrossRef]

Herman, B. M.

L. W. Thomason, B. M. Herman, and J. A. Reagan, "The effect of atmospheric attenuators with structured vertical distributions on air mass determinations and Langley plot analyses," J. Atmos. Sci. 40, 1851-1854 (1983).
[CrossRef]

Hess, M.

M. Hess, P. Koepke, and I. Schult, "Optical properties of aerosols and clouds: the software package OPAC," Bull. Am. Meteorol. Soc. 79, 831-844 (1998).
[CrossRef]

Hobbs, P. V.

J. Redemann, B. Schmid, J. A. Eilers, R. Kahn, R. C. Levy, P. B. Russell, J. M. Livingston, P. V. Hobbs, W. L. Smith, and B. N. Holben, "Suborbital measurements of spectral aerosol optical depth and its variability at subsatellite grid scales in support of CLAMS 2001," J. Atmos. Sci. 62, 993-1007 (2005).
[CrossRef]

Holben, B.

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Holben, B. N.

J. Redemann, B. Schmid, J. A. Eilers, R. Kahn, R. C. Levy, P. B. Russell, J. M. Livingston, P. V. Hobbs, W. L. Smith, and B. N. Holben, "Suborbital measurements of spectral aerosol optical depth and its variability at subsatellite grid scales in support of CLAMS 2001," J. Atmos. Sci. 62, 993-1007 (2005).
[CrossRef]

Jankowiak, I.

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Kahn, R.

J. Redemann, B. Schmid, J. A. Eilers, R. Kahn, R. C. Levy, P. B. Russell, J. M. Livingston, P. V. Hobbs, W. L. Smith, and B. N. Holben, "Suborbital measurements of spectral aerosol optical depth and its variability at subsatellite grid scales in support of CLAMS 2001," J. Atmos. Sci. 62, 993-1007 (2005).
[CrossRef]

Kasten, F.

Kaufman, Y.

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Kaufman, Y. J.

Y. J. Kaufman, D. Tanre, and O. Boucher, "A satellite view of aerosols in the climate system," Nature (London) 419, 215-223 (2002).
[CrossRef] [PubMed]

Keil, A.

A. Keil and J. M. Haywood, "Solar radiative forcing by biomass burning aerosol particles during SAFARI 2000: a case study based on measured aerosol and cloud properties," J. Geophys. Res. 108, 8467, doi: (2003).
[CrossRef]

Kerr, J. B.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Kiehl, J. T.

V. Ramanathan, P. J. Crutzen, J. T. Kiehl, and D. Rosenfeld, "Aerosols, climate and the hydrological cycle," Science 294, 2119-2124 (2001).
[CrossRef] [PubMed]

King, M.

M. King and D. Byrne, "A method for interfering total ozone content from the spectral variation of total optical depth obtained with a solar radiometer," J. Atmos. Sci. 33, 2242-2251 (1978).
[CrossRef]

King, M. D.

O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements," J. Geophys. Res. 105, 673-696 (2000).
[CrossRef]

Koepke, P.

M. Hess, P. Koepke, and I. Schult, "Optical properties of aerosols and clouds: the software package OPAC," Bull. Am. Meteorol. Soc. 79, 831-844 (1998).
[CrossRef]

Kolyer, R. W.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Lamb, K.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Lavenu, F.

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Levy, R. C.

J. Redemann, B. Schmid, J. A. Eilers, R. Kahn, R. C. Levy, P. B. Russell, J. M. Livingston, P. V. Hobbs, W. L. Smith, and B. N. Holben, "Suborbital measurements of spectral aerosol optical depth and its variability at subsatellite grid scales in support of CLAMS 2001," J. Atmos. Sci. 62, 993-1007 (2005).
[CrossRef]

Liou, K.

K. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, 2002), Vol. 84.
[CrossRef]

Livingston, J. M.

