The energy-cycle analysis of the interactions between shallow and deep atmospheric convection

Arakawa, A., andW. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment, Part I. J. Atmos. Sci., 31, 674–701. Bechtold, P., J.-P. Chaboureau, A. Beljaars, A. Betts, M. Kohler, M. Miller, and J.-L. Redelsperger, 2004: The simulation of the diurnal cycle of convective precipitation over land in a global model. Quart. J. Roy. Meteor. Soc., 139, 3119–3137. Betts, A. K., 1997: Trade cumulus: observations and modelling. In: The Physics and Parameterization of Moist Atmospheric Convection, Kluwer Academic Publ., 99–126. Emanuel, K. A., and M. Bister, 1996: Moist convective velocity and buoyancy scales. J. Atmos. Sci., 53, 3276–3285. Emanuel, K. A., J. D. Neelin, and C. S. Bretherton, 1994: On large–scale circulation in convective atmospheres. Quart. J. Roy. Meteor. Soc., 120, 1111–1143. Goldstein, H., C. Poole, and J. Safko, 2002: Classical Mechanics, 3rd Ed. Addison Wesley, San Francisco, 638pp. Grant, A. L. M. and A. R. Brown, 1999: A similarity hypothesis for shallow-cumulus transports. Quart. J. Roy. Meteor. Soc., 125, 1913–1936. Grant, A. L. M. and A. P. Lock, 2004: The turbulent kinetic energy budget for shallow cumulus convection. Quart. J. Roy. Meteor. Soc., 130, 401–422. Grabowski, W. W., P. Bechtold, A. Cheng, R. Forbes, C. Halliwell, M. Khairoutdinov, S. Lang, T. Nasuno, J. Petch, W.-K. Tao, R. Wong, X. Wu and K.-M. Xu, 2006: Daytime convective development over land: A model intercomparison based on LBA observations. Quart. J. Roy. Meteor. Soc., 132, 317–344. Guichard F., J. C. Petch, J. L. Redelsperger, P. Bechtold, J.–P. Chaboureau, S. Cheinet, W. Grabowski, H. Grenier, C. G. Jones, M. Kohler, J.–M. Piriou, R. Tailleux, and M. Tomasini, 2004: Modelling the diurnal cycle of deep precipitating convection over land with cloud-resolving models and singlecolumn models. Quart. J. Roy. Meteor. Soc., 604, 3139–3172. Hohenegger, C., and C. S. Bretherton, 2011: Simulating deep convection with a shallow convection scheme. Atmos. Chem. Phys., 11, 8385–8430. Holtslag, A. A. M., and B. A. Boville, 1993: Local versus nonlocal boundary– layer diffusion in a global climate model. J. Climate, 6, 1825–1842. Houze, R. A., Jr., and A. K. Betts, 1981: Convection in GATE, Rev. Geophys. Space Phys., 19, 541-576. Johnson, R. H., Rickenbach, T. M., Rutledge, S. A., Ciesielski, P. E., and Schubert, W. H., 1999: Trimodal characteristics of tropical convection. J. Cli- mate, 12, 2397–2418. K¨oller, M., M. Ahlgrimm, and A. Beljaars, 2011: Unified treatment of dry convective and stratocumulus–topped boundary layers in the ECMWF model. Quart. J. Roy. Meteor. Soc., 137, 43–57. Lock, A. P., 1998: The parameterization of entrainment in cloudy boundary layers. Quart. J. Roy. Meteor. Soc., 124, 2729–2753. Lock, A. P., A. R. Brown, M. R. Bush, G. M. Martin, and R. N. B. Smith, 2000: A new boundary layer mixing scheme. Part I: Scheme description and single–column model tests. Mon. Wea. Rev., 128, 3187–3199. Mapes, B. E., and R. Neale, 2011: Parameterizing convective organization to escape the entrainment dilemma. J. Adv. Model Earth System, 3, doi:10.1029/2011MS000042. Moeng, C.