Abstract

A fast narrowband transmittance model, referred to as the Fast Fitting Transmittance Model (FFTM), is developed based on rigorous line-by-line (LBL) calculations. Specifically, monochromatic transmittances are first computed from a LBL model in a spectral region from 1 to 25000 cm-1 for various pressures and temperatures ranging from 0.05 hPa to 1100 hPa and from 200 K to 320 K, respectively. Subsequently, the monochromatic transmittances are averaged over a spectral interval of 1 cm-1 to obtain narrowband transmittances that are then fitted to various values of absorber amount. A database of fitting coefficients is then created that can be used to compute narrowband transmittances for an arbitrary atmospheric profile. To apply the FFTM to an inhomogeneous atmosphere, the Curtis-Godson (C-G) approximation is employed to obtain the weighted effective coefficients. The present method is validated against the LBLRTM and also compared with the high-spectral-resolution measurements acquired by the Atmospheric Infrared Sounder (AIRS) and High-resolution Interferometer Sounder (HIS). With a spectral resolution of 1 cm-1 and a wide spectral coverage, the FFTM offers a unique combination of numerical efficiency and considerable accuracy for computing moderate- to high-spectral-resolution transmittances involved in radiative transfer simulations and remote sensing applications.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2006 (1)

2005 (3)

S. A. Clough, M. W. Shephard, E. J. Mlawer, J. S. Delamere, M. J. Iacono, K. Cady-Pereira, S. Boukabara, and P. D. Brown, "Atmospheric radiative transfer modeling: a summary of the AER codes," J. Quant. Spectrosc. Radiat. Transf. 91, 233-244 (2005).
[CrossRef]

L. S. Rothmana, D. A. Jacquemarta, A. Barbeb,  et al., "The HITRAN 2004 molecular spectroscopic database," J. Quant. Spectrosc. Radiat. Transfer. 96, 139-204 (2005).
[CrossRef]

D. P. Kratz, G. M. Mlynczak, C. J. Mertens,  et al., "An inter-comparison of far-infrared line-by-line radiative transfer models," J. Quant. Spectrosc. Radiat. Transf. 90, 323-341 (2005).
[CrossRef]

2004 (2)

J. L. Moncet, G. Uymin, and H. E. Snell, "Atmospheric radiance modeling using the optimal spectral sampling (OSS) method," Proc. SPIE 5425, 368-374 (2004).
[CrossRef]

H. L. Wei, P. Yang, J. Li, B. A. Baum, H. L. Huang, S. Platnick, Y. X. Hu, and L. L. Strow, "Retrieval of ice cloud optical thickness from Atmospheric Infrared Sounder (AIRS) measurements," IEEE Trans. Geosci. Remote Sens. 42, 2254-2267 (2004).
[CrossRef]

2003 (1)

L. L. Strow, S. E. Hannon, S. Souza-Machado, H. E. Motteler, and D. C. Tobin, "An overview of the AIRS radiative transfer model," IEEE Trans. Geosci. Remote Sens. 41, 303-313 (2003).
[CrossRef]

2000 (1)

J. A. Curry, P. V. Hobbs, M. D. King,  et al., "FIRE arctic clouds experiment," Bull. Amer. Meteorol. Soc. 81, 5-29 (2000).
[CrossRef]

1999 (3)

D. C. Tobin, F. A. Best, P. D. Brown, S. A. Clough, R. G. Dedecker, R. G. Ellingson, R. K. Garcia, H. B. Howell, R. O. Knuteson, E. J. Mlawer, H. E. Revefrcomb, J. F. Short, P. F. W. van Delst, V. P. Walden, "Downwelling spectral radiance observations at the SHEBA ice station: water vapor continuum measurements from 17 -26 μm,"J. Geophys. Res. 104, 2081-2092 (1999).
[CrossRef]

D. P. Kratz and F. G. Rose, "Accounting for molecular absorption within the spectral range of the CERES window channel," J. Quant. Spectrosc. Radiat. Transf. 61, 83-95 (1999).
[CrossRef]

R. W. Sunders, M. Matricardi, and P. Brunel, "An improved fast radiative transfer model for assimilation of satellite radiance observations," Q. J. R. Meterol. Soc.  125, 1407-1425 (1999).

