Abstract

A near-infrared airborne differential absorption lidar (DIAL) system has become operational. Horizontal and vertical water vapor profiles of the troposphere during summer (nighttime) conditions extending from the top of the planetary boundary layer (PBL) up to near the tropopause are investigated. These measurements have been performed in Southern Bavaria, Germany. The system design, the frequency control units, and an estimation of the laser line profile of the narrow-band dye laser are discussed. Effective absorption cross sections in terms of altitude are calculated. Statistical and systematic errors of the water vapor measurements are evaluated as a function of altitude. The effect of a systematic range-dependent error caused by molecular absorption is investigated by comparing the DIAL data with in situ measurements. Typical horizontal resolutions range from 4 km in the lower troposphere to 11 km in the upper troposphere, with vertical resolutions varying from 0.3 to 1 km, respectively. The lower limit of the sensitivity of the water vapor mixing ratio is calculated to be 0.01 g/kg. The total errors of these measurements range between 8% and 25%. A sine-shaped wave structure with a wavelength of 14 km and an amplitude of 20% of its mean value, detected in the lower troposphere, indicates an atmospheric gravity wave field.

© 1993 Optical Society of America

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  1. J. Cooney, K. Petri, A. Salik, “Measurements of high resolution atmospheric water vapor profiles by use of a solar blind Raman lidar,” Appl. Opt. 24, 104–108 (1985).
    [CrossRef] [PubMed]
  2. S. H. Melfi, D. N. Whiteman, R. Ferrare, “Observation of atmospheric fronts using Raman lidar moisture measurements,” J. Appl. Meteorol. 28, 789–806 (1989).
    [CrossRef]
  3. E. Voss, M. Riebesell, W. Lehmann, C. Weitkamp, W. Michaelis, “Moisture height profiler,” in Optical Systems for Space Applications, H. Lutz, G. Otrio, eds., Proc. Soc. Photo-Opt. Instrum. Eng.810, 37–41 (1987).
  4. G. Vaughan, D. P. Wareing, L. Thomas, V. Mitev, “Humidity measurements in the free troposphere using Raman backscatter,” Q. J. R. Meteorol. Soc. 114, 1471–1484 (1988).
    [CrossRef]
  5. P. W. Baker, “Atmospheric water vapor differential absorption measurements on vertical paths with a CO2 lidar,” Appl. Opt. 22, 2257–2264 (1983).
    [CrossRef] [PubMed]
  6. V. V. Zuev, V. E. Zuev, Yu. S. Makushkin, V. N. Marichev, A. A. Mitsel, “Laser sounding of atmospheric humidity: experiment,” Appl. Opt. 22, 3742–3746 (1983).
    [CrossRef] [PubMed]
  7. R. M. Hardesty, “Coherent DIAL measurement of range-resolved water vapor concentration,” Appl. Opt. 23, 2545–2553 (1984).
    [CrossRef] [PubMed]
  8. W. B. Grant, J. S. Margolis, A. M. Brothers, D. M. Tratt, “CO2 DIAL measurements of water vapor,” Appl. Opt. 26, 3033–3042 (1987).
    [CrossRef] [PubMed]
  9. R. M. Schotland, “Some observations of the vertical profile of water vapor by means of a laser optical radar,” in Proceedings of the Fourth Symposium on Remote Sensing of Environment (University of Michigan, Ann Arbor, Mich., 1966), pp. 273–277.
  10. Ch. Werner, H. Hermann, “Lidar measurements of the vertical absolute humidity distribution in the boundary layer,” J. Appl. Meteorol. 20, 476–481 (1981).
    [CrossRef]
  11. E. V. Browell, T. D. Wilkerson, T. J. McIlrath, “Water vapor differential absorption lidar development and evaluation,” Appl. Opt. 18, 3474–3483 (1979).
    [CrossRef] [PubMed]
  12. J. Bösenberg, “A DIAL system for high resolution water vapor measurements in the troposphere,” in Laser and Optical Remote Sensing: Instrumentation and Techniques, Vol. 18 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 22–25.
  13. G. Ehret, W. Renger, A. Schmitz-Pfeiffer, “Airborne water vapour DIAL,” presented at the Lower Tropospheric Profiling: Needs and Technologies Meeting, Boulder, Colo., 31 May–3 June 1988).
  14. C. Cahen, J.-L. Lesne, P. Deschamps, P. Y. Thro, “Testing the mobile meteorological DIAL system for humidity and temperature monitoring,” presented at the Fourteenth International Laser Radar Conference International Commission on Laser Atmospheric Studies, San Candido, Italy, 24–26 June 1988.
  15. M. S. Higdon, E. V. Browell, P. Ponsardin, B. E. Grossmann, “Airborne water vapor DIAL system development laser radar V,” in Proc Soc. Photo-Opt. Instrum. Eng. 1222, 183–185 (1990).
  16. S. Cha, K. P. Chan, D. K. Killinger, “Tunable 2.1-μm Ho lidar for simultaneous range-resolved measurements of atmospheric water vapor and aerosol backscatter profiles,” Appl. Opt. 30, 3938–3943 (1991).
    [CrossRef] [PubMed]
  17. C. Cahen, G. Megie, P. Flamant, “Lidar monitoring of water vapor cycle in the troposphere,” J. Appl. Meteorol. 21, 1506–1515 (1982).
    [CrossRef]
  18. E. V. Browell, A. K. Goroch, T. D. Wilkerson, S. Ismail, R. Markson, “Airborne DIAL water vapor and aerosol measurements over the gulf stream,” presented at the Twelfth International Laser Radar Conference, Aix-en-Provence, France, 13–17 August 1984.
  19. G. Ehret, W. Renger, “Atmospheric aerosol and humidity profiling using an airborne DIAL system in the near IR,” in Optical Remote Sensing of the Atmosphere, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 586–589.
  20. T. Hauf, T. L. Clark, “Three-dimensional numerical experiments on convectively forced internal gravity waves,” Q. J. R. Meteorol. Soc. 115, 309–333 (1989).
    [CrossRef]
  21. R. M. Schotland, “Errors in the lidar measurement of atmospheric gases by differential absorption,” J. Appl. Meteorol. 13, 71–77 (1974).
    [CrossRef]
  22. T. D. Wilkerson, G. Schwemmer, B. Gentry, L. P. Giver, “Intensities and N2 collision-broadening coefficients measured for selected H2O absorption lines between 715 and 732 nm,” J. Quant. Spectrosc. Radiat. Transfer 22, 315–331 (1979).
    [CrossRef]
  23. C. Young, “Calculation of the absorption coefficient for lines with combined Doppler and Lorentz broadening,” J. Quant. Spectrosc. Radiat. Transfer 5, 549–552 (1964).
    [CrossRef]
  24. J. Y. Mandin, J. P. Chevillard, C. Camy-Peyret, J. M. Flaud, J.W. Brault, “The high-resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
    [CrossRef]
  25. B. E. Grossmann, E. V. Browell, “Water vapor line broadening and shifting by air, nitrogen, oxygen, and argon in the 720-nm wavelength region,” J. Mol. Spectrosc. 138, 562–595 (1989).
    [CrossRef]
  26. B. E. Grossmann, E. V. Browell, “Spectroscopy of water vapor in the 720-nm region: line strengths, self-induced pressure broadenings and shifts, and temperature dependence of linewidths and shifts,” J. Mol. Spectrosc. 136, 264–294 (1989).
    [CrossRef]
  27. S. Ismail, E. V. Browell, “Airborne and spaceborne lidar measurements of water vapor profiles: a sensitivity analysis,” Appl. Opt. 28, 3603–3615 (1989).
    [CrossRef] [PubMed]
  28. J. Bösenberg, “Measurements of the pressure shift of water vapor absorption lines by simultaneous photoacoustic spectroscopy,” Appl. Opt. 24, 3531–3534 (1985).
    [CrossRef] [PubMed]
  29. E. V. Browell, S. Ismail, B. E. Grossmann, “Temperature sensitivity of differential absorption lidar measurements of water vapor in the 720-nm region,” Appl. Opt. 30, 1517–1524 (1991).
    [CrossRef] [PubMed]
  30. C. Cahen, G. Megie, “A spectral limitation of the range resolved differential absorption lidar technique,” J. Quant. Spectrosc. Radiat. Transfer 25, 151–157 (1981).
    [CrossRef]
  31. D. Bruneau, H. Cazeneuve, C. Loth, J. Pelon, “Double-pulse dual-wavelength alexandrite laser for atmospheric water vapor measurement,” Appl. Opt. 30, 3930–3937 (1991).
    [CrossRef] [PubMed]
  32. T. W. Hänsch, “Repetitively pulsed tunable dye laser for high resolution spectroscopy,” Appl. Opt. 11, 895–898 (1972).
    [CrossRef] [PubMed]
  33. M. Przybylski, B. Otto, H. Gerhardt, “Spectral purity of pulsed dye laser,” Appl Phys. B 49, 201–203 (1989).
    [CrossRef]
  34. J. R. Nestor, “Optogalvanic spectra of neon and argon in glow discharge lamps,” Appl. Opt. 21, 4154–4157 (1982).
    [CrossRef] [PubMed]
  35. R. Busen, “Humidity measurements on the DLR aircraft,” presented at the Proceedings of the Tropospheric Profiling: Needs and Technologies, Boulder, Colo., 10–13 September 1991.
  36. J. H. Golden, R. Serafin, V. Lally, J. Facundo, “Atmospheric sounding systems,” in Mesoscale Meteorology and Forecasting, P. S. Ray, ed. (American Meteorological Society, Boston, Mass., 1986), Chap. 4, pp. 50–57.
  37. J. Bösenberg, “A differential absorption lidar system for high resolution water vapor measurements in the troposphere,” Internal Rep. 71 (Max-Planck-Institute of Meteorology, Hamburg, Germany, 1991).
  38. A. Ansmann, J. Bösenberg, “Correction scheme for spectral broadening by Rayleigh scattering in differential absorption lidar measurements of water vapor in the troposphere,” Appl. Opt. 26, 3026–3032 (1987).
    [CrossRef] [PubMed]

