Abstract

The transmission, including all scattering orders, of a plane-parallel beam in a homogeneous scattering medium containing aerosols (e.g., water cloud) mixed with an absorbing gas (e.g., ozone) is computed with a two-stream radiative transfer model. From differential transmission the concentration of the gas is deduced. The effect of multiple-scattering on the deduced concentration is shown for conservative scattering aerosols for which the multiple scattering by the aerosols is differentially absorbed by the gas and for nonconservative scattering aerosols for which the multiple scattering is differentially absorbed by the aerosols as well as differentially absorbed by the gas. The two-stream analytical model (with no dependence on the field of view) shows good qualitative agreement (especially for a small field of view) with a numerical radiative transfer model in which the trace gas concentration is computed for the different detector’s field of view.

© 1997 Optical Society of America

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References

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  1. E. D. Hinkley, R. T. Ku, P. L. Kelly, “Techniques for detection of molecular pollutants by absorption of laser radiation,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, New York, 1976), pp. 238–295.
  2. H. C. van de Hulst, Multiple Light Scattering Tables, Formulas and Application (Academic, New York, 1980), Cap. 14, p. 477.
  3. L. Bissonnete, D. L. Hutt, “Multiply scattered aerosol lidar returns: inversion method and comparison with in situ measurements,” Appl. Opt. 34, 6959–6975 (1995).
    [CrossRef]
  4. C. M. R. Platt, “Lidar and radiometric observations of Cirrus clouds,” J. Atmos. Sci. 30, 1191–1204 (1973).
    [CrossRef]
  5. J. A. Weinman, “Effect of multiple scattering on light pulses reflected by turbid atmosphere,” J. Atmos. Sci. 33, 1763–1771 (1976).
    [CrossRef]
  6. S. R. Pal, A. I. Carswell, “Multiple scattering in atmospheric clouds: lidar observations,” Appl. Opt. 15, 1990–1995 (1976).
    [CrossRef] [PubMed]
  7. K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
    [CrossRef]
  8. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), Chap. 3, p. 56.
  9. A. Ben-David, “Wavelength dependence of backscattering and extinction of kaolin dust at CO2 laser wavelengths: effect of multiple-scattering,” Appl. Opt. 32, 1598–1605 (1993).
    [CrossRef] [PubMed]
  10. A. Ben-David, “Multiple-scattering transmission and an effective average photon path length of a plane-parallel beam in a homogeneous medium,” Appl. Opt. 34, 2802–2810 (1995).
    [CrossRef] [PubMed]
  11. B. M. Herman, S. R. Browning, “A numerical solution to the equation of radiative transfer,” J. Atmos. Sci. 32, 559–566 (1965).
    [CrossRef]
  12. G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-µm wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [CrossRef] [PubMed]
  13. M. S. Shumate, R. T. Menzies, W. B. Grant, D. S. McDougal, “Laser absorption spectrometer: remote measurement of tropospheric ozone,” Appl. Opt. 20, 545–552 (1981).
    [CrossRef] [PubMed]
  14. R. T. Menzies, M. S. Shumate, “Remote measurements of ambient air pollutants with bistatic laser system,” Appl. Opt. 15, 2080–2084 (1976).
    [CrossRef] [PubMed]
  15. A. Mayer, J. Comera, H. Charpentier, C. Jaussaud, “Absorption coefficients of various pollutant gases at CO2 laser wavelengths; application to the remote sensing of those pollutants,” Appl. Opt. 17, 391–393 (1978).
    [CrossRef]
  16. W. B. Grant, “Effect of differential spectral reflectance on DIAL measurements using topographic targets,” Appl. Opt. 21, 2390–2394 (1982).
    [CrossRef] [PubMed]
  17. L. T. Molina, M. J. Molina, “Absolute absorption cross sections of ozone in the 185- to 350-wavelength range,” J. Geophys. Res. 91, 14501–14508 (1986).
    [CrossRef]
  18. M. Cacciani, A. di Sarra, G. Fiocco, A. Amoruso, “Absolute determination of the cross sections of ozone in the wavelength region 339–355 nm at temperature 220–293 K,” J. Geophys. Res. 94, 8485–8490 (1989).
    [CrossRef]

