\begin{thebibliography}
\item Arribas, A. 2004 Results of an initial stochastic physics scheme for the Met Office Unified Model. Forecasting Research Technical Report no. 452, Met Office, UK.
\item Byun, Y.-H. \& Hong, S.-Y. 2007 Improvements in the subgrid-scale representation of moist convection in a cumulus parameterization scheme: The single-column test and its impact on seasonal prediction. \textit{Mon. Wea. Rev.} \textbf{135} 2135--2154.
\item Buizza, R., Miller, M. \& Palmer, T. N. 1999 Stochastic representation of model uncertainties in the ECMWF ensemble prediction system. \textit{Quart. J. Roy. Met. Soc.} \textbf{125}, 2887--2908.
\item Craig, G., Fraedrich, K., Lin, J., Moncrieff, M., Plant, R., Thomson, D. \& and Tompkins, A. 2005 Working Group 1 Report: Issues in convection. In: \textit{ECMWF Workshop on Representation of Sub-grid Processes using Stochastic--Dynamic Models, Reading, UK, 6-8 June 2005} pp. ix--xii.
\item Craig, G. C. \& Cohen, B. G. 2006 Fluctuations in an equilibrium convective ensemble. Part I: Theoretical formulation. \textit{J. Atmos. Sci.} \textbf{63} 1996--2004.
\item Cullen, M. J. P. 1993 The unified forecast/climate model. \textit{Meteorol. Mag.} \textbf{122} 89--94.
\item Done, J. M. 2002 Predictability and representation of convection in a mesoscale model. PhD thesis, University of Reading, UK. 180pp.
\item Ghil, M., Berloff, P., Buizza, R., Hermanson, L., Miller, M., Palmer, T., Roulstone, I., Sardeshmukh \& Williams, P. 2005 Working Group 2 Report: The parameterisation problem in weather and climate models In: \textit{ECMWF Workshop on Representation of Sub-grid Processes using Stochastic--Dynamic Models, Reading, UK, 6-8 June 2005} pp. xvii--xxii.
\item Gregory, D. \& Rowntree, P. R. R. 1990 A mass flux convection scheme with representation of cloud ensemble characteristics and stability dependent closure. \textit{Mon. Wea. Rev.} \textbf{118} 1483--1506.
\item Hack, J. J. \& Pedretti, J. A. 2000 Assessment of solution uncertainties in Single-Column Modeling frameworks. \textit{J. Clim.} \textbf{13} 352--365.
\item Horinouchi, T., Pawson, S., Shibata, K., Langematz, U., Manzini, E., Giorgetta, M. A., Sassi, F., Wilson, A. J., Hamilton, K., de Grandpr\'{e}, J. \& Scaife, A. A. 2003 Tropical cumulus convection and upward-propagating waves in middle-atmospheric GCMs. \textit{J. Atmos. Sci.} \textbf{60} 2765--2782.
\item Hume, T. \& Jakob, C. 2005 Ensemble single column modeling (ESCM) in the tropical western Pacific: Forcing data sets and uncertainty analysis. \textit{J. Geophys. Res.} \textbf{110} D13109.
\item Kain, J. S. 2004 The Kain-Fritsch convective parameterization: An update. \textit{J. Appl. Meteorol.} \textbf{43} 170--181.
\item Kain, J. S. \& J. M. Fritsch 1990 A one-dimensional entraining/detraining plume model and its application in convective parameterisation. \textit{J. Atmos. Sci.} \textbf{47} 2784--2802.
\item Lin, J. W.-B. \& Neelin, J. D. 2002 Considerations for stochastic convective parameterization \textit{J. Atmos. Sci.} \textbf{59} 959--975.
\item Martin, G. M., Ringer, M. A., Pope, V. D., Jones, A., Dearden, C. \& Hinton, T. J. 2006 The physical properties of the atmosphere in the new Hadley Centre Global Environmental Model (HadGEM1). Part I: Model description and global climatology. \textit{J. Climate} \textbf{19} 1274--1301.
