Title:4DEnVar: link with 4D state formulation of variational assimilation and different possible implementations

Author: G. Desroziers (Meteo-France)
L. Berre (Meteo-France)
E. Arbogast (Meteo-France)

The 4D-Var formulation is currently used by most operational Numerical Weather Prediction centers. However, the 4D-Var is known to be poorly scalable on computers with a large number of processors, due to its use of low-resolution versions of the linearized model. The 4DEnVar formulation has received a considerable attention in recent years. The interest in this formulation relies on different nice properties: it allows 4D flow-dependent background error covariances to be represented, it avoids (in contrast to EnKF) the localization of background error covariances in observation space, it is potentially highly parallel on new computer architectures, and it also gets rid of the development, maintenance and cost of tangent-linear and adjoint models.

The aim of this presentation is to point out the link between the weak-constraint 4D-Var formulation and its 4DEnVar counterpart. Furthermore, the 4DEnVar formulation is relatively easy to precondition, and it can potentially include a larger class of representation of model errors. The paper also aims at showing that the so far proposed implementations of the 4DEnVar implicitly rely on a preconditioning of the variational problem using the square-root of the localized 4D ensemble covariance matrix Be. Two other possible formulations are proposed, both relying on a preconditioner given by the complete Be matrix. One of them performs the minimization in the dual space (with a size given by the number of observations). The use of a hybrid covariance matrix combining a climatological matrix Bc and an ensemble matrix Be is also discussed. An application of the proposed implementations of 4DEnVar is shown with the Burgers’ model and compared to the use of 4D-Var. Preliminary results of the 4DEnVar formulation with the French global model ARPEGE are also shown.

GMAO Head: Steven Pawson Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: Feb 9 2015