Multi-level data assimilation for ocean forecasting using the shallow-water equations

Multi-level Monte Carlo methods have become an established technique in uncertainty quantification as they provide the same statistical accuracy as traditional Monte Carlo methods but with increased computational performance. Recently, similar techniques using multi-level ensembles have been applied to data assimilation problems. In this work we study the practical challenges and opportunities of applying multi-level methods to complex data assimilation problems, in the context of simplified ocean models. We simulate the shallow-water equations at different resolutions and employ a multi-level Kalman filter to assimilate sparse in-situ observations. In this context, where the shallow-water equations represent a simplified ocean model, we present numerical results from a synthetic test case, where small-scale perturbations lead to turbulent behaviour, conduct state estimation and forecast drift trajectories using multi-level ensembles. This represents a new advance towards making multi-level data assimilation feasible for real-world oceanographic applications.