Multi-level data assimilation for simplified ocean models

Abstract. Multi-level Monte Carlo methods have established as a tool in uncertainty quantification for decreasing the computational costs while maintaining the same statistical accuracy as in single-level Monte Carlo. Lately, there have also been theoretical efforts to use similar ideas to facilitate multi-level data assimilation. By applying a multi-level ensemble Kalman filter for assimilating sparse observations of ocean currents into a simplified ocean model based on the shallow-water equations, we study the practical challenges of applying these method to more complex problems. We present numerical results from a realistic test case where small-scale perturbations lead to chaotic behaviour, and in this context we conduct state estimation and drift trajectories forecasting using multi-level ensembles. This represents a new step on the path of making multi-level data assimilation feasible for real-world oceanographic applications.