Identifying seasonal patterns of phosphorus storm dynamics with dynamic time warping

Phosphorus (P) transfer during storm events represents a significant part of annual P loads in streams and contributes to eutrophication in downstream water bodies. To improve understanding of P storm dynamics, automated or semiautomated methods are needed to extract meaningful information from ever-growing water quality measurement data sets. In this paper, seasonal patterns of P storm dynamics are identified in two contrasting watersheds (arable and grassland) through Dynamic Time Warping (DTW) combined with k-means clustering. DTW was used to align discharge time series of different lengths and with differences in phase, which allowed robust application of a k-means clustering algorithm on rescaled P time series. In the arable watershed, the main storm pattern identified from autumn to winter displayed distinct export dynamics for particulate and dissolved P, which suggests independent transport mechanisms for both P forms. Conversely, the main storm pattern identified in spring displayed synchronized export of particulate and dissolved P. In the grassland watershed, the occurrence of synchronized export of dissolved and particulate P forms was not related to the season, but rather to the amplitude of storm events. Differences between the seasonal distributions of the patterns identified for the two watersheds were interpreted in terms of P sources and transport pathways. The DTW-based clustering algorithm used in this study proved useful for identifying common patterns in water quality time series and for isolating unusual events. It will open new possibilities for interpreting the high-frequency and multiparameter water quality time series that are currently acquired worldwide.