Physical consistency in subgrid-scale parameterization for climate models
 Tiffany Shaw, Department of Physics, University of Toronto

Climate models are formulated from the fundamental laws of physics represented as partial differential equations and include all physical processes relevant to climate over a discrete spatial grid covering the Earth. The effects of  processes occurring on length and time scales too small to be resolved on the grid such as convection, the breaking of small-scale internal gravity waves and boundary layer turbulence, called subgrid-scale processes, are nevertheless important for the resolved energy and momentum balances, and need to be parameterized. While energy and momentum conservation is important, little attention has been paid to the implications of these constraints in the parameterization of subgrid-scale processes.

In this talk we will examine the importance of physical consistency in subgrid-scale parameterization for climate models. The first aspect of consistency which is examined is the importance of conservation of momentum alone. Using both a simplified and a comprehensive climate model, it is shown that violating momentum conservation in the parameterization of momentum transfers by small-scale internal gravity waves leads to large errors in the modeled mean climate and non-robustness of the response to idealized ozone depletion. The second aspect of consistency which is examined is the self-consistency of energy and momentum conservation. We use both Hamiltonian geophysical fluid dynamics and multiple scale asymptotics to construct a framework for subgrid-scale parameterization that respects both conservation laws and the second law of thermodynamics. The framework provides a concise understanding of the interactions between the two scales and new measures to quantify and test the consistency of energy and momentum conservation in current subgrid-scale parameterizations.