Abstract

A variational method for retrieving the aerosol optical thickness and backscatter coefficient profiles from multiangle lidar measurements is presented and discussed. A monostatic single-wavelength low-energy lidar system was operated at different zenith angles during the Indian Ocean Experiment (INDOEX) campaign in 1999 to characterize the aerosol plumes in the Indian monsoon. The variational method was applied to lidar data to retrieve profiles of optical thickness and the backscatter coefficient for nighttime and daytime measurements. Results are obtained with an uncertainty of 10% below 3 km (nighttime) and 2.8 km (daytime) and a bias of less than 0.01. During daytime the retrieval of optical parameters is indeed limited to a lower altitude owing to the sky background signal and the atmospheric inhomogeneity. In both cases the total aerosol optical thickness is consistent (±10%) with the integrated value derived from sunphotometer measurements. Backscatter-to-extinction ratios estimated in different regions by two distinct methods compared well, which proves the capability of the method to assess optical measurements and account for the altitude dependence of the phase function.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Hitschfeld, J. Bordan, “Errors inherent in the radar measurement of rainfall at attenuating wavelengths,” J. Appl. Meteorol. 11, 58–67 (1954).
    [CrossRef]
  2. R. T. H. Collis, “Lidar: a new atmospheric probe,” Q. J. R. Meteorol. Soc. 92, 220–230 (1966).
    [CrossRef]
  3. W. Viezee, E. E. Uthe, R. T. H. Collis, “Lidar observations of airfield approach conditions: an exploratory study,” J. Appl. Meteorol. 8, 274–283 (1969).
    [CrossRef]
  4. P. A. Davis, “Analysis of lidar signatures of cirrus clouds,” Appl. Opt. 8, 2099–2102 (1969).
    [CrossRef] [PubMed]
  5. F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of aerosol height distribution by lidar,” J. Appl. Meteorol. 11, 482–489 (1972).
    [CrossRef]
  6. R. H. Kohl, “Discussion of the interpretation problem encountered in single-wavelength lidar transmissionmeters,” J. Appl. Meteorol. 17, 1034–1038 (1978).
    [CrossRef]
  7. J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
    [CrossRef] [PubMed]
  8. J. Ackermann, “The extinction-to-backscatter ratio of tropospheric aerosols: a numerical study,” J. Atmos. Ocean. Technol. 15, 1043–1050 (1998).
    [CrossRef]
  9. S. T. Shipley, D. H. Tracey, E. W. Eloranta, J. T. Trauger, J. T. Sroga, F. L. Roesler, J. A. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1: Theory and instrumentation,” Appl. Opt. 22, 3716–3724 (1983).
    [CrossRef] [PubMed]
  10. J. T. Sroga, E. W. Eloranta, S. T. Shipley, F. L. Roesler, P. J. Tryon, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 2: Calibration and data analysis,” Appl. Opt. 22, 3725–3732 (1983).
    [CrossRef] [PubMed]
  11. A. Ansmann, M. Riebesell, C. Weitkamp, “Measurement of atmospheric aerosol extinction profiles with a Raman lidar,” Opt. Lett. 15, 746–748 (1990).
    [CrossRef] [PubMed]
  12. G. J. Kunz, “Bipath method as a way to measure the spatial backscatter and extinction coefficients with lidar,” Appl. Opt. 26, 794–795 (1987).
    [CrossRef] [PubMed]
  13. H. G. Hughes, M. R. Paulson, “Double-ended lidar technique for aerosol studies,” Appl. Opt. 27, 2273–2278 (1988).
    [CrossRef] [PubMed]
  14. D. Gutkowicz-Krusin, “Multiangle lidar performance in the presence of horizontal inhomogeneities in atmospheric extinction and scattering,” Appl. Opt. 32, 3266–3272 (1993).
    [CrossRef] [PubMed]
  15. M. C. W. Sandford, “Laser scatter measurements in the mesosphere and above,” J. Atmos. Terr. Phys. 29, 1657–1662 (1967).
    [CrossRef]
  16. P. M. Hamilton, “Lidar measurement of backscatter and attenuation of atmospheric aerosol,” Atmos. Environ. 3, 221–223 (1969).
    [CrossRef]
  17. J. D. Spinhirne, J. A. Reagan, B. M. Herman, “Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique,” J. Appl. Meteorol. 19, 426–438 (1980).
    [CrossRef]
  18. P. B. Russell, J. M. Livingston, “Slant-lidar aerosol extinction measurements and their relation to measured and calculated albedo changes,” J. Clim. Appl. Meteorol. 23, 1204–1221 (1984).
    [CrossRef]
  19. H. Shimizu, Y. Sasano, H. Nakane, N. Sugimoto, I. Matsui, N. Takeuchi, “Large scale laser radar for measuring aerosol distribution over a wide area,” Appl. Opt. 24, 617–626 (1985).
    [CrossRef] [PubMed]
  20. J. Rothermel, W. Jones, “Ground-based measurements of atmospheric backscatter and absorption using coherent CO2 lidar,” Appl. Opt. 24, 3487–3496 (1985).
    [CrossRef]
  21. M. R. Paulson, “Atmospheric horizontal-inhomogeneity effects on the optical depths determined by the double-evaluation-angle lidar technique,” Rep. TD 1600, DTIC AS-A212 836 (Naval Ocean Systems Center, San Diego, Calif., 1989).
  22. S. Elouragini, “Useful algorithms to derive the optical properties of clouds from a backscatter lidar return,” J. Mod. Opt. 42, 1439–1446 (1995).
    [CrossRef]
  23. S. Young, “Analysis of lidar backscatter profiles in optically thin clouds,” Appl. Opt. 34, 7019–7031 (1995).
    [CrossRef] [PubMed]
  24. R. M. Measures, Laser Remote Sensing (Wiley-Interscience, Toronto, 1984).
  25. M. Nicolet, “On the molecular scattering in the terrestrial atmosphere,” Planet. Space Sci. 32, 1467 (1984).
    [CrossRef]
  26. V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).
  27. V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).
  28. A. Jayaraman, D. Lubin, S. Ramachandran, V. Ramanathan, E. Woodbridge, W. D. Collins, K. S. Zalpuri, “Direct observations of aerosol radiative forcing over the tropical Indian Ocean during the January–February 1996 pre-INDOEX cruise,” J. Geophys. Res. 103, 13824–13836 (1999).
  29. S. K. Satheesh, K. Krishna Moorthy, B. V. Murthy, “Spatial gradients in the aerosol characteristics over the Arabian Sea and Indian Ocean,” J. Geophys. Res. 103, 26183–26192 (1998).
    [CrossRef]
  30. J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
    [CrossRef]
  31. J. D. Spinhirne, “Micro pulse lidar,” IEEE Trans Geosci. Remote Sens. 31, 48–55 (1993).
    [CrossRef]
  32. B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
  33. J. D. Spinhirne, J. A. R. Rall, V. S. Scott, “Compact eye safe lidar systems,” Rev. Laser Eng. 23, 112–118 (1995).
    [CrossRef]
  34. E. Hamonou, P. Chazette, D. Bialis, F. Dulac, X. Schneider, E. Galani, G. Ancellet, A. Papayannis, “Characterization of the vertical structure of Saharan dust export to the Mediterranean basin,” J. Geophys. Res. 104, 22257–22270 (1999).
    [CrossRef]

