Geographic heterogeneity of activation functions in urban real-time flood forecasting: Based on seasonal trend decomposition using Loess-Temporal Convolutional Network-Gated Recurrent Unit model

Urban real-time flood forecasting is crucial for flood prevention and sustainable development, but it poses challenges due to data inputs and activation functions selection in data-driven models without sufficient focus of geographic heterogeneity. In this study, a novel Seasonal Trend Decomposition using Loess (STL)-Temporal Convolutional Network (TCN)-Gated Recurrent Unit (GRU) model is proposed to improve urban real-time flood forecasting accuracy, twenty-one different activation functions are considered for geographic heterogeneity. Experiments are conducted at six urban drainage system locations in Odense, Denmark. The results show that: (1) STL effectively prepares data for forecasting using TCN and GRU models, leading improved performance compared to single models. STL-TCN-GRU deep learning model demonstrates strong applicability in urban forecasting, achieving an overall accuracy of 0.0079, 0.0140, 0.0482 and 0.9581 in Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and Nash-Sutcliffe efficiency coefficient (NSE), respectively. (2) Softsign emerges as the best activation function for forecasting in lower drainage system locations, with average accuracy of 0.0094, 0.0018, 0.0049 and 0.9938 in MAE, RMSE, MAPE and NSE, respectively. Furthermore, Softsign proves to be the best activation function for forecasting in middle drainage system locations, with average accuracy of 0.0047, 0.0081, 0.0309 and 0.9547 in MAE, RMSE, MAPE and NSE, respectively. Swish is the best activation function for forecasting in upper drainage system locations, with average accuracy of 0.0052, 0.0080, 0.0627 and 0.9060 in MAE, RMSE, MAPE and NSE, respectively. This study provides valuable insights for urban real-time flood forecasting modeling with high accuracy and evidence for activation function selection in data-driven models like STL-TCN-GRU for geographic heterogeneity.