• Abramowitz, M., and I. A. Stegun, 1972: Handbook of Mathematical Functions. Dover Publications, 1044 pp.

  • Bechtold, P., E. Bazile, F. Guichard, P. Mascart, and E. Richard, 2001: A mass flux convection scheme for regional and global models. Quart. J. Roy. Meteor. Soc., 127 , 869886.

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

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

    • Search Google Scholar
    • Export Citation
  • Grabowski, W. W., 2001: Coupling cloud processes with the large-scale dynamics using the cloud-resolving convection parameterization. J. Atmos. Sci., 58 , 978997.

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

    • Search Google Scholar
    • Export Citation
  • Kållberg, P., P. Berrisford, B. Hoskins, A. Simmons, S. Uppala, S. Lamy-Thépaut, and R. Hine, 2005: ERA-40 atlas. ERA-40 Project Report Series No. 19, ECMWF, Reading, United Kingdom, 191 pp.

  • Khouider, B., A. J. Majda, and M. A. Katsoulakis, 2003: Coarse-grained stochastic models for tropical convection and climate. Proc. Natl. Acad. Sci. USA, 100 , 1194111946.

    • Search Google Scholar
    • Export Citation
  • Leonard, B. P., M. K. MacVean, and A. P. Lock, 1993: Positivity-preserving numerical schemes for multidimensional advection. NASA Tech. Memo. 106055 (ICOMP-93-05), 62 pp.

  • Lilly, D. K., 1983: Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci., 40 , 749761.

  • Lin, J-B., and J. Neelin, 2000: Influence of a stochastic moist convective parametrization on tropical climate variability. Geophys. Res. Lett., 27 , 36913694.

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

  • MacVean, M. K., and P. J. Mason, 1990: Cloud-top entrainment instability through small-scale mixing and its parameterization in numerical models. J. Atmos. Sci., 47 , 10121030.

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

    • Search Google Scholar
    • Export Citation
  • Martin, G. M., M. A. Ringer, V. D. Pope, A. Jones, C. Dearden, and T. J. Hinton, 2006: The physical properties of the atmosphere in the new Hadley Centre Global Environmental Model (HadGEM). Part I: Model description and global climatology. J. Climate, 19 , 12741301.

    • Search Google Scholar
    • Export Citation
  • Neale, R. B., and B. J. Hoskins, 2001: A standard test for AGCMs including their physical parametrizations: I: The proposal. Atmos. Sci. Lett., 1 , 101107.

    • Search Google Scholar
    • Export Citation
  • Palmer, T. N., 1997: On parametrizing scales that are only somewhat smaller than the smallest resolved scales, with application to convection and orography. Proc. ECMWF Workshop on New Insights and Approaches to Convective Parametrization, Reading, United Kingdom, ECMWF, 328–337.

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

    • Search Google Scholar
    • Export Citation
  • Pauluis, O., and S. Garner, 2006: Sensitivity of radiative–convective equilibrium simulations to horizontal resolution. J. Atmos. Sci., 63 , 19101923.

    • Search Google Scholar
    • Export Citation
  • Piacsek, S. A., and G. P. Williams, 1970: Conservation properties of convection difference schemes. J. Comput. Phys., 6 , 392405.

  • Randall, D., M. Khairoutdinov, A. Arakawa, and W. Grabowski, 2003: Breaking the cloud parameterization deadlock. Bull. Amer. Meteor. Soc., 84 , 15471564.

    • Search Google Scholar
    • Export Citation
  • Ricciardulli, L., and P. D. Sardeshmukh, 2002: Local time and space scales of organized tropical convection. J. Climate, 15 , 27752790.

    • Search Google Scholar
    • Export Citation
  • Shutts, G. J., 2005: A kinetic energy backscatter algorithm for use in ensemble prediction systems. Quart. J. Roy. Meteor. Soc., 131 , 30793102.

    • Search Google Scholar
    • Export Citation
  • Shutts, G. J., and T. N. Palmer, 2004: The use of high resolution numerical simulations of tropical circulation to calibrate stochastic physics scheme. Proc. ECMWF/CLIVAR Workshop on Simulation and Prediction of Intra-Seasonal Variability with Emphasis on the MJO, Reading, United Kingdom, ECMWF, 83–102.

  • Shutts, G. J., 2006: Upscale effects in simulations of tropical convection on an equatorial beta-plane. Dyn. Atmos. Oceans Sci., 42 , 3058.