\item Moncrieff, M. W., Krueger, S. K., Gregory, D., Redelsperger, J.-L. \& Tao, W.-K. 1997 GEWEX Cloud System Study (GCSS) Working Group 4: Precipitating Convective Cloud Systems. \textit{Bull. Amer. Met. Soc.} \textbf{78} 831--845.
\item Murphy, J., Sexton, D. M. H., Barnett, D. N., Jones, G. S., Webb, M. J., Collins, M. \& Staniforth, D. A. 2004 Quantification of modelling uncertainties in a large ensemble of climate change simulations. \textit{Nature} \textbf{430} 768--772.
\item Mylne, K. R., Evans, R. E. \& Clark, R. T. 2002 Multi-model multi-analysis ensembles in quasi-operational medium-range forecasting. \textit{Quart. J. Roy. Met. Soc.} \textbf{128} 361--384.
\item Mylne, K., Bowler, N., Arribas, A. \& John, S. 2005: MOGREPS (Met Office Global and Regional Ensemble Prediction System). \textit{Met Office Scientific Advisory Committee, 10 to 11 November 2005, Paper N. 10.5}
\item Palmer, T. N. 2001 A nonlinear dynamical perspective on model error: A proposal for non-local stochastic-dynamic parameterization in weather and climate prediction models. \textit{Quart. J. Roy. Met. Soc.} \textbf{127} 279--304.
\item Penland, C. 2003 A stochastic approach to nonlinear dynamics: A review \textit{Bull. Am. Meteorol. Soc.} \textbf{84} ES43--ES52.
\item Petch, J. C., Willett, M., Wong, R. Y. \& Woolnough, S. J. 2007: Modelling suppressed and active convection. Comparing a numerical weather prediction, cloud-resolving and single-column model. \textit{Quart. J. Roy. Met. Soc.} \textbf{133} 1087--1100.
\item Plant, R. S. \& Craig, G. C. 2007 A stochastic parameterization for deep convection based on equilibrium statistics. \textit{J. Atmos. Sci.} (accepted).
\item Ricciardulli, L. \& Garcia, R. R. 2000 The excitation of equatorial waves by deep convection in the NCAR Community Climate Model (CCM3) \textit{J. Atmos. Sci.} \textbf{57} 3461--3487.
\item Sobel, A. H., Bellon, G. \& Bacmeister, J. 2007 Multiple equilibria in a single-column model of the tropical atmosphere. \textit{Geophys. Res. Lett.} (submitted).
\item Shutts, G. 2005 A kinetic energy backscatter algorithm for use in ensemble prediction systems. \textit{Quart. J. Roy. Met. Soc.} \textbf{131} 3079--3102.
\item Teixeira, J. \& Reynolds, C. A. 2007 The stochastic nature of physical parameterizations in ensemble prediction: A stochastic convection approach \textit{Mon. Wea. Rev.} (accepted).
\item Tompkins, A. M. \& Berner, J. 2007 Stochastic convective input based on subgrid humidity distributions \textit{J. Geophys. Res.} (submitted).
\item Webster, P. J. \& Lukas, R. 1992: TOGA COARE: The Coupled Ocean-Atmosphere Response Experiment. \textit{Bull. Amer. Met. Soc.} \textbf{73} 1377--1416.
\item Wilks, D. S. 2005 Effects of stochastic parameterizations in the Lorenz '96 system. \textit{Quart. J. Roy. Met. Soc.} \textbf{131} 389--407.
\item Willett, M. R. \& Milton, S. F. 2006 The tropical behaviour of the convective parameterization in aquaplanet simulations and the sensitivity to timestep. Forecasting Research Technical Report no. 482, Met Office, UK.
\item Williams, P. D. 2006 Modelling climate change: the role of unresolved processes. \textit{Phil. Trans. Roy. Soc.} \textbf{363} 2931--2946.
\item Woolnough, S. J., Bechtold, P., Blossey, P., Chaboureau, J.-P., Hosomi, T., Iacobellis, S., Luo, Y., Petch, J. C., Wong, R. \& Xie, S. 2007 Convective processes during the suppressed phase of the Madden-Julian oscillation \textit{Quart. J. Roy. Met. Soc.} (to be submitted).
\end{thebibliography}