1995 (2)

1993 (1)

1989 (1)

M. Cacciani, A. di Sarra, G. Fiocco, A. Amoruso, “Absolute determination of the cross sections of ozone in the wavelength region 339–355 nm at temperature 220–293 K,” J. Geophys. Res. 94, 8485–8490 (1989).
[CrossRef]

1986 (1)

L. T. Molina, M. J. Molina, “Absolute absorption cross sections of ozone in the 185- to 350-wavelength range,” J. Geophys. Res. 91, 14501–14508 (1986).
[CrossRef]

1982 (1)

1981 (1)

1978 (1)

1976 (4)

R. T. Menzies, M. S. Shumate, “Remote measurements of ambient air pollutants with bistatic laser system,” Appl. Opt. 15, 2080–2084 (1976).
[CrossRef] [PubMed]

J. A. Weinman, “Effect of multiple scattering on light pulses reflected by turbid atmosphere,” J. Atmos. Sci. 33, 1763–1771 (1976).
[CrossRef]

S. R. Pal, A. I. Carswell, “Multiple scattering in atmospheric clouds: lidar observations,” Appl. Opt. 15, 1990–1995 (1976).
[CrossRef] [PubMed]

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

1973 (2)

C. M. R. Platt, “Lidar and radiometric observations of Cirrus clouds,” J. Atmos. Sci. 30, 1191–1204 (1973).
[CrossRef]

G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-µm wavelength region,” Appl. Opt. 12, 555–563 (1973).
[CrossRef] [PubMed]

1965 (1)

B. M. Herman, S. R. Browning, “A numerical solution to the equation of radiative transfer,” J. Atmos. Sci. 32, 559–566 (1965).
[CrossRef]

Amoruso, A.

M. Cacciani, A. di Sarra, G. Fiocco, A. Amoruso, “Absolute determination of the cross sections of ozone in the wavelength region 339–355 nm at temperature 220–293 K,” J. Geophys. Res. 94, 8485–8490 (1989).
[CrossRef]

Ben-David, A.

Bissonnete, L.

Browning, S. R.

B. M. Herman, S. R. Browning, “A numerical solution to the equation of radiative transfer,” J. Atmos. Sci. 32, 559–566 (1965).
[CrossRef]

Cacciani, M.

M. Cacciani, A. di Sarra, G. Fiocco, A. Amoruso, “Absolute determination of the cross sections of ozone in the wavelength region 339–355 nm at temperature 220–293 K,” J. Geophys. Res. 94, 8485–8490 (1989).
[CrossRef]

Carswell, A. I.

Charpentier, H.

Comera, J.

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), Chap. 3, p. 56.

di Sarra, A.

M. Cacciani, A. di Sarra, G. Fiocco, A. Amoruso, “Absolute determination of the cross sections of ozone in the wavelength region 339–355 nm at temperature 220–293 K,” J. Geophys. Res. 94, 8485–8490 (1989).
[CrossRef]

Fiocco, G.

M. Cacciani, A. di Sarra, G. Fiocco, A. Amoruso, “Absolute determination of the cross sections of ozone in the wavelength region 339–355 nm at temperature 220–293 K,” J. Geophys. Res. 94, 8485–8490 (1989).
[CrossRef]

Grant, W. B.

Hale, G. M.

Herman, B. M.

B. M. Herman, S. R. Browning, “A numerical solution to the equation of radiative transfer,” J. Atmos. Sci. 32, 559–566 (1965).
[CrossRef]

Hinkley, E. D.

E. D. Hinkley, R. T. Ku, P. L. Kelly, “Techniques for detection of molecular pollutants by absorption of laser radiation,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, New York, 1976), pp. 238–295.

Hutt, D. L.

Jaussaud, C.

Kelly, P. L.

E. D. Hinkley, R. T. Ku, P. L. Kelly, “Techniques for detection of molecular pollutants by absorption of laser radiation,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, New York, 1976), pp. 238–295.

Ku, R. T.

E. D. Hinkley, R. T. Ku, P. L. Kelly, “Techniques for detection of molecular pollutants by absorption of laser radiation,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, New York, 1976), pp. 238–295.

