We thank Dr. H. Iwabuchi for providing the data of the Monte Carlo simulations. This study was partly supported by the Ministry of Education, Culture, Sports, Science and Technology, under a Grant-in-Aid for Scientific Research [(A)17204039].
Barker, H. W., , and J. A. Davies, 1992: Cumulus cloud radiative properties and the characteristics of satellite radiance wavenumber spectra. Remote Sens. Environ., 42 , 51–64.
Cahalan, R. F., , W. Ridgway, , W. J. Wiscombe, , and S. Gollmer, and Harshvardhan, 1994: Independent pixel and Monte Carlo estimates of stratocumulus albedo. J. Atmos. Sci., 51 , 3776–3790.
Cahalan, R. F., and Coauthors, 2005: The 13RC: Bringing together the most advanced radiative transfer tools for cloudy atmospheres. Bull. Amer. Meteor. Soc., 86 , 1275–1293.
Chai, J. C., , P-f Hsu, , and Y. C. Lam, 2004: Three-dimensional transient radiative transfer modeling using the finite-volume method. J. Quant. Spectrosc. Radiat. Transfer, 86 , 299–313.
Evans, K. F., 1993: Two-dimensional radiative transfer in cloudy atmospheres: The spherical harmonic spatial grid method. J. Atmos. Sci., 50 , 3111–3124.
Evans, K. F., 1998: The spherical harmonics discrete ordinate method for three-dimensional atmospheric radiative transfer. J. Atmos. Sci., 55 , 429–446.
Gabriel, P. M., , S. Tsay, , and G. L. Stephens, 1993: A Fourier–Riccati approach to radiative transfer. Part I: Foundations. J. Atmos. Sci., 48 , 2436–2447.
Gu, Y., , and K. N. Liou, 2001: Radiation parameterization for three-dimensional inhomogeneous cirrus clouds: Application to climate models. J. Climate, 14 , 2443–2457.
Hartman, C. M., , and J. Y. Harrington, 2005: Radiative impacts on the growth of drops within simulated marine stratocumulus. Part I: Maximum solar heating. J. Atmos. Sci., 62 , 2323–2338.
Ishida, H., , and S. Asano, 2007: A quasi-analytic solution of the radiative transfer equation for three-dimensional atmospheres. J. Quant. Spectrosc. Radiat. Transfer, 103 , 371–393.
Iwabuchi, H., , and T. Hayasaka, 2002: Effects of cloud horizontal inhomogeneity on the optical thickness retrieved from moderate-resolution satellite data. J. Atmos. Sci., 59 , 2227–2242.
Moeng, C., , P. P. Sullivan, , and B. Stevens, 1999: Including radiative effects in an entrainment rate formula for buoyancy-driven PBLs. J. Atmos. Sci., 56 , 1031–1049.
Ramanathan, V., , R. D. Cess, , E. F. Harrison, , P. Minnis, , B. R. Barkstrom, , E. Ahmad, , and D. Hartmann, 1989: Cloud-radiative forcing and climate: Results from the Earth Radiation Budget Experiment. Science, 243 , 57–63.
Stephens, G. L., 1988a: Radiative transfer through arbitrarily shaped optical media. Part I: A general method of solution. J. Atmos. Sci., 45 , 1818–1836.
Stephens, G. L., 1988b: Radiative transfer through arbitrarily shaped optical media. Part II: Group theory and simple closures. J. Atmos. Sci., 45 , 1837–1848.
Varnai, T., , and A. Marshak, 2002: Observations of three-dimensional radiative effects that influence MODIS cloud optical thickness retrievals. J. Atmos. Sci., 59 , 1607–1618.
Wiscombe, W. J., 1977: The delta-M method: Rapid yet accurate radiative flux calculations for strongly asymmetric phase functions. J. Atmos. Sci., 34 , 1408–1422.
Wu, X., , and X-Z. Liang, 2005: Radiative effects of cloud horizontal inhomogeneity and vertical overlap identified from a monthlong cloud-resolving model simulation. J. Atmos. Sci., 62 , 4105–4112.