2001 (1)

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

1999 (2)

A. Jayaraman, D. Lubin, S. Ramachandran, V. Ramanathan, E. Woodbridge, W. D. Collins, K. S. Zalpuri, “Direct observations of aerosol radiative forcing over the tropical Indian Ocean during the January–February 1996 pre-INDOEX cruise,” J. Geophys. Res. 103, 13824–13836 (1999).

E. Hamonou, P. Chazette, D. Bialis, F. Dulac, X. Schneider, E. Galani, G. Ancellet, A. Papayannis, “Characterization of the vertical structure of Saharan dust export to the Mediterranean basin,” J. Geophys. Res. 104, 22257–22270 (1999).
[CrossRef]

1998 (3)

S. K. Satheesh, K. Krishna Moorthy, B. V. Murthy, “Spatial gradients in the aerosol characteristics over the Arabian Sea and Indian Ocean,” J. Geophys. Res. 103, 26183–26192 (1998).
[CrossRef]

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

J. Ackermann, “The extinction-to-backscatter ratio of tropospheric aerosols: a numerical study,” J. Atmos. Ocean. Technol. 15, 1043–1050 (1998).
[CrossRef]

1995 (3)

J. D. Spinhirne, J. A. R. Rall, V. S. Scott, “Compact eye safe lidar systems,” Rev. Laser Eng. 23, 112–118 (1995).
[CrossRef]

S. Elouragini, “Useful algorithms to derive the optical properties of clouds from a backscatter lidar return,” J. Mod. Opt. 42, 1439–1446 (1995).
[CrossRef]

