Recurrent atmospheric flow patterns are those that occur more often than expected by chance, and their identification has been an underlying theme in atmospheric science on time scales ranging from weather forecasting to inter-annual fluctuations. This chapter focuses on identifying recurrent, and also persistent flow patterns on intra-seasonal time scales. Recurrent blocking structures seen in five-day means of the 500 hPa geopotential height (Z500) field motivate the use of a new scalar planetary wave index, whose probability distribution function (pdf) is very non-Gaussian, and hints at bi-modality. The search for maxima in pdfs in higher dimensions is best done in the reduced dimensional coordinates defined by principal component analysis, with pdf density maxima assessed as significant against a multi-dimensional Gaussian null hypothesis.
Using these ideas, we apply the k-means method of cluster analysis to recover wellknown preferred structures (known as weather regimes) occurring in the Euro-Atlantic region on time scales of 10 to 90 days during boreal winter. Synthetic time series of statistically independent principal components are generated to assess statistical confidence of the analysis. We give a detailed discussion of both the generation of the synthetic time series, and the expected signal-to-noise ratio for multi-modal pdfs in higher dimensions. A layered application of cluster analysis to weather forecasts of the European Centre for Medium-Range Weather Forecasts utilizes forecast scenarios (clusters of the 51-member ensemble evolution of Z500 within a short time window) in order to synthesis information about large-scale structures from the ensemble. Verification is done against the previously defined weather regimes.
For application beyond the very robust Euro-Atlantic regimes, more sophisticated tools are needed. The mixture model approach to modeling the full pdf with a multiple Gaussian components is presented. The use of dynamical information (in the form of the time evolution of fields), as well as explicit criteria for persistence, is a feature of the Hidden Markov Method. Using the foundation provided in the earlier sections, readers will be prepared to study these and other statistical/dynamical tools.