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\begin{document}

\title{Analytical solutions to runoff on hillslopes with curvature: numerical
and laboratory verification}



\author[1]{Dana Lapides}%
\author[1]{Cy David}%
\author[1]{Anneliese Sytsma}%
\author[2]{David Dralle}%
\author[3]{Sally Thompson}%
\affil[1]{University of California Berkeley}%
\affil[2]{Sacramento State University}%
\affil[3]{University of Western Australia}%


\vspace{-1em}



  
  \date{May 04, 2024}


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\begin{abstract}
Predicting the behavior of overland flow with analytical solutions to
the kinematic wave equation is appealing due to its relative ease of
implementation. Such simple solutions, however, have largely been
constrained to applications on simple planar hillslopes. This study
presents analytical solutions to the kinematic wave equation for
hillslopes with modest topographic curvature that causes divergence or
convergence of runoff flowpaths. The solution averages flow depths along
changing hillslope contours whose lengths vary according hillslope width
function, and results in a one-dimensional approximation to the
two-dimensional flow field. The solutions are tested against both
two-dimensional numerical solutions to the kinematic wave equation (in
ParFlow) and against experiments that use rainfall simulation on
machined hillslopes with defined curvature properties. Excellent
agreement between numerical, experimental and analytical solutions is
found in all cases. The solutions show that curvature drives large
changes in maximum flow rate \emph{q\textsubscript{max}} and time of
concentration \emph{t\textsubscript{c}}, predictions frequently used in
engineering hydrologic design and analysis.%
\end{abstract}%



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