1991 (3)

1990 (1)

M. S. Higdon, E. V. Browell, P. Ponsardin, B. E. Grossmann, “Airborne water vapor DIAL system development laser radar V,” in Proc Soc. Photo-Opt. Instrum. Eng. 1222, 183–185 (1990).

1989 (6)

T. Hauf, T. L. Clark, “Three-dimensional numerical experiments on convectively forced internal gravity waves,” Q. J. R. Meteorol. Soc. 115, 309–333 (1989).
[CrossRef]

S. H. Melfi, D. N. Whiteman, R. Ferrare, “Observation of atmospheric fronts using Raman lidar moisture measurements,” J. Appl. Meteorol. 28, 789–806 (1989).
[CrossRef]

B. E. Grossmann, E. V. Browell, “Water vapor line broadening and shifting by air, nitrogen, oxygen, and argon in the 720-nm wavelength region,” J. Mol. Spectrosc. 138, 562–595 (1989).
[CrossRef]

B. E. Grossmann, E. V. Browell, “Spectroscopy of water vapor in the 720-nm region: line strengths, self-induced pressure broadenings and shifts, and temperature dependence of linewidths and shifts,” J. Mol. Spectrosc. 136, 264–294 (1989).
[CrossRef]

S. Ismail, E. V. Browell, “Airborne and spaceborne lidar measurements of water vapor profiles: a sensitivity analysis,” Appl. Opt. 28, 3603–3615 (1989).
[CrossRef] [PubMed]

M. Przybylski, B. Otto, H. Gerhardt, “Spectral purity of pulsed dye laser,” Appl Phys. B 49, 201–203 (1989).
[CrossRef]

1988 (1)

G. Vaughan, D. P. Wareing, L. Thomas, V. Mitev, “Humidity measurements in the free troposphere using Raman backscatter,” Q. J. R. Meteorol. Soc. 114, 1471–1484 (1988).
[CrossRef]

1987 (2)

1986 (1)

J. Y. Mandin, J. P. Chevillard, C. Camy-Peyret, J. M. Flaud, J.W. Brault, “The high-resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

1985 (2)

1984 (1)

1983 (2)

1982 (2)