J. Redemann, B. Schmid, J. A. Eilers, R. Kahn, R. C. Levy, P. B. Russell, J. M. Livingston, P. V. Hobbs, W. L. Smith, and B. N. Holben, "Suborbital measurements of spectral aerosol optical depth and its variability at subsatellite grid scales in support of CLAMS 2001," J. Atmos. Sci. 62, 993-1007 (2005).
[CrossRef]

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Lumpe, J. D.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

McPeters, R. D.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Nakajima, T.

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

M. Tanaka, T. Nakajima, and 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, and T. Yamauchi, "Retrieval of the optical properties of aerosols from aureole and extinction data," Appl. Opt. 22, 2951-2959 (1983).
[CrossRef] [PubMed]

Nieke, J.

J. Nieke, B. Pflug, and G. Zimmermann, "An aureole-corrected Langley-plot method developed for the calibration of HiRES grating spectrometers," J. Atmos. Sol.-Terr. Phys. 61, 739-722 (1999).
[CrossRef]

Pflug, B.

J. Nieke, B. Pflug, and G. Zimmermann, "An aureole-corrected Langley-plot method developed for the calibration of HiRES grating spectrometers," J. Atmos. Sol.-Terr. Phys. 61, 739-722 (1999).
[CrossRef]

Pitts, M. C.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Ramanathan, V.

V. Ramanathan, P. J. Crutzen, J. T. Kiehl, and D. Rosenfeld, "Aerosols, climate and the hydrological cycle," Science 294, 2119-2124 (2001).
[CrossRef] [PubMed]

Ramirez, S. R.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Randall, C. E.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Reagan, J.

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Reagan, J. A.

L. W. Thomason, B. M. Herman, and J. A. Reagan, "The effect of atmospheric attenuators with structured vertical distributions on air mass determinations and Langley plot analyses," J. Atmos. Sci. 40, 1851-1854 (1983).
[CrossRef]

Redemann, J.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

J. Redemann, B. Schmid, J. A. Eilers, R. Kahn, R. C. Levy, P. B. Russell, J. M. Livingston, P. V. Hobbs, W. L. Smith, and B. N. Holben, "Suborbital measurements of spectral aerosol optical depth and its variability at subsatellite grid scales in support of CLAMS 2001," J. Atmos. Sci. 62, 993-1007 (2005).
[CrossRef]

Rolph, G. D.

R. R. Draxler and G. D. Rolph, "HYSPLIT (HYbrid Single-Particle Lagrangian Integrated Trajectory) Model," NOAA Air Resources Laboratory, 2003, http://www.arl.noaa.gov/ready/hysplit4.html.

Rosenfeld, D.

V. Ramanathan, P. J. Crutzen, J. T. Kiehl, and D. Rosenfeld, "Aerosols, climate and the hydrological cycle," Science 294, 2119-2124 (2001).
[CrossRef] [PubMed]

Ruhtz, T.

H. Asseng, T. Ruhtz, and J. Fischer, "Sun and aureole spectrometer for airborne measurements to derive aerosol optical properties," Appl. Opt. 43, 2146-2155 (2004).
[CrossRef] [PubMed]

T. Ruhtz and J. Fischer, "Calibration of FUBISS (Free University Berlins Integrated Spectrographic System)," in Proceedings of the Fourth International Airborne Remote Sensing Conference and Exhibition, Vol. II-1 (ERIM International, 1999), Vol. II-1.

Russell, P. B.

J. Redemann, B. Schmid, J. A. Eilers, R. Kahn, R. C. Levy, P. B. Russell, J. M. Livingston, P. V. Hobbs, W. L. Smith, and B. N. Holben, "Suborbital measurements of spectral aerosol optical depth and its variability at subsatellite grid scales in support of CLAMS 2001," J. Atmos. Sci. 62, 993-1007 (2005).
[CrossRef]

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Schmid, B.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

J. Redemann, B. Schmid, J. A. Eilers, R. Kahn, R. C. Levy, P. B. Russell, J. M. Livingston, P. V. Hobbs, W. L. Smith, and B. N. Holben, "Suborbital measurements of spectral aerosol optical depth and its variability at subsatellite grid scales in support of CLAMS 2001," J. Atmos. Sci. 62, 993-1007 (2005).
[CrossRef]

B. Schmid and C. Wehrli, "Comparison of sun photometer calibration by use of the Langley technique and the standard lamp," Appl. Opt. 34, 4500-4512 (1995).
[CrossRef] [PubMed]

Schult, I.

