Abstract

To support the verification and implementation of the National Polar-Orbiting Operational Environmental Satellite System’s Visible–Infrared Imaging–Radiometric Suite (VIIRS) algorithms used for inferring cloud environmental data records, an intercomparison effort has been carried out to assess the consistency between the simulated cloudy radiances–reflectances from the University of California at Los Angeles Line-by-Line Equivalent Radiative Transfer Model and those from the Moderate-Resolution Transmission Model (MODTRAN) with the 16 stream Discrete Ordinate Radiative Transfer Model (DISORT) incorporated. For typical ice and water cloud optical depths and particle sizes, we found discrepancies in the visible and near-infrared reflectances from the two models, which presumably are due to the difference in phase function (nonspherical versus Henyey–Greenstein), different numbers of phase function expansion terms (16 versus 200 terms), and different treatment of forward peak truncation in each model. Using the MODTRAN4, we also found substantial differences in the infrared radiances for optically thick clouds. These differences led to the discovery by MODTRAN4 developers of an inconsistency in the MODTRAN4–DISORT interface. MODTRAN4 developers corrected the inconsistency, which provided dramatic reductions in the differences between the two radiative transfer models. The comparison not only affects the prospective test plan for the VIIRS cloud algorithms but also should lead to improvements in future MODTRAN releases.

© 2005 Optical Society of America

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2003 (2)

1998 (1)

L. S. Rothman31 additional authors, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN Atmospheric Workstations): 1996 Ed.,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

1995 (1)

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

1994 (1)

K. N. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

1993 (1)

1992 (2)

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]

Y. Takano, K. N. Liou, P. Minnis, “Effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

1989 (1)

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals; II. Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 3–36 (1989).
[CrossRef]

1988 (1)

1977 (1)

W. Wiscombe, “The delta-M method: rapid yet accurate radiative flux calculations for strongly asymmetric phase functions,” J. Atmos. Sci. 34, 1408–1422 (1977).
[CrossRef]

1976 (1)

Abreu, L. W.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chettwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User guide to LOWTRAN 7” (U.S. Air Force Geophysics Laboratory, 1988).

Agraveante, H.

V. Grano, T. Scalione, P. Emch, H. Agraveante, B. Hauss, J. Jackson, S. Mills, T. Samec, M. Shoucri, “End-to-end performance assessment of the National Polar-orbiting Operational Environmental Satellite System environmental data records,” in Weather and Environmental Satellites, T. H. Vonder Haar, H.- L. Huang, eds., Proc. SPIE5549, 53–59 (2004).
[CrossRef]

Anderson, G. P.

G. P. Anderson, R. H. Picard, J. H. Chetwynd, “Proceedings of the 17th Annual Review Conference on Atmospheric Transmission Models,” (Phillips Laboratory/Geophysics Directorate, Hanscom Air Force Base, 1995).

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chettwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User guide to LOWTRAN 7” (U.S. Air Force Geophysics Laboratory, 1988).

Ardanuy, P. E.

C. Welsh, H. Swenson, S. A. Cota, F. DeLuccia, J. M. Haas, C. F. Schueler, R. M. Durham, J. E. Clement, P. E. Ardanuy, “VIIRS (Visible Infrared Imager Radiometer Suite): a next-generation operational environmental sensor for NPOESS,” presented at the International Geoscience and Remote Sensing Symposium (IGARSS), Sydney, Australia, 8–14 July 2001.

Berk, A.

A. Berk, L. S. Bernstein, D. C. Robertson, “MODTRAN: A Moderate Resolution Model for LOWTRAN7,” (U.S. Air Force Geophysics Laboratory, 1989), pp. 1–38.

Bernstein, L. S.

A. Berk, L. S. Bernstein, D. C. Robertson, “MODTRAN: A Moderate Resolution Model for LOWTRAN7,” (U.S. Air Force Geophysics Laboratory, 1989), pp. 1–38.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Oxford U. Press, 1950).

Chettwynd, J. H.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chettwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User guide to LOWTRAN 7” (U.S. Air Force Geophysics Laboratory, 1988).

Chetwynd, J. H.

G. P. Anderson, R. H. Picard, J. H. Chetwynd, “Proceedings of the 17th Annual Review Conference on Atmospheric Transmission Models,” (Phillips Laboratory/Geophysics Directorate, Hanscom Air Force Base, 1995).

Clement, J. E.

