Technical note: Analysis of concentration-discharge hysteresis loops using Self-Organizing Maps

Abstract. Analyzing concentration–discharge (C–Q) hysteresis loops is essential for understanding both dissolved and particulate constituent sources and transport mechanisms in watershed hydrology. However, traditional hysteresis analysis methods, including loop classification schemes and hysteresis indices, fail to capture the full variability and gradual transitions between loop patterns. To address these limitations, we introduce an alternative approach for characterizing hysteresis patterns in watersheds using the Self-Organizing Map (SOM) algorithm, which better represents loop variability without relying on rigid categories. This technical note outlines the application – and the advantages – of SOM-based hysteresis loop characterization and presents a general workflow for its implementation to characterize C–Q hysteresis for any watershed constituent. We demonstrate the efficacy of the SOM algorithm through a proof-of-concept with sediment transport hysteresis loops. The SOM algorithm was able to classify hysteresis loops with a high degree of accuracy, correctly mapping the amplitude, direction, and concavity of hysteresis loops in the training dataset. We also used the SOM algorithm to develop a General Turbidity-Discharge (T–Q) SOM – which may be used as a standard for characterizing primary loop types in sediment hysteresis analysis. We demonstrate the use of the General T–Q SOM in describing loop frequency distributions and exploring associations with hydrologic variables to infer hydrologic controls of loop types. We found that the General T–Q SOM captures key differences in loop shape (and thus sediment transport processes) overlooked by hysteresis indices while preserving the gradual transitions between loop types that are often lost in classification schemes. Additionally, SOM-based correlation analysis effectively detected associations between loop types and hydrologic variables, enhancing understanding of their hydrologic significance. This method offers a powerful tool for advancing the identification of constituent sources and transport mechanisms at the watershed scale. To support broader adoption of the methodology described in this paper, we have developed a Python package, equipped with detailed documentation, to facilitate SOM implementation and application in future C–Q analysis.