Development and application of a mathematical model for calculating the discharge of non-standard thin-plate weirs in urban combined sewer overflow systems: a case study

The aim of this study is to address the issue of difficulty in evaluating the combined sewer overflow (CSO) pollution effectively, especially for the monitoring of overflow from non-standard thin-plate weirs (NTPWs). In order to construct a discharge calculation mathematical model (DCMM) of NTPWs in an urban combined sewer overflow system (UCSOS), which can be used to construct a real-time monitoring and early warning system, a physical model constructed firstly for obtaining hydraulic characteristic sets under three flow conditions (free, submerged, pressurized flow). Then, the coefficient function expressions are obtained under three flow conditions through genetic algorithm (GA) fitting, and a DCMM of UCSOS is established subsequently. The results indicate that DCMM exhibits high accuracy, with mean relative error (MRE) at 0.0326, root mean square error (RMSE) at 1.569, and Nash–Sutcliffe efficiency (NSE) coefficient at 0.9387. The DCMM can not only evaluate the discharge capacity under different flow conditions, but also be used to realize reliable and convenient discharge monitoring. Although the DCMM constructed in this case is not universal, the modeling method of combining physical models with GA is an effective new approach to evaluate the discharge capacity of NTPW, which also holds value for application in other cities.