Abstract

Data assimilation is broadly used in atmosphere and ocean science to correct error in initial conditions by periodically incorporating information from measurements (e.g., satellites) into the mathematical model. Ensemble data assimilation methods propagate multiple solutions (using different initial conditions with the same numerical model) to approximate the evolution of the probability distribution function of plausible states. The co-called ensemble Kalman filtering is an ensemble data assimilation method that is widely used in practice due to its robustness and accuracy in high-dimensional nonlinear setting. In this talk, after setting up a general data assimilation framework, I will introduce ensemble Kalman filtering, show the existing theoretical results on the accuracy and stability for full observations, as well as recent results for partial observations. Lastly, I will present ideas on how to estimate the dimension of the partial observation on the fly, which is a topic of the optimal experimental design.