A metric tensor approach to data assimilation with adaptive moving meshes

Adaptive moving spatial meshes are useful for solving physical models given by time-dependent partial differentialequations. However, special consideration must be when combining adaptive meshing procedures with ensemble-based data assimilation (DA) techniques. In particular, we focus on the case where each ensemble member evolvesindependently upon its own mesh and is interpolated to a common DA update. This paper outlines aframework develop reference using locations of observations metric tensors (MTs)or monitor functions that define members. We spatiallocalization scheme based tensor (MT localization). also explore how tech-niques can control inform placement points concentrate near location observations, reducingthe error observation interpolation. especially beneficial have in wouldotherwise sparse discretization. illustrate utility our results discontinuous Galerkin(DG) approximations 1D 2D inviscid Burgers equations. The numerical show MT localizationscheme compares favorably standard Gaspari-Cohn localization problems observationsare sparse, choice has direct impact performance. demonstratethe advantage DG-based interpolation over linear equation.