The authors thank the anonymous reviewers for their constructive comments. The work is supported by the State Key Development Program for Basic Research of China (Grants 2009CB421506 and 2009CB421500), CAS Pilot Special Project (Grant XDA05090204), Special Scientific Research Fund of Meteorological Public Welfare Profession of China (Grants GYHY201006007, GYHY201006008, GYHY201006016, GYHY201206006, and GYHY200906002), and the National Natural Science Foundation of China (Grant 40921160381 and 41075056).
Ayash, T., , S. Gong, , and Q. J. Charles, 2008: Implementing the delta-four-stream approximation for solar radiation computations in an atmosphere general circulation model. J. Atmos. Sci., 65, 2448–2457.
Chandrasekhar, S., 1950: Radiative Transfer. Oxford University Press, 393 pp.
Chou, M.-D., , and M. J. Suarez, 1999: A solar radiation parameterization (CLIRAD-SW) for atmospheric studies. NASA Tech. Memo. 104606, 40 pp.
Coakley, J. A., , R. D. Cess, , and F. B. Yurevich, 1983: The effect of tropospheric aerosols on the earth’s radiation budget: A parameterization for climate models. J. Atmos. Sci., 40, 116–138.
Dobbie, J. S., , J. Li, , and P. Chýlek, 1999: Two- and four-stream optical properties for water clouds and solar wavelengths. J. Geophys. Res., 104 (D2), 2067–2079.
Fu, Q., 1991: Parameterization of radiative processes in vertically nonhomogeneous multiple scattering atmospheres. Ph.D. dissertation, University of Utah, 259 pp. [Available from University Microfilm, 305 N. Zeeb Rd., Ann Arbor, MI 48106.]
Fu, Q., , K. N. Liou, , M. C. Cribb, , T. P. Charlock, , and A. Grossman, 1997: Multiple scattering parameterization in thermal infrared radiative transfer. J. Atmos. Sci., 54, 2799–2812.
Kay, M. J., , M. A. Box, , T. Trautmann, , and J. Landgraf, 2001: Actinic flux and net flux calculations in radiative transfer—A comparative study of computational efficiency. J. Atmos. Sci., 58, 3752–3761.
King, M. D., , and Harshvardhan, 1986: Comparative accuracy of selected multiple scattering approximations. J. Atmos. Sci., 43, 784–801.
Kylling, A., , K. Stamnes, , and S. C. Tsay, 1995: A reliable and efficient two-stream algorithm for spherical radiative transfer: Documentation of accuracy in realistic layered media. J. Atmos. Chem., 21, 115–150.
Li, J., , and V. Ramaswamy, 1996: Four-stream spherical harmonic expansion approximation for solar radiative transfer. J. Atmos. Sci., 53, 1174–1186.
Li, J., , S. Dobbie, , P. Raisanen, , and Q. Min, 2005: Accounting for unresolved cloud in solar radiation. Quart. J. Roy. Meteor. Soc., 131, 1607–1629.
Liou, K.-N., 2002: An Introduction to Atmospheric Radiation. 3rd ed. Academic Press, 583 pp.
Liou, K.-N., , Q. Fu, , and T. P. Ackerman, 1988: A simple formulation of the delta-four-stream approximation for radiative transfer parameterizations. J. Atmos. Sci., 45, 1940–1947.
Lu, P., , H. Zhang, , and J. Li, 2009: A new complete comparison of two-stream DISORT and Eddington radiative transfer schemes. J. Quant. Spectrosc. Radiat. Transfer, 110, 129–138.
McClatchey, R., , R. Fenn, , J. A. Selby, , F. Volz, , and J. Garing, 1972: Optical properties of the atmosphere. 3rd ed. Air Force Cambridge Research Laboratories Rep., 108 pp.
Nakajima, T., , M. Tsukamoto, , Y. Tsushima, , A. Numaguti, , and T. Kimura, 2000: Modeling of the radiative process in an atmospheric general circulation model. Appl. Opt., 39, 4869–4878.
Shen, Z., , and H. Zhang, 2009: Analysis on the factors affecting surface solar radiation and its spectral distribution. Acta Energ. Sol. Sin., 30, 1389–1395.
Shibata, K., , and A. Uchiyama, 1992: Accuracy of the delta-four-stream approximation in inhomogeneous scattering atmospheres. J. Meteor. Soc. Japan, 70, 1097–1110.
Stamnes, K., , S. C. Tsay, , W. J. Wiscombe, , and K. Jayaweera, 1988: Numerically stable algorithm for discrete ordinate method radiative transfer in multiple scattering and emitting layered media. Appl. Opt., 27, 2502–2509.
Thomas, G. E., , and K. Stamnes, 1999: Radiative Transfer in the Atmosphere and Ocean. Cambridge University Press, 517 pp.
Tian, Y., , R. E. Dickinson, , and L. Zhou, 2007: Four-stream isosector approximation for canopy radiative transfer. J. Geophys. Res.,112, D04107, doi:10.1029/2006JD007545.
Yang, W., 2004: Interaction research between radiation transfer and the scattering by particles in earth atmosphere. Ph.D. dissertation, Cold and Arid Regions Environmental and Engineering Research Institute, 188 pp.
Zhang, F., , L. Ma, , Z. Shen, , H. Zhang, , J. Sun, , and Y. Yan, 2012: A new approach to dealing with bidirectional reflectance of non-homogeneous atmosphere. Acta Phys. Sin.,61, 184–212.
Zhang, H., , T. Nakajima, , G. Shi, , T. Suzuki, , and R. Imasu, 2003: An optimal approach to overlapping bands with correlated k distribution method and its application to radiative transfer calculations. J. Geophys. Res.,108, 4641, doi:10.1029/2002JD003358.
Zhang, H., , F. Zhang, , Q. Fu, , Z. Shen, , and P. Lu, 2010: Two- and four-stream combination approximations for computation of diffuse actinic fluxes. J. Atmos. Sci., 67, 3238–3252.