Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, February 2, 2018 - 12:00 to 12:45

Location:

STAG 112

Guest Speaker:

Institution:

Nansen Environmental and Remote Sensing Center

Abstract:

In physical applications, dynamical models and observational data play dual roles in prediction and uncertainty quantification, each representing sources of incomplete and inaccurate information. In data rich problems, first-principle physical laws constrain the degrees of freedom of massive data sets, utilizing our prior insights to complex processes. Respectively, in data sparse problems, dynamical models fill spatial and temporal gaps in observational networks. The dynamical chaos characteristic of these process models is, however, among the primary sources of forecast uncertainty in complex physical systems. Observations are thus required to update predictions where there is sensitivity to initial conditions and uncertainty in model parameters. Broadly referred to as data assimilation, the techniques used to combine these disparate sources of information include methods from Bayesian inference, dynamical systems, numerical analysis and optimal control.

While the butterfly effect renders the forecasting problem inherently volatile, chaotic dynamics also put strong constraints on the evolution of errors. It is well understood in the weather prediction community that the growth of forecast uncertainty is confined to a much lower dimensional subspace corresponding to the directions of rapidly growing perturbations --- this is characterized by the unstable-neutral manifold of the state being tracked, with dimension equal to the number of non-negative Lyapunov exponents. The Assimilation in the Unstable Subspace (AUS) methodology of Trevisan et. al. offers mathematical and conceptual tools to understand the mechanisms governing the evolution of uncertainty in ensemble forecasting. With my collaborators, I am studying the mathematical foundations of ensemble based forecasting in the perspective of smooth and random dynamical systems.