Abstract

An underlying assumption of satellite data assimilation systems is that the radiative transfer model used to simulate observed satellite radiances has no errors. For practical reasons a fast-forward radiative transfer model is used instead of a highly accurate line-by-line model. The fast model usually replaces the spectral integration of spectral quantities with their monochromatic equivalents, and the errors due to these approximations are assumed to be negligible. The reflected downward flux term contains many approximations of this nature, which are shown to introduce systematic errors. In addition, many fast-forward radiative transfer models simulate the downward flux as the downward radiance along a path defined by the secant of the mean emergent angle, the diffusivity factor. The diffusivity factor is commonly set to 1.66 or to the secant of the satellite zenith angle. Neither case takes into account that the diffusivity factor varies with optical depth, which introduces further errors. I review the two most commonly used methods for simulating reflected downward flux by fast-forward radiative transfer models and point out their inadequacies and limitations. An alternate method of simulating the reflected downward flux is proposed. This method transforms the surface-to-satellite transmittance profile to a transmittance profile suitable for simulating the reflected downward flux by raising the former transmittance to the power of κ, where κ itself is a function of channel, surface pressure, and satellite zenith angle. It is demonstrated that this method reduces the fast-forward model error for low to moderate reflectivities.

© 2004 Optical Society of America

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2002

A. P. McNally, “A note on the occurance of cloud in meteorologically sensitive areas and the implications for advanced infrared sounders,” Q. J. R. Meteorol. Soc. 128, 2551–2556 (2002).
[CrossRef]

2001

B. A. Harris, G. Kelly(2001): A satellite radiance-bias correction scheme for data assimilation. Q. J. R. Meteorol. Soc. 127, 1453–1468 (2001).
[CrossRef]

L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
[CrossRef]

2000

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

D. S. Turner, “Systematic errors that are due to the monochromatic-equivalent radiative transfer approximation in thermal emission problems,” Appl. Opt. 39, 5663–5670 (2000).
[CrossRef]

1999

R. W. Saunders, M. Matricardi, P. Brunel, “An improved fast radiative transfer model for assimilation of satellite radiance observations,” Q. J. R. Meteorol. Soc. 125, 1407–1425 (1999).

L. Garand, D. S. Turner, C. Chouinard, J. Hallé, “A physical formulation of atmospheric transmittances for the massive assimilation of satellite infrared radiances,” J. Appl. Meteorol. 38, 541–554 (1999).
[CrossRef]

1998

J. C. Derber, W.-S. Wu, “The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system,” Mon. Weather Rev. 126, 2287–2299 (1998).
[CrossRef]

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

1997

1996

1995

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

D. S. Turner, “Absorption coefficient estimation using a two-dimensional interpolation procedure,” J. Quant. Spectrosc. Radiat. Transfer 53, 633–637 (1995).
[CrossRef]

1994

M. J. Uddstrom, L. M. McMillin, “System noise in the NESDIS TOVS forward model. Part I: specification,” J. Appl. Meteorol. 33, 919–938 (1994).
[CrossRef]

1993

J. R. Eyre, G. Kelly, A. P. McNally, E. Andersson, “Assimilation of TOVS radiances through one dimensional variational analysis,” Q. J. R. Meteorol. Soc. 119, 1427–1463 (1993).
[CrossRef]

1989

S. A. Clough, F. X. Kneizys, R. W. Davies, “Line shape and the water continuum,” Atmos. Res. 23, 229–241 (1989).
[CrossRef]

1988

Q. Liu, J. Schmetz, “On the problem of an analytical solution to the diffusivity factor,” Beitr. Phys. Atmosph. 61, 23–291988.

1979

W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “The TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).

Andersson, E.

J. R. Eyre, G. Kelly, A. P. McNally, E. Andersson, “Assimilation of TOVS radiances through one dimensional variational analysis,” Q. J. R. Meteorol. Soc. 119, 1427–1463 (1993).
[CrossRef]

Bates, J.

L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
[CrossRef]

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

Boukabara, S.

L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
[CrossRef]

Boulet, Ch.

Brown, L. R.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Brunel, P.

L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
[CrossRef]

R. W. Saunders, M. Matricardi, P. Brunel, “An improved fast radiative transfer model for assimilation of satellite radiance observations,” Q. J. R. Meteorol. Soc. 125, 1407–1425 (1999).

Camy-Peyret, C.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Chance, K. V.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Chevallier, F.

L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
[CrossRef]

M. Matricardi, F. Chevallier, S. Tjemkes, “An improved general fast radiative transfer model for the assimilation of radiance observations,” ECMWF Technical Memo 345, (European Centre for Medium Range Weather Forecasts, Reading, UK, 2001).

Chouinard, C.

