We would like to thank the anonymous reviewers for their constructive comments and J. Wong for his helpful comments on this paper. We would also like to thank Dr. S. C. Tsay for providing the discrete ordinate model.
Barker, H., and Z. Li, 1995: Improved simulation of clear-sky shortwave radiative transfer in the CCC-GCM. J. Climate,8, 2213–2223.
Charlson, R. J., S. E. Schwartz, J. M. Hales, R. D. Cess, J. A. Coakley, J. E. Hansen, and D. J. Hofmann, 1992: Climate forcing by anthropogenic aerosols. Science,255, 423–430.
Chýlek, P., and S. Dobbie, 1995: Radiative properties of finite inhomogeneous cirrus clouds: Monte Carlo calculations. J. Atmos. Sci.,52, 3512–3522.
Coakley, J., and P. Chýlek, 1975: The two-stream approximation in radiative transfer: Including the angle of the incident radiation. J. Atmos. Sci.,32, 409–418.
Hu, Y., and B. A. Wielicki, 1997: A sensitivity study of angular dependence models. Preprints, Ninth Conf. on Atmospheric Radiation, Long Beach, CA, Amer. Meteor. Soc., 279–282.
Joseph, J. H., W. J. Wiscombe, and J. A. Weinman, 1976: The delta Eddington approximation for radiative flux transfer. J. Atmos. Sci.,33, 2452–2459.
King, M. D., and Harshvardhan 1986: Comparative accuracy of selected multiple scattering approximations. J. Atmos. Sci.,43, 784–801.
Li, J., and V. Ramaswamy, 1996: Four-stream spherical harmonic expansion approximation for solar radiative transfer. J. Atmos. Sci.,53, 1174–1186.
Liou, K. N., 1973: A numerical experiment on Chandrasekhar’s discrete-ordinate method for radiative transfer: Applications to cloud and hazy atmosphere. J. Atmos. Sci.,30, 1303–1326.
——, Q. Fu, and T. P. Ackerman, 1988: A simple formulation of the delta-four-stream approximation for radiative transfer parameterisation. J. Atmos. Sci.,45, 1904–1947.
Meador, W. E., and W. R. Weaver, 1980: Two-stream approximations to radiative transfer in planetary atmospheres: A unified description of existing methods and a new improvement. J. Atmos. Sci.,37, 630–643.
Ross, S. L., 1974: Differential Equation. Xerox College Publishing, 712 pp.
Shettle, E. P., and J. A. Weinman, 1970: The transfer of solar irradiance through inhomogeneous turbid atmospheres evaluated by Eddington’s approximation. J. Atmos. Sci.,27, 1048–1054.
Stamnes, K., S. C. Tsay, W. Wiscombe, and K. Jayaweera, 1988: A numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. Appl. Opt.,27, 2502–2509.
Wiscombe, W., 1977: The delta-M method: Rapid yet accurate radiative flux calculations. J. Atmos. Sci.,34, 1408–1422.