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.

This evaluates the potential for a newly proposed non-linear subsurface flux equation to improve the performance of the hydrological Hillslope Link Model (HLM). The equation contains parameters that are functionally related to the hillslope steepness and the presence of tile drainage. As a result, the equation allows a better representation of hydrograph recession curves, hydrograph timing, and total runoff volume. The authors explore the new parameterization’s potential by comparing a set of diagnostic and prognostic setups in HLM. In the diagnostic approach, they configure 12 different scenarios with spatially uniform parameters over the state of Iowa. In the prognostic case, they use information from topographical maps and known locations of tile drainage to distribute parameter values. To assess performance improvements, they compare simulation results to streamflow observations during a 17-year period (2002–2018) at 140 U.S. Geological Survey (USGS) gauging stations. The operational setup of the HLM model used at the Iowa Flood Center (IFC) serves as a benchmark to quantify overall model improvement. In particular, the new equation provides better representation of recession curves and the total streamflow volumes. However, when comparing the diagnostic and prognostic setups, the authors find discrepancies in the spatial distribution of hillslope scale parameters. The results suggest that more work is required when using maps of physical attributes to parameterize hydrological models. The findings also demonstrate that the diagnostic approach is a useful strategy to evaluate models and assess changes in their formulations.