Abstract

A new radiation scheme has been developed for dynamic general-circulation modeling. An automatic determination of k-distribution parameters and a treatment of solar–terrestrial radiation interacting with gaseous and particulate matter are incorporated into the scheme by a technique that combines discrete ordinate and matrix operator methods. An accelerated scheme for cloud overlap is developed and tested. The resultant accuracy of the scheme is ±0.5 K/day to a 70-km height in clear sky better than that of the line-by-line calculation method.

© 2000 Optical Society of America

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References

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  1. A. Lacis, W. C. Wang, J. Hansen, “Correlated k-distribution method for radiative transfer in climate models: application to the effect of cirrus clouds on climate,” NASA Conf. Publ. 2076, 309–314 (1979).
  2. M.-D. Chou, “A solar radiation model for use in climate studies,” J. Atmos. Sci. 49, 762–772 (1992).
    [CrossRef]
  3. Q. Fu, K. N. Liou, “On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres,” J. Atmos. Sci. 49, 2139–2156 (1992).
    [CrossRef]
  4. K. Shibata, T. Aoki, “An infrared-radiative scheme for numerical models of weather and climate,” J. Geophys. Res. 94, 14,923–14,943 (1992).
    [CrossRef]
  5. T. Nakajima, M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 35, 13–21 (1986).
    [CrossRef]
  6. J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
    [CrossRef]
  7. K. Stamnes, S.-C. Tsay, W. Wiscombe, K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988).
    [CrossRef] [PubMed]
  8. G. N. Plass, G. W. Kattawar, F. E. Catchings, “Matrix operator theory of radiative transfer. 1. Rayleigh scattering,” Appl. Opt. 12, 314–329 (1973).
    [CrossRef] [PubMed]
  9. R. M. Goody, Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford U. Press, Oxford, 1989).
  10. G.-Y. Shi, “An accurate calculation and representation of the infrared transmission function of atmospheric constituents,” Ph.D. dissertation (Tohoku University, Sendai, Japan, 1981).
  11. E. Raschke, U. Stucke, “Approximations of band transmission functions by finite sums of exponentials,” Contrib. Atmos. Phys. 46, 203–212 (1973).
  12. A. Uchiyama, “Line-by-line computation of the atmospheric absorption spectrum using the decomposed Voigt line shape,” J. Quant. Spectrosc. Radiat. Transfer 47, 521–532 (1992).
    [CrossRef]
  13. F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran7,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).
  14. F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran6,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).
  15. S. A. Clough, F. S. Kneizys, R. Davies, R. Gamache, R. H. Tipping, “Theoretical line shape for H2O vapor: application to the continuum,” in Atmospheric Water Vapor, A. Deepak, T. D. Wilkerson, L. H. Ruhnke, eds. (Academic, New York, 1980).
  16. G.-Y. Shi, “Radiative forcing and greenhouse effect due to atmospheric trace gases,” Sci. Sin. Ser. B 35, 217–229 (1992).
  17. J.-J. Morcrette, Y. Fouquart, “The overlapping of cloud layers in shortwave radiation parameterizations,” J. Atmos. Sci. 43, 321–328 (1986).
    [CrossRef]
  18. R. E. Payne, “Albedo of the sea surface,” J. Atmos. Sci. 29, 959–970 (1972).
    [CrossRef]
  19. T. Nakajima, M. D. King, “Asymptotic theory for optically thick layers: application to the discrete ordinates method,” Appl. Opt. 31, 7669–7683 (1992).
    [CrossRef] [PubMed]
  20. Harshvardhan, M. D. King, “Comparative accuracy of diffuse radiative properties computed using the selected multiple scattering approximation,” J. Atmos. Sci. 50, 247–259 (1993).

1993 (1)

Harshvardhan, M. D. King, “Comparative accuracy of diffuse radiative properties computed using the selected multiple scattering approximation,” J. Atmos. Sci. 50, 247–259 (1993).

1992 (6)

T. Nakajima, M. D. King, “Asymptotic theory for optically thick layers: application to the discrete ordinates method,” Appl. Opt. 31, 7669–7683 (1992).
[CrossRef] [PubMed]

M.-D. Chou, “A solar radiation model for use in climate studies,” J. Atmos. Sci. 49, 762–772 (1992).
[CrossRef]

Q. Fu, K. N. Liou, “On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres,” J. Atmos. Sci. 49, 2139–2156 (1992).
[CrossRef]

K. Shibata, T. Aoki, “An infrared-radiative scheme for numerical models of weather and climate,” J. Geophys. Res. 94, 14,923–14,943 (1992).
[CrossRef]

A. Uchiyama, “Line-by-line computation of the atmospheric absorption spectrum using the decomposed Voigt line shape,” J. Quant. Spectrosc. Radiat. Transfer 47, 521–532 (1992).
[CrossRef]

G.-Y. Shi, “Radiative forcing and greenhouse effect due to atmospheric trace gases,” Sci. Sin. Ser. B 35, 217–229 (1992).

