Abstract

To calculate aerosol extinction from Raman lidar data, it is necessary to evaluate the derivative of a molecular Raman signal with respect to range. The typical approach taken in the lidar community is to make an a priori assumption about the functional behavior of the data to calculate the derivative. It has previously been shown that the use of the chi-squared technique to determine the most likely functional behavior of the data prior to actually calculating the derivative eliminates the need for making a priori assumptions. Here that technique is validated through numerical simulation and by application to a significant body of Raman lidar measurements. In general, we show that the chi-squared approach for evaluating extinction yields lower extinction uncertainty than traditional techniques. We also use the technique to study the feasibility of developing a general characterization of the extinction uncertainty that could permit the uncertainty in Raman lidar aerosol extinction measurements to be estimated accurately without the need of the chi-squared technique.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  16. W. C. Malm, J. F. Sisler, D. Huffman, R. A. Eldred, and T. A. Cahill, "Spatial and seasonal trends in particle concentration and optical extinction in the United States," J. Geophys. Res. 99, 1347-1370 (1994).
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2004

2003

D. N. Whiteman, "Examination of the traditional Raman lidar technique. I. Evaluating the temperature-dependent lidar equations," Appl. Opt. 42, 2571-2592 (2003).
[CrossRef] [PubMed]

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

2001

D. N. Whiteman, G. Schwemmer, T. Berkoff, H. Plotkin, L. Ramos-Izquierdo, and G. Pappalardo, "Performance modeling of an airborne Raman water vapor lidar," Appl. Opt. 40, 375-390 (2001).
[CrossRef]

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

1999

D. N. Whiteman and S. H. Melfi, "Cloud liquid water, mean droplet radius and number density measurements using a Raman lidar," J. Geophys. Res. 104, 31411-31419 (1999).
[CrossRef]

D. N. Whiteman, "Application of statistical methods to the determination of slope in lidar data," Appl. Opt. 38, 3360-3369 (1999).
[CrossRef]

1994

D. N. Stacey, "Rayleigh's legacy to modern physics: high resolution spectroscopy," Eur. J. Phys. 15, 236-242 (1994).
[CrossRef]

W. C. Malm, J. F. Sisler, D. Huffman, R. A. Eldred, and T. A. Cahill, "Spatial and seasonal trends in particle concentration and optical extinction in the United States," J. Geophys. Res. 99, 1347-1370 (1994).
[CrossRef]

1992

R. A. Ferrare, S. H. Melfi, D. N. Whiteman, and K. D. Evans, "Raman lidar measurements of pinatubo aerosols over southeastern Kansas during November-December 1991," Geophys. Res. Lett. 19, 1599-1602 (1992).
[CrossRef]

1990

1965

G. Marsaglia, "Ratios of normal variables and ratios of sums of uniform variables," J. Am. Stat. Assoc. 60, 193-204 (1965).
[CrossRef]

Amiridis, V.

Amodeo, A.

Ansmann, A.

G. Pappalardo, A. Amodeo, M. Pandolfi, U. Wandinger, A. Ansmann, J. Bosenberg, V. Matthias, V. Amiridis, F. De Tomasi, M. Frioud, M. Iarlori, Leonce Komguem, A. Papayannis, F. Rocadenbosch, and X. Wang, "Aerosol lidar intercomparison in the framework of the EARLINET project. 3. Raman lidar algorithm for aerosol extinction, backscatter, and lidar ratio," Appl. Opt. 43, 5370-5385 (2004).
[CrossRef] [PubMed]

A. Ansmann, M. Riebesell, and C. Weitkamp, "Measurements of atmospheric aerosol extinction profiles with a Raman lidar," Opt. Lett. 15, 746-748 (1990).
[CrossRef] [PubMed]

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Baldasano, J. M.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Balis, D.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Barlow, R. J.

R. J. Barlow, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences (Wiley, 1989).

Barnard, J.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Berkoff, T.

Bevington, P. R.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, 1992).

Böckmann, C.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Bosenberg, J.

