Research Colloquium with Jochen Bröcker (University of Reading)

Dynamical reconstruction of forcings in quasigeostrophic and transport-diffusion equations

Abstract: In this talk, we will discuss simple data assimilation schemes that not only reconstruct the underlying states of a dynamical system but simultaneously identify unknown components of the dynamics. Specifically, we focus on quasigeostrophic and transport-diffusion equations, which describe the distribution of atmospheric aerosols or tracer gases for example. We propose a simple nudging scheme to reconstruct the underlying dynamical states of these equations along with forcings, which for instance represent surface fluxes (of momentum in the case of quasigeostrophic equations or of the tracer in case of transport-diffusion equations).

We prove that the algorithm will recover the unknown forcings and states with asymptotically vanishing error, provided the observations are sufficiently ``rich'' (although they can still be finite dimensional), and provided the forcings depend on finitely many parameters in a suitable sense. Although the proposed nudging scheme is conceptually very simple (and not optimal in any way), the analysis is complicated by the fact that the considered systems are infinite dimensional.