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\begin{document}

\title{Copula-based modeling of hydraulic structures using a nonlinear
reservoir model}



\author[1]{Xin Wen}%
\author[1]{Yunze Mao}%
\author[1]{Qiaofeng Tan}%
\author[1]{Tian Jin}%
\author[1]{Zhenni Wang}%
\author[1]{Ziyu Ding}%
\affil[1]{Hohai University}%


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  \date{May 08, 2024}


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\begin{abstract}
Multivariate flood frequency analysis has been widely used in the design
and risk assessment of hydraulic structures. However, previous studies
have mostly relied on the idealized linear reservoir model in which a
linear routing process is assumed, and consequently the flood risk is
likely to be over- or under-estimated. The present study proposes a
nonlinear reservoir model in which the relationships of reservoir water
level with reservoir volume and discharge are assumed to be nonlinear in
order to more accurately describe the routing process as it takes into
consideration the interactions between hydrological loading and
different discharge structures. The structure return period is
calculated based on the copula function and compared with that based on
the linear reservoir model and the bivariate return period based on the
Kendall distribution function. The results show that the structure
return period based on the linear model leads to an underestimation of
the flood risk under the conditions of high reservoir water level. For
the same reservoir, linear and nonlinear reservoir models give quite
different reservoir volume-water level and discharge-water level curves,
and therefore they differ substantially in the sensitivity to flood
events with different combinations of flood peak and volume. We also
analyze the effects of the parameters involved in the reservoir
volume-water level and discharge-water level relationships on the
maximum water level at different return periods in order to better
understand the applicability and effectiveness of the proposed method
for different hydraulic projects.%
\end{abstract}%



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