Clustering of Cyclostationary Signals with Applications to Climate Station Sitings, Eliminations, and Merges

This paper considers methods to classify and discriminate the multidimensional cyclostationary climatological time series. The methods take into account both the seasonal mean cycles and random behavior in the series, simultaneously considering means and all component-by-component autocovariances. This improves classical Hotelling T2 statistics that classify through mean changes only, and constant-mean speech methods that classify exclusively through sample autocovariance differences. Here, two series are compared by assuming that both follow the same time series model; from this, a test statistic representing a distance between the two series is developed from linear prediction theory. This construction generates a level- α test statistic for Gaussian data that can be used to assess how different the two series are. The derived distances can be used in a clustering algorithm, e.g., to group series with similar behavior. Such information is useful to eliminate or merge the climate stations whose data are redundant to another station or to optimally locate a collection of stations. The techniques are first tested on simulated series with known structures, and then applied to 11 two-dimensional series in the National Oceanic and Atmospheric Administration's data buoy catalog. Natural clusters emerge which are geographically realistic. Specifically, the methods were able to perfectly group stations in the Gulf of Mexico, the Carolina Coast, the Pacific Ocean, and offshore New England.