|Title||Will the 4D-Var approach be defeated by nonlinearity?|
|Publication Type||Technical memorandum|
|Secondary Title||ECMWF Technical Memoranda|
|Authors||Andersson, E, Fisher, M, Hólm, EV, Isaksen, L, Radnóti, G, Trémolet, Y|
|Place Published||Shinfield Park, Reading|
Some of the issues involved in extending the current 4D-Var algorithm to higher resolution and/or longer assimilation window in the presence of nonlinearity, are investigated and discussed. Tests have been conducted within the context of the global numerical weather prediction (NWP) system at ECMWF. The accuracy of the 4D Var solution algorithm and its convergence are investigated with respect to nonlinearities and their dependence on analysis resolution and length of the assimilation window. From a literature review and some new results in an idealized setting (the Lorenz-1995 40 parameter model) we conclude that a long-window weak-constraint 4D-Var has exciting prospects, alleviating the severity of the linearity assumption compared to the strong-constraint formulation. In weak-constraint 4D-Var a sequence of model states are estimated (rather than just the initial state), with the consequence that the tangent linear assumption is relied upon only for the shorter time segment between successive state estimates, and not for propagation of information throughout the assimilation window. This property makes a weak-constraint 4D-Var an attractive prospect that should be pursued as a main avenue of research in the coming years, with the goal to lengthen the assimilation window. Conclusions are drawn with respect to the ECMWF research plans.