Ensemble data assimilation using optimal control in the Wasserstein metric

Abstract

An ensemble data assimilation method is proposed that is based on optimal control minimizing the cost of mismatch in the Wasserstein metric on the observation space. The new method achieved the optimal state without calculating the posterior distribution of the particle state and the particle states are evolved deterministically, which is easy to be implemented. The method is appropriate for systems in which multiple, noisy, partial observations are available (e.g. citizen weather stations or smart phones). The method is demonstrated for: (i) deterministic dynamics with uncertain initial conditions, (ii) multiple noisy observations of a randomly forced ordinary differential equation (ODE), (iii) observations from multiple sample paths from a stochastic differential equation (SDE). A bi-modal measure and a measure supported on a strange attractor are tested. The numerical results show that our method performs a relatively small Wasserstein distance which measures the approximation performance. But numerical implementation is a bit expensive due to the complexity of Wasserstein distance computation, especially with large set of particles.