–H., 1998: Stratocumulus–topped atmospheric planetary boundary layer. In: Buoyant Convection in Geophysical Flows, E. J. Plate, E. E. Fedorovich, D. X. Viegas, and J. C.Wyngaard, Eds., Kulwer Academic Publ., 421–440. Neggers, R., M. K¨oller, and A. Beljaars, 2009: A dual mass flux framework for boundary–layer convection. Part I: Transport. J. Atmos. Sci., 66, 1465– 1487. Pan, D.-M., and D. A. Randall, 1998: A cumulus parameterization with prognostic closure, Quart. J. Roy. Meteor. Soc., 124, 949–981. Parodi, A., and K. Emanuel, 2009: A theory for buoyancy and velocity scales in deep moist convection. J. Atmos. Sci., 66, 3449–3463. Plant, R. S., 2012: A new modelling framework for statistical cumulus dynamics. Phil. Trans. Roy. Soc., A370, 1041–1060. Randall, D. A., and D.-M. Pan, 1993: Implementation of the Arakawa-Schubert cumulus parameterization with a prognostic closure. In: The Representa- tion of Cumulus Convection in Numerical Models, K. A. Emanuel and D. J. Raymond (Eds.), Meteorological Monographs 46, Amer. Meteor. Soc., 137–144. Riehl, H., C. Yeh, J. S. Malkus, and N. E. LaSeur, 1951: The north–east trade of the Pacific Ocean. Quart. J. Roy. Meteor. Soc., 77, 598–626. Redelsperger, J.–L., 1997: The mesoscale organization of deep convection. In: The Physics and Parameterization of Moist Atmospheric Convection, R. K. Smith (Ed.), Kluwer Academic Publ., 59–98. Riehl, H., and J. S. Malkus, 1958: On the heat balance in the equatorial trough zone. Geophysica, 6, 503–538. Shutts, G. J., and M. E. B. Gray, 1999: Numerical simulations of convective equilibrium under prescribed forcing. Quart. J. Roy. Meteor. Soc., 125, 2767–2787. Stevens, B., 2005: Atmospheric moist convection. Ann. Rev. Earth Planet. Sci., 33, 605–643. Tiedtke, M., 1989: A comprehensive mass flux scheme of cumulus parameterization in large–scale models. Mon. Wea. Rev., 117, 1779–1800. Tung, W. W., C. Lin, B. Chen, M. Yanai, and A. Arakawa, 1999: Basic mode of cumulus heating and drying observed during TOGA–COARE IOP. Geophys. Res. Lett., 26, 117–120. Wyant, M. C., C. S. Bretherton, A. Chlond, B. M. Griffin, H. Kitagawa, C.–L. Lappen, V. E. Larson, A. Lock, S. Park, S. R. de Roode, J. Uchida, M. Zhao, A. S. Ackerman, 2007: A single–column model intercomparison of a heavily drizzling stratocumulus–topped boundary layer. J. Geophys. Res., 112, D24204, doi:10.1029/2007JD008536. Yano, J.-I., J.-L. Redelsperger, F. Guichard, and P. Bechtold, 2005: Mode decomposition as a methodology for developing convective-scale representations in global models. Quart. J. Roy. Meteor. Soc., 131, 2313–2336. Yano, J.-I., and R. S. Plant, 2012a: Finite departure from convective quasiequilibrium: Periodic cycle and discharge-recharge mechanism. Quart. J. Roy. Meteor. Soc., 138, 626–637. Yano, J.-I., and R. S. Plant 2012b: Interactions between shallow and deep convection under a finite departure from convective quasi–equilibrium. J. Atmos. Sci., 69, 3463–3470. Yano, J.-I., and R. S. Plant, 2012c: Convective quasi–equilibrium. Rev. Geo- phys., 50, RG4004, doi:10.1029/2011RG000378. Yano, J.-I., 2013: Convective Kinetic Energy Equation Under the Mass-flux Subgrid-scale Parameterization. In preparation. Yano J.-I., M. Bister, Z. Fuchs, L. Gerard, V. Phillips, S. Barkidija, and J.-M. Piriou, 2013: Phenomenology of convection-parameterization closure. At- mos. Chem. Phys., 13, 4111–4131. Zhang, C., 2005: Madden–Julian oscillation. Rev. Geophys,43, 8755–1209/05/2005RG000158. 56