Nonlinear data-assimilation using implicit models

Abstract. We show how the traditional 4D-Var method can be adapted for implicit time-integration and extended for multi-parameter estimation. We present the algorithm for this new method, which we call I4D-Var, and demonstrate its performance using a fully-implicit barotropic quasi-geostrophic model of the wind-driven double-gyre ocean circulation. For the latter model, the different regimes of flow behavior and the regime boundaries (i.e. bifurcation points) are well known and hence the parameter estimation problem can be systematically studied. It turns out that I4D-Var is able to correctly estimate parameter values, even when background flow and "observations" are in different dynamical regimes.