G. Pappalardo, A. Amodeo, M. Pandolfi, U. Wandinger, A. Ansmann, J. Bosenberg, V. Matthias, V. Amiridis, F. De Tomasi, M. Frioud, M. Iarlori, Leonce Komguem, A. Papayannis, F. Rocadenbosch, and X. Wang, "Aerosol lidar intercomparison in the framework of the EARLINET project. 3. Raman lidar algorithm for aerosol extinction, backscatter, and lidar ratio," Appl. Opt. 43, 5370-5385 (2004).
[CrossRef] [PubMed]

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Bösenberg, J.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Cadirola, M.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Cahill, T. A.

W. C. Malm, J. F. Sisler, D. Huffman, R. A. Eldred, and T. A. Cahill, "Spatial and seasonal trends in particle concentration and optical extinction in the United States," J. Geophys. Res. 99, 1347-1370 (1994).
[CrossRef]

Calpini, B.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Chaikovsky, A.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Clough, S.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Cook, D.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

De Tomasi, F.

Demoz, B.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Eldred, R. A.

W. C. Malm, J. F. Sisler, D. Huffman, R. A. Eldred, and T. A. Cahill, "Spatial and seasonal trends in particle concentration and optical extinction in the United States," J. Geophys. Res. 99, 1347-1370 (1994).
[CrossRef]

Eloranta, E. W.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Evans, K. D.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

R. A. Ferrare, S. H. Melfi, D. N. Whiteman, and K. D. Evans, "Raman lidar measurements of pinatubo aerosols over southeastern Kansas during November-December 1991," Geophys. Res. Lett. 19, 1599-1602 (1992).
[CrossRef]

Feltz, W.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Feltz, W. F.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Ferrare, R.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Ferrare, R. A.

R. A. Ferrare, S. H. Melfi, D. N. Whiteman, and K. D. Evans, "Raman lidar measurements of pinatubo aerosols over southeastern Kansas during November-December 1991," Geophys. Res. Lett. 19, 1599-1602 (1992).
[CrossRef]

Flamant, P.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Frioud, M.

Goldsmith, J.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Gutman, S.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Gutman, S. I.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Hågård, A.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Halthore, R.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Huffman, D.

W. C. Malm, J. F. Sisler, D. Huffman, R. A. Eldred, and T. A. Cahill, "Spatial and seasonal trends in particle concentration and optical extinction in the United States," J. Geophys. Res. 99, 1347-1370 (1994).
[CrossRef]

Iarlori, M.

Jedlovec, G. J.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Knuteson, R. O.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Komguem, Leonce

Lesht, B.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Liljegren, J.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Linne, H.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Malm, W. C.

W. C. Malm, J. F. Sisler, D. Huffman, R. A. Eldred, and T. A. Cahill, "Spatial and seasonal trends in particle concentration and optical extinction in the United States," J. Geophys. Res. 99, 1347-1370 (1994).
[CrossRef]

Marsaglia, G.

G. Marsaglia, "Ratios of normal variables and ratios of sums of uniform variables," J. Am. Stat. Assoc. 60, 193-204 (1965).
[CrossRef]

Matthias, V.

Melfi, S. H.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

D. N. Whiteman and S. H. Melfi, "Cloud liquid water, mean droplet radius and number density measurements using a Raman lidar," J. Geophys. Res. 104, 31411-31419 (1999).
[CrossRef]

R. A. Ferrare, S. H. Melfi, D. N. Whiteman, and K. D. Evans, "Raman lidar measurements of pinatubo aerosols over southeastern Kansas during November-December 1991," Geophys. Res. Lett. 19, 1599-1602 (1992).
[CrossRef]

Michalsky, J.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Mitev, V.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Morris, V.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Pandolfi, M.

Papayannis, A.

