Introducing the Coincidence Index: A Novel Diagnostic and Production‐Based Framework for Water Body Interaction Analysis and Its Application to Study the Interaction of River Plumes

Abstract

Quantifying interactions between distinct water bodies is critical yet challenging for understanding ocean and estuarine dynamics. We introduce the coincidence index (CI), defined as the product of two arbitrary tracers (, ), to diagnose where two water masses coexist and mix. By deriving a transport equation for the CI, we identify a single active production term, , that pinpoints physical mixing locations, while advection and diffusion only redistribute CI. We apply this method in two numerical models: Oceananigans for a Large‐Eddy simulation of river confluence, and General Estuarine Transport Model for the analysis of the interaction of water masses from the Elbe and Weser river plumes in the German Bight. In both, the CI accurately highlights mixing interfaces; for example, the CI pattern from the river confluence simulation matches observations from the Lancang River. In the German Bight, the CI reveals a narrow, persistent interface between river plumes, with vertical diffusion dominating production. Artificial numerical production of CI, arising from the discretization of advection, is also diagnosed but found to be less significant. The CI method thus enables precise, quantitative diagnostics of water mass mixing from laboratory to realistic estuarine systems, advancing our understanding of transport and mixing processes central to aquatic environments.