Subgrid-Scale Parameterization with Conditional Markov Chains

Abstract

A new approach is proposed for stochastic parameterization of subgrid-scale processes in models of atmospheric or oceanic circulation. The new approach relies on two key ingredients: first, the unresolved processes are represented by a Markov chain whose properties depend on the state of the resolved model variables; second, the properties of this conditional Markov chain are inferred from data. The parameterization approach is tested by implementing it in the framework of the Lorenz ?96 model. Performance of the parameterization scheme is assessed by inspecting probability distributions, correlation functions, and wave properties, and by carrying out ensemble forecasts. For the Lorenz ?96 model, the parameterization algorithm is shown to give good results with a Markov chain with a few states only and to outperform several other parameterization schemes.