C. Welsh, H. Swenson, S. A. Cota, F. DeLuccia, J. M. Haas, C. F. Schueler, R. M. Durham, J. E. Clement, P. E. Ardanuy, “VIIRS (Visible Infrared Imager Radiometer Suite): a next-generation operational environmental sensor for NPOESS,” presented at the International Geoscience and Remote Sensing Symposium (IGARSS), Sydney, Australia, 8–14 July 2001.

Clough, S. A.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chettwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User guide to LOWTRAN 7” (U.S. Air Force Geophysics Laboratory, 1988).

Cota, S. A.

C. Welsh, H. Swenson, S. A. Cota, F. DeLuccia, J. M. Haas, C. F. Schueler, R. M. Durham, J. E. Clement, P. E. Ardanuy, “VIIRS (Visible Infrared Imager Radiometer Suite): a next-generation operational environmental sensor for NPOESS,” presented at the International Geoscience and Remote Sensing Symposium (IGARSS), Sydney, Australia, 8–14 July 2001.

d’Almeida, G. A.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols, Global Climatology and Radiative Characteristics (Deepak Publishing, 1991).

DeLuccia, F.

C. Welsh, H. Swenson, S. A. Cota, F. DeLuccia, J. M. Haas, C. F. Schueler, R. M. Durham, J. E. Clement, P. E. Ardanuy, “VIIRS (Visible Infrared Imager Radiometer Suite): a next-generation operational environmental sensor for NPOESS,” presented at the International Geoscience and Remote Sensing Symposium (IGARSS), Sydney, Australia, 8–14 July 2001.

Durham, R. M.

C. Welsh, H. Swenson, S. A. Cota, F. DeLuccia, J. M. Haas, C. F. Schueler, R. M. Durham, J. E. Clement, P. E. Ardanuy, “VIIRS (Visible Infrared Imager Radiometer Suite): a next-generation operational environmental sensor for NPOESS,” presented at the International Geoscience and Remote Sensing Symposium (IGARSS), Sydney, Australia, 8–14 July 2001.

Emch, P.

V. Grano, T. Scalione, P. Emch, H. Agraveante, B. Hauss, J. Jackson, S. Mills, T. Samec, M. Shoucri, “End-to-end performance assessment of the National Polar-orbiting Operational Environmental Satellite System environmental data records,” in Weather and Environmental Satellites, T. H. Vonder Haar, H.- L. Huang, eds., Proc. SPIE5549, 53–59 (2004).
[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, L. W. Abreu, J. H. Chettwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User guide to LOWTRAN 7” (U.S. Air Force Geophysics Laboratory, 1988).

George, A.

S. C. Ou, Y. Takano, K. N. Liou, G. J. Higgins, A. George, R. Slonaker, “Remote sensing of cirrus cloud optical thickness and effective size for the National Polar-orbiting Operational Environmental Satellite System Visible–Infrared Imager Radiometer Suite: sensitivity to instrument noise and uncertainties in environmental parameters,” Appl. Opt. 42, 7202–72142003.
[CrossRef]

S. C. Ou, K. N. Liou, Y. Takano, G. J. Higgins, A. George, R. Slonaker, “VIIRS cloud effective particle size and cloud optical depth algorithm theoretical basis document,” Algorithm Theoretical Basis Document, Version 5, Rev. 1 (Raytheon, Lanham, Md., 2002).

Grano, V.

V. Grano, T. Scalione, P. Emch, H. Agraveante, B. Hauss, J. Jackson, S. Mills, T. Samec, M. Shoucri, “End-to-end performance assessment of the National Polar-orbiting Operational Environmental Satellite System environmental data records,” in Weather and Environmental Satellites, T. H. Vonder Haar, H.- L. Huang, eds., Proc. SPIE5549, 53–59 (2004).
[CrossRef]

Haas, J. M.

C. Welsh, H. Swenson, S. A. Cota, F. DeLuccia, J. M. Haas, C. F. Schueler, R. M. Durham, J. E. Clement, P. E. Ardanuy, “VIIRS (Visible Infrared Imager Radiometer Suite): a next-generation operational environmental sensor for NPOESS,” presented at the International Geoscience and Remote Sensing Symposium (IGARSS), Sydney, Australia, 8–14 July 2001.

Hauss, B.

V. Grano, T. Scalione, P. Emch, H. Agraveante, B. Hauss, J. Jackson, S. Mills, T. Samec, M. Shoucri, “End-to-end performance assessment of the National Polar-orbiting Operational Environmental Satellite System environmental data records,” in Weather and Environmental Satellites, T. H. Vonder Haar, H.- L. Huang, eds., Proc. SPIE5549, 53–59 (2004).
[CrossRef]

Higgins, G. J.

