Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 12 4 2005 10.5194/npg-12-515-2005 http://www.nonlin-processes-geophys.net/12/515/2005/ http://www.nonlin-processes-geophys.net/12/515/2005/npg-12-515-2005.html http://www.nonlin-processes-geophys.net/12/515/2005/npg-12-515-2005.pdf 515 525 2005-05-19 Nonlinear data-assimilation using implicit models A. D. Terwisscha van Scheltinga H. A. Dijkstra Institute for Marine and Atmospheric research Utrecht, Department of Physics and Astronomy, Utrecht University, The Netherlands Department of Atmospheric Science, Colorado State University, Fort Collins, CO, USA 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.