M. Hess, P. Koepke, and I. Schult, "Optical properties of aerosols and clouds: the software package OPAC," Bull. Am. Meteorol. Soc. 79, 831-844 (1998).
[CrossRef]

Setzer, A.

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Shetter, R. E.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Shiobara, M.

Slusser, J.

B. Bodhaine, N. Wood, E. Dutton, and J. Slusser, "On Rayleigh optical depth calculations," J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
[CrossRef]

Slutsker, I.

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Smirnov, A.

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Smith, W. L.

J. Redemann, B. Schmid, J. A. Eilers, R. Kahn, R. C. Levy, P. B. Russell, J. M. Livingston, P. V. Hobbs, W. L. Smith, and B. N. Holben, "Suborbital measurements of spectral aerosol optical depth and its variability at subsatellite grid scales in support of CLAMS 2001," J. Atmos. Sci. 62, 993-1007 (2005).
[CrossRef]

Swartz, W. H.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Tanaka, M.

Tanre, D.

Y. J. Kaufman, D. Tanre, and O. Boucher, "A satellite view of aerosols in the climate system," Nature (London) 419, 215-223 (2002).
[CrossRef] [PubMed]

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Thomason, L. W.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

L. W. Thomason, B. M. Herman, and J. A. Reagan, "The effect of atmospheric attenuators with structured vertical distributions on air mass determinations and Langley plot analyses," J. Atmos. Sci. 40, 1851-1854 (1983).
[CrossRef]

Trepte, C. R.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Vermote, E.

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Wehrli, C.

Wiscombe, W.

Wood, N.

B. Bodhaine, N. Wood, E. Dutton, and J. Slusser, "On Rayleigh optical depth calculations," J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
[CrossRef]

Yamauchi, T.

Yee, J.-H.

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Young, A.

Zimmermann, G.

J. Nieke, B. Pflug, and G. Zimmermann, "An aureole-corrected Langley-plot method developed for the calibration of HiRES grating spectrometers," J. Atmos. Sol.-Terr. Phys. 61, 739-722 (1999).
[CrossRef]

Adv. Geophys. (1)

K. Bullrich, "Scattered radiation in the atmosphere and the natural aerosol," Adv. Geophys. 10, 99-256 (1964).
[CrossRef]

Appl. Opt. (6)

Atmos. Chem. Phys. (1)

J. M. Livingston, B. Schmid, P. B. Russell, J. A. Eilers, R. W. Kolyer, J. Redemann, S. R. Ramirez, J.-H. Yee, W. H. Swartz, C. R. Trepte, L. W. Thomason, M. C. Pitts, M. A. Avery, C. E. Randall, J. D. Lumpe, R. M. Bevilacqua, M. Bittner, T. Erbertseder, R. D. McPeters, R. E. Shetter, E. V. Browell, J. B. Kerr, and K. Lamb, "Retrieval of ozone column content from airborne sun photometer measurements during SOLVE II: comparison with coincident satellite and aircraft measurements," Atmos. Chem. Phys. 5, 2035-2054 (2005).
[CrossRef]

Bull. Am. Meteorol. Soc. (1)

M. Hess, P. Koepke, and I. Schult, "Optical properties of aerosols and clouds: the software package OPAC," Bull. Am. Meteorol. Soc. 79, 831-844 (1998).
[CrossRef]

J. Atmos. Ocean. Technol. (1)

B. Bodhaine, N. Wood, E. Dutton, and J. Slusser, "On Rayleigh optical depth calculations," J. Atmos. Ocean. Technol. 16, 1854-1861 (1999).
[CrossRef]

