[4-2] February 27, 15:00-15:20

The ECMWF weak constraint 4D-Var formulation

Yannick Tremolet (ECMWF), Jacky Goddard (ECMWF), Martin Leutbecher (ECMWF), Simon Lang (ECMWF), Sarah-Jane Lock (ECMWF), Patrick Laloyaux (ECMWF)

In most operational implementations of four-dimensional variational data assimilation, it is assumed that the model used in the data assimilation process is perfect or, at least, that errors in the model can be neglected when compared to other errors in the system. ECMWF has been developing a weak-constraint 4D-Var formulation where a model-error forcing term is explicitly estimated to take into account model imperfections. This problem is very similar in nature to strong constraint 4D-Var as it is essentially an initial-condition problem with parameter estimation where the additional parameters represent model error.

ECMWF has implemented a new version of its forecasting system in November 2016 where the weak constraint option of 4D-Var has been reactivated using a model error forcing term active in the stratosphere above 40 hPa. The model error covariance matrix is based on statistics generated by special runs of the ensemble predication system with identical initial conditions but with different realisations of model error from the SPPT and SKEB stochastic physics schemes. Future work will aim to improve the specification of the model error covariance matrix and the interaction with the variational bias correction.