|Title||Weak-constraint and long window 4DVAR|
|Publication Type||Technical memorandum|
|Year of Publication||2011|
|Secondary Title||ECMWF Technical Memorandum|
|Authors||Fisher, M, Trémolet, Y, Auvinen, H, Tan, DGH, Poli, P|
We describe recent progress in weak-constraint and long-window 4D-Var. Experiments in a two-layer quasi-geostrophic system confirm the results obtained by Fisher et al. (2005) for the Lorenz (1995) model. The experiments show that increasing the length of the analysis window in 4D-Var improves the analysis. Moreover, this benefit is present even if the model error is induced by systematic error in the model parameters, and is imperfectly described by the analysis system. We present results using the full ECMWF analysis system showing that the analysis window can usefully be extended to 24 hours. It is expected that 24 hour 4D-Var will be implemented in 2012. We also present results using a degraded observation network comprising surface pressure observations only. We find that a 24-hour analysis window gives better results than a 12-hour analysis window, and the improvement is even more significant when the 24-hour windows are overlapped by performing an analysis every 12 hours. The importance of properly taking into account the mean component of model error is highlighted in both the two-layer quasi-geostrophic context, and in experiments conducted using an Reanalysis configuration of the ECMWF assimilation system in which only historical surface pressure observations are assimilated. A major potential benefit of weak-constraint 4D-Var is that it allows parallelisation of the inner loops of 4D-Var. We discuss how this benefit might be realised, and present a new parallel algorithm which we call the saddle point formulation of 4D-Var. We demonstrate the algorithm using the two-layer quasi-geostrophic system.