1988 (1)

1986 (2)

J.-J. Morcrette, Y. Fouquart, “The overlapping of cloud layers in shortwave radiation parameterizations,” J. Atmos. Sci. 43, 321–328 (1986).
[CrossRef]

T. Nakajima, M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 35, 13–21 (1986).
[CrossRef]

1979 (1)

A. Lacis, W. C. Wang, J. Hansen, “Correlated k-distribution method for radiative transfer in climate models: application to the effect of cirrus clouds on climate,” NASA Conf. Publ. 2076, 309–314 (1979).

1976 (1)

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
[CrossRef]

1973 (2)

G. N. Plass, G. W. Kattawar, F. E. Catchings, “Matrix operator theory of radiative transfer. 1. Rayleigh scattering,” Appl. Opt. 12, 314–329 (1973).
[CrossRef] [PubMed]

E. Raschke, U. Stucke, “Approximations of band transmission functions by finite sums of exponentials,” Contrib. Atmos. Phys. 46, 203–212 (1973).

1972 (1)

R. E. Payne, “Albedo of the sea surface,” J. Atmos. Sci. 29, 959–970 (1972).
[CrossRef]

Abreu, L. W.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran7,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran6,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Anderson, G. P.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran7,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

Aoki, T.

K. Shibata, T. Aoki, “An infrared-radiative scheme for numerical models of weather and climate,” J. Geophys. Res. 94, 14,923–14,943 (1992).
[CrossRef]

Catchings, F. E.

Chetwynd, J. H.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran7,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran6,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Chou, M.-D.

M.-D. Chou, “A solar radiation model for use in climate studies,” J. Atmos. Sci. 49, 762–772 (1992).
[CrossRef]

Clough, S. A.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran7,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran6,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

S. A. Clough, F. S. Kneizys, R. Davies, R. Gamache, R. H. Tipping, “Theoretical line shape for H2O vapor: application to the continuum,” in Atmospheric Water Vapor, A. Deepak, T. D. Wilkerson, L. H. Ruhnke, eds. (Academic, New York, 1980).

Davies, R.

S. A. Clough, F. S. Kneizys, R. Davies, R. Gamache, R. H. Tipping, “Theoretical line shape for H2O vapor: application to the continuum,” in Atmospheric Water Vapor, A. Deepak, T. D. Wilkerson, L. H. Ruhnke, eds. (Academic, New York, 1980).

Fenn, R. W.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran6,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Fouquart, Y.

J.-J. Morcrette, Y. Fouquart, “The overlapping of cloud layers in shortwave radiation parameterizations,” J. Atmos. Sci. 43, 321–328 (1986).
[CrossRef]

Fu, Q.

Q. Fu, K. N. Liou, “On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres,” J. Atmos. Sci. 49, 2139–2156 (1992).
[CrossRef]

Gallery, W. O.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran6,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran7,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

Gamache, R.

S. A. Clough, F. S. Kneizys, R. Davies, R. Gamache, R. H. Tipping, “Theoretical line shape for H2O vapor: application to the continuum,” in Atmospheric Water Vapor, A. Deepak, T. D. Wilkerson, L. H. Ruhnke, eds. (Academic, New York, 1980).

Goody, R. M.

R. M. Goody, Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford U. Press, Oxford, 1989).

Hansen, J.

A. Lacis, W. C. Wang, J. Hansen, “Correlated k-distribution method for radiative transfer in climate models: application to the effect of cirrus clouds on climate,” NASA Conf. Publ. 2076, 309–314 (1979).

Harshvardhan,

Harshvardhan, M. D. King, “Comparative accuracy of diffuse radiative properties computed using the selected multiple scattering approximation,” J. Atmos. Sci. 50, 247–259 (1993).

Jayaweera, K.

Joseph, J. H.

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
[CrossRef]

Kattawar, G. W.

King, M. D.

Harshvardhan, M. D. King, “Comparative accuracy of diffuse radiative properties computed using the selected multiple scattering approximation,” J. Atmos. Sci. 50, 247–259 (1993).

T. Nakajima, M. D. King, “Asymptotic theory for optically thick layers: application to the discrete ordinates method,” Appl. Opt. 31, 7669–7683 (1992).
[CrossRef] [PubMed]

Kneizys, F. S.

