• Arakawa, A., 2004: The cumulus parameterization problem: Past, present, and future. J. Climate, 17 , 24932525.

  • Arakawa, A., and W. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment, Part I. J. Atmos. Sci., 31 , 674701.

    • Search Google Scholar
    • Export Citation
  • Bjerknes, J., 1938: Saturated-adiabatic ascent of air through a dry-adiabatically descending environment. Quart. J. Roy. Meteor. Soc., 64 , 325330.

    • Search Google Scholar
    • Export Citation
  • Bretherton, C., 1988: A theory for nonprecipitating convection between two parallel plates. Part II: Nonlinear theory and cloud field organization. J. Atmos. Sci., 45 , 23912415.

    • Search Google Scholar
    • Export Citation
  • Bretherton, C., P. Blossey, and M. Khairoutdinov, 2005: An energy-balance analysis of deep convective self-aggregation above uniform SST. J. Atmos. Sci., 62 , 42734292.

    • Search Google Scholar
    • Export Citation
  • Bright, D., and S. Mullen, 2002: Short-range ensemble forecasts of precipitation during the southwest monsoon. Wea. Forecasting, 17 , 10801100.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., 1997: Potential forecast skill of ensemble prediction and spread and skill distributions of the ECMWF Ensemble Prediction System. Mon. Wea. Rev., 125 , 99119.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., M. Miller, and T. Palmer, 1999: Stochastic representation of model uncertainties in the ECMWF ensemble prediction system. Quart. J. Roy. Meteor. Soc., 125 , 28872908.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., P. Houtekamer, Z. Toth, G. Pellerin, M. Wei, and Y. Zhu, 2005: A comparison of the ECMWF, MSC, and NCEP global ensemble prediction systems. Mon. Wea. Rev., 133 , 10761096.

    • Search Google Scholar
    • Export Citation
  • Chaboureau, J., F. Guichard, J. Redelsperger, and J. Lafore, 2004: The role of stability and moisture in the diurnal cycle of convection over land. Quart. J. Roy. Meteor. Soc., 130 , 31053117.

    • Search Google Scholar
    • Export Citation
  • Cohen, B., 2001: Fluctuations in an ensemble of cumulus clouds. Ph.D. thesis, University of Reading, 165 pp.

  • Cohen, B., and G. Craig, 2004: The response time of a convective cloud ensemble to a change of forcing. Quart. J. Roy. Meteor. Soc., 130 , 933944.

    • Search Google Scholar
    • Export Citation
  • Cohen, B., and G. Craig, 2006: Fluctuation in an equilibrium convective ensemble. Part II: Numerical experiments. J. Atmos. Sci., 63 , 20052015.

    • Search Google Scholar
    • Export Citation
  • Collins, M., B. Booth, G. Harris, J. Murphy, D. Sexton, and M. Webb, 2006: Towards quantifying uncertainty in transient climate change. Climate Dyn., 27 , 127147.

    • Search Google Scholar
    • Export Citation
  • Craig, G., and B. Cohen, 2006: Fluctuation in an equilibrium convective ensemble. Part I: Theoretical formulation. J. Atmos. Sci., 63 , 19962004.

    • Search Google Scholar
    • Export Citation
  • Davies, L., 2008: Self-organisation of convection as a mechanism for memory. Ph.D. thesis, University of Reading, 157 pp.

  • Done, J., G. Craig, S. Gray, P. Clark, and M. Gray, 2006: Mesoscale simulations of organized convection: Importance of convective equilibrium. Quart. J. Roy. Meteor. Soc., 132 , 737756.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K., 1994: Atmospheric Convection. Oxford University Press, 550 pp.

  • Emanuel, K., and M. Bister, 1996: Moist convective velocity and buoyancy scales. J. Atmos. Sci., 53 , 32763285.

  • Guichard, F., and Coauthors, 2004: Modelling the diurnal cycle of deep precipitating convection over land with cloud-resolving models and single-column models. Quart. J. Roy. Meteor. Soc., 130 , 31393172.

    • Search Google Scholar
    • Export Citation
  • Hou, D., E. Kalnay, and K. Droegemeier, 2001: Objective verification of the SAMEX ’98 ensemble forecasts. Mon. Wea. Rev., 129 , 7391.

    • Search Google Scholar
    • Export Citation
  • Kain, J., and M. Fritsch, 1990: A one-dimensional entraining/detraining plume model and its application in convective parameterization. J. Atmos. Sci., 47 , 27842802.

    • Search Google Scholar
    • Export Citation
  • Kain, J., and M. Fritsch, 1993: Convective parameterization in mesoscale models: The Kain–Fritsch scheme. The Representation of Cumulus Convection in Numerical Models, Meteor. Monogr., No. 46, Amer. Meteor. Soc., 165–170.

