Model complexity versus ensemble size: allocating resources for climate prediction

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.