Urban Runoff Evaluation via the StaP Index Under Storm and First-Flush Conditions Using Hybrid Mechanistic–ML Modeling

This study introduces and validates the StaP (Stationarity and Predictability) index as a novel integral metric for the quality assessment of urban surface runoff under storm and first-flush conditions. The StaP index simultaneously accounts for both the stationarity and predictability of water quality time series and explicitly represents episodic structures, including high-risk first-flush events. Using a hybrid methodology that combines mechanistic modeling and machine learning, experimental validation was performed with pilot-scale filtration columns simulating urban and industrial runoff scenarios, with 1344 analytical data points collected per scenario. The results demonstrate that StaP outperforms classical indices such as the Water Quality Index (WQI) and single-parameter metrics (e.g., COD) in terms of discriminatory power, invariance to sampling frequency, and sensitivity to episodic variability. The index proved robust in real time and at different monitoring resolutions, reliably distinguishing between runoff types, aligning closely with expert assessments and biotests, and reducing misclassification in event-dominated regimes. The adoption of StaP facilitates automated, adaptive-quality management of urban water systems, supporting LID/WSUD frameworks and digital platforms (SCADA/IoT). The proposed approach addresses current gaps in urban water diagnostics and offers improved operational support for risk-informed decision making.