C. Cahen, G. Megie, P. Flamant, “Lidar monitoring of water vapor cycle in the troposphere,” J. Appl. Meteorol. 21, 1506–1515 (1982).
[CrossRef]

J. R. Nestor, “Optogalvanic spectra of neon and argon in glow discharge lamps,” Appl. Opt. 21, 4154–4157 (1982).
[CrossRef] [PubMed]

1981 (2)

C. Cahen, G. Megie, “A spectral limitation of the range resolved differential absorption lidar technique,” J. Quant. Spectrosc. Radiat. Transfer 25, 151–157 (1981).
[CrossRef]

Ch. Werner, H. Hermann, “Lidar measurements of the vertical absolute humidity distribution in the boundary layer,” J. Appl. Meteorol. 20, 476–481 (1981).
[CrossRef]

1979 (2)

E. V. Browell, T. D. Wilkerson, T. J. McIlrath, “Water vapor differential absorption lidar development and evaluation,” Appl. Opt. 18, 3474–3483 (1979).
[CrossRef] [PubMed]

T. D. Wilkerson, G. Schwemmer, B. Gentry, L. P. Giver, “Intensities and N2 collision-broadening coefficients measured for selected H2O absorption lines between 715 and 732 nm,” J. Quant. Spectrosc. Radiat. Transfer 22, 315–331 (1979).
[CrossRef]

1974 (1)

R. M. Schotland, “Errors in the lidar measurement of atmospheric gases by differential absorption,” J. Appl. Meteorol. 13, 71–77 (1974).
[CrossRef]

1972 (1)

1964 (1)

C. Young, “Calculation of the absorption coefficient for lines with combined Doppler and Lorentz broadening,” J. Quant. Spectrosc. Radiat. Transfer 5, 549–552 (1964).
[CrossRef]

Ansmann, A.

Baker, P. W.

Bösenberg, J.

A. Ansmann, J. Bösenberg, “Correction scheme for spectral broadening by Rayleigh scattering in differential absorption lidar measurements of water vapor in the troposphere,” Appl. Opt. 26, 3026–3032 (1987).
[CrossRef] [PubMed]

J. Bösenberg, “Measurements of the pressure shift of water vapor absorption lines by simultaneous photoacoustic spectroscopy,” Appl. Opt. 24, 3531–3534 (1985).
[CrossRef] [PubMed]

J. Bösenberg, “A differential absorption lidar system for high resolution water vapor measurements in the troposphere,” Internal Rep. 71 (Max-Planck-Institute of Meteorology, Hamburg, Germany, 1991).

J. Bösenberg, “A DIAL system for high resolution water vapor measurements in the troposphere,” in Laser and Optical Remote Sensing: Instrumentation and Techniques, Vol. 18 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 22–25.

Brault, J.W.

J. Y. Mandin, J. P. Chevillard, C. Camy-Peyret, J. M. Flaud, J.W. Brault, “The high-resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

Brothers, A. M.

Browell, E. V.

E. V. Browell, S. Ismail, B. E. Grossmann, “Temperature sensitivity of differential absorption lidar measurements of water vapor in the 720-nm region,” Appl. Opt. 30, 1517–1524 (1991).
[CrossRef] [PubMed]

M. S. Higdon, E. V. Browell, P. Ponsardin, B. E. Grossmann, “Airborne water vapor DIAL system development laser radar V,” in Proc Soc. Photo-Opt. Instrum. Eng. 1222, 183–185 (1990).

B. E. Grossmann, E. V. Browell, “Spectroscopy of water vapor in the 720-nm region: line strengths, self-induced pressure broadenings and shifts, and temperature dependence of linewidths and shifts,” J. Mol. Spectrosc. 136, 264–294 (1989).
[CrossRef]

B. E. Grossmann, E. V. Browell, “Water vapor line broadening and shifting by air, nitrogen, oxygen, and argon in the 720-nm wavelength region,” J. Mol. Spectrosc. 138, 562–595 (1989).
[CrossRef]

S. Ismail, E. V. Browell, “Airborne and spaceborne lidar measurements of water vapor profiles: a sensitivity analysis,” Appl. Opt. 28, 3603–3615 (1989).
[CrossRef] [PubMed]

E. V. Browell, T. D. Wilkerson, T. J. McIlrath, “Water vapor differential absorption lidar development and evaluation,” Appl. Opt. 18, 3474–3483 (1979).
[CrossRef] [PubMed]

E. V. Browell, A. K. Goroch, T. D. Wilkerson, S. Ismail, R. Markson, “Airborne DIAL water vapor and aerosol measurements over the gulf stream,” presented at the Twelfth International Laser Radar Conference, Aix-en-Provence, France, 13–17 August 1984.

Bruneau, D.

Busen, R.

R. Busen, “Humidity measurements on the DLR aircraft,” presented at the Proceedings of the Tropospheric Profiling: Needs and Technologies, Boulder, Colo., 10–13 September 1991.

Cahen, C.

C. Cahen, G. Megie, P. Flamant, “Lidar monitoring of water vapor cycle in the troposphere,” J. Appl. Meteorol. 21, 1506–1515 (1982).
[CrossRef]

C. Cahen, G. Megie, “A spectral limitation of the range resolved differential absorption lidar technique,” J. Quant. Spectrosc. Radiat. Transfer 25, 151–157 (1981).
[CrossRef]

C. Cahen, J.-L. Lesne, P. Deschamps, P. Y. Thro, “Testing the mobile meteorological DIAL system for humidity and temperature monitoring,” presented at the Fourteenth International Laser Radar Conference International Commission on Laser Atmospheric Studies, San Candido, Italy, 24–26 June 1988.

Camy-Peyret, C.

J. Y. Mandin, J. P. Chevillard, C. Camy-Peyret, J. M. Flaud, J.W. Brault, “The high-resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

Cazeneuve, H.

Cha, S.

Chan, K. P.

Chevillard, J. P.

J. Y. Mandin, J. P. Chevillard, C. Camy-Peyret, J. M. Flaud, J.W. Brault, “The high-resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

Clark, T. L.