G. Pappalardo, A. Amodeo, M. Pandolfi, U. Wandinger, A. Ansmann, J. Bosenberg, V. Matthias, V. Amiridis, F. De Tomasi, M. Frioud, M. Iarlori, Leonce Komguem, A. Papayannis, F. Rocadenbosch, and X. Wang, "Aerosol lidar intercomparison in the framework of the EARLINET project. 3. Raman lidar algorithm for aerosol extinction, backscatter, and lidar ratio," Appl. Opt. 43, 5370-5385 (2004).
[CrossRef] [PubMed]

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Pappalardo, G.

Pelon, J.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Plotkin, H.

Porch, W.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Ramos-Izquierdo, L.

Resendes, D.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Revercomb, H. E.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Richardson, S.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Riebesell, M.

Robinson, D. K.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, 1992).

Rocadenbosch, F.

Schmid, B.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Schmidlin, F. J.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Schneider, J.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Schwemmer, G.

Schwemmer, G. K.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Sisler, J. F.

W. C. Malm, J. F. Sisler, D. Huffman, R. A. Eldred, and T. A. Cahill, "Spatial and seasonal trends in particle concentration and optical extinction in the United States," J. Geophys. Res. 99, 1347-1370 (1994).
[CrossRef]

Spinelli, N.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Splitt, M.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Stacey, D. N.

D. N. Stacey, "Rayleigh's legacy to modern physics: high resolution spectroscopy," Eur. J. Phys. 15, 236-242 (1994).
[CrossRef]

Starr, D. O'C.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Tobin, D.

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

Tobin, D. C.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Trickl, T.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Turner, D. D.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Van Hove, T.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Vaughan, G.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Visconti, G.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Wandinger, U.

Wang, X.

Weitkamp, C.

Westwater, E.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Whiteman, D.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Whiteman, D. N.

D. N. Whiteman, "Examination of the traditional Raman lidar technique. I. Evaluating the temperature-dependent lidar equations," Appl. Opt. 42, 2571-2592 (2003).
[CrossRef] [PubMed]

D. N. Whiteman, G. Schwemmer, T. Berkoff, H. Plotkin, L. Ramos-Izquierdo, and G. Pappalardo, "Performance modeling of an airborne Raman water vapor lidar," Appl. Opt. 40, 375-390 (2001).
[CrossRef]

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

D. N. Whiteman, "Application of statistical methods to the determination of slope in lidar data," Appl. Opt. 38, 3360-3369 (1999).
[CrossRef]

D. N. Whiteman and S. H. Melfi, "Cloud liquid water, mean droplet radius and number density measurements using a Raman lidar," J. Geophys. Res. 104, 31411-31419 (1999).
[CrossRef]

R. A. Ferrare, S. H. Melfi, D. N. Whiteman, and K. D. Evans, "Raman lidar measurements of pinatubo aerosols over southeastern Kansas during November-December 1991," Geophys. Res. Lett. 19, 1599-1602 (1992).
[CrossRef]

Wiegner, M.

J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

Wietkamp, C.

C. Wietkamp, Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere (Springer Science & Business Media, 2005).

Appl. Opt.

Bull. Am. Meteorol. Soc.

H. E. Revercomb, D. D. Turner, D. C. Tobin, R. O. Knuteson, W. F. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Linne, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The ARM program's water vapor intensive observation periods--Overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Eur. J. Phys.

D. N. Stacey, "Rayleigh's legacy to modern physics: high resolution spectroscopy," Eur. J. Phys. 15, 236-242 (1994).
[CrossRef]

Geophys. Res. Lett.

R. A. Ferrare, S. H. Melfi, D. N. Whiteman, and K. D. Evans, "Raman lidar measurements of pinatubo aerosols over southeastern Kansas during November-December 1991," Geophys. Res. Lett. 19, 1599-1602 (1992).
[CrossRef]

J. Am. Stat. Assoc.

G. Marsaglia, "Ratios of normal variables and ratios of sums of uniform variables," J. Am. Stat. Assoc. 60, 193-204 (1965).
[CrossRef]

J. Geophys. Res.

D. N. Whiteman and S. H. Melfi, "Cloud liquid water, mean droplet radius and number density measurements using a Raman lidar," J. Geophys. Res. 104, 31411-31419 (1999).
[CrossRef]