S. C. Ou, Y. Takano, K. N. Liou, G. J. Higgins, A. George, R. Slonaker, “Remote sensing of cirrus cloud optical thickness and effective size for the National Polar-orbiting Operational Environmental Satellite System Visible–Infrared Imager Radiometer Suite: sensitivity to instrument noise and uncertainties in environmental parameters,” Appl. Opt. 42, 7202–72142003.
[CrossRef]

S. C. Ou, K. N. Liou, Y. Takano, G. J. Higgins, A. George, R. Slonaker, “VIIRS cloud effective particle size and cloud optical depth algorithm theoretical basis document,” Algorithm Theoretical Basis Document, Version 5, Rev. 1 (Raytheon, Lanham, Md., 2002).

Jackson, J.

V. Grano, T. Scalione, P. Emch, H. Agraveante, B. Hauss, J. Jackson, S. Mills, T. Samec, M. Shoucri, “End-to-end performance assessment of the National Polar-orbiting Operational Environmental Satellite System environmental data records,” in Weather and Environmental Satellites, T. H. Vonder Haar, H.- L. Huang, eds., Proc. SPIE5549, 53–59 (2004).
[CrossRef]

Jayaweera, K.

Kneizys, F. X.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chettwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User guide to LOWTRAN 7” (U.S. Air Force Geophysics Laboratory, 1988).

Koepke, P.

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols, Global Climatology and Radiative Characteristics (Deepak Publishing, 1991).

Liou, K. N.

S. C. Ou, Y. Takano, K. N. Liou, G. J. Higgins, A. George, R. Slonaker, “Remote sensing of cirrus cloud optical thickness and effective size for the National Polar-orbiting Operational Environmental Satellite System Visible–Infrared Imager Radiometer Suite: sensitivity to instrument noise and uncertainties in environmental parameters,” Appl. Opt. 42, 7202–72142003.
[CrossRef]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

K. N. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

Y. Takano, K. N. Liou, “Transfer of polarized infrared radiation in optically anisotropic media: application to horizontally oriented ice crystals,” J. Opt. Soc. Am. A 10, 1243–1256 (1993).
[CrossRef]

Y. Takano, K. N. Liou, P. Minnis, “Effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (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]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals; II. Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 3–36 (1989).
[CrossRef]

K. N. Liou, An Introduction to Atmospheric Radiation, 2nd ed., Vol. 84 of Academic International Geophysics Series (Academic, 2002).

S. C. Ou, K. N. Liou, Y. Takano, G. J. Higgins, A. George, R. Slonaker, “VIIRS cloud effective particle size and cloud optical depth algorithm theoretical basis document,” Algorithm Theoretical Basis Document, Version 5, Rev. 1 (Raytheon, Lanham, Md., 2002).

Mills, S.

V. Grano, T. Scalione, P. Emch, H. Agraveante, B. Hauss, J. Jackson, S. Mills, T. Samec, M. Shoucri, “End-to-end performance assessment of the National Polar-orbiting Operational Environmental Satellite System environmental data records,” in Weather and Environmental Satellites, T. H. Vonder Haar, H.- L. Huang, eds., Proc. SPIE5549, 53–59 (2004).
[CrossRef]

Minnis, P.

Y. Takano, K. N. Liou, P. Minnis, “Effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

Ou, S. C.

S. C. Ou, Y. Takano, K. N. Liou, G. J. Higgins, A. George, R. Slonaker, “Remote sensing of cirrus cloud optical thickness and effective size for the National Polar-orbiting Operational Environmental Satellite System Visible–Infrared Imager Radiometer Suite: sensitivity to instrument noise and uncertainties in environmental parameters,” Appl. Opt. 42, 7202–72142003.
[CrossRef]

S. C. Ou, K. N. Liou, Y. Takano, G. J. Higgins, A. George, R. Slonaker, “VIIRS cloud effective particle size and cloud optical depth algorithm theoretical basis document,” Algorithm Theoretical Basis Document, Version 5, Rev. 1 (Raytheon, Lanham, Md., 2002).

Picard, R. H.

G. P. Anderson, R. H. Picard, J. H. Chetwynd, “Proceedings of the 17th Annual Review Conference on Atmospheric Transmission Models,” (Phillips Laboratory/Geophysics Directorate, Hanscom Air Force Base, 1995).

Robertson, D. C.

A. Berk, L. S. Bernstein, D. C. Robertson, “MODTRAN: A Moderate Resolution Model for LOWTRAN7,” (U.S. Air Force Geophysics Laboratory, 1989), pp. 1–38.

Rothman, L. S.

