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\begin{document}

\title{Evaluating Uncertainty in FEMA Flood Insurance Rate Maps (FIRMs) using
Bayesian Model Averaging (BMA) and Hierarchical BMA}



\author[1]{Tao Huang}%
\author[1]{Venkatesh Merwade}%
\affil[1]{Purdue University}%


\vspace{-1em}



  
  \date{June 15, 2024}


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\begin{abstract}
Flood Insurance Rate Maps (FIRMs) managed by the Federal Emergency
Management Agency (FEMA) have been providing ongoing flood information
to most of the communities in the United States over the past half
century. However, the uncertainty associated with the modeling of the
FIRMs, some of which are created by using a single HEC-RAS
one-dimensional (1D) steady flow model, may have adverse effects on the
reliability of flood stage and inundation extent. Therefore, a
systematic understating of the uncertainty in the modeling process of
FIRMs is important and necessary. The Bayesian model averaging (BMA),
which is a statistical approach that can combine estimations from
multiple models and produce reliable probabilistic predictions, is
applied to evaluating the uncertainty associated with the FIRMs. In this
study, both the BMA and HBMA approaches are 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 the bridges, channel
roughness, floodplain roughness, and upstream flow input. The BMA weight
and the variance for each model member are obtained given the ensemble
predictions and the observed water stage data in the training period,
and then the BMA prediction ability is validated for the observed data
from the later period. The results indicate that BMA prediction is more
robust than the original FEMA model as well as the ensemble mean.
Different types of uncertainty coefficients based on the BMA prediction
distribution are also proposed to evaluate the FEMA models. Furthermore,
the HBMA framework shows that both the channel roughness and the
upstream flow input have a larger impact on prediction variance than
bridges, and hence provides some insights for modelers into the relative
impact of individual uncertainty sources in the flood modeling process.%
\end{abstract}%



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