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Keywords:

  • convective-scale numerical weather prediction

Abstract

We review the limits of 4D-Var, particularly its ability to work well for a wide range of scales, and discuss the relationship to the atmospheric butterfly effect. As a concrete example, we consider how 4D-Var might be applied to a global, convective-scale model. Deterministic 4D-Var, finding the most likely model evolution to fit observations, does not work in the limit of high resolution. Statistical 4D-Var, minimising the mean-square errors and estimating the mean of possible states, might work. We address the optimal regularisation of models for this. It requires a means of forecasting the evolution of the best estimate state and a perturbation model optimised for a range of finite perturbations. The parametrisation of uncertain scales in such models is discussed.

For several more practical reasons, as well as the difficulties of building such models, a seamless NWP system, based on 4D-Var and capable of forecasting from convective to global scales, is unlikely. However, the concepts introduced are still useful in designing practical high-resolution 4D-Var systems. © Crown Copyright 2007. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd