Cluster analysis of the Northern Hemisphere wintertime 500-hPa height field : spatial patterns

Hierarchical cluster analysis based on the method of Ward is performed on the Northern Hemisphere wintertime 10-day low-pass-filtered 500-hPa height field, using the NMC operational analyses for the period 1946-85. Input data are gridded fields at 5-day intervals, a total of 702 maps, each with 445 grid points. The measure of similarity between maps is the squared height difference, averaged over all grid points; that is, the squared ``distance'' between the maps in multidimensional phase space. The closest two of the 702 maps are merged to form a cluster that, in subsequent calculations, replaces the maps from which it was formed. This procedure (modified slightly, to deal with the differing numbers of maps in the clusters) is repeated 701 times until all the maps have been merged to form a single cluster whose centroid corresponds to the climatological mean map. The two clusters involved in the final merger, the pair of smaller clusters that merged to form each of them, and so on, are represented in terms of a ``family tree'' that is traced back to the point where the clusters become too small to be of practical interest. The reproducibility of the larger clusters is compared by seeing how well various ones are replicated when the analysis is repeated on randomly chosen halves of the dataset in an ensemble of 50 runs. The three most reproducible clusters, which together account for similar to 1/3 of the 702 maps in the dataset, can be reconstructed remarkably well from linear combinations of the two leading EOFs of the covariance matrix. They are related to features of the probability density function (PDF) in a two-dimensional phase space defined by the expansion coefficients of these EOFs. One is marked by a closed anticyclone over the southern tip of Greenland, one by a ridge over the Gulf of Alaska, and one by a ridge over the Rockies. In comparison to other clusters of comparable size, their centroids are conspicuously far from the climatological mean map. Positive 500-hPa height anomalies in excess of 200 m are observed in association with the first two clusters, over regions of large variance and strong positive skewness of the 500-hPa height field. Occurrences of these two clusters have often been marked by extreme cold over parts of North America. Similar clusters are obtained when the analysis is performed on the Pacific/North American and Atlantic/European sectors of the hemisphere. The results are compared with those obtained in other studies