A great many individuals and organizations contributed to this work. We would like to thank, in particular, Paul Ciesielski, Richard Johnson, and Steven Krueger for providing and assisting with the TOGA COARE datasets; Steven Lord, Hua-Lu Pan, Zavisa Janjic, and Tom Black of NCEP for providing the convection schemes used for the comparison tests; and Joel Sloman for his assistance in preparing the manuscript. Three anonymous reviewers made helpful criticisms of the original manuscript, and the authors are especially grateful to Steve Lord and Zavisa Janjic for their thoughtful comments on this paper. This work was supported by the Department of Energy under Grant DE-FG02-91ER61220.
Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment, Part I. J. Atmos. Sci.,31, 674–701.
Betts, A. K., 1982: Saturation point analysis of moist convective overturning. J. Atmos. Sci.,39, 1484–1505.
——, 1986: A new convective adjustment scheme. Part I: Observational and theoretical basis. Quart. J. Roy. Meteor. Soc.,112, 677–691.
——, and M. J. Miller, 1986: A new convective adjustment scheme. Part II: Single column tests using GATE wave, BOMEX, ATEX and arctic air-mass data sets. Quart. J. Roy. Meteor. Soc.,112, 693–709.
Bretherton, C. S., and P. K. Smolarkiewicz, 1989: Gravity waves, compensating subsidence, and detrainment around cumulus clouds. J. Atmos. Sci.,46, 740–759.
Carpenter, R. L., Jr., K. K. Droegemeier, and A. M. Blyth, 1998: Entrainment and detrainment in numerically simulated cumulus congestus clouds. Part I: General results. J. Atmos. Sci.,55, 3417–3432.
Cess, R. D., and Coauthors, 1990: Intercomparison and interpretation of climate feedback processes in 19 atmospheric general circulation models. J. Geophys. Res.,95, 16 601–16 615.
Cheng, M.-D., and A. Arakawa, 1997: Inclusion of rainwater budget and convective downdrafts in the Arakawa–Schubert cumulus parameterization. J. Atmos. Sci.,54, 1359–1378.
Colman, B. R., 1990: Thunderstorms above frontal surfaces in environments without positive CAPE. Part I: A climatology. Mon. Wea. Rev.,118, 1103–1121.
Cox, S. K., and K. T. Griffith, 1979: Estimates of radiative divergence during Phase III of the GARP Atlantic Tropical Experiment. Part II: Analysis of Phase III results. J. Atmos. Sci.,36, 586–601.
Emanuel, K. A., 1991: A scheme for representing cumulus convection in large-scale models. J. Atmos. Sci.,48, 2313–2335.
——, and R. T. Pierrehumbert, 1996: Microphysical and dynamical control of tropospheric water vapor. Clouds, Chemistry and Climate, P. J. Crutzen and V. Ramanathan, Eds., Springer-Verlag, 264 pp.
Gyakum, J. R., and Coauthors, 1996: A regional model intercomparison using a case of explosive oceanic cyclogenesis. Wea. Forecasting,11, 521–543.
Hall, M. C. G., 1986: Application of adjoint sensitivity theory to an atmospheric general circulation model. J. Atmos. Sci.,43, 2644–2651.
Jabouille, P., J. L. Redelsperger, and J. P. LaFore, 1996: Modification of surface fluxes by atmospheric convection in the TOGA COARE region. Mon. Wea. Rev.,124, 816–837.
Janjic, Z. I., 1994: The step-mountain eta coordinate model: Further developments of the convection, viscous sublayer, and turbulence closure schemes. Mon. Wea. Rev.,122, 927–945.
Kessler, E., 1969: On the Distribution and Continuity of Water Substance in Atmospheric Circulation. Amer. Meteor. Soc., 84 pp.
Kuo, H.-L., 1974: Further studies of the parameterization of the influence of cumulus convection on large-scale flow. J. Atmos. Sci.,31, 1232–1240.
LeMone, M. A., G. M. Barnes, E. J. Szoke, and E. J. Zipser, 1984: The tilt of the leading edge of mesoscale tropical convective lines. Mon. Wea. Rev.,112, 510–519.
Lin, X., and R. H. Johnson, 1996: Kinematic and thermodynamic characteristics of the flow over the western Pacific warm pool during TOGA COARE. J. Atmos. Sci.,53, 695–715.
Lindzen, R. S., 1990: Some coolness concerning global warming. Bull. Amer. Meteor. Soc.,71, 288–299.
Manabe, S., J. Smagorinsky, and R. F. Strickler, 1965: Simulated climatology of a general circulation model with a hydrologic cycle. Mon. Wea. Rev.,93, 769–798.
