Rainfall–runoff prediction in an ungauged catchment using an integrated HEC-HMS and machine learning framework

Abstract

Predicting discharge in ungauged catchments remains a major challenge because of the lack of observed discharge data. This study proposes an integrated framework combining a physically based model (HEC-HMS) with machine learning approaches (ANN, Random Forest, and XGBoost) for daily discharge prediction. The models were developed and evaluated in the gauged Kebir catchment and subsequently transferred to the ungauged Saf-Saf catchment. In the gauged catchment, all three machine learning models achieved strong predictive performance. ANN provided the best overall results, with R² = 0.962, RMSE = 8.168 m³/s, NSE = 0.962, and PI = 0.963, followed by Random Forest (R² = 0.959, RMSE = 8.450 m³/s, NSE = 0.959, and PI = 0.961) and XGBoost (R² = 0.953, RMSE = 9.084 m³/s, NSE = 0.953, and PI = 0.954). Random Forest achieved the lowest MAE (3.046 m³/s), compared with 3.137 and 3.238 m³/s for ANN and XGBoost, respectively. The positive PI values demonstrate that all three models outperformed the one-step persistence benchmark, indicating predictive skill beyond simply carrying forward the discharge observed at the previous day. In the ungauged catchment, model outputs were assessed indirectly using flow duration curves, seasonal regime, coefficient of variation, and uncertainty behavior. Random Forest exhibited the most stable behavior, with the lowest coefficient of variation (CV = 2.568), while all models reproduced plausible discharge dynamics consistent with the hydrological characteristics of the study area. Uncertainty analysis revealed a positive relationship between prediction interval width (ICwidth) and discharge, with correlation coefficients of 0.688, 0.716, and 0.676 for ANN, Random Forest, and XGBoost, respectively, indicating flow-dependent uncertainty. Overall, the proposed framework provides a physically informed and comparative approach for daily discharge estimation and one-step-ahead prediction in data-scarce environments, although direct validation in the ungauged catchment remains unavailable and sub-daily storm dynamics cannot be resolved from the available daily observations.