Applying MERIS time series and dynamic time warping for delineating areas with similar temporal behaviour in the northern Baltic Sea

Abstract Coastal waters are subject to ongoing long-term developments, cycles of varying lengths and random variations. Assessments of water quality should not be based only on temporally sparse sampling and inter-annual comparisons of periodical data, but also on their temporal behaviour as an entity. In the latter approach, regions having similar inter- and intra-annual temporal pattern are classified together, regardless of the differing levels of the observed parameter. Altogether 4602 time series, containing Medium Resolution Imaging Spectrometer (MERIS) remote sensing reflectance data R rs (443), R rs (560) and R rs (665) and one band ratio R rs (681)/R rs (620), were formed for the Gulf of Bothnia in the Northern Baltic Sea, covering the ice free periods of 1.6.–30.9. in 2004–2011. I was interested in the similarities in temporal shapes of the reflectance time series, and the time series were standardized by their annual means and standard deviation before further processing. Dynamic time warping (DTW) was used to measure the dissimilarity between the standardized time series, which were clustered in order to find areas having similar temporal character. In partitional clustering, a random initial centroid time series is selected for each cluster, which is then adjusted according to the selected centroid function to find coherent clusters. With DTW, a specific DTW barycentric averaging (DBA) is commonly used for this purpose. Appropriate configurations for DTW and clustering were searched by evaluating the clustering results with two cluster validity indices. Two key settings in DTW are 1) step pattern, which defines how the minimum distances between the observations are searched, and 2) window constraint, which constrain the allowed time difference between the observations to be compared. The performance of two step patterns, symmetricP0 and symmetricP1, and three window constraints, +−1, +−7 and +−21 days, were tested. The partitions may vary due to randomness in the selection of the initial centroid time series. The stability of the repeated clustering was evaluated by Variation of Information–index (VI). With this metric, symmetricP1 step pattern performed slightly better than symmetricP0. Longer window constraints produced more labile partitions. Allowing a certain amount of temporal distortion is however desirable, and because the VI showed satisfactory results also with window constraint of +−7 days, it was selected for further computation. A Silhouette index was used to evaluate the appropriate number of clusters (k). Regardless the number of k, the clusters were neither internally coherent nor clearly deviating from each other. Although the time series did not form strong clusters in the terms of clustering, they formed spatially distinctive and coherent groups on a map. The groups reflected the surface layer circulation pattern of the Gulf of Bothnia, rivers with fresh water input and terrestrial washed-out materials being among the most recognisable phenomena. Hard partitions gave, however, too simplified view on spatiality of temporal patterns. To avoid visual mis-interpretations, the prototypes of each cluster were calculated with DBA and distances in DTW space from these prototypes to all the other time series were visualized. In this way, clustering was used to define the macro-areas of similar temporal pattern, but similarities were defined in continuous DTW scale. This allowed more precise evaluation of the spatial–temporal relationships.