Quantifying Structural Uncertainty in Hydrologic Models

Abstract

Hydrologic models are essential tools for understanding watershed processes and supporting water resource management. However, their predictions are inherently uncertain due to imperfect model structures (structural uncertainty), parameter estimation challenges (parameter uncertainty), and limitations in observational data and model forcings (input uncertainty). Bayesian inference has become a widely used framework for quantifying these uncertainties because it enables probabilistic parameter estimation and prediction while formally incorporating prior information and observational evidence. Despite these advantages, the application of Bayesian methods to complex hydrologic models remains computationally demanding, and the resulting predictive uncertainty often represents a combination of multiple uncertainty sources (including input, parameter, and structural uncertainties) that are difficult to interpret individually. These limitations reduce the effectiveness of Bayesian uncertainty analysis as a diagnostic tool for improving hydrologic models. This thesis develops methodological advances to improve the efficiency and interpretability of Bayesian uncertainty quantification in hydrologic modeling. The research focuses on two challenges: improving the computational feasibility of Bayesian inference for complex models and separating the sources of uncertainty represented within Bayesian predictive distributions. To address these challenges, new methods are developed and evaluated using both regional and continental-scale hydrologic datasets. 1. A machine learning–assisted framework is developed to improve the efficiency of Bayesian joint inference for hydrologic models. The proposed approach integrates machine learning techniques with Bayesian calibration to facilitate exploration of complex posterior parameter distributions and reduce the computational burden associated with traditional sampling methods. The framework is evaluated using twelve watersheds from the MOPEX dataset and demonstrates improved inference performance while maintaining reliable uncertainty quantification. 2. A variance decomposition methodology is introduced to identify and quantify the sources of uncertainty embedded within Bayesian predictions. While Bayesian calibration provides probabilistic estimates of model outputs, it does not directly attribute predictive uncertainty to individual components of the modeling framework. The proposed method decomposes posterior predictive uncertainty into interpretable components, enabling a clearer understanding of how different aspects of the modeling process contribute to overall uncertainty. 3. The proposed uncertainty decomposition framework is applied to a large-scale hydrologic analysis across approximately 3,000 watersheds in North America. This continental-scale application enables the systematic evaluation of spatial patterns in hydrologic model uncertainty and reveals how dominant uncertainty sources vary across hydroclimatic and physiographic regions. Together, the contributions of this thesis improve both the computational efficiency and the interpretability of Bayesian uncertainty estimates in hydrologic modeling. The proposed approaches provide tools for diagnosing uncertainty sources and evaluating model reliability, which can support more transparent hydrological predictions across a range of environmental and water resource applications.