T. Hauf, T. L. Clark, “Three-dimensional numerical experiments on convectively forced internal gravity waves,” Q. J. R. Meteorol. Soc. 115, 309–333 (1989).
[CrossRef]

Cooney, J.

Deschamps, P.

C. Cahen, J.-L. Lesne, P. Deschamps, P. Y. Thro, “Testing the mobile meteorological DIAL system for humidity and temperature monitoring,” presented at the Fourteenth International Laser Radar Conference International Commission on Laser Atmospheric Studies, San Candido, Italy, 24–26 June 1988.

Ehret, G.

G. Ehret, W. Renger, A. Schmitz-Pfeiffer, “Airborne water vapour DIAL,” presented at the Lower Tropospheric Profiling: Needs and Technologies Meeting, Boulder, Colo., 31 May–3 June 1988).

G. Ehret, W. Renger, “Atmospheric aerosol and humidity profiling using an airborne DIAL system in the near IR,” in Optical Remote Sensing of the Atmosphere, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 586–589.

Facundo, J.

J. H. Golden, R. Serafin, V. Lally, J. Facundo, “Atmospheric sounding systems,” in Mesoscale Meteorology and Forecasting, P. S. Ray, ed. (American Meteorological Society, Boston, Mass., 1986), Chap. 4, pp. 50–57.

Ferrare, R.

S. H. Melfi, D. N. Whiteman, R. Ferrare, “Observation of atmospheric fronts using Raman lidar moisture measurements,” J. Appl. Meteorol. 28, 789–806 (1989).
[CrossRef]

Flamant, P.

C. Cahen, G. Megie, P. Flamant, “Lidar monitoring of water vapor cycle in the troposphere,” J. Appl. Meteorol. 21, 1506–1515 (1982).
[CrossRef]

Flaud, J. M.

J. Y. Mandin, J. P. Chevillard, C. Camy-Peyret, J. M. Flaud, J.W. Brault, “The high-resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

Gentry, B.

T. D. Wilkerson, G. Schwemmer, B. Gentry, L. P. Giver, “Intensities and N2 collision-broadening coefficients measured for selected H2O absorption lines between 715 and 732 nm,” J. Quant. Spectrosc. Radiat. Transfer 22, 315–331 (1979).
[CrossRef]

Gerhardt, H.

M. Przybylski, B. Otto, H. Gerhardt, “Spectral purity of pulsed dye laser,” Appl Phys. B 49, 201–203 (1989).
[CrossRef]

Giver, L. P.

T. D. Wilkerson, G. Schwemmer, B. Gentry, L. P. Giver, “Intensities and N2 collision-broadening coefficients measured for selected H2O absorption lines between 715 and 732 nm,” J. Quant. Spectrosc. Radiat. Transfer 22, 315–331 (1979).
[CrossRef]

Golden, J. H.

J. H. Golden, R. Serafin, V. Lally, J. Facundo, “Atmospheric sounding systems,” in Mesoscale Meteorology and Forecasting, P. S. Ray, ed. (American Meteorological Society, Boston, Mass., 1986), Chap. 4, pp. 50–57.

Goroch, A. K.

E. V. Browell, A. K. Goroch, T. D. Wilkerson, S. Ismail, R. Markson, “Airborne DIAL water vapor and aerosol measurements over the gulf stream,” presented at the Twelfth International Laser Radar Conference, Aix-en-Provence, France, 13–17 August 1984.

Grant, W. B.

Grossmann, B. E.

E. V. Browell, S. Ismail, B. E. Grossmann, “Temperature sensitivity of differential absorption lidar measurements of water vapor in the 720-nm region,” Appl. Opt. 30, 1517–1524 (1991).
[CrossRef] [PubMed]

M. S. Higdon, E. V. Browell, P. Ponsardin, B. E. Grossmann, “Airborne water vapor DIAL system development laser radar V,” in Proc Soc. Photo-Opt. Instrum. Eng. 1222, 183–185 (1990).

B. E. Grossmann, E. V. Browell, “Spectroscopy of water vapor in the 720-nm region: line strengths, self-induced pressure broadenings and shifts, and temperature dependence of linewidths and shifts,” J. Mol. Spectrosc. 136, 264–294 (1989).
[CrossRef]

B. E. Grossmann, E. V. Browell, “Water vapor line broadening and shifting by air, nitrogen, oxygen, and argon in the 720-nm wavelength region,” J. Mol. Spectrosc. 138, 562–595 (1989).
[CrossRef]

Hänsch, T. W.

Hardesty, R. M.

Hauf, T.

T. Hauf, T. L. Clark, “Three-dimensional numerical experiments on convectively forced internal gravity waves,” Q. J. R. Meteorol. Soc. 115, 309–333 (1989).
[CrossRef]

Hermann, H.

Ch. Werner, H. Hermann, “Lidar measurements of the vertical absolute humidity distribution in the boundary layer,” J. Appl. Meteorol. 20, 476–481 (1981).
[CrossRef]

Higdon, M. S.

M. S. Higdon, E. V. Browell, P. Ponsardin, B. E. Grossmann, “Airborne water vapor DIAL system development laser radar V,” in Proc Soc. Photo-Opt. Instrum. Eng. 1222, 183–185 (1990).

Ismail, S.

E. V. Browell, S. Ismail, B. E. Grossmann, “Temperature sensitivity of differential absorption lidar measurements of water vapor in the 720-nm region,” Appl. Opt. 30, 1517–1524 (1991).
[CrossRef] [PubMed]

S. Ismail, E. V. Browell, “Airborne and spaceborne lidar measurements of water vapor profiles: a sensitivity analysis,” Appl. Opt. 28, 3603–3615 (1989).
[CrossRef] [PubMed]

E. V. Browell, A. K. Goroch, T. D. Wilkerson, S. Ismail, R. Markson, “Airborne DIAL water vapor and aerosol measurements over the gulf stream,” presented at the Twelfth International Laser Radar Conference, Aix-en-Provence, France, 13–17 August 1984.

Killinger, D. K.

Lally, V.

J. H. Golden, R. Serafin, V. Lally, J. Facundo, “Atmospheric sounding systems,” in Mesoscale Meteorology and Forecasting, P. S. Ray, ed. (American Meteorological Society, Boston, Mass., 1986), Chap. 4, pp. 50–57.