S. Young, “Analysis of lidar backscatter profiles in optically thin clouds,” Appl. Opt. 34, 7019–7031 (1995).
[CrossRef] [PubMed]

1993 (2)

1990 (1)

1988 (1)

1987 (1)

1985 (2)

1984 (2)

P. B. Russell, J. M. Livingston, “Slant-lidar aerosol extinction measurements and their relation to measured and calculated albedo changes,” J. Clim. Appl. Meteorol. 23, 1204–1221 (1984).
[CrossRef]

M. Nicolet, “On the molecular scattering in the terrestrial atmosphere,” Planet. Space Sci. 32, 1467 (1984).
[CrossRef]

1983 (2)

1981 (1)

1980 (1)

J. D. Spinhirne, J. A. Reagan, B. M. Herman, “Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique,” J. Appl. Meteorol. 19, 426–438 (1980).
[CrossRef]

1978 (1)

R. H. Kohl, “Discussion of the interpretation problem encountered in single-wavelength lidar transmissionmeters,” J. Appl. Meteorol. 17, 1034–1038 (1978).
[CrossRef]

1972 (1)

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of aerosol height distribution by lidar,” J. Appl. Meteorol. 11, 482–489 (1972).
[CrossRef]

1969 (3)

W. Viezee, E. E. Uthe, R. T. H. Collis, “Lidar observations of airfield approach conditions: an exploratory study,” J. Appl. Meteorol. 8, 274–283 (1969).
[CrossRef]

P. M. Hamilton, “Lidar measurement of backscatter and attenuation of atmospheric aerosol,” Atmos. Environ. 3, 221–223 (1969).
[CrossRef]

P. A. Davis, “Analysis of lidar signatures of cirrus clouds,” Appl. Opt. 8, 2099–2102 (1969).
[CrossRef] [PubMed]

1967 (1)

M. C. W. Sandford, “Laser scatter measurements in the mesosphere and above,” J. Atmos. Terr. Phys. 29, 1657–1662 (1967).
[CrossRef]

1966 (1)

R. T. H. Collis, “Lidar: a new atmospheric probe,” Q. J. R. Meteorol. Soc. 92, 220–230 (1966).
[CrossRef]

1954 (1)

W. Hitschfeld, J. Bordan, “Errors inherent in the radar measurement of rainfall at attenuating wavelengths,” J. Appl. Meteorol. 11, 58–67 (1954).
[CrossRef]

Ackermann, J.

J. Ackermann, “The extinction-to-backscatter ratio of tropospheric aerosols: a numerical study,” J. Atmos. Ocean. Technol. 15, 1043–1050 (1998).
[CrossRef]

Alfaro, S. C.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

Ancellet, G.

E. Hamonou, P. Chazette, D. Bialis, F. Dulac, X. Schneider, E. Galani, G. Ancellet, A. Papayannis, “Characterization of the vertical structure of Saharan dust export to the Mediterranean basin,” J. Geophys. Res. 104, 22257–22270 (1999).
[CrossRef]

Ansmann, A.

Bialis, D.

E. Hamonou, P. Chazette, D. Bialis, F. Dulac, X. Schneider, E. Galani, G. Ancellet, A. Papayannis, “Characterization of the vertical structure of Saharan dust export to the Mediterranean basin,” J. Geophys. Res. 104, 22257–22270 (1999).
[CrossRef]

Bonnazola, M.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

Bordan, J.

W. Hitschfeld, J. Bordan, “Errors inherent in the radar measurement of rainfall at attenuating wavelengths,” J. Appl. Meteorol. 11, 58–67 (1954).
[CrossRef]

Buis, J. P.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Cautenet, S.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

Chazette, P.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

E. Hamonou, P. Chazette, D. Bialis, F. Dulac, X. Schneider, E. Galani, G. Ancellet, A. Papayannis, “Characterization of the vertical structure of Saharan dust export to the Mediterranean basin,” J. Geophys. Res. 104, 22257–22270 (1999).
[CrossRef]

Clarke, A.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Coakley, J.

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

Coakley, J. A.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Collins, W. D.

A. Jayaraman, D. Lubin, S. Ramachandran, V. Ramanathan, E. Woodbridge, W. D. Collins, K. S. Zalpuri, “Direct observations of aerosol radiative forcing over the tropical Indian Ocean during the January–February 1996 pre-INDOEX cruise,” J. Geophys. Res. 103, 13824–13836 (1999).

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Collis, R. T. H.

