Cluster-based XGBoost framework for short-term rainfall–runoff prediction under uncertainty in the Sieber watershed, Germany

Abstract

The study focuses on the Sieber River watershed in northern Germany, a small mountainous catchment characterized by rapid rainfall–runoff response, limited hydrological data availability, and substantial short-term flow variability. These characteristics make the region an ideal testbed for developing robust, data-efficient short-term runoff prediction models. This research proposes a novel hybrid modeling framework combining eXtreme Gradient Boosting (XGBoost) with clustering algorithms (K-means and X-means) to improve multi-step-ahead rainfall–runoff forecasting under uncertainty. Hourly precipitation–runoff data and lagged precipitation inputs (P t to P t–36 ) are used to generate predictions at 1-, 2-, 3-, and 6-hour horizons. The hybrid models are benchmarked against standalone XGBoost, Principal Component Regression (PCR), and the conceptual Event-Based Approach for Small and Ungauged Basins (EBA4SUB). Model performance is evaluated using RMSE, MAE, NSE, R², and uncertainty bounds. Clustering rainfall–runoff conditions into homogeneous hydrometeorological regimes considerably enhances prediction accuracy. The XGBoost–K-means model provides the best performance, achieving low predictive error (6-hour ahead: RMSE = 0.580 m³/s, NSE = 0.954) and the narrowest uncertainty range (WUCB = 2.274). These findings demonstrate that cluster-enhanced machine learning models offer a reliable and computationally efficient solution for operational short-term forecasting in small catchments like the Sieber watershed. The hybrid approach supports improved flood early warning, real-time water management, and decision-making in data-scarce environments. • This study presents the first integration of X-means clustering with XGBoost. • The proposed hybrid framework improves short-term rainfall–runoff forecasts. • Lagged precipitation inputs up to 36 h are optimized for better prediction. • Event-based testing confirms robustness under both high-flow and normal cases. • The hybrid models reduce predictive uncertainty and surpass conceptual models.