Lehmann, W.

E. Voss, M. Riebesell, W. Lehmann, C. Weitkamp, W. Michaelis, “Moisture height profiler,” in Optical Systems for Space Applications, H. Lutz, G. Otrio, eds., Proc. Soc. Photo-Opt. Instrum. Eng.810, 37–41 (1987).

Lesne, J.-L.

C. Cahen, J.-L. Lesne, P. Deschamps, P. Y. Thro, “Testing the mobile meteorological DIAL system for humidity and temperature monitoring,” presented at the Fourteenth International Laser Radar Conference International Commission on Laser Atmospheric Studies, San Candido, Italy, 24–26 June 1988.

Loth, C.

Makushkin, Yu. S.

Mandin, J. Y.

J. Y. Mandin, J. P. Chevillard, C. Camy-Peyret, J. M. Flaud, J.W. Brault, “The high-resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

Margolis, J. S.

Marichev, V. N.

Markson, R.

E. V. Browell, A. K. Goroch, T. D. Wilkerson, S. Ismail, R. Markson, “Airborne DIAL water vapor and aerosol measurements over the gulf stream,” presented at the Twelfth International Laser Radar Conference, Aix-en-Provence, France, 13–17 August 1984.

McIlrath, T. J.

Megie, G.

C. Cahen, G. Megie, P. Flamant, “Lidar monitoring of water vapor cycle in the troposphere,” J. Appl. Meteorol. 21, 1506–1515 (1982).
[CrossRef]

C. Cahen, G. Megie, “A spectral limitation of the range resolved differential absorption lidar technique,” J. Quant. Spectrosc. Radiat. Transfer 25, 151–157 (1981).
[CrossRef]

Melfi, S. H.

S. H. Melfi, D. N. Whiteman, R. Ferrare, “Observation of atmospheric fronts using Raman lidar moisture measurements,” J. Appl. Meteorol. 28, 789–806 (1989).
[CrossRef]

Michaelis, W.

E. Voss, M. Riebesell, W. Lehmann, C. Weitkamp, W. Michaelis, “Moisture height profiler,” in Optical Systems for Space Applications, H. Lutz, G. Otrio, eds., Proc. Soc. Photo-Opt. Instrum. Eng.810, 37–41 (1987).

Mitev, V.

G. Vaughan, D. P. Wareing, L. Thomas, V. Mitev, “Humidity measurements in the free troposphere using Raman backscatter,” Q. J. R. Meteorol. Soc. 114, 1471–1484 (1988).
[CrossRef]

Mitsel, A. A.

Nestor, J. R.

Otto, B.

M. Przybylski, B. Otto, H. Gerhardt, “Spectral purity of pulsed dye laser,” Appl Phys. B 49, 201–203 (1989).
[CrossRef]

Pelon, J.

Petri, K.

Ponsardin, P.

M. S. Higdon, E. V. Browell, P. Ponsardin, B. E. Grossmann, “Airborne water vapor DIAL system development laser radar V,” in Proc Soc. Photo-Opt. Instrum. Eng. 1222, 183–185 (1990).

Przybylski, M.

M. Przybylski, B. Otto, H. Gerhardt, “Spectral purity of pulsed dye laser,” Appl Phys. B 49, 201–203 (1989).
[CrossRef]

Renger, W.

G. Ehret, W. Renger, A. Schmitz-Pfeiffer, “Airborne water vapour DIAL,” presented at the Lower Tropospheric Profiling: Needs and Technologies Meeting, Boulder, Colo., 31 May–3 June 1988).

G. Ehret, W. Renger, “Atmospheric aerosol and humidity profiling using an airborne DIAL system in the near IR,” in Optical Remote Sensing of the Atmosphere, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 586–589.

Riebesell, M.

E. Voss, M. Riebesell, W. Lehmann, C. Weitkamp, W. Michaelis, “Moisture height profiler,” in Optical Systems for Space Applications, H. Lutz, G. Otrio, eds., Proc. Soc. Photo-Opt. Instrum. Eng.810, 37–41 (1987).

Salik, A.

Schmitz-Pfeiffer, A.

G. Ehret, W. Renger, A. Schmitz-Pfeiffer, “Airborne water vapour DIAL,” presented at the Lower Tropospheric Profiling: Needs and Technologies Meeting, Boulder, Colo., 31 May–3 June 1988).

Schotland, R. M.

R. M. Schotland, “Errors in the lidar measurement of atmospheric gases by differential absorption,” J. Appl. Meteorol. 13, 71–77 (1974).
[CrossRef]

R. M. Schotland, “Some observations of the vertical profile of water vapor by means of a laser optical radar,” in Proceedings of the Fourth Symposium on Remote Sensing of Environment (University of Michigan, Ann Arbor, Mich., 1966), pp. 273–277.

Schwemmer, G.

T. D. Wilkerson, G. Schwemmer, B. Gentry, L. P. Giver, “Intensities and N2 collision-broadening coefficients measured for selected H2O absorption lines between 715 and 732 nm,” J. Quant. Spectrosc. Radiat. Transfer 22, 315–331 (1979).
[CrossRef]

Serafin, R.

J. H. Golden, R. Serafin, V. Lally, J. Facundo, “Atmospheric sounding systems,” in Mesoscale Meteorology and Forecasting, P. S. Ray, ed. (American Meteorological Society, Boston, Mass., 1986), Chap. 4, pp. 50–57.

Thomas, L.

G. Vaughan, D. P. Wareing, L. Thomas, V. Mitev, “Humidity measurements in the free troposphere using Raman backscatter,” Q. J. R. Meteorol. Soc. 114, 1471–1484 (1988).
[CrossRef]

Thro, P. Y.

C. Cahen, J.-L. Lesne, P. Deschamps, P. Y. Thro, “Testing the mobile meteorological DIAL system for humidity and temperature monitoring,” presented at the Fourteenth International Laser Radar Conference International Commission on Laser Atmospheric Studies, San Candido, Italy, 24–26 June 1988.

Tratt, D. M.

Vaughan, G.

