Methods of Ensemble Data Assimilation on Adaptive Moving Meshes

• Main Author: Guider, Colin Thomas
• Other Authors: College of Arts and Sciences, Department of Mathematics, Jones, Chris, Budhiraja, Amarjit, Sampson, Christian, Carrassi, Alberto, Newhall, Katie
• Format: Doctoral or Postdoctoral Thesis
• Language: English
• Published: University of North Carolina at Chapel Hill Graduate School 2019
• Subjects: data assimilation; ensemble kalman filter; Mathematics; moving mesh; adaptive mesh; Sea ice
• Online Access: https://doi.org/10.17615/bwc6-3891; https://cdr.lib.unc.edu/downloads/h702qb840?file=thumbnail; https://cdr.lib.unc.edu/downloads/h702qb840

Numerical models solved on adaptive moving meshes have become increasingly prevalent in recent years. In particular, neXtSIM is a 2D model of sea-ice that is numerically solved on a Lagrangian mesh that does not conserve the number of mesh points. In this dissertation, we present two novel approaches to the formulation of ensemble data assimilation for models with this underlying computational structure. Specifically, we map ensemble members onto a common reference mesh, where the Ensemble Kalman Filter (EnKF) can be performed. Numerical experiments are carried out using 1D prototypical models: Burgers and Kuramoto-Sivashinsky equations, with both Eulerian and Lagrangian synthetic observations assimilated. One of the approaches is very effective, while the other is significantly less so. We also present a novel approach in the formulation of the Local Ensemble Transform Kalman Filter (LETKF) on a conservative moving mesh model. This is also achieved by mapping the ensemble members onto a common reference mesh, but it done in a significantly different manner than from the previous two approaches. Specifically, the common mesh is formed by taking an equidistributing mesh for the previous output of the algorithm. The preliminary results of this method from an application to Burgers equation are encouraging. Doctor of Philosophy