L. S. Rothman31 additional authors, “THE HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001,” J. Quant Spectrosc. Radiat. Transfer 82, 5–44 (2003).
[CrossRef]

L. S. Rothman31 additional authors, “The HITRAN molecular spectroscopic database and HAWKS (HITRAN Atmospheric Workstations): 1996 Ed.,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Samec, T.

V. Grano, T. Scalione, P. Emch, H. Agraveante, B. Hauss, J. Jackson, S. Mills, T. Samec, M. Shoucri, “End-to-end performance assessment of the National Polar-orbiting Operational Environmental Satellite System environmental data records,” in Weather and Environmental Satellites, T. H. Vonder Haar, H.- L. Huang, eds., Proc. SPIE5549, 53–59 (2004).
[CrossRef]

Scalione, T.

V. Grano, T. Scalione, P. Emch, H. Agraveante, B. Hauss, J. Jackson, S. Mills, T. Samec, M. Shoucri, “End-to-end performance assessment of the National Polar-orbiting Operational Environmental Satellite System environmental data records,” in Weather and Environmental Satellites, T. H. Vonder Haar, H.- L. Huang, eds., Proc. SPIE5549, 53–59 (2004).
[CrossRef]

Schueler, C. F.

C. Welsh, H. Swenson, S. A. Cota, F. DeLuccia, J. M. Haas, C. F. Schueler, R. M. Durham, J. E. Clement, P. E. Ardanuy, “VIIRS (Visible Infrared Imager Radiometer Suite): a next-generation operational environmental sensor for NPOESS,” presented at the International Geoscience and Remote Sensing Symposium (IGARSS), Sydney, Australia, 8–14 July 2001.

Selby, J. E. A.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chettwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User guide to LOWTRAN 7” (U.S. Air Force Geophysics Laboratory, 1988).

Shettle, E. P.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chettwynd, G. P. Anderson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “User guide to LOWTRAN 7” (U.S. Air Force Geophysics Laboratory, 1988).

G. A. d’Almeida, P. Koepke, E. P. Shettle, Atmospheric Aerosols, Global Climatology and Radiative Characteristics (Deepak Publishing, 1991).

Shoucri, M.

V. Grano, T. Scalione, P. Emch, H. Agraveante, B. Hauss, J. Jackson, S. Mills, T. Samec, M. Shoucri, “End-to-end performance assessment of the National Polar-orbiting Operational Environmental Satellite System environmental data records,” in Weather and Environmental Satellites, T. H. Vonder Haar, H.- L. Huang, eds., Proc. SPIE5549, 53–59 (2004).
[CrossRef]

Slonaker, R.

S. C. Ou, Y. Takano, K. N. Liou, G. J. Higgins, A. George, R. Slonaker, “Remote sensing of cirrus cloud optical thickness and effective size for the National Polar-orbiting Operational Environmental Satellite System Visible–Infrared Imager Radiometer Suite: sensitivity to instrument noise and uncertainties in environmental parameters,” Appl. Opt. 42, 7202–72142003.
[CrossRef]

S. C. Ou, K. N. Liou, Y. Takano, G. J. Higgins, A. George, R. Slonaker, “VIIRS cloud effective particle size and cloud optical depth algorithm theoretical basis document,” Algorithm Theoretical Basis Document, Version 5, Rev. 1 (Raytheon, Lanham, Md., 2002).

Stamnes, K.

Swenson, H.

C. Welsh, H. Swenson, S. A. Cota, F. DeLuccia, J. M. Haas, C. F. Schueler, R. M. Durham, J. E. Clement, P. E. Ardanuy, “VIIRS (Visible Infrared Imager Radiometer Suite): a next-generation operational environmental sensor for NPOESS,” presented at the International Geoscience and Remote Sensing Symposium (IGARSS), Sydney, Australia, 8–14 July 2001.

Takano, Y.

S. C. Ou, Y. Takano, K. N. Liou, G. J. Higgins, A. George, R. Slonaker, “Remote sensing of cirrus cloud optical thickness and effective size for the National Polar-orbiting Operational Environmental Satellite System Visible–Infrared Imager Radiometer Suite: sensitivity to instrument noise and uncertainties in environmental parameters,” Appl. Opt. 42, 7202–72142003.
[CrossRef]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. III. Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

K. N. Liou, Y. Takano, “Light scattering by nonspherical particles: remote sensing and climatic implications,” Atmos. Res. 31, 271–298 (1994).
[CrossRef]