G. Vaughan, D. P. Wareing, L. Thomas, V. Mitev, “Humidity measurements in the free troposphere using Raman backscatter,” Q. J. R. Meteorol. Soc. 114, 1471–1484 (1988).
[CrossRef]

Voss, E.

E. Voss, M. Riebesell, W. Lehmann, C. Weitkamp, W. Michaelis, “Moisture height profiler,” in Optical Systems for Space Applications, H. Lutz, G. Otrio, eds., Proc. Soc. Photo-Opt. Instrum. Eng.810, 37–41 (1987).

Wareing, D. P.

G. Vaughan, D. P. Wareing, L. Thomas, V. Mitev, “Humidity measurements in the free troposphere using Raman backscatter,” Q. J. R. Meteorol. Soc. 114, 1471–1484 (1988).
[CrossRef]

Weitkamp, C.

E. Voss, M. Riebesell, W. Lehmann, C. Weitkamp, W. Michaelis, “Moisture height profiler,” in Optical Systems for Space Applications, H. Lutz, G. Otrio, eds., Proc. Soc. Photo-Opt. Instrum. Eng.810, 37–41 (1987).

Werner, Ch.

Ch. Werner, H. Hermann, “Lidar measurements of the vertical absolute humidity distribution in the boundary layer,” J. Appl. Meteorol. 20, 476–481 (1981).
[CrossRef]

Whiteman, D. N.

S. H. Melfi, D. N. Whiteman, R. Ferrare, “Observation of atmospheric fronts using Raman lidar moisture measurements,” J. Appl. Meteorol. 28, 789–806 (1989).
[CrossRef]

Wilkerson, T. D.

T. D. Wilkerson, G. Schwemmer, B. Gentry, L. P. Giver, “Intensities and N2 collision-broadening coefficients measured for selected H2O absorption lines between 715 and 732 nm,” J. Quant. Spectrosc. Radiat. Transfer 22, 315–331 (1979).
[CrossRef]

E. V. Browell, T. D. Wilkerson, T. J. McIlrath, “Water vapor differential absorption lidar development and evaluation,” Appl. Opt. 18, 3474–3483 (1979).
[CrossRef] [PubMed]

E. V. Browell, A. K. Goroch, T. D. Wilkerson, S. Ismail, R. Markson, “Airborne DIAL water vapor and aerosol measurements over the gulf stream,” presented at the Twelfth International Laser Radar Conference, Aix-en-Provence, France, 13–17 August 1984.

Young, C.

C. Young, “Calculation of the absorption coefficient for lines with combined Doppler and Lorentz broadening,” J. Quant. Spectrosc. Radiat. Transfer 5, 549–552 (1964).
[CrossRef]

Zuev, V. E.

Zuev, V. V.

Appl Phys. B (1)

M. Przybylski, B. Otto, H. Gerhardt, “Spectral purity of pulsed dye laser,” Appl Phys. B 49, 201–203 (1989).
[CrossRef]

Appl. Opt. (14)

J. R. Nestor, “Optogalvanic spectra of neon and argon in glow discharge lamps,” Appl. Opt. 21, 4154–4157 (1982).
[CrossRef] [PubMed]

D. Bruneau, H. Cazeneuve, C. Loth, J. Pelon, “Double-pulse dual-wavelength alexandrite laser for atmospheric water vapor measurement,” Appl. Opt. 30, 3930–3937 (1991).
[CrossRef] [PubMed]

T. W. Hänsch, “Repetitively pulsed tunable dye laser for high resolution spectroscopy,” Appl. Opt. 11, 895–898 (1972).
[CrossRef] [PubMed]

S. Ismail, E. V. Browell, “Airborne and spaceborne lidar measurements of water vapor profiles: a sensitivity analysis,” Appl. Opt. 28, 3603–3615 (1989).
[CrossRef] [PubMed]

J. Bösenberg, “Measurements of the pressure shift of water vapor absorption lines by simultaneous photoacoustic spectroscopy,” Appl. Opt. 24, 3531–3534 (1985).
[CrossRef] [PubMed]

E. V. Browell, S. Ismail, B. E. Grossmann, “Temperature sensitivity of differential absorption lidar measurements of water vapor in the 720-nm region,” Appl. Opt. 30, 1517–1524 (1991).
[CrossRef] [PubMed]

P. W. Baker, “Atmospheric water vapor differential absorption measurements on vertical paths with a CO2 lidar,” Appl. Opt. 22, 2257–2264 (1983).
[CrossRef] [PubMed]

V. V. Zuev, V. E. Zuev, Yu. S. Makushkin, V. N. Marichev, A. A. Mitsel, “Laser sounding of atmospheric humidity: experiment,” Appl. Opt. 22, 3742–3746 (1983).
[CrossRef] [PubMed]

R. M. Hardesty, “Coherent DIAL measurement of range-resolved water vapor concentration,” Appl. Opt. 23, 2545–2553 (1984).
[CrossRef] [PubMed]

W. B. Grant, J. S. Margolis, A. M. Brothers, D. M. Tratt, “CO2 DIAL measurements of water vapor,” Appl. Opt. 26, 3033–3042 (1987).
[CrossRef] [PubMed]

J. Cooney, K. Petri, A. Salik, “Measurements of high resolution atmospheric water vapor profiles by use of a solar blind Raman lidar,” Appl. Opt. 24, 104–108 (1985).
[CrossRef] [PubMed]

E. V. Browell, T. D. Wilkerson, T. J. McIlrath, “Water vapor differential absorption lidar development and evaluation,” Appl. Opt. 18, 3474–3483 (1979).
[CrossRef] [PubMed]

S. Cha, K. P. Chan, D. K. Killinger, “Tunable 2.1-μm Ho lidar for simultaneous range-resolved measurements of atmospheric water vapor and aerosol backscatter profiles,” Appl. Opt. 30, 3938–3943 (1991).
[CrossRef] [PubMed]

A. Ansmann, J. Bösenberg, “Correction scheme for spectral broadening by Rayleigh scattering in differential absorption lidar measurements of water vapor in the troposphere,” Appl. Opt. 26, 3026–3032 (1987).
[CrossRef] [PubMed]

J. Appl. Meteorol. (4)

C. Cahen, G. Megie, P. Flamant, “Lidar monitoring of water vapor cycle in the troposphere,” J. Appl. Meteorol. 21, 1506–1515 (1982).
[CrossRef]

