Saddle Point Preconditioners for Weak Constraint Four-Dimensional Variational Data Assimilation

Abstract: Data assimilation algorithms blend observation data together with prior information from a numerical model to obtain an improved estimate of the current state of a dynamical system of interest. In this setting, the use of correlated observation error covariance matrices has produced many opportunities for improved initial conditions for weather forecasts, but at the risk of more ill-conditioned linear systems which can be prohibitively expensive to solve.

In this talk I will present novel preconditioners for a saddle point formulation of the weak-constraint 4DVar data assimilation problem, with a focus on the correlated observation error setting. I will present a number of new preconditioners that improve on current state-of-the-art, and allow for reductions in computational cost through the use of parallel architectures or matrix-oriented iterative methods. This is work with John Pearson (University of Edinburgh).

Bio: Jemima Tabeart is an Assistant Professor in the Computational Science group at TU Eindhoven. She completed her PhD at the University of Reading. After her PhD, she undertook postdoctoral positions at ICERM (Brown University) and the University of Edinburgh and then spent a year as a Hooke Fellow at the University of Oxford. Her research interests lie at the intersection of numerical linear algebra and data assimilation for high-dimensional applications.