1996 (1)

L. S. Bernstein, A. Berk, P. K. Acharya,  et al., "Very narrow band model calculations of atmospheric flux and cooling rates," J. Atmos. Sci. 53, 2887-2904 (1996).
[CrossRef]

1995 (2)

S. A. Clough and M. J. Iacono, "Line-by-line calculations of atmospheric fluxes and cooling rates: Part II: Application to carbon dioxide, ozone, methane, nitrous oxide, and the halocarbons," J. Geophys. Res. 100, 16519-16535 (1995).
[CrossRef]

L. M. McMillin, T. J. Kleespies, and L. J. Crone, "Atmospheric transmittance of an absorbing gas. 5. Improvements to the OPTRAN approach," Appl. Opt. 34, 8396-8399 (1995).
[CrossRef] [PubMed]

1992 (2)

Q. Fu and K. N. Liou, "On the correlated K-distribution method for radiative transfer in non-homogeneous atmospheres," J. Atmos. Sci. 49, 2139-2156 (1992).
[CrossRef]

Q. Fu and K. N. Liou, "A three-parameter approximation for radiative transfer nonhomogeneous atmosphere: application to the O3 9.6 μm band," J. Geophys. Res. 97, 13051-13058 (1992).
[CrossRef]

Appl. Opt. (2)

Bull. Amer. Meteorol. Soc. (1)

J. A. Curry, P. V. Hobbs, M. D. King,  et al., "FIRE arctic clouds experiment," Bull. Amer. Meteorol. Soc. 81, 5-29 (2000).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

H. L. Wei, P. Yang, J. Li, B. A. Baum, H. L. Huang, S. Platnick, Y. X. Hu, and L. L. Strow, "Retrieval of ice cloud optical thickness from Atmospheric Infrared Sounder (AIRS) measurements," IEEE Trans. Geosci. Remote Sens. 42, 2254-2267 (2004).
[CrossRef]

L. L. Strow, S. E. Hannon, S. Souza-Machado, H. E. Motteler, and D. C. Tobin, "An overview of the AIRS radiative transfer model," IEEE Trans. Geosci. Remote Sens. 41, 303-313 (2003).
[CrossRef]

J. Atmos. Sci. (2)

Q. Fu and K. N. Liou, "On the correlated K-distribution method for radiative transfer in non-homogeneous atmospheres," J. Atmos. Sci. 49, 2139-2156 (1992).
[CrossRef]

L. S. Bernstein, A. Berk, P. K. Acharya,  et al., "Very narrow band model calculations of atmospheric flux and cooling rates," J. Atmos. Sci. 53, 2887-2904 (1996).
[CrossRef]

J. Geophys. Res. (3)

D. C. Tobin, F. A. Best, P. D. Brown, S. A. Clough, R. G. Dedecker, R. G. Ellingson, R. K. Garcia, H. B. Howell, R. O. Knuteson, E. J. Mlawer, H. E. Revefrcomb, J. F. Short, P. F. W. van Delst, V. P. Walden, "Downwelling spectral radiance observations at the SHEBA ice station: water vapor continuum measurements from 17 -26 μm,"J. Geophys. Res. 104, 2081-2092 (1999).
[CrossRef]

Q. Fu and K. N. Liou, "A three-parameter approximation for radiative transfer nonhomogeneous atmosphere: application to the O3 9.6 μm band," J. Geophys. Res. 97, 13051-13058 (1992).
[CrossRef]

S. A. Clough and M. J. Iacono, "Line-by-line calculations of atmospheric fluxes and cooling rates: Part II: Application to carbon dioxide, ozone, methane, nitrous oxide, and the halocarbons," J. Geophys. Res. 100, 16519-16535 (1995).
[CrossRef]

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

D. P. Kratz, G. M. Mlynczak, C. J. Mertens,  et al., "An inter-comparison of far-infrared line-by-line radiative transfer models," J. Quant. Spectrosc. Radiat. Transf. 90, 323-341 (2005).
[CrossRef]

D. P. Kratz and F. G. Rose, "Accounting for molecular absorption within the spectral range of the CERES window channel," J. Quant. Spectrosc. Radiat. Transf. 61, 83-95 (1999).
[CrossRef]

S. A. Clough, M. W. Shephard, E. J. Mlawer, J. S. Delamere, M. J. Iacono, K. Cady-Pereira, S. Boukabara, and P. D. Brown, "Atmospheric radiative transfer modeling: a summary of the AER codes," J. Quant. Spectrosc. Radiat. Transf. 91, 233-244 (2005).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer. (1)

L. S. Rothmana, D. A. Jacquemarta, A. Barbeb,  et al., "The HITRAN 2004 molecular spectroscopic database," J. Quant. Spectrosc. Radiat. Transfer. 96, 139-204 (2005).
[CrossRef]

Proc. SPIE (1)

J. L. Moncet, G. Uymin, and H. E. Snell, "Atmospheric radiance modeling using the optimal spectral sampling (OSS) method," Proc. SPIE 5425, 368-374 (2004).
[CrossRef]

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

R. W. Sunders, M. Matricardi, and P. Brunel, "An improved fast radiative transfer model for assimilation of satellite radiance observations," Q. J. R. Meterol. Soc.  125, 1407-1425 (1999).

