We thank S. Weckmann for useful discussions. The work for the clouds and the Clouds and the Earth's Radiant Energy System (CERES) project was supported by the NASA Langley Research Center Grant NAG-1-1963 to Hampton University and Cooperative Agreement NCC-1-405 to Virginia Polytechnic Institute and State University.
Barker, H. W., 1996: A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds. Part I: Methodology and homogeneous biases. J. Atmos. Sci, 53 , 2289–2303.
Barker, H. W., B. A. Wielicki, and L. Parker, 1996: A parameterization for computing grid-averaged solar fluxes for inhomogeneous marine boundary layer clouds. Part II: Validation using satellite data. J. Atmos. Sci, 53 , 2304–2316.
Barker, H. W., J-J. Morcrette, and G. D. Alexander, 1998: Broadband solar fluxes and heating rates for atmospheres with 3D broken clouds. Quart. J. Roy. Meteor. Soc, 124 , 1245–1271.
Cahalan, R. F., W. Ridgway, W. J. Wiscombe, S. Gollmer, and Harshvardhan, 1994: Independent pixel and Monte Carlo estimates of stratocumulus albedo. J. Atmos. Sci, 51 , 3776–3790.
Geleyn, J-F., and A. Hollingsworth, 1979: An economical analytical method for the computation of the interaction between scattering and line absorption of radiation. Contrib. Atmos. Phys, 52 , 1–16.
Kato, S., T. P. Ackerman, J. H. Mather, and E. E. Clothiaux, 1999: The k-distribution method and correlated-k approximation for a shortwave radiative transfer model. J. Quant. Spectrosc. Radiat. Transfer, 62 , 109–121.
Liou, K-N., 1975: Applications of the discrete-ordinate method for radiative transfer to inhomogeneous aerosol atmospheres. J. Geophys. Res, 80 , 3434–3440.
McClatchey, R. A., R. W. Fenn, J. E. A. Selby, F. E. Volz, and J. S. Garing, 1972: Optical properties of the atmosphere. 3d ed. Environmental Research Paper 411, Air Force Cambridge Research Laboratories, Bedford, MA, 110 pp.
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.
Oreopoulos, L., and H. W. Barker, 1999: Accounting for subgrid-scale cloud variability in a multi-layer 1D solar radiative transfer algorithm. Quart. J. Roy. Meteor. Soc, 125 , 301–330.
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 , 1048–1055.
Stamnes, K., and R. A. Swanson, 1981: A new look at the discrete ordinate method for radiative transfer calculations in anisotropically scattering atmospheres. J. Atmos. Sci, 38 , 387–399.
Stamnes, K., S-C. Tsay, W. 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.
Stephens, G. L., 1988: Radiative transfer through arbitrarily shaped optical media. Part II: Group theory and simple closures. J. Atmos. Sci, 45 , 1837–1848.
Stephens, G. L., P. M. Gabriel, and S-C. Tsay, 1991: Statistical radiative transport in one-dimensional media and its application to the terrestrial atmosphere. Trans. Theor. Stat. Phys, 20 , 139–175.
Toon, O. B., C. P. Mckay, T. P. Ackerman, and K. Santhanam, 1989:: Rapid calculation of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres. J. Geophys. Res, 94 , 16287–16301.
Wiscombe, W. J., 1977: The delta-Eddington approximation for a vertically inhomogeneous atmosphere. Tech. Note TN-121+STR, National Center for Atmospheric Research, Boulder, CO, 66 pp.