D. N. Whiteman, K. D. Evans, B. Demoz, D. O'C. Starr, E. W. Eloranta, D. Tobin, W. Feltz, G. J. Jedlovec, S. I. Gutman, G. K. Schwemmer, M. Cadirola, S. H. Melfi, and F. J. Schmidlin, "Raman lidar measurements of water vapor and cirrus clouds during the passage of Hurricane Bonnie," J. Geophys. Res. 106, 5211-5225 (2001).
[CrossRef]

W. C. Malm, J. F. Sisler, D. Huffman, R. A. Eldred, and T. A. Cahill, "Spatial and seasonal trends in particle concentration and optical extinction in the United States," J. Geophys. Res. 99, 1347-1370 (1994).
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Opt. Lett.

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J. Bösenberg, A. Ansmann, J. M. Baldasano, D. Balis, C. Böckmann, B. Calpini, A. Chaikovsky, P. Flamant, A. Hågård, V. Mitev, A. Papayannis, J. Pelon, D. Resendes, J. Schneider, N. Spinelli, T. Trickl, G. Vaughan, G. Visconti, and M. Wiegner, "EARLINET: a European aerosol research lidar network," in Advances in Laser Remote Sensing, A.Dabas, C.Loth, and J.Pelon, eds. (Editions de L'Ecole Polytechnique, 2001), pp. 155-158.

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Figures (13)

Fig. 1
Fig. 1

Simulated extinction profiles that were used to simulate N signals. (a) Extinction profile decreasing with altitude in the boundary layer. (b) Lofted aerosol layer with increasing aerosol content in the boundary layer.

Fig. 2
Fig. 2

Examples of simulated N2 Raman signals with 600   s averaging time acquired along the vertical direction. (a) Signal simulated with the aerosol extinction in Fig. 1(a) (Ext1). (b) Signal simulated with the aerosol extinction in Fig. 1(b).

Fig. 3
Fig. 3

Percentage differences between the simulated extinction and the retrieved extinctions calculated using different combinations of order of polynomials for z 2 P ( z ) and N(z). The extinction profiles used here were generated simulating a N2 Raman signal with 1200 s averaging times and the simulated extinction Ext1. (a) The first order of polynomial is used for the regression of the term N(z) and linear (Lin), quadratic (Quad), and cubic (Cub) polynomials are used for the term z 2 P ( z ) . (b) The second-order model is used for the regression of the term N(z) and the linear, quadratic, and cubic models are used for the term z 2 P ( z ) . (c) The third-order regression is used for the regression of the term N(z). It is important to note that the combinations that result in lower random variability of the differences are those in which the same order of regression is used for both the terms z 2 P ( z ) and N(z). Moreover, the order of regression of the term z 2 P ( z ) that results in an unbiased retrieval is the third order.

Fig. 4
Fig. 4

Average results of the retrieval of the aerosol extinction from the statistical ensemble (200 profiles) of simulated data with a 600 s averaging time. (a), (e) Average extinction profiles retrieved using the linear (Lin), quadratic (Quad), cubic (Cub) regression on z 2 P ( z ) , and the chi-squared technique (Chosen) for both (a) Ext1 and (e) Ext2. (b), (f) Average percentage differences between simulated and retrieved extinction with the different orders of regression and the chi-squared technique. (c), (g) Average extinction uncertainties calculated using each different order of regression and the chi-squared technique. (d), (h) Standard deviations of the average uncertainties obtained using different orders of polynomials and using the chi-squared technique.

Fig. 5
Fig. 5

Frequencies of the chosen models for the 200 profiles simulated using Ext1 [(a)–(c)] and Ext2 [(d)–(f)] and 60 s [(a) and (d)], 600 s [(b) and (e)], and 6000   s [(c) and (f)] averaging times.