Y. Takano, K. N. Liou, “Transfer of polarized infrared radiation in optically anisotropic media: application to horizontally oriented ice crystals,” J. Opt. Soc. Am. A 10, 1243–1256 (1993).
[CrossRef]

Y. Takano, K. N. Liou, P. Minnis, “Effects of small ice crystals on cirrus infrared radiative properties,” J. Atmos. Sci. 49, 1487–1493 (1992).
[CrossRef]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals; II. Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 3–36 (1989).
[CrossRef]

S. C. Ou, K. N. Liou, Y. Takano, G. J. Higgins, A. George, R. Slonaker, “VIIRS cloud effective particle size and cloud optical depth algorithm theoretical basis document,” Algorithm Theoretical Basis Document, Version 5, Rev. 1 (Raytheon, Lanham, Md., 2002).

Thekaekara, M. P.

Tsay, S.-C.

Welsh, C.

C. Welsh, H. Swenson, S. A. Cota, F. DeLuccia, J. M. Haas, C. F. Schueler, R. M. Durham, J. E. Clement, P. E. Ardanuy, “VIIRS (Visible Infrared Imager Radiometer Suite): a next-generation operational environmental sensor for NPOESS,” presented at the International Geoscience and Remote Sensing Symposium (IGARSS), Sydney, Australia, 8–14 July 2001.

Wiscombe, W.

W. Wiscombe, “The delta-M method: rapid yet accurate radiative flux calculations for strongly asymmetric phase functions,” J. Atmos. Sci. 34, 1408–1422 (1977).
[CrossRef]

Wiscombe, W. J.

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Figures (5)

Fig. 1
Fig. 1

Flow chart of the UCLA LBLE radiative transfer code.

Fig. 2
Fig. 2

(a) Schematic depiction of the components of the forward-scattering peak of a nonspherical ice crystal phase function, assuming random orientation. (b) Comparison of nonspherical ice crystal (Cs, De = 42 μm) phase function with a H–G phase function.

Fig. 3
Fig. 3

Comparison of 0.672, 1.61, and 2.25 μm ice cloud reflectances as functions of solar zenith angles in terms of percentage differences (Δr/rUCLA) for ice cloud with θ = 0°, De = 42 μm, and surface albedo of As = 0.05, where (a) Δr = rM1rUCLA and (b) Δr = rM3rUCLA. Ranges of computational (CPU) time are 0.7–2.5 and 8–38 s for the LBLE and M1, respectively.

Fig. 4
Fig. 4

Comparison of the algebraic and finite (16 and 200) term expanded H–G phase functions, as given in Eq. (2).

Fig. 5
Fig. 5

Comparison of water cloud reflectances from the LBLE and M1 with re = 8 μm, As = 0.05, and the U.S. Standard Atmosphere. Ranges of CPU time are 0.7–2.5 and 8–35 s for LBLE and M3, respectively.

Tables (9)

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Table 1 Summary of Single-Scattering Properties Incorporated into LBLE, M1, M3, and M4

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Table 2 Comparison of 3.7 μm Top-of-Atmosphere Radiancea for Ice Cloud

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Table 3 Comparison of 10.8 μm Top-of-Atmosphere Radiancea for Ice Cloud

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Table 4 Comparison of 3.7 μm Top-of-Atmosphere Radiancea for Water Cloud

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Table 5 Comparison of 10.8 μm Top-of-Atmosphere Radiancea for Water Cloud

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Table 6 Percentage Difference [ΔR/RUCLA(%)]a of 3.7 μm Top-of-Atmosphere Radiance for Ice Cloud

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Table 7 Percentage Difference [ΔR/RUCLA(%)]a of 10.8 μm Top-of-Atmosphere Radiance for Ice Cloud

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Table 8 Percentage Difference [ΔR/RUCLA(%)]a of 3.7 μm Top-of-Atmosphere Radiance for Water Cloud

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Table 9 Percentage Difference [ΔR/RUCLA(%)]a of 10.8 μm Top-of-Atmosphere Radiance for Water Cloud

Equations (2)

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P ( Θ ) = P ( μ , ϕ ; μ , ϕ ) = i = 0 N ϖ l P l [ μ μ + ( 1 - μ 2 ) 1 / 2 ( 1 - μ 2 ) × cos [ ϕ - ϕ ) ] = m = 0 M l = m N ϖ l m P l m ( μ ) P l m ( μ ) cos m ( ϕ - ϕ ) ,
P HG ( cos Θ ) = ( 1 - g 2 ) / ( 1 + g 2 - 2 g cos Θ ) 3 / 2 = t = 0 N ( 2 l + 1 ) g l P l ( cos Θ ) .

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