Modeling Large-Scale Atmospheric Flow Using a Mixture of Local Linear Empirical Models

Linear inverse modeling is a well-established technique in the atmospheric and climate sciences. An empirical linear model is estimated from data, augmented with additive or multiplicative stochastic noise, and used for prediction or simulation purposes. This contribution extends this approach to nonlinear inverse modeling by combining several empirical linear models locally in state space. The technique harnesses nonlinear correlations as state-dependent means and covariances. Also the noise terms are local, amounting to multiplicative noise. Three different methods for defining the localisation are considered: (i) a cluster-weighted model, linking the local models to clusters in state space; (ii) a Markov-switching model; and (iii) a model based on nearest-neighbor localisation. Model parameter estimation is still simple, stable and computationally inexpensive. The method is exemplified on a data set from the NCAR CCM0 atmospheric general circulation model. The analysis is performed in the space of the leading empirical orthogonal functions (EOFs). The focus is on extended-range prediction. Both deterministic and probabilistic forecasts are evaluated. Nonlinear inverse modeling is shown to considerably outperform the more traditional linear inverse modeling.