Quantifying uncertainties in data and model: a prediction model for extreme rainfall events with application to Beijing subway

Extreme rainfall is the primary cause of flooding at subway stations, and accurate prediction of rainfall volumes is essential for early flood warning systems. While previous research mostly focuses on point-by-point predictions based on rainfall spatiotemporal characteristics, it frequently ignores the uncertainties associated with rainfall data and predictive models, leading to unreliable rainfall forecasts. To address these limitations, we introduce a new model for predicting probability density (PD-STGCN) that systematically integrates data and model uncertainty quantification. This model provides both point predictions (PP) and probability density predictions (PDP) for extreme rainfall events. We specifically combine Monte Carlo Dropout (MC Dropout) and prediction variance into a Spatiotemporal Graph Convolutional Network (STGCN) architecture to quantify uncertainties in both the model and the data, and then build a new loss function to train the model based on the quantification results. Additionally, based on the sample set obtained by the trained model, and Gaussian Kernel Density Estimation (KDE) is used to calculate the rainfall probability density function (PDF) at the predicted moments. Validation using two distinct extreme rainfall events in Beijing shows that our proposed model outperforms various benchmark models in both tasks for point prediction and probability density prediction. These findings provide urban flood management with a novel predictive tool that combines high accuracy with strong reliability.