Articles | Volume 24, issue 4
Research article
01 Dec 2017
Research article |  | 01 Dec 2017

The Onsager–Machlup functional for data assimilation

Nozomi Sugiura

Abstract. When taking the model error into account in data assimilation, one needs to evaluate the prior distribution represented by the Onsager–Machlup functional. Through numerical experiments, this study clarifies how the prior distribution should be incorporated into cost functions for discrete-time estimation problems. Consistent with previous theoretical studies, the divergence of the drift term is essential in weak-constraint 4D-Var (w4D-Var), but it is not necessary in Markov chain Monte Carlo with the Euler scheme. Although the former property may cause difficulties when implementing w4D-Var in large systems, this paper proposes a new technique for estimating the divergence term and its derivative.

Short summary
The optimisation of simulation paths is sometimes misleading. We can find a path with the highest probability by the method of least squares. However, it is not necessarily the route where the paths are most concentrated. This paper clarifies how we can find the mode of a distribution of paths by optimisation.