Modern Applied Mathematics for the Atmospheric and Oceanic Sciences

July 14 - August 2, 2003

Overview

MAMAOS is a three week summer-school designed to train graduate students in the application of modern applied mathematics to important problems in the atmospheric and oceanic sciences. The school will focus on three themes at the interface between the disciplines: numerics, asymptotics and stochastics, with one theme being covered per week of school. Each week’s theme will be presented by teams of five distinguished lecturers drawn from leading institutions of atmospheric/oceanic sciences and applied mathematics.

  • Week 1: Numerics

    Lectures by Dale Durran (U. Washington), Bjorn Engquist (Princeton), Stan Osher (UCLA), Eitan Tadmor (Maryland), and Bjorn Stevens (UCLA) will emphasize modern numerical methods for the representation of conservation laws. In particular methods for interface tracking (level sets) and the representation of advection/diffusion processes where the diffusion is often associated with small scale turbulent (rather than molecular) processes and thus tends to be flow dependent, rather than fluid dependent will be discussed. Some background in numerical methods is preferred.

  • Week 2: Asymptotics

    Lectures by Gregory Hakim (U. Washington), Rupert Klein (Potsdam, Germany), Peter Kramer (Rensselaer Polytechnic), Andrew Majda (Courant Institute, NYU), and Jim McWilliams (UCLA) will cover the fundamentals of asymptotic methods, e.g., dimensional, similarity and perturbation analysis. Geophysical context will be provided by a discussion of large-scale balanced flows in the atmosphere/ocean and the applicability of multi-scale asymptotics as well as asymptotically adaptive numerical methods to these problems. Some background in PDEs is preferred.

  • Week 3: Stochastics

    Lectures by George Craig & (University of Reading, England), Kerry Emanuel (MIT), Markos Katsoulakis (UMass), Dave Levermore (Maryland) and Eric Vanden Eijnden (Courant Institute, NYU) will cover basics of atmospheric thermodynamics and moist convection, basics of probability, kinetic theory, interacting particle systems, and stochastic modeling. An emphasis will be placed on constructing simple stochastic models for the representation of deep moist convection. Some background in probability is preferred.

In addition to introducing geophysically-minded students to new mathematical techniques selected for their applicability to important outstanding problems, mathematically-minded students will be introduced to new problems selected to inspire the development of new mathematics. Twenty students per week will be funded to participate in the school. Students may apply to participate in one, all or some contiguous subset of the three themes.

Students will be organized into interdisciplinary groups to work on research projects. The groups will be mentored by the lecturers and by post-doctoral fellows. The participation of the fellows will help enhance the learning and productivity of project groups in part by providing tutoring/mentoring sessions for students to aide in mastering new concepts.

IPAM gratefully acknowledges support for this program from a grant from the Collaborations for Mathematical Geosciences initiative of the National Science Foundation.

Organizing Committee

Bjorn Stevens (UCLA, Atmospheric Sciences)