Downscaling Data Assimilation Algorithm for Dissipative Evolution Models Employing Coarse Mesh Observables

Edriss Titi, Texas A&M University, USA - 11:15

One of the main characteristics of infinite-dimensional dissipative evolution equations, such as the Navier-Stokes equations and reaction-diffusion systems, is that their long-time dynamics is determined by finitely many parameters -- finite number of determining modes, nodes, volume elements and other determining interpolants. In this talk I  will show how to explore this finite-dimensional feature of the long-time behavior of infinite-dimensional dissipative systems  to design  nudging downscaling data assimilation algorithms for weather prediction based on discrete coarse mesh measurements. Moreover, I will also demonstrate uniform in time error estimates of the numerical discretization of these algorithms, which makes reliable upon implementation computationally. Furthermore, I will also present some recent results concerning a statistical version of these algorithms.

Invited by Sebastian Reich