W. Viezee, E. E. Uthe, R. T. H. Collis, “Lidar observations of airfield approach conditions: an exploratory study,” J. Appl. Meteorol. 8, 274–283 (1969).
[CrossRef]

R. T. H. Collis, “Lidar: a new atmospheric probe,” Q. J. R. Meteorol. Soc. 92, 220–230 (1966).
[CrossRef]

Crutzen, P. J.

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Davis, P. A.

Dickerson, R.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

Dulac, F.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

E. Hamonou, P. Chazette, D. Bialis, F. Dulac, X. Schneider, E. Galani, G. Ancellet, A. Papayannis, “Characterization of the vertical structure of Saharan dust export to the Mediterranean basin,” J. Geophys. Res. 104, 22257–22270 (1999).
[CrossRef]

Eck, T. F.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Eloranta, E. W.

Elouragini, S.

S. Elouragini, “Useful algorithms to derive the optical properties of clouds from a backscatter lidar return,” J. Mod. Opt. 42, 1439–1446 (1995).
[CrossRef]

Fahey, D.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Fernald, F. G.

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of aerosol height distribution by lidar,” J. Appl. Meteorol. 11, 482–489 (1972).
[CrossRef]

Flamant, C.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

Foret, G.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

Galani, E.

E. Hamonou, P. Chazette, D. Bialis, F. Dulac, X. Schneider, E. Galani, G. Ancellet, A. Papayannis, “Characterization of the vertical structure of Saharan dust export to the Mediterranean basin,” J. Geophys. Res. 104, 22257–22270 (1999).
[CrossRef]

Gandrud, B.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Gaudichet, A.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

Gomes, L.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

Gutkowicz-Krusin, D.

Hamilton, P. M.

P. M. Hamilton, “Lidar measurement of backscatter and attenuation of atmospheric aerosol,” Atmos. Environ. 3, 221–223 (1969).
[CrossRef]

Hamonou, E.

E. Hamonou, P. Chazette, D. Bialis, F. Dulac, X. Schneider, E. Galani, G. Ancellet, A. Papayannis, “Characterization of the vertical structure of Saharan dust export to the Mediterranean basin,” J. Geophys. Res. 104, 22257–22270 (1999).
[CrossRef]

Herman, B. M.

J. D. Spinhirne, J. A. Reagan, B. M. Herman, “Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique,” J. Appl. Meteorol. 19, 426–438 (1980).
[CrossRef]

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of aerosol height distribution by lidar,” J. Appl. Meteorol. 11, 482–489 (1972).
[CrossRef]

Heymsfield, A.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

Hitschfeld, W.

W. Hitschfeld, J. Bordan, “Errors inherent in the radar measurement of rainfall at attenuating wavelengths,” J. Appl. Meteorol. 11, 58–67 (1954).
[CrossRef]

Holben, B. N.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Hughes, H. G.

Inamdar, S. R.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

Jankowiak, I.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Jayaraman, A.

A. Jayaraman, D. Lubin, S. Ramachandran, V. Ramanathan, E. Woodbridge, W. D. Collins, K. S. Zalpuri, “Direct observations of aerosol radiative forcing over the tropical Indian Ocean during the January–February 1996 pre-INDOEX cruise,” J. Geophys. Res. 103, 13824–13836 (1999).

Jones, W.

Kaufman, Y. J.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Kiehl, J.

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

Kiehl, J. T.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Klett, J. D.

Kley, D.

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

Kohl, R. H.

R. H. Kohl, “Discussion of the interpretation problem encountered in single-wavelength lidar transmissionmeters,” J. Appl. Meteorol. 17, 1034–1038 (1978).
[CrossRef]

Krishna Moorthy, K.

S. K. Satheesh, K. Krishna Moorthy, B. V. Murthy, “Spatial gradients in the aerosol characteristics over the Arabian Sea and Indian Ocean,” J. Geophys. Res. 103, 26183–26192 (1998).
[CrossRef]

Krishnamurti, T.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Krishnamurti, T. N.

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

Kuettner, J.

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Kunz, G. J.

Lavenu, F.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Lelieved, J.

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

Léon, J.-F.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

Livingston, J. M.

P. B. Russell, J. M. Livingston, “Slant-lidar aerosol extinction measurements and their relation to measured and calculated albedo changes,” J. Clim. Appl. Meteorol. 23, 1204–1221 (1984).
[CrossRef]

Lubin, D.