S. A. Clough, F. S. Kneizys, R. Davies, R. Gamache, R. H. Tipping, “Theoretical line shape for H2O vapor: application to the continuum,” in Atmospheric Water Vapor, A. Deepak, T. D. Wilkerson, L. H. Ruhnke, eds. (Academic, New York, 1980).

Kneizys, F. X.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran7,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran6,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Lacis, A.

A. Lacis, W. C. Wang, J. Hansen, “Correlated k-distribution method for radiative transfer in climate models: application to the effect of cirrus clouds on climate,” NASA Conf. Publ. 2076, 309–314 (1979).

Liou, K. N.

Q. Fu, K. N. Liou, “On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres,” J. Atmos. Sci. 49, 2139–2156 (1992).
[CrossRef]

Morcrette, J.-J.

J.-J. Morcrette, Y. Fouquart, “The overlapping of cloud layers in shortwave radiation parameterizations,” J. Atmos. Sci. 43, 321–328 (1986).
[CrossRef]

Nakajima, T.

T. Nakajima, M. D. King, “Asymptotic theory for optically thick layers: application to the discrete ordinates method,” Appl. Opt. 31, 7669–7683 (1992).
[CrossRef] [PubMed]

T. Nakajima, M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 35, 13–21 (1986).
[CrossRef]

Payne, R. E.

R. E. Payne, “Albedo of the sea surface,” J. Atmos. Sci. 29, 959–970 (1972).
[CrossRef]

Plass, G. N.

Raschke, E.

E. Raschke, U. Stucke, “Approximations of band transmission functions by finite sums of exponentials,” Contrib. Atmos. Phys. 46, 203–212 (1973).

Selby, J. E. A.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran7,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran6,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

Shettle, E. P.

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran6,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran7,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

Shi, G.-Y.

G.-Y. Shi, “Radiative forcing and greenhouse effect due to atmospheric trace gases,” Sci. Sin. Ser. B 35, 217–229 (1992).

G.-Y. Shi, “An accurate calculation and representation of the infrared transmission function of atmospheric constituents,” Ph.D. dissertation (Tohoku University, Sendai, Japan, 1981).

Shibata, K.

K. Shibata, T. Aoki, “An infrared-radiative scheme for numerical models of weather and climate,” J. Geophys. Res. 94, 14,923–14,943 (1992).
[CrossRef]

Stamnes, K.

Stucke, U.

E. Raschke, U. Stucke, “Approximations of band transmission functions by finite sums of exponentials,” Contrib. Atmos. Phys. 46, 203–212 (1973).

Tanaka, M.

T. Nakajima, M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 35, 13–21 (1986).
[CrossRef]

Tipping, R. H.

S. A. Clough, F. S. Kneizys, R. Davies, R. Gamache, R. H. Tipping, “Theoretical line shape for H2O vapor: application to the continuum,” in Atmospheric Water Vapor, A. Deepak, T. D. Wilkerson, L. H. Ruhnke, eds. (Academic, New York, 1980).

Tsay, S.-C.

Uchiyama, A.

A. Uchiyama, “Line-by-line computation of the atmospheric absorption spectrum using the decomposed Voigt line shape,” J. Quant. Spectrosc. Radiat. Transfer 47, 521–532 (1992).
[CrossRef]

Wang, W. C.

A. Lacis, W. C. Wang, J. Hansen, “Correlated k-distribution method for radiative transfer in climate models: application to the effect of cirrus clouds on climate,” NASA Conf. Publ. 2076, 309–314 (1979).

Weinman, J. A.

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
[CrossRef]

Wiscombe, W.

Wiscombe, W. J.

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
[CrossRef]

Yung, Y. L.

R. M. Goody, Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford U. Press, Oxford, 1989).

Appl. Opt. (3)

Contrib. Atmos. Phys. (1)

E. Raschke, U. Stucke, “Approximations of band transmission functions by finite sums of exponentials,” Contrib. Atmos. Phys. 46, 203–212 (1973).

J. Atmos. Sci. (6)

J. H. Joseph, W. J. Wiscombe, J. A. Weinman, “The delta-Eddington approximation for radiative flux transfer,” J. Atmos. Sci. 33, 2452–2459 (1976).
[CrossRef]

J.-J. Morcrette, Y. Fouquart, “The overlapping of cloud layers in shortwave radiation parameterizations,” J. Atmos. Sci. 43, 321–328 (1986).
[CrossRef]

R. E. Payne, “Albedo of the sea surface,” J. Atmos. Sci. 29, 959–970 (1972).
[CrossRef]

M.-D. Chou, “A solar radiation model for use in climate studies,” J. Atmos. Sci. 49, 762–772 (1992).
[CrossRef]

Q. Fu, K. N. Liou, “On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres,” J. Atmos. Sci. 49, 2139–2156 (1992).
[CrossRef]

Harshvardhan, M. D. King, “Comparative accuracy of diffuse radiative properties computed using the selected multiple scattering approximation,” J. Atmos. Sci. 50, 247–259 (1993).

