A simple model for long-term prediction of sewage flow in a changing climate

With more frequent extreme weather under climate change, sewage flow has become increasingly variable. A significant driver of this variability is rainfall-derived inflow and infiltration (RDII); currently, its long-term impact on sewage flow dynamics has been little studied. Existing flow prediction models, initially developed for other purposes, face inherent limitations in terms of complexity, data requirements, and interpretability, highlighting the need for a more practical and transparent approach. This study presents a novel and simple model for predicting long-term sewage flow patterns using rainfall forecasts as the sole input. The model integrates data-driven learning with physically meaningful structures. Built on a convolutional framework, it employs B-spline-based instantaneous response functions to automatically learn the rainfall-RDII relationship without presetting the response pattern. The response function adapts to soil saturation levels, enabling the model to generalise across varying conditions. Both simulation studies under various synthetic rainfall and sewer deterioration scenarios and three real-world case studies demonstrated stable performance, with the Kling-Gupta efficiency consistently above 0.7 and normalised root mean square error below 12%, demonstrating the stable accuracy and generalisability of the model.