S. H. Melfi, D. N. Whiteman, R. Ferrare, “Observation of atmospheric fronts using Raman lidar moisture measurements,” J. Appl. Meteorol. 28, 789–806 (1989).
[CrossRef]

Ch. Werner, H. Hermann, “Lidar measurements of the vertical absolute humidity distribution in the boundary layer,” J. Appl. Meteorol. 20, 476–481 (1981).
[CrossRef]

R. M. Schotland, “Errors in the lidar measurement of atmospheric gases by differential absorption,” J. Appl. Meteorol. 13, 71–77 (1974).
[CrossRef]

J. Mol. Spectrosc. (3)

J. Y. Mandin, J. P. Chevillard, C. Camy-Peyret, J. M. Flaud, J.W. Brault, “The high-resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

B. E. Grossmann, E. V. Browell, “Water vapor line broadening and shifting by air, nitrogen, oxygen, and argon in the 720-nm wavelength region,” J. Mol. Spectrosc. 138, 562–595 (1989).
[CrossRef]

B. E. Grossmann, E. V. Browell, “Spectroscopy of water vapor in the 720-nm region: line strengths, self-induced pressure broadenings and shifts, and temperature dependence of linewidths and shifts,” J. Mol. Spectrosc. 136, 264–294 (1989).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (3)

T. D. Wilkerson, G. Schwemmer, B. Gentry, L. P. Giver, “Intensities and N2 collision-broadening coefficients measured for selected H2O absorption lines between 715 and 732 nm,” J. Quant. Spectrosc. Radiat. Transfer 22, 315–331 (1979).
[CrossRef]

C. Young, “Calculation of the absorption coefficient for lines with combined Doppler and Lorentz broadening,” J. Quant. Spectrosc. Radiat. Transfer 5, 549–552 (1964).
[CrossRef]

C. Cahen, G. Megie, “A spectral limitation of the range resolved differential absorption lidar technique,” J. Quant. Spectrosc. Radiat. Transfer 25, 151–157 (1981).
[CrossRef]

Proc Soc. Photo-Opt. Instrum. Eng. (1)

M. S. Higdon, E. V. Browell, P. Ponsardin, B. E. Grossmann, “Airborne water vapor DIAL system development laser radar V,” in Proc Soc. Photo-Opt. Instrum. Eng. 1222, 183–185 (1990).

Q. J. R. Meteorol. Soc. (2)

T. Hauf, T. L. Clark, “Three-dimensional numerical experiments on convectively forced internal gravity waves,” Q. J. R. Meteorol. Soc. 115, 309–333 (1989).
[CrossRef]

G. Vaughan, D. P. Wareing, L. Thomas, V. Mitev, “Humidity measurements in the free troposphere using Raman backscatter,” Q. J. R. Meteorol. Soc. 114, 1471–1484 (1988).
[CrossRef]

Other (10)

E. Voss, M. Riebesell, W. Lehmann, C. Weitkamp, W. Michaelis, “Moisture height profiler,” in Optical Systems for Space Applications, H. Lutz, G. Otrio, eds., Proc. Soc. Photo-Opt. Instrum. Eng.810, 37–41 (1987).

R. M. Schotland, “Some observations of the vertical profile of water vapor by means of a laser optical radar,” in Proceedings of the Fourth Symposium on Remote Sensing of Environment (University of Michigan, Ann Arbor, Mich., 1966), pp. 273–277.

E. V. Browell, A. K. Goroch, T. D. Wilkerson, S. Ismail, R. Markson, “Airborne DIAL water vapor and aerosol measurements over the gulf stream,” presented at the Twelfth International Laser Radar Conference, Aix-en-Provence, France, 13–17 August 1984.

G. Ehret, W. Renger, “Atmospheric aerosol and humidity profiling using an airborne DIAL system in the near IR,” in Optical Remote Sensing of the Atmosphere, Vol. 4 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 586–589.

J. Bösenberg, “A DIAL system for high resolution water vapor measurements in the troposphere,” in Laser and Optical Remote Sensing: Instrumentation and Techniques, Vol. 18 of 1987 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 22–25.

G. Ehret, W. Renger, A. Schmitz-Pfeiffer, “Airborne water vapour DIAL,” presented at the Lower Tropospheric Profiling: Needs and Technologies Meeting, Boulder, Colo., 31 May–3 June 1988).

C. Cahen, J.-L. Lesne, P. Deschamps, P. Y. Thro, “Testing the mobile meteorological DIAL system for humidity and temperature monitoring,” presented at the Fourteenth International Laser Radar Conference International Commission on Laser Atmospheric Studies, San Candido, Italy, 24–26 June 1988.

R. Busen, “Humidity measurements on the DLR aircraft,” presented at the Proceedings of the Tropospheric Profiling: Needs and Technologies, Boulder, Colo., 10–13 September 1991.

J. H. Golden, R. Serafin, V. Lally, J. Facundo, “Atmospheric sounding systems,” in Mesoscale Meteorology and Forecasting, P. S. Ray, ed. (American Meteorological Society, Boston, Mass., 1986), Chap. 4, pp. 50–57.

J. Bösenberg, “A differential absorption lidar system for high resolution water vapor measurements in the troposphere,” Internal Rep. 71 (Max-Planck-Institute of Meteorology, Hamburg, Germany, 1991).

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Figures (16)

Fig. 1
Fig. 1

Schematic experimental setup of the airborne water vapor DIAL.

Fig. 2
Fig. 2

Optogalvanic spectra of the atomic neon transition 2p53s to 2p53p as a function of wavenumber detuning of the narrow-band dye laser around the center frequency, 13798.53 cm−1, with a step size of 0.004 cm−1. The measured profile is compared with a theoretical profile obtained from a least-squares fit.

Fig. 3
Fig. 3

Calculated spectral energy distribution of the narrow-band dye laser in comparison with both measured and fitted neon line profiles from Fig. 2. To help in visualizing the spectral impurity of the dye laser around the center frequency, the ordinate scaling from Fig. 2 has been magnified by a factor of 10. Both the measured profile and the laser line profile are normalized to their maximum value.