L. Garand, D. S. Turner, C. Chouinard, J. Hallé, “A physical formulation of atmospheric transmittances for the massive assimilation of satellite infrared radiances,” J. Appl. Meteorol. 38, 541–554 (1999).
[CrossRef]

Chouinard, C. B.

D. S. Turner, C. B. Chouinard, “An attempt to understand and correct some of the errors of forward radiative transfer models,” in Technical Proceedings of the Ninth International TOVS Study Conference (European Centre for Medium-Range Weather Forecasts, Reading, UK, 1997), pp. 499–508.

Clough, S. A.

S. A. Clough, F. X. Kneizys, R. W. Davies, “Line shape and the water continuum,” Atmos. Res. 23, 229–241 (1989).
[CrossRef]

Crone, L. J.

Dana, V.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Davies, R. W.

S. A. Clough, F. X. Kneizys, R. W. Davies, “Line shape and the water continuum,” Atmos. Res. 23, 229–241 (1989).
[CrossRef]

de Souza-Machado, S.

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

S. De Souza-Machado, L. L. Strow, D. Tobin, S. E. Hannon, “Improved atmospheric radiance calculations using P/R-branch line mixing,” in Satellite Remote Sensing of Clouds and Atmosphere IV, J. E. Russell, ed., Proc. SPIE3867, 188–195 (1999).

DeBlonde, G.

L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
[CrossRef]

Derber, J. C.

J. C. Derber, W.-S. Wu, “The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system,” Mon. Weather Rev. 126, 2287–2299 (1998).
[CrossRef]

Edwards, D. P.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Ellingson, B.

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

Engelen, R.

L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
[CrossRef]

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

Eyre, J. R.

J. R. Eyre, G. Kelly, A. P. McNally, E. Andersson, “Assimilation of TOVS radiances through one dimensional variational analysis,” Q. J. R. Meteorol. Soc. 119, 1427–1463 (1993).
[CrossRef]

J. R. Eyre, “A bias correction scheme for simulated TOVS brightness temperatures,” ECMWF Research Department Technical Memo 186 (European Centre for Medium-Range Weather Forecasts, Reading, UK, 1992).

Flaud, J.-M.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Gamache, R. R.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Garand, L.

L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
[CrossRef]

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

L. Garand, D. S. Turner, C. Chouinard, J. Hallé, “A physical formulation of atmospheric transmittances for the massive assimilation of satellite infrared radiances,” J. Appl. Meteorol. 38, 541–554 (1999).
[CrossRef]

Goldman, A.

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L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
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B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
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B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
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B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
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L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
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W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “The TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).

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B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
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B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

Solodov, A. M.

Strow, L.

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

Strow, L. L.

S. De Souza-Machado, L. L. Strow, D. Tobin, S. E. Hannon, “Improved atmospheric radiance calculations using P/R-branch line mixing,” in Satellite Remote Sensing of Clouds and Atmosphere IV, J. E. Russell, ed., Proc. SPIE3867, 188–195 (1999).

Thibault, F.

Tjemkes, S.

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

M. Matricardi, F. Chevallier, S. Tjemkes, “An improved general fast radiative transfer model for the assimilation of radiance observations,” ECMWF Technical Memo 345, (European Centre for Medium Range Weather Forecasts, Reading, UK, 2001).

Tobin, D.

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

S. De Souza-Machado, L. L. Strow, D. Tobin, S. E. Hannon, “Improved atmospheric radiance calculations using P/R-branch line mixing,” in Satellite Remote Sensing of Clouds and Atmosphere IV, J. E. Russell, ed., Proc. SPIE3867, 188–195 (1999).

Turner, D.

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

Turner, D. S.

L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
[CrossRef]

D. S. Turner, “Systematic errors that are due to the monochromatic-equivalent radiative transfer approximation in thermal emission problems,” Appl. Opt. 39, 5663–5670 (2000).
[CrossRef]

L. Garand, D. S. Turner, C. Chouinard, J. Hallé, “A physical formulation of atmospheric transmittances for the massive assimilation of satellite infrared radiances,” J. Appl. Meteorol. 38, 541–554 (1999).
[CrossRef]

D. S. Turner, “Absorption coefficient estimation using a two-dimensional interpolation procedure,” J. Quant. Spectrosc. Radiat. Transfer 53, 633–637 (1995).
[CrossRef]

D. S. Turner, C. B. Chouinard, “An attempt to understand and correct some of the errors of forward radiative transfer models,” in Technical Proceedings of the Ninth International TOVS Study Conference (European Centre for Medium-Range Weather Forecasts, Reading, UK, 1997), pp. 499–508.

Uddstrom, M. J.

M. J. Uddstrom, L. M. McMillin, “System noise in the NESDIS TOVS forward model. Part I: specification,” J. Appl. Meteorol. 33, 919–938 (1994).
[CrossRef]

van Delst, P.

