Uncertainty in estimating the relative change of design floods under climate change: a stylized experiment with process-based, deep learning, and hybrid models

The resilience of water systems to future hydrology depends on reliable projections of hydrological change. Process-based and, more recently, machine learning-based hydrological models are commonly used for such projections. To account for model uncertainties, hydrologists often report relative (i.e., percent) changes in hydrologic design statistics rather than absolute values, assuming model biases cancel out when estimating relative change. While extensive research has addressed uncertainty quantification in hydrologic modeling, little work has examined uncertainty in relative change estimates and its relationship to structural, parametric, and input uncertainties. In this study, we conduct a stylized experiment across 30 basins in Massachusetts, USA to evaluate uncertainty in design flood change estimates from six hydrological models: three process-based models of varying complexity, a deep learning model, and two hybrid models combining process models with deep learning post-processors. We assess each model’s ability to predict changes in design floods under different climate scenarios and levels of historical precipitation error, compared to another model taken as the true hydrologic system. Our findings reveal considerable variance and some bias in estimated design flood change, even with no historical precipitation error. Uncertainty increases only marginally with more precipitation error, suggesting structural limitations and equifinality dominate uncertainty. The deep learning model provides competitive estimates of change, while deep learning post-processors generally reduce bias but not variance of change estimates. Pooling estimates of design flood change across sites significantly reduces error variance, improving reliability. Overall, these insights can guide model and methodological choices for hydrological change assessments supporting long-term planning.