A. Jayaraman, D. Lubin, S. Ramachandran, V. Ramanathan, E. Woodbridge, W. D. Collins, K. S. Zalpuri, “Direct observations of aerosol radiative forcing over the tropical Indian Ocean during the January–February 1996 pre-INDOEX cruise,” J. Geophys. Res. 103, 13824–13836 (1999).

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Maring, H.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Matsui, I.

Measures, R. M.

R. M. Measures, Laser Remote Sensing (Wiley-Interscience, Toronto, 1984).

Mitra, A. P.

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

Murthy, B. V.

S. K. Satheesh, K. Krishna Moorthy, B. V. Murthy, “Spatial gradients in the aerosol characteristics over the Arabian Sea and Indian Ocean,” J. Geophys. Res. 103, 26183–26192 (1998).
[CrossRef]

Nakajima, T.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Nakane, H.

Nicolet, M.

M. Nicolet, “On the molecular scattering in the terrestrial atmosphere,” Planet. Space Sci. 32, 1467 (1984).
[CrossRef]

Ogren, J.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Papayannis, A.

E. Hamonou, P. Chazette, D. Bialis, F. Dulac, X. Schneider, E. Galani, G. Ancellet, A. Papayannis, “Characterization of the vertical structure of Saharan dust export to the Mediterranean basin,” J. Geophys. Res. 104, 22257–22270 (1999).
[CrossRef]

Paulson, M. R.

H. G. Hughes, M. R. Paulson, “Double-ended lidar technique for aerosol studies,” Appl. Opt. 27, 2273–2278 (1988).
[CrossRef] [PubMed]

M. R. Paulson, “Atmospheric horizontal-inhomogeneity effects on the optical depths determined by the double-evaluation-angle lidar technique,” Rep. TD 1600, DTIC AS-A212 836 (Naval Ocean Systems Center, San Diego, Calif., 1989).

Pelon, J.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

Prospero, J.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

Rall, J. A. R.

J. D. Spinhirne, J. A. R. Rall, V. S. Scott, “Compact eye safe lidar systems,” Rev. Laser Eng. 23, 112–118 (1995).
[CrossRef]

Ramachandran, S.

A. Jayaraman, D. Lubin, S. Ramachandran, V. Ramanathan, E. Woodbridge, W. D. Collins, K. S. Zalpuri, “Direct observations of aerosol radiative forcing over the tropical Indian Ocean during the January–February 1996 pre-INDOEX cruise,” J. Geophys. Res. 103, 13824–13836 (1999).

Ramanathan, V.

A. Jayaraman, D. Lubin, S. Ramachandran, V. Ramanathan, E. Woodbridge, W. D. Collins, K. S. Zalpuri, “Direct observations of aerosol radiative forcing over the tropical Indian Ocean during the January–February 1996 pre-INDOEX cruise,” J. Geophys. Res. 103, 13824–13836 (1999).

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

Rasch, P. J.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Reagan, J. A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

J. D. Spinhirne, J. A. Reagan, B. M. Herman, “Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique,” J. Appl. Meteorol. 19, 426–438 (1980).
[CrossRef]

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of aerosol height distribution by lidar,” J. Appl. Meteorol. 11, 482–489 (1972).
[CrossRef]

Riebesell, M.

Roesler, F. L.

Rothermel, J.

Russell, P. B.

P. B. Russell, J. M. Livingston, “Slant-lidar aerosol extinction measurements and their relation to measured and calculated albedo changes,” J. Clim. Appl. Meteorol. 23, 1204–1221 (1984).
[CrossRef]

Sadourny, R.

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

Sandford, M. C. W.

M. C. W. Sandford, “Laser scatter measurements in the mesosphere and above,” J. Atmos. Terr. Phys. 29, 1657–1662 (1967).
[CrossRef]

Sarode, P. R.

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

Sasano, Y.

Satheesh, S. K.

S. K. Satheesh, K. Krishna Moorthy, B. V. Murthy, “Spatial gradients in the aerosol characteristics over the Arabian Sea and Indian Ocean,” J. Geophys. Res. 103, 26183–26192 (1998).
[CrossRef]

Savoie, D.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Schneider, X.

E. Hamonou, P. Chazette, D. Bialis, F. Dulac, X. Schneider, E. Galani, G. Ancellet, A. Papayannis, “Characterization of the vertical structure of Saharan dust export to the Mediterranean basin,” J. Geophys. Res. 104, 22257–22270 (1999).
[CrossRef]

Scott, V. S.

