Phil. Trans. R. Soc. A (2012) 370, 1087–1099 doi:10.1098/rsta.2011.0307 Model complexity versus ensemble size: allocating resources for climate prediction BY CHRISTOPHER A. T. FERRO 1,2, *, TIM E. JUPP 2 , F. HUGO LAMBERT 2 , CHRIS HUNTINGFORD 3 AND PETER M. COX 2 1 National Centre for Atmospheric Science, and 2 Mathematics Research Institute, University of Exeter, Harrison Building, North Park Road, Exeter EX4 4QF, UK 3 Centre for Ecology and Hydrology, Wallingford OX10 8BB, UK A perennial question in modern weather forecasting and climate prediction is whether to invest resources in more complex numerical models or in larger ensembles of simulations. If this question is to be addressed quantitatively, then information is needed about how changes in model complexity and ensemble size will affect predictive performance. Information about the effects of ensemble size is often available, but information about the effects of model complexity is much rarer. An illustration is provided of the sort of analysis that might be conducted for the simplified case in which model complexity is judged in terms of grid resolution and ensemble members are constructed only by perturbing their initial conditions. The effects of resolution and ensemble size on the performance of climate simulations are described with a simple mathematical model, which is then used to define an optimal allocation of computational resources for a range of hypothetical prediction problems. The optimal resolution and ensemble size both increase with available resources, but their respective rates of increase depend on the values of two parameters that can be determined from a small number of simulations. The potential for such analyses to guide future investment decisions in climate prediction is discussed. Keywords: general circulation models; initial condition ensembles; mean-squared error; resolution; weather forecasting 1. Introduction Two of the main drivers of improved weather forecasts and climate predictions in recent decades have been the increasing complexity of general circulation models and the increasing number of trajectories simulated with those models. Both of these advances place greater demands on computational resources and so a trade- off emerges: should future resources be invested in more complex models or in larger ensembles of simulations? This question pertains to forecasting on all time scales. We believe that answers to this question would benefit from quantitative analysis, but efforts are rarely made to collect the necessary data. In this paper, *Author for correspondence (c.a.t.ferro@exeter.ac.uk). One contribution of 13 to a Theme Issue ‘Climate predictions: the influence of nonlinearity and randomness’. This journal is © 2012 The Royal Society 1087