A Physics-Aware Machine Learning-Based Framework for Minimizing Prediction Uncertainty of Hydrological Models

Modeling hydrological processes for managing the available water resources effectively is often complex due to the existence of high nonlinearity, and the associated prediction uncertainty mainly arising from model inputs, parameters, and structure. Despite several attempts to quantify the model prediction uncertainty, reducing the same for improving the reliability of models is indispensable for their wider acceptance. This paper presents a novel modeling framework for minimizing the prediction uncertainty in the streamflow simulation of the conceptual hydrological model (HBV) by integrating with the Bayesian-based Particle Filter technique (PF) and machine learning algorithm (Random Forest algorithm, RF). Initially, the streamflow prediction interval (PI) is derived from the stochastically estimated parameters of the HBV model through the PF technique (HBV-PF model). As the HBV-PF model quantifies only parametric uncertainty, the RF algorithm was employed (HBV-PF-RF model) for further minimizing the prediction uncertainty by inherently taking care of different sources of uncertainty. The RF algorithm inherently combines the physics of the hydrological system (i.e., process-based variables) with machine learning-based approach to minimize the overall prediction uncertainty. The proposed framework was analyzed on Nepal and India's Sunkoshi and Beas River basins, through several statistical performance indices for assessing the accuracy and uncertainty of the model prediction. The framework was observed to be consistently improving the model performance minimizing the uncertainty in both watersheds. Therefore, the proposed framework can be considered to be more reliable in improving the prediction capability of hydrological models.