J. D. Spinhirne, J. A. R. Rall, V. S. Scott, “Compact eye safe lidar systems,” Rev. Laser Eng. 23, 112–118 (1995).
[CrossRef]

Setzer, A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Shaw, G.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Shimizu, H.

Shipley, S. T.

Slutsker, I.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Smirnov, A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Spinhirne, J. D.

J. D. Spinhirne, J. A. R. Rall, V. S. Scott, “Compact eye safe lidar systems,” Rev. Laser Eng. 23, 112–118 (1995).
[CrossRef]

J. D. Spinhirne, “Micro pulse lidar,” IEEE Trans Geosci. Remote Sens. 31, 48–55 (1993).
[CrossRef]

J. D. Spinhirne, J. A. Reagan, B. M. Herman, “Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique,” J. Appl. Meteorol. 19, 426–438 (1980).
[CrossRef]

Sroga, J. T.

Sugimoto, N.

Takeuchi, N.

Tanré, D.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Tracey, D. H.

Trauger, J. T.

Tryon, P. J.

Tuck, A.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Uthe, E. E.

W. Viezee, E. E. Uthe, R. T. H. Collis, “Lidar observations of airfield approach conditions: an exploratory study,” J. Appl. Meteorol. 8, 274–283 (1969).
[CrossRef]

Valero, F. P. J.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

Vermote, E.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Viezee, W.

W. Viezee, E. E. Uthe, R. T. H. Collis, “Lidar observations of airfield approach conditions: an exploratory study,” J. Appl. Meteorol. 8, 274–283 (1969).
[CrossRef]

Weinman, J. A.

Weitkamp, C.

Woodbridge, E.

A. Jayaraman, D. Lubin, S. Ramachandran, V. Ramanathan, E. Woodbridge, W. D. Collins, K. S. Zalpuri, “Direct observations of aerosol radiative forcing over the tropical Indian Ocean during the January–February 1996 pre-INDOEX cruise,” J. Geophys. Res. 103, 13824–13836 (1999).

Woodbridge, E. L.

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Young, S.

Zalpuri, K. S.

A. Jayaraman, D. Lubin, S. Ramachandran, V. Ramanathan, E. Woodbridge, W. D. Collins, K. S. Zalpuri, “Direct observations of aerosol radiative forcing over the tropical Indian Ocean during the January–February 1996 pre-INDOEX cruise,” J. Geophys. Res. 103, 13824–13836 (1999).

Zhang, G.

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

Appl. Opt. (10)

P. A. Davis, “Analysis of lidar signatures of cirrus clouds,” Appl. Opt. 8, 2099–2102 (1969).
[CrossRef] [PubMed]

J. D. Klett, “Stable analytical inversion solution for processing lidar returns,” Appl. Opt. 20, 211–220 (1981).
[CrossRef] [PubMed]

S. T. Shipley, D. H. Tracey, E. W. Eloranta, J. T. Trauger, J. T. Sroga, F. L. Roesler, J. A. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1: Theory and instrumentation,” Appl. Opt. 22, 3716–3724 (1983).
[CrossRef] [PubMed]

J. T. Sroga, E. W. Eloranta, S. T. Shipley, F. L. Roesler, P. J. Tryon, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 2: Calibration and data analysis,” Appl. Opt. 22, 3725–3732 (1983).
[CrossRef] [PubMed]

H. Shimizu, Y. Sasano, H. Nakane, N. Sugimoto, I. Matsui, N. Takeuchi, “Large scale laser radar for measuring aerosol distribution over a wide area,” Appl. Opt. 24, 617–626 (1985).
[CrossRef] [PubMed]

J. Rothermel, W. Jones, “Ground-based measurements of atmospheric backscatter and absorption using coherent CO2 lidar,” Appl. Opt. 24, 3487–3496 (1985).
[CrossRef]

G. J. Kunz, “Bipath method as a way to measure the spatial backscatter and extinction coefficients with lidar,” Appl. Opt. 26, 794–795 (1987).
[CrossRef] [PubMed]

H. G. Hughes, M. R. Paulson, “Double-ended lidar technique for aerosol studies,” Appl. Opt. 27, 2273–2278 (1988).
[CrossRef] [PubMed]

D. Gutkowicz-Krusin, “Multiangle lidar performance in the presence of horizontal inhomogeneities in atmospheric extinction and scattering,” Appl. Opt. 32, 3266–3272 (1993).
[CrossRef] [PubMed]

S. Young, “Analysis of lidar backscatter profiles in optically thin clouds,” Appl. Opt. 34, 7019–7031 (1995).
[CrossRef] [PubMed]