Pan, H.-L., and W.-S. Wu, 1995: Implementing a mass flux convection parameterization package for the NMC Medium-Range Forecast Model. NMC Office Note 409, 40 pp. [Available form the National Centers for Environmental Prediction, Stop 9910, 4700 Silver Hill Road, Washington, DC 20233-9910.].
Pierrehumbert, R. T., and H. Yang, 1993: Global chaotic mixing on isentropic surfaces. J. Atmos. Sci.,50, 2462–2480.
Randall, D. A., K.-M. Xu, R. J. C. Somerville, and S. Iacobellis, 1996: Single-column models and cloud ensemble models as links between observations and climate models. J. Climate,9, 1683–1697.
Raymond, D. J., 1995: Regulation of moist convection over the west Pacific warm pool. J. Atmos. Sci.,52, 3945–3959.
——, and A. M. Blyth, 1986: A stochastic model for nonprecipitating cumulus clouds. J. Atmos. Sci.,43, 2708–2718.
Rennó, N. O., K. A. Emanuel, and P. H. Stone, 1994: Radiative-convective model with an explicit hydrological cycle. 1: Formulation and sensitivity to model parameters. J. Geophys. Res.,99, 14 429–14 441.
Rossow, W. B., and Y.-C. Zhang, 1995: Calculation of surface and top of atmosphere radiative fluxes from physical quantities based on ISCCP data sets. 2: Validation and first results. J. Geophys. Res.,100, 1167–1197.
Spencer, R. W., and W. D. Braswell, 1997: How dry is the tropical free troposphere? Implications for global warming theory. Bull. Amer. Meteor. Soc.,78, 1097–1106.
Sud, Y. C., and G. K. Walker, 1993: A rain evaporation and downdraft parameterization to complement a cumulus updraft scheme and its evaluation using GATE data. Mon. Wea. Rev.,121, 3019–3039.
Sun, D.-Z., and A. H. Oort, 1995: Humidity–temperature relationships in the tropical troposphere. J. Climate,8, 1974–1987.
Taylor, G. R., and M. B. Baker, 1991: Entrainment and detrainment in cumulus clouds. J. Atmos. Sci.,48, 112–121.
Thompson, R. M., Jr., S. W. Payne, E. E. Recker, and R. J. Reed, 1979: Structure and properties of synoptic-scale wave disturbances in the intertropical convergence zone of the eastern Atlantic. J. Atmos. Sci.,36, 53–72.
Tziperman, E., and W. C. Thacker, 1989: An optimal-control/adjoint-equations approach to studying the oceanic general circulation. J. Phys. Oceanogr.,19, 1471–1485.
Velden, C. S., and J. A. Young, 1994: Satellite observations during TOGA COARE: Large-scale descriptive overview. Mon. Wea. Rev.,122, 2426–2441.
Vukicevic, T., and R. M. Errico, 1993: Linearization and adjoint of parameterized moist diabatic processes. Tellus,45A, 493–510.
Wang, Z. I., M. Navon, X. Zou, and F. X. Le Dimet, 1995: A truncated Newton Optimization algorithm in meteorology applications with analytic Hessian/vector products. Comput. Optim. Appl.,4, 241–262.
Warner, J., 1970: On steady-state one-dimensional models of cumulus convection. J. Atmos. Sci.,27, 1035–1040.
Wei, D., A. M. Blyth, and D. J. Raymond, 1998: Buoyancy of convective clouds in TOGA COARE. J. Atmos. Sci.,55, 3381–3391.
Weller, R. A., and S. P. Anderson, 1996: Surface meteorology and air–sea fluxes in the western equatorial Pacific warm pool during TOGA Coupled Ocean–Atmosphere Response Experiment. J. Climate,9, 1959–1990.
Zhang, M. H., and J. L. Lin, 1997: Constrained variational analysis of sounding data based on column-integrated budgets of mass, heat, moisture, and momentum: Approach and application to ARM measurements. J. Atmos. Sci.,54, 1503–1524.
Zhang, Y.-C., W. B. Rossow, and A. A. Lacis, 1995: Calculation of surface and top of atmosphere radiative fluxes from physical quantities based on ISCCP data sets. 1: Method and sensitivity to input data uncertainties. J. Geophys. Res.,100, 1149–1165.
Živković, M., 1997: Variational optimization of sub-grid scale convection parameters. Final Report, Department of Energy, 58 pp. [Available from Atmospheric and Environmental Research, 840 Memorial Drive, Cambridge, MA 02139.].
——, J.-F. Louis, and J.-L. Moncet, 1995: Sensitivity analysis of a radiation parameterization. J. Geophys. Res.,100 (D7), 13 827–13 840.