Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs

Applied math perspectives on stochastic climate models

Andrew Majda

New York University

We are entering a new era of Stochastic Climate Modeling. Such an approach is needed for several reason: 1) to model crucial poorly represented processes in contemporary comprehensive computer models such as intermittent organized tropical convention in the atmosphere and mesocale/submesoscale eddies in the ocean; 2) to quantify uncertainty in intermediate and long range forecasts where both uncertainty in initial data and forcing play a role 3) to represent unresolved stochastic backscatter from small scales to large scales in midlatitude dynamics. This lecture has three parts which illustrate how contemporary applied mathematics contributes novel stochastic ideas and potentially practical algorithms for these important problems. The use of judicious simplified but complex mathematical models for turbulent dynamical systems will be emphasized throughout the lecture. The first topic is joint work with Boualem Khouider and Yevgeniy Frenkel, the second topic with Themis Sapsis, and the third topic with Ian Grooms. All of the references in this lecture can be found at http://www.math.nyu.edu/faculty/majda/.