Kunkel, K. E.

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

Mayer, A.

McDougal, D. S.

Menzies, R. T.

Molina, L. T.

L. T. Molina, M. J. Molina, “Absolute absorption cross sections of ozone in the 185- to 350-wavelength range,” J. Geophys. Res. 91, 14501–14508 (1986).
[CrossRef]

Molina, M. J.

L. T. Molina, M. J. Molina, “Absolute absorption cross sections of ozone in the 185- to 350-wavelength range,” J. Geophys. Res. 91, 14501–14508 (1986).
[CrossRef]

Pal, S. R.

Platt, C. M. R.

C. M. R. Platt, “Lidar and radiometric observations of Cirrus clouds,” J. Atmos. Sci. 30, 1191–1204 (1973).
[CrossRef]

Querry, M. R.

Shumate, M. S.

Weinman, J. A.

J. A. Weinman, “Effect of multiple scattering on light pulses reflected by turbid atmosphere,” J. Atmos. Sci. 33, 1763–1771 (1976).
[CrossRef]

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

Appl. Opt. (9)

L. Bissonnete, D. L. Hutt, “Multiply scattered aerosol lidar returns: inversion method and comparison with in situ measurements,” Appl. Opt. 34, 6959–6975 (1995).
[CrossRef]

S. R. Pal, A. I. Carswell, “Multiple scattering in atmospheric clouds: lidar observations,” Appl. Opt. 15, 1990–1995 (1976).
[CrossRef] [PubMed]

A. Ben-David, “Wavelength dependence of backscattering and extinction of kaolin dust at CO2 laser wavelengths: effect of multiple-scattering,” Appl. Opt. 32, 1598–1605 (1993).
[CrossRef] [PubMed]

A. Ben-David, “Multiple-scattering transmission and an effective average photon path length of a plane-parallel beam in a homogeneous medium,” Appl. Opt. 34, 2802–2810 (1995).
[CrossRef] [PubMed]

G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-µm wavelength region,” Appl. Opt. 12, 555–563 (1973).
[CrossRef] [PubMed]

M. S. Shumate, R. T. Menzies, W. B. Grant, D. S. McDougal, “Laser absorption spectrometer: remote measurement of tropospheric ozone,” Appl. Opt. 20, 545–552 (1981).
[CrossRef] [PubMed]

R. T. Menzies, M. S. Shumate, “Remote measurements of ambient air pollutants with bistatic laser system,” Appl. Opt. 15, 2080–2084 (1976).
[CrossRef] [PubMed]

A. Mayer, J. Comera, H. Charpentier, C. Jaussaud, “Absorption coefficients of various pollutant gases at CO2 laser wavelengths; application to the remote sensing of those pollutants,” Appl. Opt. 17, 391–393 (1978).
[CrossRef]

W. B. Grant, “Effect of differential spectral reflectance on DIAL measurements using topographic targets,” Appl. Opt. 21, 2390–2394 (1982).
[CrossRef] [PubMed]

J. Atmos. Sci. (4)

B. M. Herman, S. R. Browning, “A numerical solution to the equation of radiative transfer,” J. Atmos. Sci. 32, 559–566 (1965).
[CrossRef]

K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

C. M. R. Platt, “Lidar and radiometric observations of Cirrus clouds,” J. Atmos. Sci. 30, 1191–1204 (1973).
[CrossRef]

J. A. Weinman, “Effect of multiple scattering on light pulses reflected by turbid atmosphere,” J. Atmos. Sci. 33, 1763–1771 (1976).
[CrossRef]

J. Geophys. Res. (2)

L. T. Molina, M. J. Molina, “Absolute absorption cross sections of ozone in the 185- to 350-wavelength range,” J. Geophys. Res. 91, 14501–14508 (1986).
[CrossRef]

M. Cacciani, A. di Sarra, G. Fiocco, A. Amoruso, “Absolute determination of the cross sections of ozone in the wavelength region 339–355 nm at temperature 220–293 K,” J. Geophys. Res. 94, 8485–8490 (1989).
[CrossRef]

Other (3)

E. D. Hinkley, R. T. Ku, P. L. Kelly, “Techniques for detection of molecular pollutants by absorption of laser radiation,” in Laser Monitoring of the Atmosphere, E. D. Hinkley, ed. (Springer-Verlag, New York, 1976), pp. 238–295.