J. Geophys. Res. (1)

K. Shibata, T. Aoki, “An infrared-radiative scheme for numerical models of weather and climate,” J. Geophys. Res. 94, 14,923–14,943 (1992).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

T. Nakajima, M. Tanaka, “Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 35, 13–21 (1986).
[CrossRef]

A. Uchiyama, “Line-by-line computation of the atmospheric absorption spectrum using the decomposed Voigt line shape,” J. Quant. Spectrosc. Radiat. Transfer 47, 521–532 (1992).
[CrossRef]

NASA Conf. Publ. (1)

A. Lacis, W. C. Wang, J. Hansen, “Correlated k-distribution method for radiative transfer in climate models: application to the effect of cirrus clouds on climate,” NASA Conf. Publ. 2076, 309–314 (1979).

Sci. Sin. Ser. B (1)

G.-Y. Shi, “Radiative forcing and greenhouse effect due to atmospheric trace gases,” Sci. Sin. Ser. B 35, 217–229 (1992).

Other (5)

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran7,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

F. X. Kneizys, E. P. Shettle, W. O. Gallery, J. H. Chetwynd, L. W. Abreu, J. E. A. Selby, S. A. Clough, R. W. Fenn, “Atmospheric transmittance/radiance: computer code lowtran6,” (U. S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1983).

S. A. Clough, F. S. Kneizys, R. Davies, R. Gamache, R. H. Tipping, “Theoretical line shape for H2O vapor: application to the continuum,” in Atmospheric Water Vapor, A. Deepak, T. D. Wilkerson, L. H. Ruhnke, eds. (Academic, New York, 1980).

R. M. Goody, Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford U. Press, Oxford, 1989).

G.-Y. Shi, “An accurate calculation and representation of the infrared transmission function of atmospheric constituents,” Ph.D. dissertation (Tohoku University, Sendai, Japan, 1981).

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Figures (12)

Fig. 1
Fig. 1

Matrix operators that characterize the radiative process in a homogeneous layer.

Fig. 2
Fig. 2

System of sublayers as an approximation of an inhomogeneous atmosphere.

Fig. 3
Fig. 3

Concept of k distribution.

Fig. 4
Fig. 4

Sorting of absorption coefficients. Water-vapor absorption in the spectral range of 3700–3800 cm-1 is taken as an example. The key sorting wave number is that for P = 50 hPa. (Reproduced from Ref. 10).

Fig. 5
Fig. 5

Treatment of overlapping band absorption for two gases in the k-distribution method.

Fig. 6
Fig. 6

Optimized frequency distributions for overlapping bands of water vapor and CO2 in the spectral range 550–770 cm-1.

Fig. 7
Fig. 7

(a) Vertical profiles of heating rate and error for calculating long-wave flux. (b) Same as in (a) but for the near-infrared region. Six AFGL atmospheres and clear-sky conditions are assumed. ———, tropical; — — —, mid-latitude summer; – – – – – – – –, mid-latitude winter; – — – — – — –, Subarctic summer; — – – — –, subarctic winter; — – – – —, U.S. Standard.

Fig. 8
Fig. 8

System of partial cloud layers.

Fig. 9
Fig. 9

Heating-rate profiles for atmospheres with clouds located at 2, 6, and 9 km.

Fig. 10
Fig. 10

Heating-rate and error profiles for a partial cloud system calculated by random and semirandom methods.

Fig. 11
Fig. 11

Spectra of the co-albedo for several band allocations and a and s averages.

Fig. 12
Fig. 12

(a) Comparison of heating-rate profiles calculated by several methods of averaging to obtain band-averaged parameters of particulate matter. The cloud optical thickness is 10.5. (b) Same as in (a) but with a cloud optical thickness of 31.5. ———, short-wave (sw) true (T); –––, long-wave (LW) T; true; —○—, SW 17-band a average; —○—, LW 17-band a average; —△—, SW 12-band a average; —△—, LW 12-band a average; —▲—, SW 17-band s average; —▲—, LW 17-band s average; —□—, SW 12-band s average; —□— LW 12-band s average.

