Functional data clustering as a powerful tool to group streamflow regimes and flood hydrographs

Grouping catchments according to their seasonal streamflow or flood behavior can be essential in regionalization studies, climate impact assessments, or model choice and evaluation. Classical clustering approaches often rely on a selection of indices derived from streamflow/flood hydrographs to identify groups of similar hydrographs and ignore valuable information provided through the temporal (auto-)correlation pattern. To exploit this temporal information, we propose a functional clustering approach to identify catchments with similar streamflow regimes or flood hydrographs. Functional data clustering expresses hydrograph shapes as continuous functions by projecting them onto a set of basis functions (here B-splines) and clusters the resulting basis coefficients using classical clustering algorithms such as hierarchical or k-means clustering.
We apply this functional clustering approach to (1) a large set of catchments in the United States in order to identify regions with similar streamflow regimes and (2) a large set of catchments in Switzerland in order to identify regions with similar flood reactivity. We show that both the streamflow regime and flood reactivity regions are not only similar in terms of their streamflow/hydrograph behavior but also in terms of physiography and climate. We use the streamflow regime clusters derived using functional data clustering to assess future streamflow regime changes in the United States and demonstrate that they are beneficial in climate impact assessments, e.g. to indicate which types of catchments are particularly prone to future change. Further, we use the flood reactivity regions in a regionalization study to derive design hydrographs in ungauged catchments. We conclude that functional clustering approaches are beneficial in climate impact assessments and regionalization studies and might potentially also be valuable to cluster other types of hydrological phenomena such as drought events or long-term streamflow behavior.