Clustering Monitoring Stations Based on Two Rank-Based Criteria of Similarity of Temporal Profiles

To support evaluation of water quality trends, a water quality variable may be measured at a series of points in time, at multiple stations. Summarization of such data and detection of spatiotemporal patterns may benefit from the application of multivariate methods. We propose hierarchical cluster analysis methods that group stations according to similarities among temporal profiles, relying on standard clustering algorithms combined with two proposed, rank-based criteria of similarity. An approach complementary to standard environmental trend evaluation relies on the incremental sum of squares clustering algorithm and a criterion of similarity related to a standard test for trend heterogeneity. Relevance to the context of trend evaluation is enhanced by transforming dendrogram edge lengths to reflect cluster homogeneity according to a standard test. However, the standard homogeneity criterion may not be sensitive to patterns with possible practical significance, such as region-specific reversal in the sign of a trend. We introduce a second criterion, which is based on concordance of changes in the water quality variable between pairs of stations from one measurement time to the next, that may be sensitive to a wider range of patterns. Our suggested criteria are illustrated and compared based on application to measurements of dissolved oxygen in the James River of Virginia, USA. Results have limited similarity between the two methods, but agree in identifying a cluster associated with a locality that is characterized by pronounced negative trends at multiple stations.