Uncertainty Analysis and Quantification in Flood Insurance Rate Maps Using Bayesian Model Averaging and Hierarchical BMA

Abstract

Flood Insurance Rate Maps (FIRMs) managed by FEMA have been providing ongoing flood information to most communities in the United States over the past half-century. However, the uncertainty associated with the modeling of FIRMs, some of which are created by using a single Hydrologic Engineering Center River Analysis System (HEC-RAS) one-dimensional (1D) steady-flow model, may have adverse effects on the reliability of flood stage and inundation extent predictions. Therefore, a systematic understanding of the uncertainty in the modeling process of FIRMs is necessary. Bayesian model averaging (BMA), which is a statistical approach that can combine estimations from multiple models and produce reliable probabilistic predictions, was applied to evaluating the uncertainty associated with FIRMs. In this study, both the BMA and hierarchical BMA (HBMA) approaches were used to quantify the uncertainty within the detailed FEMA models of the Deep River and the Saint Marys River in the state of Indiana based on water stage predictions from 150 HEC-RAS 1D unsteady-flow model configurations that incorporate four uncertainty sources including bridges, channel roughness, floodplain roughness, and upstream flow input. Given the ensemble predictions and the observed water stage data in the training period, the BMA weight and the variance for each model member were obtained, and then the BMA prediction ability was validated for the observed data from the later period. The results indicate that the BMA prediction is more robust than both the original FEMA model and the ensemble mean. Furthermore, the HBMA framework explicitly shows the propagation of various uncertainty sources, and both the channel roughness and the upstream flow input have a larger impact on prediction variance than bridges. Hence, it provides insights for modelers into the relative impact of individual uncertainty sources in the flood modeling process. The results show that the probabilistic flood maps developed based on the BMA analysis could provide more reliable predictions than the deterministic FIRMs.