Physical Consistency in Subgrid-scale Parameterization for Climate Models

It is well known that the transfers of energy and momentum by subgrid- scale processes such as convection, the breaking of small-scale internal gravity waves and boundary layer turbulence are important for the energy and momentum budgets of the resolved scales in a climate model. While energy and momentum conservation is important in general, 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. We will present a framework for subgrid-scale parameterization that respects energy and momentum conservation as well as the second law of thermodynamics, which is derived using Hamiltonian geophysical fluid dynamics and multiple scale asymptotics. The framework provides a concise understanding of the interactions between the resolved and subgrid scale energy and momentum by appealing to wave activity conservation laws. It also provides new measures to quantify and test the consistency of energy and momentum conservation in current subgrid-scale parameterizations. We will present the results of climate model simulations which clearly demonstrate that nonconservation in the parameterization of momentum transfers by small-scale internal gravity waves leads to non-negligible errors which occur throughout the depth of the atmosphere.