Data-based stochastic subgrid-scale parametrization: an approach using cluster-weighted modelling.

A new approach for data-based stochastic parametrization of unresolved scales and processes in numerical weather and climate prediction models is introduced. The subgrid-scale model is conditional on the state of the resolved scales, consisting of a collection of local models. A clustering algorithm in the space of the resolved variables is combined with statistical modelling of the impact of the unresolved variables. The clusters and the parameters of the associated subgrid models are estimated simultaneously from data. The method is implemented and explored in the framework of the Lorenz '96 model using discrete Markov processes as local statistical models. Performance of the cluster-weighted Markov chain scheme is investigated for long-term simulations as well as ensemble prediction. It clearly outperforms simple parametrization schemes and compares favourably with another recently proposed subgrid modelling scheme also based on conditional Markov chains.