Data assimilation for moving mesh methods with an application to ice sheet modelling
Bertrand Bonan, Nancy K. Nichols, Michael J. Baines, and Dale Partridge
School of Mathematical, Physical and Computational Sciences, University of Reading, Reading, United Kingdom
Received: 22 Aug 2016 – Accepted for review: 09 Sep 2016 – Discussion started: 12 Sep 2016
Abstract. We develop data assimilation techniques for nonlinear dynamical systems modelled by moving mesh methods. Such techniques are valuable for explicitly tracking interfaces and boundaries in evolving systems. The unique aspect of these assimilation techniques is that both the states of the system and the positions of the mesh points are updated simultaneously using physical observations. Covariances between states and mesh points are generated either by a correlation structure function in a variational context or by ensemble methods. The application of the techniques is demonstrated on a one-dimensional model of a grounded shallow ice sheet. It is shown, using observations of surface elevation and/or surface ice velocities, that the techniques predict the evolution of the ice sheet margin and the ice thickness accurately and efficiently. This approach also allows the straightforward assimilation of observations of the position of the ice sheet margin.
Bonan, B., Nichols, N. K., Baines, M. J., and Partridge, D.: Data assimilation for moving mesh methods with an application to ice sheet modelling, Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-45, in review, 2016.