H. C. van de Hulst, Multiple Light Scattering Tables, Formulas and Application (Academic, New York, 1980), Cap. 14, p. 477.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969), Chap. 3, p. 56.

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Figures (12)

Fig. 1
Fig. 1

Contours of ΔC(ppb) (thin curves) and the total transmission T(%) (thick curves) at the on-resonant wavelength as a function of the aerosol number density N(cm-3) and the ozone concentration C(ppb) for the transmission of a normally incident plane-parallel beam through a layer of L = 1 km aerosol cloud C.1 homogeneously mixed with ozone. The on-resonant wavelength is the 9 p 14 CO2 laser wavelength and the off-resonant wavelength is the 9 p 22 CO2 laser wavelength. The aerosol optical depth N σ1p L and the ozone optical depth k1 CL for the on-resonant wavelength are also shown. ΔC(ppb) and T(%) are computed with Eqs. (8) and (5) of the two-stream radiative transfer model.

Fig. 2
Fig. 2

Contours of the ratio of the on-resonant multiple-scattering optical depth and the off-resonant multiple-scattering optical depth τms1ms2 [computed with Eq. (6)] as a function of the aerosol number density N(cm-3) and the ozone concentration C(ppb) for Fig. 1.

Fig. 3
Fig. 3

Contours of ΔC(ppb) as a function of the aerosol number density N (cm-3) and the ozone concentration C(ppb) for a layer of L = 1 km aerosol cloud C.1 homogeneously mixed with ozone, when the off-resonant (9 p 22) aerosol parameters (σ2p, a2p, g2p) were set to be the same as the on-resonant (9 p 14) aerosol parameters (σ1p, a1p, g1p) in the two-stream radiative transfer model.

Fig. 4
Fig. 4

Contours of ΔC(ppb) (thin curves) and the total transmission T(%) (thick curves) at the on-resonant wavelength as a function of the path length L(km) in homogeneous layer with aerosol number density N = 60 cm-3 and ozone concentration C(ppb), computed with the two-stream radiative transfer model. The on-resonant wavelength is the 9 p 14 CO2 laser wavelength and the off-resonant wavelength is the 9 p 22 CO2 laser wavelength. The aerosol optical depth N σ1p L and the ozone optical depth k1 CL for L = 1 km at the on-resonant wavelength are also shown.

Fig. 5
Fig. 5

Same as Fig. 1, but for the UV wavelength pair (308 nm, 355 nm) where the on-resonant wavelength is 308 nm (XeCl excimer laser) and the off-resonant wavelength is 355 nm (third harmonic of a Nd:YAG laser).

Fig. 6
Fig. 6

Contours of the ratio of the on-resonant multiple-scattering optical depth and the off-resonant multiple-scattering optical depth τms1ms2 as a function of the aerosol number density N (cm-3) and the ozone concentration C(ppb) for Fig. 5.

Fig. 7
Fig. 7

Contours of ΔC(ppb) as a function of the aerosol number density N (cm-3) and the ozone concentration C(ppb) for a layer of L = 1 km aerosol cloud C.1 homogeneously mixed with ozone, when the off-resonant (308 nm) aerosol parameters (σ2p, a2p, g2p) were set to be the same as the on-resonant (355 nm) aerosol parameters (σ1p, a1p, g1p) in the two-stream radiative transfer model.

Fig. 8
Fig. 8

Same as Fig. 1 except for the UV wavelength pair (266 nm, 299 nm), where the on-resonant wavelength is 266 nm (fourth harmonic of a Nd:YAG laser) and the off-resonant wavelength is 299 nm (a shifted stimulated Raman scattering in hydrogen).

Fig. 9
Fig. 9

Contours of the ratio of the on-resonant multiple-scattering optical depth and the off-resonant multiple-scattering optical depth τms1ms2 as a function of the aerosol number density N (cm-3) and the ozone concentration C(ppb) for Fig. 8.