L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
[CrossRef]

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

Varanasi, P.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Wark, D. Q.

W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “The TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).

Wattson, R. B.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Weber, A.

Wehr, T.

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

Woolf, H.

L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
[CrossRef]

Woolf, H. M.

W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “The TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).

Wu, W.-S.

J. C. Derber, W.-S. Wu, “The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system,” Mon. Weather Rev. 126, 2287–2299 (1998).
[CrossRef]

Yoshino, K.

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Appl. Opt.

Atmos. Res.

S. A. Clough, F. X. Kneizys, R. W. Davies, “Line shape and the water continuum,” Atmos. Res. 23, 229–241 (1989).
[CrossRef]

Beitr. Phys. Atmosph.

Q. Liu, J. Schmetz, “On the problem of an analytical solution to the diffusivity factor,” Beitr. Phys. Atmosph. 61, 23–291988.

Bull. Am. Meteorol. Soc.

B. Soden, S. Tjemkes, J. Schmetz, R. Saunders, J. Bates, B. Ellingson, R. Engelen, L. Garand, D. Jackson, G. Jedlovec, T. Kleespies, D. Randel, P. Rayer, E. Salathe, D. Schwarzkopf, N. Scott, B. Sohn, S. de Souza-Machado, L. Strow, D. Tobin, D. Turner, P. van Delst, T. Wehr, “An intercomparison of radiation codes for retrieving upper-tropospheric humidity in the 6.3 μm band: a report from the first GvaP workshop,” Bull. Am. Meteorol. Soc. 81, 797–808 (2000).
[CrossRef]

W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “The TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).

J. Appl. Meteorol.

L. Garand, D. S. Turner, C. Chouinard, J. Hallé, “A physical formulation of atmospheric transmittances for the massive assimilation of satellite infrared radiances,” J. Appl. Meteorol. 38, 541–554 (1999).
[CrossRef]

M. J. Uddstrom, L. M. McMillin, “System noise in the NESDIS TOVS forward model. Part I: specification,” J. Appl. Meteorol. 33, 919–938 (1994).
[CrossRef]

J. Geophys. Rev.

L. Garand, D. S. Turner, M. Larocque, J. Bates, S. Boukabara, P. Brunel, F. Chevallier, G. DeBlonde, R. Engelen, M. Hollingshead, D. Jackson, G. Jedlovec, J. Joiner, T. Kleespies, D. S. McKague, L. McMillin, J.-L. Moncet, J. R. Pardo, P. J. Rayer, E. Salathe, R. Saunders, N. A. Scott, P. van Delst, H. Woolf, “Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels,” J. Geophys. Rev. 106, 24017–24031 (2001).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

D. S. Turner, “Absorption coefficient estimation using a two-dimensional interpolation procedure,” J. Quant. Spectrosc. Radiat. Transfer 53, 633–637 (1995).
[CrossRef]

L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Mon. Weather Rev.

J. C. Derber, W.-S. Wu, “The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system,” Mon. Weather Rev. 126, 2287–2299 (1998).
[CrossRef]

Q. J. R. Meteorol. Soc.

R. W. Saunders, M. Matricardi, P. Brunel, “An improved fast radiative transfer model for assimilation of satellite radiance observations,” Q. J. R. Meteorol. Soc. 125, 1407–1425 (1999).

J. R. Eyre, G. Kelly, A. P. McNally, E. Andersson, “Assimilation of TOVS radiances through one dimensional variational analysis,” Q. J. R. Meteorol. Soc. 119, 1427–1463 (1993).
[CrossRef]

B. A. Harris, G. Kelly(2001): A satellite radiance-bias correction scheme for data assimilation. Q. J. R. Meteorol. Soc. 127, 1453–1468 (2001).
[CrossRef]

A. P. McNally, “A note on the occurance of cloud in meteorologically sensitive areas and the implications for advanced infrared sounders,” Q. J. R. Meteorol. Soc. 128, 2551–2556 (2002).
[CrossRef]

Other

J. R. Eyre, “A bias correction scheme for simulated TOVS brightness temperatures,” ECMWF Research Department Technical Memo 186 (European Centre for Medium-Range Weather Forecasts, Reading, UK, 1992).

S. De Souza-Machado, L. L. Strow, D. Tobin, S. E. Hannon, “Improved atmospheric radiance calculations using P/R-branch line mixing,” in Satellite Remote Sensing of Clouds and Atmosphere IV, J. E. Russell, ed., Proc. SPIE3867, 188–195 (1999).

W. G. Planet, “Data extraction and calibration of TIROS-N/NOAA radiometers,” NOAA Technical Memo NESS 107 (National Oceanic and Atmospheric Administration, Washington, D.C., 1988).

