Stream gauge clustering and analysis for non-stationary time series through complex networks

Abstract

Stream gauge clustering enables diverse studies, such as the analysis of spatial patterns and the physical reasons for these patterns. The clustering of monitoring gauges through complex networks combined with community detection algorithms is a strong alternative to classical methods. However, this approach involves several particularities that impact the clustering results, and the non-stationarity commonly present in streamflow series is typically not accounted for in studies that use this methodology. This article presents the application of a new framework developed to cluster stream gauge stations and to analyse changes in the clustering results across time. Weighted networks were created through Mutual Information combined with an automated threshold. Complex networks were obtained for the entire series and for sliding windows to investigate if significant differences occur across time. A more in-depth analysis was carried out with selected time windows through the perspective of Network Science and Complex Network Analysis, and the results were compared to those from a classic clustering approach. The framework provided robust and physically coherent clustering results and a more detailed clustering result than the classic approach. The weighted networks construction procedure successfully diminished time delimited effects induced by non-stationarity. However, the sliding windows networks results demonstrated that significant changes occurred across time, and three different community configurations were obtained. These results indicate that the use a single network can result in a misrepresentation of local characteristic and lead to wrong conclusions. The communities’ evolution across time showed spatial-time coherence with both the physical phenomenology of the study area and previous studies. The changes observed were associated with phase shifts of low-frequency sea surface temperature oscillations of both the Atlantic and the Pacific Oceans through the phase shifts’ direct and indirect influence on the South Atlantic Convergence Zone. The in-depth analysis resulted in the identification of a spatially coherent transition zone within the clusters obtained and attested the reliability of the framework results based on network typologies. Thus, the proposed framework can aid in clustering problems and provide better comprehension of local characteristics. Although the framework was developed for stream gauge clustering, its use can be extended to the clustering of any data with nonlinear and nonstationary characteristics.