Variational data assimilation for Hamiltonian problems

We investigate the conservation properties of Hamiltonian systems in variational data assimilation. We set up a four-dimensional data assimilation scheme for the two-body (Kepler) system using a symplectic scheme to model the non-linear problem. We use our completed scheme to investigate the observability of the system and the effect of different background constraints. We find that the addition of these constraints gives an improved solution for the cases we have investigated. Copyright (c) 2005 John Wiley & Sons, Ltd.