Balancing Efficiency and Accuracy: Simplifying Complex PDEs in Collection Systems Hydraulic and Hydrologic Modeling with Continuous Data Assimilation – A Case Study.

Accurate hydraulic and hydrologic simulation of gravity collection systems typically requires solving high-dimensional, nonlinear partial differential equations (PDEs), which can be computationally demanding for real-time and predictive applications, as well as difficult to calibrate. To overcome these challenges, we propose a novel approach that replaces selected portions of the governing equations with simplified alternatives and compensates for any added model error through continuous data assimilation. Specifically, we employ the Ensemble Kalman Filter (EnKF) to assimilate real-time observations into an ensemble of model forecasts at regular intervals, continuously updating the defined model states for both hydrologic and hydraulic engines.We demonstrate our approach on a sewer collection system in Oregon (United States), showing that incorporating data assimilation into a simplified PDE model can outperform a more complex, full-physics model. Compared to the traditional computationally intensive approach, the proposed method achieves a 10% reduction in root-mean-square error (RMSE) of the resulting Hydraulic Gradeline (HGL) while also delivering a 78% improvement in computational efficiency. These gains are particularly valuable for applications such as near-real-time system state forecasting and predictive storm response for proactive decision-making to prevent Sanitary Sewer Overflow (SSO) risk, where both accuracy and speed are crucial.By leveraging available observations to update the state of a simplified model through the application of data assimilation, our methodology bridges the gap between computational tractability and physical realism. Furthermore, its adaptability makes it broadly applicable to other hydraulic and hydrologic systems—including river networks, irrigation canals, and urban drainage infrastructure—where continuous data assimilation can significantly improve predictive performance and operational reliability.