4D-Var and the butterfly effect: Statistical four-dimensional data assimilation for a wide range of scales
✍ Scribed by Andrew C. Lorenc; Tim Payne
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 163 KB
- Volume
- 133
- Category
- Article
- ISSN
- 0035-9009
- DOI
- 10.1002/qj.36
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✦ Synopsis
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