Large-scale length and time scales for use with stochastic convective parameterization
Plant, R. S. and Keane, R. J. (2011) Large-scale length and time scales for use with stochastic convective parameterization. Quarterly Journal of the Royal Meteorological Society, 138 (666). pp. 1150-1164. ISSN 1477-870X
To link to this article DOI: 10.1002/qj.992
Many numerical models for weather prediction and climate studies are run at resolutions that are too coarse to resolve convection explicitly, but too fine to justify the local equilibrium assumed by conventional convective parameterizations. The Plant-Craig (PC) stochastic convective parameterization scheme, developed in this paper, solves this problem by removing the assumption that a given grid-scale situation must always produce the same sub-grid-scale convective response. Instead, for each timestep and gridpoint, one of the many possible convective responses consistent with the large-scale situation is randomly selected. The scheme requires as input the large-scale state as opposed to the instantaneous grid-scale state, but must nonetheless be able to account for genuine variations in the largescale situation. Here we investigate the behaviour of the PC scheme in three-dimensional simulations of radiative-convective equilibrium, demonstrating in particular that the necessary space-time averaging required to produce a good representation of the input large-scale state is not in conflict with the requirement to capture large-scale variations. The resulting equilibrium profiles agree well with those obtained from established deterministic schemes, and with corresponding cloud-resolving model simulations. Unlike the conventional schemes the statistics for mass flux and rainfall variability from the PC scheme also agree well with relevant theory and vary appropriately with spatial scale. The scheme is further shown to adapt automatically to changes in grid length and in forcing strength.
Ball MA, Plant RS. 2008. Comparison of stochastic parameterization approaches in a single-column model. Phil. Trans. Roy. Soc. A 366: 2605–2623. Bechtold P, K¨ohler M, Jung T, Doblas-Reyes F, Leutbecher M, Rodwell MJ, Vitart F, Balsamo G. 2008. Advances in simulating atmospheric variabilty with the ECMWF model: From synoptic to decadal timescales. Q. J. R. Meteorol. Soc. 134: 1337–1351. Bowler NE, Arribas A, Mylne KR, Robertson KB, Beare SE. 2008. The MOGREPS short-range ensemble prediction system. Q. J. R. Meteorol. Soc. 134: 703–722. Bright DR, Mullen SL. 2002. Short-range ensemble forecasts of precipitation during the southwest monsoon. Weather and Forecasting 17: 1080–1100. Buizza R. 1997. Potential forecast skill of ensemble prediction and spread and skill distributions of the ECMWF ensemble prediction system. Monthly Weather Rev. 125: 99–119. Buizza R, Houtekamer PL, Toth Z, Pellerin G, Wei M, Zhu Y. 2005. A comparison of the ECMWF, MSC, and NCEP global ensemble prediction systems. Monthly Weather Rev. 133: 1076–1097. Buizza R, Miller M, Palmer TN. 1999. Stochastic representation of model uncertainties in the ECMWF Ensemble Prediction System. Q. J. R. Meteorol. Soc. 125: 2887–2908. Cohen BG. 2001. Fluctuations in an ensemble of cumulus clouds. PhD thesis, University of Reading. Cohen BG, Craig GC. 2006. Fluctuations in an equilibrium convective ensemble. Part II: Numerical experiments. J. Atmos. Sci. 63(8): 2005– 2015. Craig GC, Cohen BG. 2006. Fluctuations in an equilibrium convective ensemble. Part I: Theoretical formulation. J. Atmos. Sci. 63(8): 1996– 2004. Davies L. 2008. Self-organization of convection as a mechanism for memory. PhD thesis, University of Reading. Davies L, Jakob C. 2011. On convective cloud properties at radiativeconvective equilibrium. To be submitted to: J. Geophys. Res. . Davies T, Cullen MJP, Malcolm AJ, Mawson MH, Staniforth A, White AA, Wood N. 2005. A new dynamical core for the Met Office’s global and regional modelling of the atmosphere. Q. J. R. Meteorol. Soc. 131: 1759–1782. Davoudi J, McFarlane NA, Birner T. 2010. Fluctuation of mass flux in a cloud-resolving simulation with interactive radiation. J. Atmos. Sci. 67: 400–418. Emanuel KA. 2000. Quasi-equilibrium thinking. In: General circulation model development, Randall DA (ed), ch. 8, Elsevier, p. 225255. Gregory D, Rowntree PR. 1990. A mass flux convection scheme with representation of cloud ensemble characteristics and stabilitydependent closure. Monthly Weather Rev. 118: 1483–1506. Groenemeijer PH, Craig GC. 2011. Ensemble forecasting with a stochastic convective parametrization based on equilibrium statistics. Submitted to Atmos. Chem. Phys. . Held IM, Zhao M. 2008. Horizontally homogeneous rotating radiativeconvective equilibria at GCM resolution. J. Atmos. Sci. 65: 2003–2013. Held IM, Zhao M, Wyman B. 2007. Dynamic radiative-convective equilibria using GCM column physics. J. Atmos. Sci. 64: 228–238. Holloway CE, Neelin JD. 2010. Temporal relations of column water vapor and tropical precipitation. J. Atmos. Sci. 67: 1091–1105. Jones TR, Randall DA. 2011. Quantifying the limits of convective parameterizations. J. Geophys. Res. 116: D08 210. Kain JS. 2004. The Kain-Fritsch convective parameterization: An update. J. Appl. Meteor. 43: 170–181. Kain JS, Fritsch JM. 1990. A one-dimensional entraining / detraining plume model and its application in convective parameterization. J. Atmos. Sci. 47(23): 2784–2802. Kuo YH, Bresch JF, Cheng MD, Kain J, Parsons DB, Tao WK, Zhang DL. 1997. Summary of a mini workshop on cumulus parameterization for mesoscale models. Bull. Am. Meteorol. Soc. 78: 475–491. Lander J, Hoskins BJ. 1997. Believable scales and parameterizations in a spectral transform model. Monthly Weather Rev. 125: 292–303. LeMone MA, Zipser EJ. 1980. Cumulonimbus vertical velocity events in GATE. Part II: Synthesis and model core structure. J. Atmos. Sci. 37: 2458–2469. Lin JWB, Neelin JD. 2003. Toward stochastic deep convective parameterization in general circulation models. Geophys. Res. Lett. 30(4): 1162. Lock AP, Brown AR, Bush MR, Martin GM, Smith RNB. 2000. A new boundary layer mixing scheme. Part I: Scheme description and singlecolumn model tests. Monthly Weather Rev. 128: 3187–3199. Lucas C, Zipser EJ, LeMone MA. 1994. Vertical velocity in oceanic convection off tropical Australia. J. Atmos. Sci. 51: 3183–3193. Martin GM, Ringer MA, Pope VD, Jones A, Dearden C, Hinton TJ. 2006. The physical properties of the atmosphere in the new Hadley centre global environmental model (HadGEM1). Part I:Model description and global climatology. J. Clim. 19: 1274–1301. May PT, Rajopadhyaya DK. 1999. Vertical velocity characteristics of deep convection over darwin, Australia. Monthly Weather Rev. 127: 1056– 1071. Moron V, Robertson AW,Ward MN, Camberlin P. 2007. Spatial coherence of tropical rainfall at the regional scale. J. Clim. 20: 5244–5263. Parodi A, Emanuel K. 2009. A theory for buoyancy and velocity scales in deep moist convection. J. Atmos. Sci. 66: 3449–3463. Paulius O, Garner S. 2006. Sensitivity of radiative-convective equilibrium simulations to horizontal resolution. J. Atmos. Sci. 63: 1910–1923. Plant RS. 2010. A review of the theoretical basis for bulk mass flux convective parameterization. Atmos. Chem. Phys. 10: 3529–3544. Plant RS, Craig GC. 2008. A stochastic parameterization for deep convection based on equilibrium statistics. J. Atmos. Sci. 65(1): 87–105. Ricciardulli L, Sardeshmukh PD. 2002. Local time- and space scales of organized tropical deep convection. J. Clim. 15: 2775–2790. Robe FR, Emanuel KA. 1996. Moist convective scaling: Some inferences from three-dimensional cloud ensemble simulations. J. Atmos. Sci. 53(22): 3265–3275. Shutts G. 2005. A kinetic energy backscatter algorithm for use in ensemble prediction systems. Q. J. R. Meteorol. Soc. 131: 3079–3102. Shutts GJ, Gray MEB. 1999. Numerical simulations of convective equilibrium under prescribed forcing. Q. J. R. Meteorol. Soc. 125: 2767–2787. Shutts GJ, Palmer TN. 2007. Convective forcing fluctuations in a cloudresolving model: Relevance to the stochastic parameterization problem. J. Clim. 20: 187–202. Smith DF, Gasiewski AJ, Jackson DL, Wick GA. 2005. Spatial scales of tropical precipitation inferred from TRMM microwave imager data. IEEE Trans. Geophys. Remote Sens. 43: 1542–1551. Stiller O. 2009. Efficient moist physics schemes for data assimilation. II: Deep convection. Q. J. R. Meteorol. Soc. 135: 721–738. Willett MR, Milton SF. 2006. The tropical behaviour of the convective parameterization in aquaplanet simulations and the sensitivity to timestep. Forecasting Research Technical Report 482, Met Office, UK. Williams PD, Palmer TN (eds). 2009. Stochastic physics and climate modelling. Cambridge University Press. 496pp. Wilson DR, Ballard SP. 1999. A microphysically based precipitation scheme for the UK Meteorological Office Unified Model. Q. J. R. Meteorol. Soc. 125: 1607–1636. Xu KM, Arakawa A, Krueger SK. 1992. The macroscopic behavior of cumulus ensembles simulated by a cumulus ensemble model. J. Atmos. Sci. 49(24): 2402–2420. Zhang F, Snyder C, Rotunno R. 2003. Effects of moist convection on mesoscale predictability. J. Atmos. Sci. 60: 1173–1185. Zhang GJ, McFarlane NA. 1995. Sensitivity of climate simulations to the parameterization of cumulus convection in the Canadian climate centre general circulation model. Atmosphere-Ocean 33: 407–446.