    • Search Google Scholar
    • Export Citation
  • Khouider, B., A. Majda, and A. Katsoulakis, 2003: Coarse-grained stochastic models for tropical convection and climate. Proc. Natl. Acad. Sci. USA, 100 , 1194111946.

    • Search Google Scholar
    • Export Citation
  • Kuang, Z., 2008: Modeling the interaction between cumulus convection and linear gravity waves using a limited-domain cloud system–resolving model. J. Atmos. Sci., 65 , 576591.

    • Search Google Scholar
    • Export Citation
  • Küpper, C., J. Thuburn, G. C. Craig, and T. Birner, 2004: Mass and water transport into the tropical stratosphere: A cloud-resolving simulation. J. Geophys. Res., 109 , D10111. doi:10.1029/2004JD004541.

    • Search Google Scholar
    • Export Citation
  • Landau, L., and E. Lifshitz, 1968: Statistical Physics. Pergamon Press, 512 pp.

  • LeMone, M., and E. Zipser, 1980: Cumulonimbus vertical velocity events in GATE. Part II: Diameter, intensity and mass flux. J. Atmos. Sci., 37 , 24442457.

    • Search Google Scholar
    • Export Citation
  • Lin, J. W-B., and J. D. Neelin, 2000: Influence of stochastic moist convective parameterization on tropical climate variability. Geophys. Res. Lett., 27 , 36913694.

    • Search Google Scholar
    • Export Citation
  • Lin, J. W-B., and J. D. Neelin, 2002: Considerations for stochastic convective parameterization. J. Atmos. Sci., 59 , 959975.

  • Lin, J. W-B., and J. D. Neelin, 2003: Towards stochastic deep convective parameterization in general circulation models. Geophys. Res. Lett., 30 , 1162. doi:10.1029/2002GL016203.

    • Search Google Scholar
    • Export Citation
  • Majda, A., and B. Khouider, 2002: Stochastic and mesoscopic models for tropical convection. Proc. Natl. Acad. Sci. USA, 99 , 11231128.

    • Search Google Scholar
    • Export Citation
  • Medhi, J., 1994: Stochastic Processes. New Age International Publishers, 598 pp.

  • Murphy, J., D. Sexton, D. Barnett, G. Jones, M. Webb, M. Collins, and D. Stainforth, 2004: Quantification of modelling uncertainties in a large ensemble of climate change simulations. Nature, 430 , 768772.

    • Search Google Scholar
    • Export Citation
  • Mylne, K., R. Evans, and R. Clark, 2002: Multi-model multi-analysis ensembles in quasi-operational medium-range forecasting. Quart. J. Roy. Meteor. Soc., 128 , 361384.

    • Search Google Scholar
    • Export Citation
  • Palmer, T. N., 2001: A nonlinear dynamical perspective on model error: A proposal for non-local stochastic-dynamic parametrization in weather and climate prediction models. Quart. J. Roy. Meteor. Soc., 127 , 279304.

    • Search Google Scholar
    • Export Citation
  • Pan, D., and D. Randall, 1998: A cumulus parameterization with a prognostic closure. Quart. J. Roy. Meteor. Soc., 124 , 949981.

  • Petch, J., 2004: The predictability of deep convection in cloud-resolving simulations over land. Quart. J. Roy. Meteor. Soc., 130 , 31733187.

    • Search Google Scholar
    • Export Citation
  • Petch, J., A. Brown, and M. Gray, 2002: The impact of horizontal resolution on the simulations of convective development over land. Quart. J. Roy. Meteor. Soc., 128 , 20312044.

    • Search Google Scholar
    • Export Citation
  • Piriou, J-M., J-L. Redelsperger, J-F. Geleyn, J-P. Lafore, and F. Guichard, 2007: An approach for convective parameterization with memory: Separating microphysics and transport in grid-scale equations. J. Atmos. Sci., 64 , 41274139.

    • Search Google Scholar
    • Export Citation
  • Plant, R., and G. Craig, 2008: A stochastic parameterization for deep convection based on equilibrium statistics. J. Atmos. Sci., 65 , 87105.

    • Search Google Scholar
    • Export Citation
  • Robe, F., and K. Emanuel, 1996: Moist convective scaling: Some inferences from three-dimensional cloud ensemble simulations. J. Atmos. Sci., 53 , 32653275.

    • Search Google Scholar
    • Export Citation
  • Sheldon, M. R., 1992: Applied Probability Models with Optimization Applications. Dover, 198 pp.

  • Stirling, A., and J. Petch, 2004: The impacts of spatial variability on the development of convection. Quart. J. Roy. Meteor. Soc., 130 , 31893206.

    • Search Google Scholar
    • Export Citation
  • Taylor, H., and S. Karlin, 1994: An Introduction to Stochastic Modelling. Academic Press, 631 pp.

  • Teixeira, J., and C. Reynolds, 2008: Stochastic nature of physical parameterizations in ensemble prediction: A stochastic convection approach. Mon. Wea. Rev., 136 , 483496.