Tables (2)

Tables Icon

Table 1 Band and Channel Allocation for a High-Resolution Model

Tables Icon

Table 2 Band and Channel Allocation for a Low-Resolution Model

Equations (66)

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

μ duτ, μ, ϕdτ=-uτ, μ, ϕ+ω-11dμ 02πdϕPμ, μ, ϕ-ϕuτ, μ, ϕ+ωPμ, μ0, ϕexp-τ/μ0F0+1-ωBτ,
±Mdu±τdτ=-u±τ+P±Wu+τ+PWu-τ+SS± exp-τ/μ0+SBτ,
u±=02π uτ, ±μi, μ0, ϕcos mϕdϕ|i=1, N,
P±=ω 02π P±μi, μj, ϕcos mϕdϕ|i, j=1, N,
SS±=ω 02π P±μi, μ0, ϕcos mϕdF0|i=1, N,
SB±=2πδ0m1-ωBτ|i=1, N,
M=μiδij|i=1, N;  W=wiδij|i=1, N,
u±τ±wμu±τ±=Ruτ±+T±u±τ+ε±,
Px=n=0N2n+14π gnPnx.
g0=1, g=g1, f=g2.
τ1-ωfτ, ω1-f1-ωf ω, gg-f1-f.
P0±μ, μ02π P±μ, μ, ϕdϕ=½1±3gμμ.
Bτ=n=0Nb bnτ-τ-n.
bnbn1-ωfn.
e=Cext/V, s0=Csca/V, s1=Cscag1/V,, s4=Cscag4/V
τP=m=1expmVm,
σP,n=m=1 snmVm,
ωP=σP,0/τ;  gP,n=σP,n/σP,0.
01exp-x/μμdμ½ exp-x/d,  d1.66.
μ1/d,  Fπu.
F±=μwu±+μ0 exp-τ/μ0F0,  λ<4 μm,
F±=πu±,  λ4 μm,
kvkv*.
F=1νB-νAνAνB Fvdν=1νB-νAνAνB Fν*dν*=01 Fgdg,
gk=ν*k-νAνB-νA.
Fn=1K Fknwn,
kn=knP, T.
kn=k*gn.
SP, T=c1F+-Ftrue+2+F--Ftrue-2+c2H-Htrue2,
Hz=1CpρddzF+z-F-z.
τO2=AO2ρΔz,
τO3=n=02 AnO3T/T0nρrO3Δz,
τH2O=AH2O+BH2OTrH2OrH2OρΔz,
τCFC=n=116 AnCFCrnCFCρΔz.
τCON=τH2O+τO3+τO2+τCFC.
τKD=m=1 kmCm,
km=expi=0j=0 Aijmln PiT-T0j,
τ=τP+τR+τCON+τKD,
ω=ωPτP+ωRτR/τ,
gn=ωPτPgP,n+ωRτRgR,n/ωPτP+ωRτR,
Rk>,  Tk,
Q=nQc+1-nQs,
t1,k=k=1K tk,
t=exp-τ/μ0.
εk=εB,k+εS,kt1,k.
Ag=expi=13j=15 Cijtiμ0j,
ev=sv+avsv+av,
χ=1-ω1-s/a+s1/2,
av=χ21-χ2 sv.
R=12X1+E-λ1-EX1+E+λ1-E+X1-E-λ1+EX1-E+λ1+E,
T=12X1+E-λ1-EX1+E+λ1-E-X1-E/λ-1+EX1-E/λ+1+E,
X±=1μ1-P0μ, μ±P0-μ, μw, X=X-, Y=X+,
G=XY, λ=G, E=exp-λΔτ.
ε-=V0--RV0+-TV1-, ε+=V1+-TV0+-RV1-,
σS±=W-ωP0μ, μ0±P0-μ, μ0,
VS±=121±1Xμ0σS+Xμ0+σS-Gμ0-1/μ0±σS-X,
W-=w/μ,
cn=2π1-ωW-bn,
DO±=2c2/G+c0/Yc1/G, D1±=c1/Y2c2/G, D2±=c2/Y.
V0±=VS± exp-τ-/μ0F0+D0±,
V1±=VS± exp-τ+/μ0F0+D0±+D1±Δτ+D2±Δτ2.
ε±=εS± exp-τ-/μ0F0+εB±.
R1,2+=R1++T1-I-R2+R1--1R2+T1+, T1,2-=T1-I-R2+R1--1T2-,
ε1,2-=ε1-+T1-I-R2+R1--1R2+ε1++ε2-.
ε1,2+=ε2++T2+ε1++R1-I-R2+R1--1×R2+ε1++ε2-.
u+=I-R1-R2+-1R1-ε2-+ε1+, u-=R2+u++ε2-.

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