Workshop II: Numerical Hierarchies for Climate Modeling

April 12 - 16, 2010

Overview

Covering processes from the microphysics and turbulence in clouds to planetary motions and the evolution of the climate, Atmosphere-Ocean flows are characterized by an extremely broad range of spatio-temporal scales. Since it is, and will be for some time, neither possible nor interesting to represent this entire scale range in one and the same model, we encounter a resolution hierarchy of computational models whose members describe differing ranges of spatio-temporal scales. This workshop will focus on advanced computational techniques which allow us to cover a wide range of scales in a single simulation, and which operate reliably at various resolutions. Of particular interest will be mechanisms for selecting non-resolved scale parameterizations as a function of grid resolution and for controlling the interplay of numerical truncation with subgrid scale process representations.

This line of thought leads us to a hierarchy of numerical balances: As discussed, inter alia, in workshop on “Equation Hierarchies”, processes that can be associated with a specific, relatively narrow scale range generally follow simplified balanced dynamics described successfully by related simplified equation sets. Examples are the incompressible Boussinesq, anelastic or pseudo-incompressible, quasi, semi, or planetary geostrophic, and the hydrostatic primitive equation models. Correctly reflecting these balances numerically constitutes a persistent challenge in the construction of computational models. This challenge is severely compounded in scale-adaptive models which must incorporate correctly the balances associated with all the scales that they may dynamically tap into during a simulation.

Closely related is the parameterization hierarchy: When deciding, statically or dynamically, to not explicitly represent the spatio-temporal scales below a certain threshold, we must at the same time incorporate means to capture the net effects of the non-resolved scales on the resolved ones. Whereas it is long-standing practice to develop and implement associated subgrid scale parameterizations in computational models with static resolution, how to do this in models that allow the user to quite freely choose the resolution or in scale-adaptive models is a wide open question.

Finally, there is the hierarchy of conservation laws: We know that mass and total energy are preserved in continuum mechanical problems. At the same time, there is a host of derived quantities that are also conserved under particular simplifying circumstances. Examples are potential temperature, potential vorticity, enstrophy, helicity, and linear or angular momentum. We will discuss which of these conservation principles are how important in which modeling context, and how to realize them computationally.

The above constitutes the framework of this workshop. To trigger the discussions, we will specifically concentrate on the following set of issues:

  • Formulation of mathematical equations–continuous or discrete, deterministic or stochastic–which jointly represent the dynamics AND physics above some given spatio-temporal scales.
  • Properties of numerical schemes for unstructured grids, structured grids with variable resolution, and dynamically adaptive grids when process resolution becomes marginal.
  • Interplay of non-resolved scale parameterizations with the numerical schemes of dynamical cores. Among others, we will address the competition between numerical truncation and subgrid scale closures, techniques for on-the-fly control of parameterizations in dynamically adaptive models, and the consequences of including stochastic parameterization in the construction of dynamical cores.
  • Coupling of models for different processes, such as atmosphere-ocean; (dry) dynamics-(moist) physics; continuum flows-suspended particles and droplets.

Organizing Committee

Francis Giraldo (Naval Postgraduate School)
Christiane Jablonowski (University of Michigan, Department of Atmospheric, Oceanic & Space Sciences)
Rupert Klein (Freie Universität Berlin, Mathematics)
Sebastian Reich (Universität Potsdam)