Atmos. Environ. (1)

P. M. Hamilton, “Lidar measurement of backscatter and attenuation of atmospheric aerosol,” Atmos. Environ. 3, 221–223 (1969).
[CrossRef]

IEEE Trans Geosci. Remote Sens. (1)

J. D. Spinhirne, “Micro pulse lidar,” IEEE Trans Geosci. Remote Sens. 31, 48–55 (1993).
[CrossRef]

J. Appl. Meteorol. (5)

W. Hitschfeld, J. Bordan, “Errors inherent in the radar measurement of rainfall at attenuating wavelengths,” J. Appl. Meteorol. 11, 58–67 (1954).
[CrossRef]

J. D. Spinhirne, J. A. Reagan, B. M. Herman, “Vertical distribution of aerosol extinction cross section and inference of aerosol imaginary index in the troposphere by lidar technique,” J. Appl. Meteorol. 19, 426–438 (1980).
[CrossRef]

W. Viezee, E. E. Uthe, R. T. H. Collis, “Lidar observations of airfield approach conditions: an exploratory study,” J. Appl. Meteorol. 8, 274–283 (1969).
[CrossRef]

F. G. Fernald, B. M. Herman, J. A. Reagan, “Determination of aerosol height distribution by lidar,” J. Appl. Meteorol. 11, 482–489 (1972).
[CrossRef]

R. H. Kohl, “Discussion of the interpretation problem encountered in single-wavelength lidar transmissionmeters,” J. Appl. Meteorol. 17, 1034–1038 (1978).
[CrossRef]

J. Atmos. Ocean. Technol. (1)

J. Ackermann, “The extinction-to-backscatter ratio of tropospheric aerosols: a numerical study,” J. Atmos. Ocean. Technol. 15, 1043–1050 (1998).
[CrossRef]

J. Atmos. Terr. Phys. (1)

M. C. W. Sandford, “Laser scatter measurements in the mesosphere and above,” J. Atmos. Terr. Phys. 29, 1657–1662 (1967).
[CrossRef]

J. Clim. Appl. Meteorol. (1)

P. B. Russell, J. M. Livingston, “Slant-lidar aerosol extinction measurements and their relation to measured and calculated albedo changes,” J. Clim. Appl. Meteorol. 23, 1204–1221 (1984).
[CrossRef]

J. Geophys. Res. (4)

A. Jayaraman, D. Lubin, S. Ramachandran, V. Ramanathan, E. Woodbridge, W. D. Collins, K. S. Zalpuri, “Direct observations of aerosol radiative forcing over the tropical Indian Ocean during the January–February 1996 pre-INDOEX cruise,” J. Geophys. Res. 103, 13824–13836 (1999).

S. K. Satheesh, K. Krishna Moorthy, B. V. Murthy, “Spatial gradients in the aerosol characteristics over the Arabian Sea and Indian Ocean,” J. Geophys. Res. 103, 26183–26192 (1998).
[CrossRef]

J.-F. Léon, P. Chazette, F. Dulac, J. Pelon, C. Flamant, M. Bonnazola, G. Foret, S. Cautenet, S. C. Alfaro, A. Gaudichet, L. Gomes, F. Lavenu, S. R. Inamdar, P. R. Sarode, “Large scale advection of continental aerosols during INDOEX,” J. Geophys. Res. 108, 28427–28440 (2001).
[CrossRef]

E. Hamonou, P. Chazette, D. Bialis, F. Dulac, X. Schneider, E. Galani, G. Ancellet, A. Papayannis, “Characterization of the vertical structure of Saharan dust export to the Mediterranean basin,” J. Geophys. Res. 104, 22257–22270 (1999).
[CrossRef]

J. Mod. Opt. (1)

S. Elouragini, “Useful algorithms to derive the optical properties of clouds from a backscatter lidar return,” J. Mod. Opt. 42, 1439–1446 (1995).
[CrossRef]

Opt. Lett. (1)

Planet. Space Sci. (1)

M. Nicolet, “On the molecular scattering in the terrestrial atmosphere,” Planet. Space Sci. 32, 1467 (1984).
[CrossRef]

Q. J. R. Meteorol. Soc. (1)

R. T. H. Collis, “Lidar: a new atmospheric probe,” Q. J. R. Meteorol. Soc. 92, 220–230 (1966).
[CrossRef]

Remote Sens. Environ. (1)

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, ”AERONET - A federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).

