Combining uncertainty quantification and entropy-inspired concepts into a single objective function for rainfall-runoff model calibration

A novel metric for rainfall-runoff model calibration and performance assessment is proposed. By integrating entropy and mutual information concepts as well as uncertainty quantification through the Brisk Local Uncertainty Estimator for Hydrological Simulations and Predictions (BLUECAT) (likelihood-free approach), the ratio of uncertainty to mutual information (RUMI) offers a robust framework for quantifying the shared information between observed and simulated streamflows. RUMI's capability to calibrate rainfall-runoff models is demonstrated using the GR4J rainfall-runoff model over 99 catchments from various macroclimatic zones, ensuring a comprehensive evaluation. Four additional performance metrics and 50 hydrological signatures are also used for performance assessment. Key findings indicate that RUMI-based simulations provide more consistent and reliable results compared to the traditional Kling-Gupta efficiency (KGE), with improved performance across multiple metrics and reduced variability. Additionally, RUMI includes uncertainty quantification as a core computation step, offering a more holistic view of model performance. This study highlights the potential of RUMI to enhance hydrological modelling through better performance metrics and uncertainty assessment, contributing to more accurate and reliable hydrological predictions.