By Didier Auroux, Université Côte d'Azur (Nice Sophia Antipolis)

Abstract 

Nudging is a simple data assimilation method that uses dynamical relaxation to adjust a model towards observations. The standard nudging algorithm consists in adding a feedback term, proportional to the difference between the observations and the corresponding model state, to the model equations. Also known as the Luenberger (or asymptotic) observer, it theoretically requires an infinite time window to converge.
The Back and Forth Nudging algorithm has been introduced in order to extend the efficiency of nudging to finite/small time windows. It consists in alternately solving the model forwards and backwards in time, with a nudging term in both cases, over the assimilation window.
These approaches can be extended to more complex observers, for which non-observed variables can also be corrected with observed ones. We will give an overview of nudging, observers, and backward-forward algorithms, with applications to oceanography and fluid dynamics, for state and/or parameter estimation