An easy-to-implement and efficient data assimilation method for the identification of the initial condition: the Back and Forth Nudging (BFN) algorithm

Abstract

This paper deals with a new data assimilation algorithm called the Back and Forth Nudging. The standard nudging technique consists in adding to the model equations a relaxation term, which is supposed to force the model to the observations. The BFN algorithm consists of repeating forward and backward resolutions of the model with relaxation (or nudging) terms, that have opposite signs in the direct and inverse resolutions, so as to make the backward evolution numerically stable. We then applied the Back and Forth Nudging algorithm to a simple non-linear model: the ID viscous Burgers' equations. The tests were carried out through several cases relative to the precision and density of the observations. These simulations were then compared with both the variational assimilation (VAR) and quasi-inverse (QIL) algorithms. The comparisons deal with the programming, the convergence, and time computing for each of these three algorithms.