J. Atmos. Sci. (3)

L. W. Thomason, B. M. Herman, and J. A. Reagan, "The effect of atmospheric attenuators with structured vertical distributions on air mass determinations and Langley plot analyses," J. Atmos. Sci. 40, 1851-1854 (1983).
[CrossRef]

J. Redemann, B. Schmid, J. A. Eilers, R. Kahn, R. C. Levy, P. B. Russell, J. M. Livingston, P. V. Hobbs, W. L. Smith, and B. N. Holben, "Suborbital measurements of spectral aerosol optical depth and its variability at subsatellite grid scales in support of CLAMS 2001," J. Atmos. Sci. 62, 993-1007 (2005).
[CrossRef]

M. King and D. Byrne, "A method for interfering total ozone content from the spectral variation of total optical depth obtained with a solar radiometer," J. Atmos. Sci. 33, 2242-2251 (1978).
[CrossRef]

J. Atmos. Sol.-Terr. Phys. (1)

J. Nieke, B. Pflug, and G. Zimmermann, "An aureole-corrected Langley-plot method developed for the calibration of HiRES grating spectrometers," J. Atmos. Sol.-Terr. Phys. 61, 739-722 (1999).
[CrossRef]

J. Geophys. Res. (2)

A. Keil and J. M. Haywood, "Solar radiative forcing by biomass burning aerosol particles during SAFARI 2000: a case study based on measured aerosol and cloud properties," J. Geophys. Res. 108, 8467, doi: (2003).
[CrossRef]

O. Dubovik and M. D. King, "A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements," J. Geophys. Res. 105, 673-696 (2000).
[CrossRef]

Nature (1)

Y. J. Kaufman, D. Tanre, and O. Boucher, "A satellite view of aerosols in the climate system," Nature (London) 419, 215-223 (2002).
[CrossRef] [PubMed]

Remote Sens. Environ. (1)

B. Holben, T. Eck, I. Slutsker, D. Tanre, J. Buis, A. Setzer, E. Vermote, J. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov, "AERONET--A federated instrument network and data archive for aerosol characterization," Remote Sens. Environ. 66, 1-6 (1998).
[CrossRef]

Science (1)

V. Ramanathan, P. J. Crutzen, J. T. Kiehl, and D. Rosenfeld, "Aerosols, climate and the hydrological cycle," Science 294, 2119-2124 (2001).
[CrossRef] [PubMed]

Other (6)

K. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, 2002), Vol. 84.
[CrossRef]

T. Ruhtz and J. Fischer, "Calibration of FUBISS (Free University Berlins Integrated Spectrographic System)," in Proceedings of the Fourth International Airborne Remote Sensing Conference and Exhibition, Vol. II-1 (ERIM International, 1999), Vol. II-1.

R. R. Draxler and G. D. Rolph, "HYSPLIT (HYbrid Single-Particle Lagrangian Integrated Trajectory) Model," NOAA Air Resources Laboratory, 2003, http://www.arl.noaa.gov/ready/hysplit4.html.

Data can be accessed from the website of the Tropospheric Emission Monitoring Internet Service, http://www.temis.nl.

Data can be accessed from the website of the World Ozone and Ultraviolet Radiation Data Centre, http://es-ee.tor.ec.gc.ca/e/ozone/ozoneworld.htm.

Carl Zeiss OEM Sensorik/Prozessanalytik, "Produktinformation MMS 1 Monolithische Miniatur-Spektrometer," D-73446 Oberkochen, Germany.

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Figures (9)

Fig. 1
Fig. 1

Modeled aureole index aui for ten different aerosol types. (a) Spectral dependence of aui at 50 % relative humidity, (b) Ångström exponent α 500 - 862   nm versus aui at 500   nm , (c) α 500 - 862   nm versus spectral slope of aui, (d) single scattering albedo ω 0 versus spectral slope of aui. The figures (b)–(d) include the results for all relative humidities for each aerosol type (see text).

