Donald Bren School of Information and Computer Sciences

Mixture model clustering is applied to Northern Hemisphere (NH) 700-mb geopotential height anomalies. A mixture model is a flexible probability density estimation technique, consisting of a linear combination of k component densities. A key feature of the mixture modeling approach to clustering is the ability to estimate a posterior probability distribution for k, the number of clusters, given the data and the model, and thus objectively determine the number of clusters that is most likely to fit the data.

A data set of 44 winters of NH 700-mb fields is projected onto its two leading empirical orthogonal functions (EOFs) and analyzed using mixtures of Gaussian components. Cross-validated likelihood is used to determine the best value of k, the number of clusters. The posterior probability so determined peaks at k = 3 and thus yields clear evidence for 3 clusters in the NH 700-mb data. The 3-cluster result is found to be robust with respect to variations in data preprocessing and data analysis parameters. The spatial patterns of the 3 clusters' centroids bear a high degree of qualitative similarity to the 3 clusters obtained independently by X. Cheng and J. M. Wallace, using hierarchical clustering on 500-mb NH winter data: A for Gulf-of-Alaska ridge, G for high over southern Greenland, and R for enhanced climatological ridge over the Rockies.

Separating the 700-mb data into Pacific (PAC) and Atlantic (ATL) sector maps reveals that the optimal k-value is 2 for both the PAC and ATL sectors. The respective clusters consist of M. Kimoto and M. Ghil's Pacific/North-American (PNA) and reverse PNA (RNA) regimes, as well as the zonal (ZNAO) and blocked (BNAO) phases of the North Atlantic Oscillation (NAG). The connections between our sectorial and hemispheric results are discussed from the perspective of large-scale atmospheric dynamics.