Workshop I: Equation Hierarchies for Climate Modeling

March 22 - 26, 2010


The atmosphere-ocean system is a unique one in science in that the dynamical equations are essentially known. However in order to distill the nonlinearity and turbulence of the forced-dissipative fluid equations on a rotating sphere into a more readily understandable system requires a hierarchical approach. This workshop will focus on the development, use, and study of “equation hierarchies”: sets of equations and models which make idealizations in order to construct progressively simpler (and more understandable), but self-consistent frameworks for the study of climate dynamics.

The use of hierarchies of equations has been remarkably successful in developing understanding of climate and weather phenomena: e.g., the quasi-geostrophic equations for study of baroclinic instability, the semi-geostrophic equations for frontogenesis, and the diffusive energy balance model to investigate ice sheet growth as a function of solar intensity. Since diabatic terms are fundamentally important in climate dynamics, the topic of equation hierarchies naturally connects to the development of parameterizations to handle convection, clouds, etc., at different scales or levels of complexity within models.

Equation hierarchies are closely connected to the other topics in this program: the choice of equations to use colors the numerical methods one would use to integrate the equations, the experimental design in a given set of simulations, and influences how one interprets data from observations or models. While each of these will be discussed within this workshop, the equation hierarchies week will focus the discussion on problems such as: 1) the development of new balanced systems of equations using techniques such as multiple scales asymptotics, 2) the use of simplified sets of equations as models of the Earth or other planetary climates, 3) balance dynamics and the breakdown of balance, and 4) the role of latent heating in the dynamics of the tropical and extratropical atmosphere and simplified ways to account for condensation in models.

Organizing Committee

Simona Bordoni (California Institute of Technology)
Dargan Frierson (University of Washington)
Andrew Majda (New York University, Courant Institute of Mathematical Sciences)
Jonathan Mitchell (University of California, Los Angeles (UCLA))