Fig. 4
Fig. 4

Residual errors from the line profile fit shown in Fig. 3 expressed as a percentage of the maximum value of the fitted profile.

Fig. 5
Fig. 5

Water vapor absorption in the near infrared. The spectra indicates the measured photoacoustic signal versus frequency detuning of the dye laser from 13 831 to 13 793 cm−1 at a step size of 0.02 cm−1 and a laser bandwidth of 0.2 cm−1. The highly resolved spectra of the line doublet on the right-hand side of this figure is obtained by tuning the narrow-band dye laser from Fig. 3 over the indicated spectral region. These lines are chosen for the DIAL measurements reported in Section 4.

Fig. 6
Fig. 6

Laser frequency calibration measurement. The photoacoustic signal of the s-line calibration as a function of the shot-pair number is shown during the airborne DIAL measurement in the lower troposphere at an altitude of 3600 m.

Fig. 7
Fig. 7

CCD intensity of the Fizeau spectrometer versus pixel number for one shot pair on- and off-line. The dashed curve marks the measured data, and the solid curve results from a smoothing algorithm using a FFT. The corresponding pixel number for the maximum value of the smoothed curve is used to determine the laser frequency position on a relative frequency scale with a resolution of 0.002 cm−1.

Fig. 8
Fig. 8

Laser frequency position measurement. This figure illustrates a statistical distribution of the pixel numbers associated to the maximum values of the smoothed data in Fig. 7 for each shot-pair number on line and off line. The rms value of 2.4 in the case of the on-line measurements corresponds to a laser line position inaccuracy of only 0.005 cm−1.

Fig. 9
Fig. 9

Range-resolved aerosol backscattering from the middle (a) and upper (b) trophosphere after averaging over 100 shot pairs. The strong peak at 1600 m results from cloud top backscattering in (a).

Fig. 10
Fig. 10

Effective absorption cross sections as a function of altitude height for the s and l lines of Fig. 5 for a standard summer atmosphere.

Fig. 11
Fig. 11

Horizontal water vapor distributions as a function of time and number of shot pairs horizontally averaged. These data result from calculations with lidar returns from atmospheric backscatter regions lying 900 m below the aircraft at 4300-m altitude. The vertical range resolution of the profiles is 300 m. For a better comparison, the mean values of those profiles where 10 and 50 shot pairs are averaged have been shifted by a constant amount (0.5 g/kg) against each other as indicated on the left. The true mean values are given on the right. The flight time of approximately 280 s corresponds to a horizontal distance of approximately 40 km at a flight speed at 140 m/s.

Fig. 12
Fig. 12

Water vapor mixing ratios as a function of time and altitude ranges, calculated from lidar returns in the lower and middle troposphere. The vertical resolution of these profiles is 300 m, and the horizontal resolution ranges between 4 km for the profiles at 2800 m and 5 km for those at 5200 m.

Fig. 13
Fig. 13

Water vapor mixing ratios as a function of time and altitude ranges in the upper troposphere. The vertical resolution of these profiles is 900 m, the horizontal resolution lies between 11 and 12 km. The reduced spatial resolution of these profiles compared with those from Fig. 12 results from a 200 shot-pair average and an increased flight speed of the aircraft in the upper troposphere of nearly 180 m/s. The flight time of approximately 200 s corresponds here to a horizontal distance of approximately 36 km.

Fig. 14
Fig. 14

Two-dimensional water vapor mixing ratio plot: Vertical cut through the atmosphere with a vertical resolution of 300 m and a horizontal resolution of 4 km. The ordinate shows the altitude in meters, and the abscissa shows the horizontal measurement time and range.

Fig. 15
Fig. 15

Water vapor profiles as a function of altitude in comparison with in situ measurements in the lower and middle (a) as well as the middle and upper troposphere (b). For the calculation of the DIAL data vertically spaced by 150 m, the signal averaging procedure indicated in Table 3 has been applied.

Fig. 16
Fig. 16

Uncorrected and corrected water vapor mixing ratio profiles as a function of altitude calculated from the 6-km altitude measurement in comparison with the in situ data and the two-way optical depth (upper abscissa). The corrected profile fits quite well with in situ data up to an optical depth of ∼2.5.

Tables (4)

Tables Icon

Table 1 Water Vapor DIAL System Parameters

Tables Icon

Table 2 Line Parameters of Selected Water Vapor Lines Indicated in Fig. 5 According to Grossman et al.a

Tables Icon

Table 3 Signal Averaging Data for the Calculation of the Vertical Water Vapor Profiles Presented in Fig. 15

Tables Icon

Table 4 Estimated Systematical Errors (in percent) of Water Vapor Mixing Ratios as a Function of Altitude Ranges (in kilometers)

Equations (14)

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

N ¯ ( R ) = 1 2 σ Δ R ln P off ( R 2 ) P on ( R 1 ) P on ( R 2 ) P off ( R 1 ) ,
σ = σ on σ off ,
σ ( ν ) = S γ π 3 / 2 + exp ( ξ 2 ) 1 + ( x ξ y ) 2 d ξ ,
y = γ γ D ( ln 2 ) 1 / 2 , x = ν ν 0 γ D ( ln 2 ) 1 / 2 .
S = S 0 ( T 0 T ) 1.5 exp [ E h c k ( 1 T 0 1 T ) ] ,
γ = γ 0 P P 0 ( T 0 T ) n ,
γ D = ν 0 c ( 2 k T ln 2 m ) 1 / 2 ,
σ eff = 0 σ ( ν ) [ L ( ν ν on ) L ( ν ν off ) ] d ν 0 L ( ν ) d ν .
m r = N ¯ N ¯ air 0.622 ,
L ( ν , ν 0 ) = L 0 { P 1 exp [ ( ν ν 0 ) 2 γ 1 2 l n 2 ] + P 2 exp [ ( ν ν 0 ) 2 γ 2 2 l n 2 ] } ,
Δ m r = 0.622 Δ R σ eff N L n x n y S / N ,
τ ( R ) = 2 0 R N ( r ) σ ( r ) d r ,
P 1 ( R ) = P 1 exp [ τ ( R ) ] ,
J , K a , K c

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