Other (1)

L. Moy, D. C. Tobin, P. Delst, and H. Woolf, "Clear sky forward model development for GIFTS," (2004), http://ams.confex.com/ams/pdfpapers/71971>pdf.

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Figures (13)

Fig. 1.
Fig. 1.

The mean optical depth averaged with a spectral resolution of 1 cm-1 and the monochromatic optical depth for water vapor at t=290 K, p=100 hPa, and u=670 gcm-2.

Fig. 2.
Fig. 2.

CO2 absorption coefficient (in units of atm-cm) as a function of wavenumber within a one-wavenumber spectral interval centered at 2336.0 cm-1 for a pressure of 0.1 hPa and a temperature of 200 K.

Fig. 3.
Fig. 3.

Fitting coefficients Ci for CO2 at 2383.0 cm-1 and the variations of these coefficients versus (a) temperature and (b) pressure.

Fig. 4.
Fig. 4.

CO2 transmittance computed from the LBLRTM and the FFTM with a spectral resolution of 1 cm-1 for a spectral interval centered at 2336 cm-1 for various pressures and absorber amounts.

Fig. 5.
Fig. 5.

H2O transmittance computed from LBLRTM and the FFTM with a spectral resolution of 1 cm-1 for a spectral interval centered at 5030 cm-1 for various pressures, temperatures, and absorber amounts.

Fig. 6.
Fig. 6.

Comparison between LBLRTM and the corrected FFTM for the O3 9.6 μm band for various paths and model atmospheres.

Fig. 7.
Fig. 7.

Comparison of the mean spectral optical depth for water vapor, computed from LBLRTM and the present FFTM for a homogeneous path with t=250 K, p=1100 hPa, and u=3271 atm-cm.

Fig. 8.
Fig. 8.

Comparison of the mean spectral transmittance of water vapor, computed from the LBLRTM algorithm and the fitting method for a homogeneous path with t=200 K, p=1100 hPa, and u=100 atm-cm.

Fig. 9.
Fig. 9.

Same as Fig. 8, but for a lower pressure (p= 0.1 hPa).

Fig. 10.
Fig. 10.

Comparison of the mean spectral transmittances for water vapor, which are computed from the LBLRTM algorithm and the present fitting method for an inhomogeneous path from 100 to 0 km. The mid-latitude summer atmospheric profile is used.

Fig. 11.
Fig. 11.

Transmittance computed from the FFTM, LBLRTM, and Modtran4.0 for a vertical path from 0 to 100 km. The AFGL Mid-latitude summer atmospheric profile is used.

Fig. 12.
Fig. 12.

The comparison between the HIS observation and FFTM calculation in the bands 1 and 2 (600–1700 cm-1)

Fig. 13.
Fig. 13.

The observed AIRS radiance and the calculated radiance by FFTM

Equations (10)

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T ̅ ν t p u = ν Δ ν 2 ν + Δ ν 2 exp [ k ν ( t , p ) u ] ν Δ ν 2 ν + Δ ν 2 .
T ̅ ν t p u = exp [ u k ̅ ν t p u ] ,
k ̅ ν t p u = exp ( i = 0 i = M C i ( t , p ) [ log ( u ) ] i ) .
C ˜ i = C i ( t , p ) k ¯ ∙du ( t , p ) k ̅ ∙du ( t , p ) ,
T ν ( U ) = exp { U exp ( i = 0 i = M C ˜ i [ log ( U ) ] i } ,
U = du ( t , p ) .
C ˜ i = C i ( t , p ) du ( t , p ) du ( t , p ) .
T O 3 ν ( U ) = exp { U f ν ( U U 0 ) exp ( i = 0 i = M C ˜ i ) [ log ( U ) ] i } ,
T ν t p u 1 u 2 .... u n = T cn ν u 1 u 2 .... u n k = 1 N exp { u k exp ( i = 0 i = M C ik ( t , p ) [ log ( u k ) ] i ) } .
T ν U 1 U 2 .... U n = T cn ν U 1 U 2 .... U n k = 1 N exp { U k exp ( i = 0 i = M C ̅ ik ( t , p ) [ log ( U k ) ] i ) } .

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