Advances in numerical weather prediction represent a quiet revolution because they have resulted from a steady accumulation of scientific knowledge and technological advances over many years that, with only a few exceptions, have not been associated with the aura of fundamental physics breakthroughs. Nonetheless, the impact of numerical weather prediction is among the greatest of any area of physical science. As a computational problem, global weather prediction is comparable to the simulation of the human brain and of the evolution of the early Universe, and it is performed every day at major operational centres across the world.

The range of possibilities for future climate evolution needs to be taken into account when planning climate change mitigation and adaptation strategies. This requires ensembles of multi-decadal simulations to assess both chaotic climate variability and model response uncertainty. Statistical estimates of model response uncertainty, based on observations of recent climate change, admit climate sensitivities--defined as the equilibrium response of global mean temperature to doubling levels of atmospheric carbon dioxide--substantially greater than 5 K. But such strong responses are not used in ranges for future climate change because they have not been seen in general circulation models. Here we present results from the 'climateprediction.net' experiment, the first multi-thousand-member grand ensemble of simulations using a general circulation model and thereby explicitly resolving regional details. We find model versions as realistic as other state-of-the-art climate models but with climate sensitivities ranging from less than 2 K to more than 11 K. Models with such extreme sensitivities are critical for the study of the full range of possible responses of the climate system to rising greenhouse gas levels, and for assessing the risks associated with specific targets for stabilizing these levels.

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Numerical simulations of two-dimensional deep convection are analysed using analytical models extended to include shallow downdraughts and non-constant shear. The cumulonimbus are initiated by Iowlevel convergence created by a finite amplitude downdraught. These experiments have constant low-level shear and differ only in the profile of mid-and upper-level winds. Quasi-steady convection is produced if the mid-and upper-level flow has small shear and the low-level shear is large. The surface precipitation is maximized for no initial relative flow aloft and, if stationary, this storm ( P ( 0 ) ) can give prodigious localized rainfall; P(0) is the two-dimensional equivalent of the supercell. These results are placed in context with previous two-dimensional simulations. Attention is drawn to the similarity with squall lines in central and eastern U.S.A. Storm P(0) is analysed by construction of time-averaged fields of streamfunction, vorticity, temperature, and height deviation. The smoothness of these fields suggests a conceptual model of the storm dynamics which involves cooperation between distinct characteristic flows; an overturning updraught, a jump type updraught, a shallow downdraught, a low-level rotor, and a boundary layer.An idealized analytical model is described by solution of the equations for steady convection. These solutions, for the remote flow, are derived from energy conservation, mass continuity and a momentum budget, and they give relationships between the non-dimensional parameters of the problem. It is apparent that the convection is a high Froude (or low Richardson) number flow demanding the existence of a crossstorm pressure gradient. Inherent in this idealized model is a vortex sheet between updraught and downdraught and it is considered that the dynamical instability of this sheet is related to complexities in the numerical simulation. Furthermore, these results show that in two-dimensions both non-constant shear and a shallow downdraught are necessary to maintain steady convection.