Fig. 10
Fig. 10

Contours of ΔC(Ω) (ppb) (thin curves) and the total transmission T (L, Ω) (%) (thick curves) at the on-resonant wavelength as a function of the aerosol number density N (cm-3) and the ozone concentration C(ppb) for the transmission of a plane-parallel beam incident at angle θ0 = 5° through a layer of L = 1 km aerosol cloud C.1 homogeneously mixed with ozone. The on-resonant wavelength is the 9 p 14 CO2 laser wavelength and the off-resonant wavelength is the 9 p 22 CO2 laser wavelength. The aerosol optical depth N σ1p L and the ozone optical depth k1 CL for the on-resonant wavelength are also shown. Contours of ΔC(Ω) and T(L, Ω) are computed with a numerical radiative transfer model11 [Eqs. (11) and (12)]: (a) field of view (half-width) Ω = 20°; (b) field of view (half-width) Ω = 40° (c) field of view (half-width) Ω = 60°; and (d) field of view (half-width) Ω = 90°.

Fig. 11
Fig. 11

Same as Fig. 10, but for the UV wavelength pair (308 nm, 355 nm) where the on-resonant wavelength is 308 nm (XeCl excimer laser) and the off-resonant wavelength is 355 nm (third harmonic of a Nd:YAG laser): (a) field of view (half-width) Ω = 20°; (b) field of view (half-width) Ω = 40°; (c) field of view (half-width) Ω = 60°; and (d) field of view (half-width) Ω = 90°.

Fig. 12
Fig. 12

Same as Fig. 10, but for the UV wavelength pair (266 nm, 299 nm) where the on-resonant wavelength is 266 nm (fourth harmonic of a Nd:YAG laser) and the off-resonant wavelength is 299 nm (a shifted stimulated Raman scattering in hydrogen): (a) field of view (half-width) Ω = 20°; (b) field of view (half-width) Ω = 40°; (c) field of view (half-width) Ω = 60°; and (d) field of view (half-width) Ω = 90°.

Tables (2)

Tables Icon

Table 1 Optical Parameters (volume extinction coefficient N σp, single-scattering albedo ap, asymmetry parameter gp, volume backscattering coefficient N βp) of Cloud C.1 with Aerosol Number Density N = 100 cm-3 and Absorption Coefficient, k, of ozone

Tables Icon

Table 2 Error ΔC0 = N1p - σ2p)/(k1 - k2) for Ozone due to Aerosol Differential Extinction of Cloud C.1 with Aerosol Number Density N = 100 cm-3, and Error ΔCβ L = ln(β21)/(k1 - k2) for Cloud C.1 Differential Reflectivity and Path Length L in the Ozone Trace Gas

Equations (13)

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Tτ=exp-τ=T0τexpτms,
C*=lnT2/T1k1-k2L=C+τ1p-τ2pk1-k2L+τms2-τms1k1-k2L,
C*=C+ΔC0+ΔCms,
ΔC=ΔC0+ΔCms=τ1p-τms1-τ2p-τms2k1-k2L.
Tτ, a, g=coshτz+x sinhτz/z-1=T0τexpτms,
τms=τ-lncoshτz+x sinhτz/z.
τ=Nσp+k C L=τp+k C L,a=NσpapNσp+k C=τpapτp+k C L,g=gp, x=1-1+ga/2, z=1-a1-ag1/2,
ΔC=lncoshτ1z1+x1 sinhτ1z1/z1coshτ2z2+x2 sinhτ2z2/z2k1-k2L-C.
τms|τz>1=τ1-z+ln21+x/z
τms|τz<1=τ-ln1+τx+τz2/2+τz2τx/6,
ΔC|τ1z1>1,τ2z2>1=τ1z1-k1CL-τ2z2-k2CL+ln1+x1/z1/1+x2/z2k1-k2L.
TL, Ω=exp-NσpL+k C L/cosθ0+ϕ=02πdϕθ=0ΩIL, θ, ϕcosθsinθdθcosθ0,
ΔCΩ=lnT2L, Ω/T1L, Ωk1-k2L/cosθ0-C.

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