M. Matricardi, F. Chevallier, S. Tjemkes, “An improved general fast radiative transfer model for the assimilation of radiance observations,” ECMWF Technical Memo 345, (European Centre for Medium Range Weather Forecasts, Reading, UK, 2001).

D. S. Turner, C. B. Chouinard, “An attempt to understand and correct some of the errors of forward radiative transfer models,” in Technical Proceedings of the Ninth International TOVS Study Conference (European Centre for Medium-Range Weather Forecasts, Reading, UK, 1997), pp. 499–508.

K. N. Liou, “Diffusivity factor in infrared radiative transfer” in Radiation and Cloud Processes in the Atmosphere (Oxford U. Press, New York, 1992), pp. 41–43.

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Figures (8)

Fig. 1
Fig. 1

Comparison of the bias and stdv of the BT difference between the FLBL and model 1 across the dependent set as a function of surface pressure, emissivity, and sec θ for HIRS 8, 9, and 11.

Fig. 2
Fig. 2

Comparison of the bias and stdv of the BT difference between the FLBL and model 2 across the dependent set as a function of surface pressure, emissivity, and sec θ for HIRS 8, 9, and 11.

Fig. 3
Fig. 3

Bias of the BT difference between the rF (p s )T s (θ, p s )〉 and its monochromatic equivalent, rF (p s )〉〈T s (θ, p s )〉 across the dependent set as a function of surface pressure and sec θ for HIRS 8, 9, and 11. The value of r has been set to .05π-1 (i.e., ∊ = 0.95).

Fig. 4
Fig. 4

Comparison of the bias and stdv of the BT difference between the exact downward flux and the approximate flux for models 1 and 2 across the dependent set for HIRS 8, 9, and 11. The bias and stdv are functions of surface pressure and sec θ for model 1 and a function of surface pressure only for model 2. The model 2 bias and stdv curves are the solid and dotted curves, respectively.

Fig. 5
Fig. 5

Illustration of the minimization curve for κ. The optimal κ is at the intersection of the target radiance [first term of relation (8)], ℛ0 = 1, and ℛ(κ) [second term of relation (8)]. Generally ℛ(κ) is well behaved (thick curve), and the intersection of ℛ0 and ℛ(κ) is easy to determine. The dotted curve represents a more difficult case. Here the minimization becomes unstable at κ = B after ℛ(κ) exceeds the target radiance at point A. In some cases, usually for very opaque atmospheres, the first discontinuity occurs infinitesimally just beyond κ = A.

Fig. 6
Fig. 6

Values of κ as a function of p s and sec θ for HIRS 8, 9, and 11.

Fig. 7
Fig. 7

Comparison of the bias and stdv of the BT difference between the FLBL and model 3 across the dependent set as a function of surface pressure, emissivity, and sec θ for HIRS 8, 9, and 11.

Fig. 8
Fig. 8

Comparison of the bias and stdv of the BT difference between the FLBL and model 3 across the independent set as a function of surface pressure, emissivity, and sec θ for HIRS 8, 9, and 11.

Tables (3)

Tables Icon

Table 1 List of Model’s Fixed Pressure Levels and Surface Pressures (hPa)

Tables Icon

Table 2 NOAA-14 HIRS Characteristicsa

Tables Icon

Table 3 Comparison of the Bias and Stdv (Quoted Below the Bias) for the Three Models (M1, M2, M3)a

Equations (13)

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

, θ, ps=BpsTθ, ps+0ps BpdTθ, p+rTθ, psFps,
Fps=02π 0π/2 0ps BpdTp, θcos θ sin θdθdϕ=2π 0ps BpdE3p,
2πrTθ, ps 0ps BpdE3p.
2BpdE3pBpdTp, ϕ,
, θ, ps=BsTsθ+k=1sTkθ-Tk+1θB¯k+πrTsθk=1sTkϕ-Tk+1ϕB¯k.
Tkϕ=TsϕTkϕ-TsϕTk-1ϕ,
, θ, ps=BsTsθ+k=1sTkθ-Tk+1θB¯k+πrTsθk=1sTk-1ϕ-TkϕTk-1ϕTkϕB¯kTsϕ.
, θ, ps=BsTsθ+k=1sTkθ-Tk+1θ×B¯k+πrTsθ×k=1sTk-1ϕ-TkϕTk-1ϕTkϕ B¯kTsϕ,
lnTijTij-1=k aijkXijk,
TUMG+H2OTUMGorTUMG+H2O+O3TUMG+H2O.
Tsϕ k=1sTk-1ϕ-TkϕTk-1ϕTkϕ B¯k,
πrTsθk=1sTk-1θκps,θ-Tkθκps,θTk-1θκps,θTkθκps,θ B¯k×Tsθκps,θ.
Tθ, psFps-Tsθ×k=1sTk-1θκps,θ-Tkθκps,θTk-1θκps,θTkθκps,θB¯k×Tsθκps,θδ

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