Flood inundation maps serve as an important tool in decision making related to minimizing losses from flooding. Generally, flood risk management is based on the prediction of flood inundation for the design flood event (e.g., the 100 years). Flood inundation modeling includes hydraulic modeling, hydrologic modeling, and terrain analysis. The accuracy of flood prediction is influenced by various internal and external uncertainties in flood inundation modeling. To address the issue of uncertainty in flood inundation modeling, the objectivities of this study are: (1) to estimate the uncertainty propagation from model variables into flood inundation prediction; (2) to quantify the uncertainty in flood inundation mapping using generalized likelihood uncertainty estimation (GLUE) and sensitivity analysis; and (3) to assess the role of prior and posterior probability distribution functions on the subjectivities in uncertainty quantification using the GLUE methodology. Three variables, namely, discharge, topography, and Manning's n are used for uncertainty analysis in this study. The objectives of this study are accomplished by using a 1D HEC-RAS model and data from study areas including the East Fork White River near Seymour, Indiana (Seymour reach) and the Strouds reach in Orange County, North Carolina (Strouds reach).

Estimation of uncertainty propagation using the FOA method shows that the uncertainty of a single variable is propagated differently to the flood inundation area, depending on the role of other variables in the overall process. In addition, the results from HSY sensitivity analysis show that topography is a major contributor to the uncertainty in the flood inundation area at the Seymour reach, and discharge is the major contributor at the Strouds reach.

Performance of GLUE is assessed by selecting three likelihood functions including the sum of absolute error (SAE) in water surface elevation and inundation width, sum of squared error (SSE) in water surface elevation and inundation width, and a statistic (F-statistic) based on the area of observed and simulated flood inundation map. Results showed that the uncertainty in topography, roughness and flow information created an uncertainty bound in the inundation area that ranged from 1.4 to 4.6% for Seymour reach and 4 to 29% for Strouds reach of the base inundation areas.

The prior and posterior PDFs for model variables are used to investigate the consistency of datasets for behavioral models in the GLUE methodology. The results show that the type of prior probability distribution functions affects the uncertainty bounds for the Seymour reach. The small number of dataset leads to approximate uncertainty bounds, but the use of the effective range provides a reasonable number of datasets to quantify the uncertainty in flood inundation mapping.