Fig. 6
Fig. 6

Comparison of extinction uncertainties obtained with the linear and chosen models. (a), (b) Points selected for the comparison. (c) Frequencies with which the linear model results in extinction uncertainties higher than the chosen model as a function of the averaging time on a logarithmic scale. The data used for the comparison correspond to 60, 300, 600, 1200, and 6000 s averaging times. The linear model results in an extinction uncertainty larger than the chosen model more than 90 % of the time except for points C and F with 60 s averaging times. For these two points, that have higher noise, the linear model results in extinction uncertainty larger than the chosen model more than 65 % of the time.

Fig. 7
Fig. 7

Diagrams showing the ability of the chi-squared test to distinguish the underlying functional form of the data as a function of the magnitude of aerosol extinction and signal random error. (a) corresponds to the simulated data obtained using the extinction profile Ext1, (b) corresponds to the simulated data obtained using the extinction profile Ext2. The white pixels indicate values of extinction and signal random error for which the difference between the frequency of choice of the cubic model as the most probable by the chi-squared technique is more than 30 % larger than the frequency of choice of the linear model. Here the third-order model is chosen as a reference, since it will be shown that it is the most chosen when the chi-squared technique is applied to the experimental data. The gray pixels indicate the values of aerosol extinction and signal random error for which the frequency of the cubic model was less than 30 % larger than the linear model. The white pixels indicate the values of the aerosol extinction and signal uncertainty for which the chi-squared test was able to clearly distinguish the underlying functional shape of the data, while the gray pixel indicates confusion between linear and cubic models.

Fig. 8
Fig. 8

Example of aerosol extinction values included in the statistics. (a) Three extinction profiles acquired by SRL on 13, 14, and 18 September 1996. (b) Average extinction profile and corresponding standard deviation of the data used for this study.

Fig. 9
Fig. 9

(a) The model chosen by the chi-squared technique as a function of aerosol extinction and signal random error for all the experimental data acquired during the WVIOPs and (b) the corresponding average extinction uncertainties. The model that is most frequently chosen as the most likely is the cubic model ( 80 % ) .

Fig. 10
Fig. 10

An example of regression of five points using linear, quadratic, and cubic polynomials. (a) Data points (Sim) simulated with a lidar model using the parameters in Table 1 and 40 s averaging time, the linear (Lin), quadratic (Quad), and cubic (Cub) regression. (b) The deviations of each fit function from the data points in terms of percentage difference. The lines labeled signal σ and signal + σ indicate, respectively, the 1 σ range of random error of the data points. The chi-squared cumulative probabilities of the different models were, respectively, 1 , 0.69 , and 0.47 for the linear, quadratic, and cubic model. Therefore the cubic model was chosen as the most likely model to represent the data.

Fig. 11
Fig. 11

Panels showing an example of regression of five points using linear, quadratic, and cubic polynomials. (a) Data points simulated with a lidar model using the parameters in Table 1 and 10 s averaging time, the linear, quadratic, and cubic regression. (b) Deviations of each fit function from the data points in terms of percentage difference. The lines labeled signal σ and signal + σ indicate, respectively, the 1 σ range of random error of the data points. The chi-squared cumulative probabilities of the different models were, respectively, 1 , 0.9 , and 0.003 for the linear, quadratic, and cubic model. The quadratic model was chosen as the most likely model to represent the data. The chi-squared cumulative probability value for the cubic models is small with respect to the expected value (0.5) because the cubic fit is reproducing the data points too closely with respect to their uncertainty, as can be seen in (b).

Fig. 12
Fig. 12

Example selection of models by the chi-squared technique in case a seven-point window is used to regress the data. The N2 Raman signal used here was simulated with the aerosol extinction Ext1, using the parameters in Table 1 and an averaging time of 600 s. (a) and (b) show, respectively, the chosen model as a function of altitude and the cumulative probability of the chosen model in case a window of seven points is used for the regression and the linear, quadratic, and cubic models are tested. (c) and (d) show, respectively, the chosen model as a function of altitude and the cumulative probability of the chosen model in case the same window of seven points is used but five models (linear, quadratic, cubic, fourth order, and fifth order) are used. The set of models that results in a cumulative probability closest to 0.5 is that containing the maximum order possible of regression of the seven-point window, namely, the set composed by five models.

