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\begin{document}

\title{Considering Uncertainty of Historical Ice Jam Flood Records in a
Bayesian Frequency Analysis for the Peace-Athabasca Delta}



\author[1]{Jared D. Smith}%
\author[2]{Jonathan R Lamontagne}%
\author[3]{Martin Jasek}%
\affil[1]{Department of Engineering Systems and Environment, University of Virginia}%
\affil[2]{Department of Civil and Environmental Engineering, Tufts University}%
\affil[3]{BC Hydro}%


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  \date{June 05, 2024}


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\begin{abstract}
The Peace-Athabasca Delta in Alberta, Canada has numerous perched basins
that are primarily recharged after large ice jams cause floods (an
ecological benefit). Previous studies have estimated that such large
floods are likely to decrease in frequency under various climate
projections. However, there is a sizeable uncertainty range in these
predicted flood probabilities, in part due to the short 60-year
systematic record that contained few large ice jam floods. An additional
50 years of historical data are available from various sources, with
expert-interpreted flood categories; however, these categorizations are
uncertain in magnitude and occurrence. We developed a Bayesian framework
that considers magnitude and occurrence uncertainties within a logistic
regression model that predicts the annual probability of a large flood.
The Bayesian regression estimates the joint distribution of parameters
describing the effects of climatic factors and parameters that describe
the probability that historical flood magnitudes were recorded as large
(or not) when a truly large (or not) flood occurred. We compare four
models for hindcasting and projecting large ice jam flood probabilities
in future climates. The models consider: 1) historical data uncertainty,
2) no historical data uncertainty, 3) only the systematic record, and 4)
the systematic record with a different model structure. Neglecting
historical data uncertainty provides inaccurate estimates, while using
only the systematic record provides wider prediction intervals than
considering the full record with uncertain historical data. Thus, we
demonstrate that including uncertain historical information can
effectively extend the record length and improve flood frequency
analyses.%
\end{abstract}%



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