Thursday, 11 June 2009

Stowe Room (Stoweflake Resort and Confernce Center)

**Frank Kwasniok**, University of Exeter, Exeter, United Kingdom

The approach of modeling large-scale atmospheric dynamics with empirical linear models is extended to a nonlinear framework by using a mixture of local linear models instead of one global linear model. The study is performed within a three-level quasigeostrophic (QG) model with realistic climatological mean state and variance pattern as well as Pacific/North America and North Atlantic Oscillation teleconnection patterns. The empirical model is constructed in the space of the leading empirical orthogonal function(EOFs) of the QG model. The methodology of cluster-weighted modeling is used to design an optimized mixture of local discrete linear Markov models. Each of the local models has a Gaussian cluster in the space of EOFs defining a regime in the large-scale circulation and an associated predictive linear regression model with Gaussian uncertainty into the space of EOFs some time lag ahead. The whole model is a state-dependent weighted mixture of the local models, interpolating between them, resulting in a locally linear but globally nonlinear system driven by multiplicative noise. The approach identifies and harnesses nonlinear correlations in the system by dealing with state-dependent means and covariances. The parameters of the model are determined consistently from a large data set of the QG model; only the number of clusters has to be given beforehand. A well-established and robust algorithm is available for this parameter estimation. For only one cluster, the method degenerates to a single globally linear Markov model with purely additive noise.

The predictive skill of the cluster-weighted model is investigated. The method provides probabilistic predictions; the predictive distribution is propagated in time using the unscented transform. As a byproduct, a deterministic prediction can be obtained by restricting attention to the mean of the predictive distribution. Both in deterministic and probabilistic prediction, a mixture of two and three local models outperforms a single linear model in standard skill scores. While this improvement is only moderate for deterministic prediction it is more substantial for probabilistic prediction. This is due to a superior propagation of prediction uncertainty. A portrait of predictability in state space is produced from the properties of the local linear models.

The results indicate that the nonlinear propagator in the space of the leading EOFs in an atmospheric model can be efficiently approximated by a mixture of linear models; locally linear dynamics driven by multiplicative noise may serve as a paradigm model for large-scale atmospheric dynamics.

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