    • Search Google Scholar
    • Export Citation
  • Tompkins, A., 2001: Organization of tropical convection in low vertical wind shears: The role of cold pools. J. Atmos. Sci., 58 , 16501672.

    • Search Google Scholar
    • Export Citation
  • Tompkins, A., and G. Craig, 1998a: Radiative–convective equilibrium in a three-dimensional cloud-ensemble model. Quart. J. Roy. Meteor. Soc., 124 , 20732097.

    • Search Google Scholar
    • Export Citation
  • Tompkins, A., and G. Craig, 1998b: Time scales of adjustment to radiative–convective equilibrium in the tropical atmosphere. Quart. J. Roy. Meteor. Soc., 124 , 26932713.

    • Search Google Scholar
    • Export Citation
  • Wilks, D., 2005: Effects of stochastic parametrizations in the Lorenz ’96 system. Quart. J. Roy. Meteor. Soc., 131 , 389407.

  • Zhang, F., C. Synder, and R. Rotunno, 2003: Effects of moist convection on mesoscale predictability. J. Atmos. Sci., 60 , 11731185.

  • Zipser, E., and M. LeMone, 1980: Cumulonimbus vertical velocity events in GATE. Part II: Synthesis and model core structure. J. Atmos. Sci., 37 , 24582469.

    • Search Google Scholar
    • Export Citation
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Fluctuation of Mass Flux in a Cloud-Resolving Simulation with Interactive Radiation

J. DavoudiDepartment of Physics, University of Toronto, Toronto, Ontario, Canada

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N. A. McFarlaneDepartment of Physics, University of Toronto, Toronto, Ontario, Canada

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T. BirnerDepartment of Physics, University of Toronto, Toronto, Ontario, Canada

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Abstract

It was shown by Craig and Cohen that fluctuations of cumulus clouds under homogeneous large-scale forcing satisfy the Gibbs canonical ensemble in a strict radiative–convective equilibrium (RCE). In the limit of random noninteracting convective cells, an analytical expression for the distribution function of total mass flux over a region of given size was derived.

The authors examine the consistency of the Gibbs canonical ensemble as a representation for the mass flux fluctuations when the large-scale forcing is time dependent. A cloud-resolving simulation (CRM) with interactive radiation, fixed imposed surface temperature, and diurnally varying solar forcing to mimic the diurnal cycle over the tropical ocean is used.

As a necessary condition for the existence of a state of quasi-equilibrium, the time-scale separation between convective processes and forcing is studied. Detailed evaluation of time scales of convective adjustment and memory in a three-month run confirms the hypothesis of time-scale separation.

The Craig and Cohen theory, in a varying range of heights between the cloud base up to the level of neutral buoyancy (LNB), is tested. It is shown that, although the theory is capable of reproducing the qualitative features of the variability, systematic deviations are detected. By quantifying the spatial distribution of the clouds, the authors suggest that deviations are associated with clustering effects.

* Additional affiliation: Canadian Centre for Climate Modelling and Analysis, University of Victoria, Victoria, British Columbia, Canada.

+ Current affiliation: Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado.

Corresponding author address: Jahanshah Davoudi, Department of Physics, University of Toronto, 60 St. George St., Toronto ON M5S 1A7, Canada. Email: jahan@atmosp.physics.utoronto.ca

Abstract

It was shown by Craig and Cohen that fluctuations of cumulus clouds under homogeneous large-scale forcing satisfy the Gibbs canonical ensemble in a strict radiative–convective equilibrium (RCE). In the limit of random noninteracting convective cells, an analytical expression for the distribution function of total mass flux over a region of given size was derived.

The authors examine the consistency of the Gibbs canonical ensemble as a representation for the mass flux fluctuations when the large-scale forcing is time dependent. A cloud-resolving simulation (CRM) with interactive radiation, fixed imposed surface temperature, and diurnally varying solar forcing to mimic the diurnal cycle over the tropical ocean is used.

As a necessary condition for the existence of a state of quasi-equilibrium, the time-scale separation between convective processes and forcing is studied. Detailed evaluation of time scales of convective adjustment and memory in a three-month run confirms the hypothesis of time-scale separation.

The Craig and Cohen theory, in a varying range of heights between the cloud base up to the level of neutral buoyancy (LNB), is tested. It is shown that, although the theory is capable of reproducing the qualitative features of the variability, systematic deviations are detected. By quantifying the spatial distribution of the clouds, the authors suggest that deviations are associated with clustering effects.

* Additional affiliation: Canadian Centre for Climate Modelling and Analysis, University of Victoria, Victoria, British Columbia, Canada.

+ Current affiliation: Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado.

Corresponding author address: Jahanshah Davoudi, Department of Physics, University of Toronto, 60 St. George St., Toronto ON M5S 1A7, Canada. Email: jahan@atmosp.physics.utoronto.ca

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