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ODE representation of tile drainage on hillslopes of varying topography
Conference poster

ODE representation of tile drainage on hillslopes of varying topography

Morgan Fonley, Nicolás Velásquez, Ricardo Mantilla, Keyu Qiu and Nathaniel Haut
Earth and Space Science Open Archive
AGU 2019 Fall Meeting (San Francisco, CA, USA, 12/09/2019–12/13/2019)
2020
DOI: 10.1002/essoar.10501838.1

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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.

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