Abstract

Floods are the most common natural disaster, causing widespread damage to lives and infrastructure worldwide. In fluvial flooding, where rivers overflow their banks, channel geometry-discharge relationships play a crucial role in flood prediction. Conventionally, this relationship is estimated deterministically using rating curves that adopt the power-law relationship between stage and discharge. The deterministic approach cannot adequately explain or account for the inherent uncertainties in this relationship, which arise from climate variability, morphological alterations in the riverbed, and anthropogenic modifications. Additionally, from a fluid dynamics perspective, during unsteady flows caused by intense precipitation or reservoir releases, the stage-discharge relationship exhibits hysteresis, deviating significantly from power-law behavior. This study proposes a stochastic approach to better characterize channel geometry-discharge relationships and account for these uncertainties. For this purpose, different copula-based Bayesian frameworks, along with the Inventory of Field Measurements for Hydraulic Attributes (IFMHA) dataset, were used to describe stage-discharge relationships. The resulting probabilistic rating curves are integrated with the Office of Water Prediction (OWP) Height Above Nearest Drainage (HAND) Flood Inundation Mapping (OWP HAND-FIM) model to generate probabilistic flood inundation maps. The results demonstrate that the copula-based Bayesian approach can capture a wider range of stage-discharge variations with 90% confidence compared to the conventional power-law-based deterministic approach. Consequently, the flood inundation mapping (FIM) ensembles derived from different stage scenarios provide a more comprehensive understanding of potential flood extents. This study emphasizes that accounting for inherent uncertainty in natural systems, given the heterogeneity of watersheds, the stochastic nature of turbulent flow, and the variability of erosion processes, leads to more realistic and interpretable representation of these systems. In this case, the probabilistic stage-discharge relationships and subsequent inundation extent estimations can guide improved flood response strategies and emergency action plans.