We thank Marat Khairoutdinov for the stimulating discussion that lead to Eq. (11) and Bjorn Stevens for providing his LES code. Bjorn Stevens, Charlie Cohen, and Steve Burk are thanked for their comments on the manuscript. The constructive comments of the anonymous reviewers are greatly appreciated. This work was started when S. Wang was affiliated with Universities Space Research Association and supported by the NASA FIRE III and EOS programs. Most of the analyses and writing were done when S. Wang was at Naval Research Laboratory, and supported by the Office of Naval Research under PE 0602435N. Q. Wang was supported by NSF Grants ATM-9700845 and ATM-9900496. G. Feingold acknowledges support from the NSF/NOAA EPIC program.
Ackerman, A. S., O. B. Toon, and P. V. Hobbs, 1995: A model for particle microphysics, turbulent mixing, and radiative transfer in the stratocumulus-topped marine boundary layer and comparison with measurements. J. Atmos. Sci., 52 , 1204–1236.
Albrecht, B. A., M. P. Jensen, and W. J. Syrett, 1995: Marine boundary layer structure and fractional cloudiness. J. Geophys. Res., 100 , 14209–14222.
Bott, A., T. Trautmann, and W. Zdunkowki, 1996: A numerical model of cloud-topped planetary boundary-layer: Radiation, turbulence and spectral microphysics in marine stratus. Quart. J. Roy. Meteor. Soc., 122 , 635–667.
Clark, T. L., 1973: Numerical modeling of the dynamics and microphysics of warm cumulus convection. J. Atmos. Sci., 30 , 857–878.
Considine, G. D., 1997: Modeling the diurnal variability in cloud microphysics in boundary layer clouds. J. Geophys. Res., 102 , 1717–1726.
Cooper, W. A., 1989: Effects of variable droplet growth histories on droplet size distributions. Part I: Theory. J. Atmos. Sci., 46 , 1301–1311.
Deardorff, J. W., 1980: Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound.-Layer Meteor., 18 , 495–527.
Feingold, G., B. Stevens, W. R. Cotton, and R. L. Walko, 1994: An explicit cloud microphysical/LES model designed to simulate the Twomey effect. Atmos. Res., 33 , 207–233.
Feingold, G., B. Stevens, W. R. Cotton, and R. L. Walko, 1998: Simulations of marine stratocumulus using a new microphysical parameterization scheme. Atmos. Res., 47–48 , 505–523.
Fu, Q., S. K. Krueger, and K. N. Liou, 1995: Interactions of radiation and convection in simulated tropical cloud clusters. J. Atmos. Sci., 52 , 2139–2156.
Khairoutdinov, M., and Y. Kogan, 2000: A new cloud physics parameterization in a large-eddy simulation model of marine stratocumulus. Mon. Wea. Rev., 128 , 229–243.
Khvorostyanov, V. I., and J. Curry, 1999: Toward the theory of stochastic condensation in clouds. Part I: A general kinetic equation. J. Atmos. Sci., 56 , 3985–3996.
Kogan, Y. L., M. P. Khairoutinov, D. K. Lilly, Z. N. Kogan, and Q. Fu, 1995: Modeling of stratocumulus clouds layers in a large-eddy simulation model with explicit microphysics. J. Atmos. Sci., 52 , 2923–2940.
Lappen, C-L., and D. A. Randall, 2001: Toward a unified parameterization of the boundary layer and moist convection. Part I: A new type of mass-flux model. J. Atmos. Sci., 58 , 2021–2036.
Moeng, C-H., 1986: Large-eddy simulation of a stratus-topped boundary layer. Part I: Structure and budgets. J. Atmos. Sci., 43 , 2886–2900.
Moeng, C-H., and J. C. Wyngaard, 1986: An analysis of closures for pressure-scalar covariances in the convective boundary layer. J. Atmos. Sci., 43 , 2499–2513.
Nicholls, S., 1984: The dynamics of stratocumulus: Aircraft observations and comparisons with a mixed-layer model. Quart. J. Roy. Meteor. Soc., 110 , 783–820.
Paluch, I. R., and D. H. Lenschow, 1991: Stratiform cloud formation in the marine boundary layer. J. Atmos. Sci., 48 , 2141–2158.
Sigg, R., 2000: Use of pseudoadiabatic adjustment of turbulence for a simplified nighttime stratocumulus case: A one-dimensional study. Mon. Wea. Rev., 128 , 2317–2328.
Sommeria, G., and J. W. Deardorff, 1977: Subgrid-scale condensation in models of nonprecipitating clouds. J. Atmos. Sci., 34 , 344–355.
Stevens, B., G. Feingold, W. R. Cotton, and R. L. Walko, 1996a: Elements of the microphysical structure of numerically simulated nonprecipitating stratocumulus. J. Atmos. Sci., 53 , 980–1006.
Stevens, B., R. L. Walko, W. R. Cotton, and G. Feingold, 1996b: The spurious production of cloud-edge supersaturation by Eulerian models. Mon. Wea. Rev., 124 , 1034–1041.
Stevens, B., W. R. Cotton, and G. Feingold, 1998a: A critique of one- and two-dimensional models of boundary layer clouds with a binned representations of drop microphysics. Atmos. Res., 47–48 , 529–553.
Stevens, B., W. R. Cotton, G. Feingold, and C-H. Moeng, 1998b: Large-eddy simulations of strongly precipitating, shallow, stratocumulus-topped boundary layers. J. Atmos. Sci., 55 , 3616–3638.
Stevens, B., C-H. Moeng, and P. P. Sullivan, 1999: Large-eddy simulation of radiatively driven convection: Sensitivities to the representation of small scales. J. Atmos. Sci., 56 , 3963–3984.
Wang, Q., H. Zuo, S. Wang, C. Zhao, and D. L. Westphal, 1998: A new turbulence closure model with explicit microphysics for marine stratocumulus. Preprints, Conf. on Cloud Physics, Everett, WA, Amer. Meteor. Soc.,. 325–328.
Wang, S., and Q. Wang, 1994: Roles of drizzle in a one-dimensional third-order turbulence closure model of the nocturnal stratus-topped marine boundary layer. J. Atmos. Sci., 51 , 1559–1576.
Wang, S., and Q. Wang, 1999: On condensation and evaporation in turbulence cloud parameterizations. J. Atmos. Sci., 56 , 3338–3344.
Wang, S., and B. Stevens, 2000: Top-hat representation of turbulence statistics in cloud-topped boundary layers: A large eddy simulation study. J. Atmos. Sci., 57 , 423–440.
Wang, S., and Q. Wang, 2000: A cloud microphysical parameterization for higher-order turbulence closure models. Proc. 13th Int. Conf. on Clouds and Precipitation, Reno, NV, ICCP,. 557–560.
Wyngaard, J. C., and C-H. Moeng, 1992: Parameterizing turbulent diffusion through the joint probability density. Bound.-Layer Meteor., 60 , 1–13.