Data Assimilation Meetings at Reading

Date Meeting type Speakers
26 June 2013 Invited Speaker David Fairbairn (Met Office)
Comparisons between 4DVar and 4DEnVar on the Met Office global model (pdf)
Trials have shown that hybrid 4DVar beats hybrid 4DEnVar on the Met Office global model. Single observation experiments are used to gain understanding of these methods, and to help explain these results. Hybrid 4DVar combines a 3D climatological background-error covariance (B) and 3D ensemble background-error covariance (Pb, from the ETKF) and propagates these using the perturbation forecast model (similar to a tangent linear model). Localization of Pb is performed only at the first timestep. Hybrid 4DEnVar uses a 4D Pb that requires 4D localization. In hybrid 4DEnVar the same 3D B is used at each timestep, and therefore has no flow-dependence at all (unlike 4DVar, which propagates this using the linear model: MBM^T). It is importance to recognize firstly, that the 3DVar and 3DEnVar are equivalent. The differences between 4DVar and 4DEnVar are caused by the time dimension in the assimilation window, which we describe as 4D differences. The 4D errors are calculated in order to compare the methods. The single observation experiments provide an ideal test of the ability of the background error covariance to spread information through the assimilation window.
Two examples are chosen:
1. Jet stream (where |Pb|~|B|)
2. Hurricane Sandy (where |Pb|>>|B|)
With a 50:50 ratio B:Pb, hybrid 4DVar performs much better than hybrid 4DEnVar for the jet stream case. Hybrid 4DVar performs better because it can propagate B through the assimilation window, unlike hybrid 4DEnVar, where the 3D B is used throughout the window. The 4D localization also degrades the time correlations of the 4DEnVar Pb, but this effect appears to be much less significant than the former. These results may explain why hybrid 4DEnVar performed worse than hybrid 4DVar in the trials, but further experiments are required.

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