    • Search Google Scholar
    • Export Citation
  • Swann, H., 1998: Sensitivity to the representation of precipitating ice in CRM simulations of deep convection. Atmos. Res., 48 , 415435.

    • Search Google Scholar
    • Export Citation
  • Vallis, G. K., G. J. Shutts, and M. E. B. Gray, 1997: Balanced mesoscale motion and stratified turbulence forced by convection. Quart. J. Roy. Meteor. Soc., 123 , 16211652.

    • Search Google Scholar
    • Export Citation
  • Xu, K-M., A. Arakawa, and S. Krueger, 1992: The macroscopic behavior of cumulus ensembles simulated by a cumulus ensemble model. J. Atmos. Sci., 49 , 24022420.

    • Search Google Scholar
    • Export Citation
  • Yanai, M., S. Esbensen, and J-H. Chu, 1973: Determination of bulk properties of tropical cloud clusters from large-scale heat and moisture budgets. J. Atmos. Sci., 30 , 611627.

    • Search Google Scholar
    • Export Citation
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Convective Forcing Fluctuations in a Cloud-Resolving Model: Relevance to the Stochastic Parameterization Problem

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  • 1 Met Office, Exeter, United Kingdom
  • | 2 ECMWF, Reading, United Kingdom
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Abstract

Idealized cloud-resolving model (CRM) simulations spanning a large part of the tropical atmosphere are used to evaluate the extent to which deterministic convective parameterizations fail to capture the statistical fluctuations in deep-convective forcing, and to provide probability distribution functions that may be used in stochastic parameterization schemes for global weather and climate models. A coarse-graining methodology is employed to deduce an effective convective warming rate appropriate to the grid scale of a forecast model, and a convective parameterization scheme is used to bin these computed tendencies into different ranges of convective forcing strength. The dependence of the probability distribution functions for the coarse-grained temperature tendency on parameterized tendency is then examined.

An aquaplanet simulation using a climate model, configured with similar horizontal resolution to that of the coarse-grained CRM fields, was used to compare temperature tendency variation (less the effect of advection and radiation) with that deduced as an effective forcing function from the CRM. The coarse-grained temperature tendency of the CRM is found to have a substantially broader probability distribution function than the equivalent quantity in the climate model.

The CRM-based probability distribution functions of precipitation rate and convective warming are related to the statistical mechanics theory of Craig and Cohen and the “stochastic physics” scheme of Buizza et al. It is found that the standard deviation of the coarse-grained effective convective warming is an approximately linear function of its mean, thereby providing some support for the Buizza et al. scheme, used operationally by ECMWF.

Corresponding author address: G. J. Shutts, Met Office, Fitzroy Road, Exeter, Devon, EX1 3PB, United Kingdom. Email: glenn.shutts@metoffice.gov.uk

Abstract

Idealized cloud-resolving model (CRM) simulations spanning a large part of the tropical atmosphere are used to evaluate the extent to which deterministic convective parameterizations fail to capture the statistical fluctuations in deep-convective forcing, and to provide probability distribution functions that may be used in stochastic parameterization schemes for global weather and climate models. A coarse-graining methodology is employed to deduce an effective convective warming rate appropriate to the grid scale of a forecast model, and a convective parameterization scheme is used to bin these computed tendencies into different ranges of convective forcing strength. The dependence of the probability distribution functions for the coarse-grained temperature tendency on parameterized tendency is then examined.

An aquaplanet simulation using a climate model, configured with similar horizontal resolution to that of the coarse-grained CRM fields, was used to compare temperature tendency variation (less the effect of advection and radiation) with that deduced as an effective forcing function from the CRM. The coarse-grained temperature tendency of the CRM is found to have a substantially broader probability distribution function than the equivalent quantity in the climate model.

The CRM-based probability distribution functions of precipitation rate and convective warming are related to the statistical mechanics theory of Craig and Cohen and the “stochastic physics” scheme of Buizza et al. It is found that the standard deviation of the coarse-grained effective convective warming is an approximately linear function of its mean, thereby providing some support for the Buizza et al. scheme, used operationally by ECMWF.

Corresponding author address: G. J. Shutts, Met Office, Fitzroy Road, Exeter, Devon, EX1 3PB, United Kingdom. Email: glenn.shutts@metoffice.gov.uk

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