Rev. Laser Eng. (1)

J. D. Spinhirne, J. A. R. Rall, V. S. Scott, “Compact eye safe lidar systems,” Rev. Laser Eng. 23, 112–118 (1995).
[CrossRef]

Other (4)

V. Ramanathan, P. J. Crutzen, J. Coakley, R. Dickerson, A. Heymsfield, J. Kiehl, D. Kley, T. N. Krishnamurti, J. Kuettner, J. Lelieved, A. P. Mitra, J. Prospero, R. Sadourny, F. P. J. Valero, E. L. Woodbridge, Indian Ocean Experiment (INDOEX) White Paper, Center for Clouds, Chemistry and Climate (C4) Publ. 143 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1995).

V. Ramanathan, P. J. Crutzen, J. A. Coakley, A. Clarke, W. D. Collins, R. Dickerson, D. Fahey, B. Gandrud, A. Heymsfield, J. T. Kiehl, J. Kuettner, T. Krishnamurti, D. Lubin, H. Maring, J. Ogren, J. Prospero, P. J. Rasch, D. Savoie, G. Shaw, A. Tuck, F. P. J. Valero, E. L. Woodbridge, G. Zhang, Indian Ocean Experiment (INDOEX), A multiagency proposal for a field experiment in the Indian Ocean, Center for Clouds, Chemistry and Climate (C4) Publ. 162 (Scripps Institution of Oceanography, UCSD, La Jolla, Calif. 92093-0239, 1996).

R. M. Measures, Laser Remote Sensing (Wiley-Interscience, Toronto, 1984).

M. R. Paulson, “Atmospheric horizontal-inhomogeneity effects on the optical depths determined by the double-evaluation-angle lidar technique,” Rep. TD 1600, DTIC AS-A212 836 (Naval Ocean Systems Center, San Diego, Calif., 1989).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Overlap factor of the MPL lidar versus distance measured in a horizontal layer of the atmosphere on 11 March 1999: bold solid curve, average overlap factor, light dotted curves, ten profiles.

Fig. 2
Fig. 2

Logarithm of the lidar signal versus altitude and horizontal distance obtained (a) Wednesday, 10 March 1999 during nighttime between 13:34 and 15:03 UTC and (b) Thursday, 11 March 1999 during daytime between 9:33 and 10:59 UTC at Goa University, India. (c) SNR versus altitude; (d) the angle on the same days.

Fig. 3
Fig. 3

Aerosol optical thickness profile at 523.5 nm retrieved with the variational method from multiangle lidar profiles obtained (a) on Wednesday, 10 March 1999, between 13:34 and 15:03 UTC and (b) on Thursday, 11 March 1999, between 9:33 and 10:59 UTC, at Goa University, India. The τeq is the integrated equivalent aerosol optical thickness from the sunphotometer.

Fig. 4
Fig. 4

Aerosol backscatter coefficient profile retrieved with the variational method (solid curve) from multiangle lidar profiles obtained (a) on Wednesday, 10 March 1999, between 13:34 and 15:03 UTC and (b) on Thursday, 11 March 1999, between 9:33 and 10:59 UTC, at Goa University, India. The aerosol backscatter coefficient profiles retrieved with the Klett method from the zenith lidar profile with different values of k π are also reported.

Fig. 5
Fig. 5

Aerosol backscatter coefficient retrieved with the variational method as a function of altitude and horizontal distance from multiangle lidar profiles obtained (a) on Wednesday, 10 March 1999, between 13:34 and 15:03 UTC and (b) on Thursday, 11 March 1999, between 9:33 and 10:59 UTC, at Goa University, India.

Fig. 6
Fig. 6

Monte Carlo method.

Fig. 7
Fig. 7

(a) Bias and (b) relative error on the optical thickness retrieved with the variational method versus zenith SNR for four different values of τ; dotted curves with asterisks, optical thickness of 0.6 with an angular error.

Equations (7)

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

Pz, φ=K Fz, φβz, φcos2 φz-z02exp-2τz, φ,
Sz, φ=Kβz, φexp-2τz, φ.
τijz=-121cos φi-1cos φj-1 lnSizSjz.
Jz=1in1jnijlnSizSjz+2cos φi-2cos φjτz2.
τz=-1in1jnij QijzlnSizSjz1cos φi-1cos φj2 1in1jnij Qijz1cos φi-1cos φj2.
Qijz=minSNRiz, SNRjz1in1jnijminSNRiz, SNRjz.
βiz=SizSizref βzrefexp-2cos φiτzref-τz,

Metrics