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\begin{document}

\title{ODE representation of tile drainage on hillslopes of varying topography}



\author[1]{Morgan Fonley}%
\author[2]{Nicolás Velásquez}%
\author[3]{Ricardo Mantilla}%
\author[2]{Keyu Qiu}%
\author[1]{Nathaniel Haut}%
\affil[1]{Alma College}%
\affil[2]{The University of Iowa}%
\affil[3]{University of Iowa}%


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  \date{June 18, 2024}


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\begin{abstract}
We use numerical solutions of the Richard's Equations for 3D porous
media to investigate the influence of agricultural subsurface drainage
as a hydrologic process and its effect on the hydrologic regime of a
watershed. Specifically, we determine the relation between subsurface
seepage and subsurface storage in hillslopes with (drained) and without
(undrained) subsurface drainage. Simulations are performed in Hydrus3D
and the output is analyzed with MATLAB's curve fitting tools, to create
simple ordinary differential equations that represent the relationship
between subsurface flow and subsurface storage for hillslopes of varying
topographical gradients and shapes. We have determined an `activation
point' below which the seepage/storage relationship is roughly linear,
and above which the drained and undrained simulations behave according
to different nonlinear functional forms. Although the seepage/storage
relationship of flat hillslopes have parametric consistencies
independent of the hillslope gradient, the addition of curvature
increases the complexity. In this work, we describe approximations to
account for curved hillslopes. From our formulation, subsurface flow for
varying hillslopes can be approximated using only the water storage and
the topography of the hillslope. Reducing the system from partial
differential equations (Hydrus) to ordinary differential equations
improves scalability of the model. Simplified equations are used to
study the consequences of large-scale changes in agricultural landscapes
due to subsurface drainage.%
\end{abstract}%



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