Fig. 13
Fig. 13

Calculation of the effective spatial resolution of the linear, quadratic, and cubic regression on a window of five points spaced by 75   m following the Rayleigh criterion. (a) Simulated peaked extinction profile with 160   m separation and the corresponding retrieved extinction using the cubic regression. The retrieved extinction value in the center of the two peaks is 62% of the value of the extinction in the peaks. (b) Simulated peaked extinction profile with 260   m separation and the corresponding retrieved extinction using the linear and quadratic regressions. Note that the linear and quadratic retrievals are almost identical. The extinction value in the center of the two peaks is 65% of the value of the extinction in the peaks for both models.

Tables (1)

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Table 1 Configuration of SRL during the Campaigns WVIOP, WVIOP2, and WVIOP3

Equations (5)

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α aer ( λ L , z ) = d d z ln [ N N ( z ) z 2 P ( λ N , z ) ] α mol ( λ L , z ) α mol ( λ N , z ) 1 + ( λ L λ N ) k ( z ) ,
d d z ln [ N N ( z ) z 2 P ( λ N , z ) ] = 1 N N ( z ) d N N ( z ) d z 1 z 2 P ( λ N , z ) × d d z [ z 2 P ( λ N , z ) ] .
f ( z ) = g ( z ) g ( z ) h ( z ) h ( z ) = b + 2 c z + 3 d z 2 a + b z + c z 2 + d z 3
f + 2 g z + 3 h z 2 e + f z + g z 2 + h z 3 ,
σ f ( z ) 2 = 1 ( a + b z + c z 2 + d z 3 ) 4 [ σ a 2 ( b + 2 c z + 3 d z 2 ) 2 + σ b 2 ( a c z 2 2 d z 3 ) 2 + σ c 2 ( 2 a z + b z 2 d z 4 ) 2 + σ d 2 ( 3 a z 2 + 2 b z 3 + c z 4 ) 2 + 2 σ ab 2 ( a + c z 2 + 2 d z 3 ) ( b + 2 c z + 3 d z 2 ) + 2 σ ac 2 ( - 2 az b z 2 + d z 4 ) ( b + 2 c z + 3 d z 2 ) + 2 σ bc 2 ( 2 a z + b z 2 d z 4 ) ( a c z 2 2 d z 3 ) 2 σ ad 2 ( 3 a + 2 b z + c z 2 ) ( b + 2 c z + 3 d z 2 ) + 2 σ bd 2 ( 3 a z 2 + 2 b z 3 + c z 4 ) ( a c z 2 2 d z 3 ) 2 σ cd 2 ( 2 a z 3 b z 4 + d z 6 ) ( 3 a + 2 b z + c z 2 ) ] + 1 ( e + f z + g z 2 + h z 3 ) 4 [ σ e 2 ( f + 2 g z + 3 h z 2 ) 2 + σ f 2 ( e g z 2 2 h z 3 ) 2 + σ g 2 ( 2 e z + f z 2 h z 4 ) 2 + σ h 2 ( 3 e z 2 + 2 f z 3 + g z 4 ) 2 + 2 σ ef 2 ( e + g z 2 + 2 h z 3 ) ( f + 2 g z + 3 h z 2 ) + 2 σ eg 2 ( 2 e z f z 2 + h z 4 ) ( f + 2 g z + 3 h z 2 ) + 2 σ fg 2 ( 2 e z + f z 2 h z 4 ) ( e g z 2 2 h z 3 ) 2 σ eh 2 ( 3 e + 2 f z + g z 2 ) ( f + 2 g z + 3 h z 2 ) + 2 σ fh 2 ( 3 e z 2 + 2 f z 3 + g z 4 ) ( e g z 2 2 h z 3 ) 2 σ gh 2 ( 2 e z 3 f z 4 + h z 6 ) ( 3 e + 2 f z + g z 2 ) ] .

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