Fig. 2
Fig. 2

Aerosol optical depth τ a measured on 9 June 2006 during AgriSAR 2006 with FUBISS-ASA2 (black curve) and a CIMEL 318NE (triangles) at 500   nm . Both were ground-based measurements.

Fig. 3
Fig. 3

(a) FUBISS-ASA2 measuring head seen from above. First aureole path (A), direct sun path (B), second aureole path (C), and sun tracker (D). (b) It is installed in the rear part of the FUB Cessna 207 T and records out of the open rear side window.

Fig. 4
Fig. 4

Schematic setup of the FUBISS-ASA2 measuring head. Three entrance optics: two aureole paths (A and C) and the direct sun path (B) (dashed lines: field of view) are mounted on a central plate (D). They are connected via fiber cables (E) to three identical Zeiss MMS-1 spectrometers below the central plate (not shown), their frontend electronic is mounted on the side of the measuring head (F). The entrance optics are orientated towards the sun with a sun tracker system (below the entrance optics, not shown) and driven by two servo-motors (G and H).

Fig. 5
Fig. 5

Airborne Langley plot (at 500   nm ) performed on 16 January 2006 south of Berlin, Germany. Only the upper 10 % percentile of the recorded irradiance values (black crosses) were used for the linear extrapolation (black line).

Fig. 6
Fig. 6

Calibration of the extraterrestrial solar irradiance using the aureole calibration technique performed on 4 July 2006. (a) Forenoon measurement, where a synchronous Langley plot was successfully recorded. (b) Afternoon measurement on the same day, where the Langley plot technique failed. (c) Ratio of ln   I 0,AureoleCal to ln   I 0,Langley for the forenoon and the afternoon measurements. The aureole calibration can be performed with the aureole recording of the 4° (solid curve) and the 6° aureole entrance optic (dotted curve).

Fig. 7
Fig. 7

Vertical profiles measured with FUBISS-ASA2 on 3 May 2006 in northern Germany during AgriSAR 2006: Altitude versus (a) aerosol optical depth τ a , (b) aerosol extinction coefficient σ a , and (c) aureole index aui. Six channels from 412 to 862   nm were analyzed [color code in (b)].

Fig. 8
Fig. 8

Vertical profile of the Ångström exponent α 500 - 862   nm .

Fig. 9
Fig. 9

Vertical profile of the spectral slope of the aureole index aui.

Tables (2)

Tables Icon

Table 1 Technical Data of FUBISS-ASA2

Tables Icon

Table 2 Technical Data of the Zeiss MMS1 [19] Spectrometers

Equations (12)

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

τ a = ln   z I 0 ln   I d m τ r τ x   with   z = ( r 0 r ) 2 ,
τ a = β λ α ,
α = ln ( τ a ( λ 1 ) / τ a ( λ 2 ) ) ln ( λ 1 / λ 2 ) .
β a = ω 0 P a τ a = I a I d m Δ Ω P r τ r .
a u i ( λ ) := β a 1 β a 2 = P a 1 P a 2 ,
a u i ( λ ) = ( z 1 I a 1 P r 1 τ r z 2 I d m Δ Ω a 1 ) Δ Ω a 2 ( I a 2 P r 2 τ r z 2 I d m Δ Ω a 2 ) Δ Ω a 1 .
z 1 = I a 2 ¯ Δ Ω a 1 I a 1 ¯ Δ Ω a 2 , z 2 = I a 2 ¯ Δ Ω d I d ¯ Δ Ω a 2 ,
ln   I d = ln   I 0 m tot τ tot
ln   I d + m r τ r = ln   I 0 m ˜ τ ˜ .
ln   I d = ln   I 0 τ * ,
τ * = m τ = 1 ω 0 P Δ Ω I a I d .
σ a ¯ = Δ τ a Δ h .

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