A semi-analytical model for transient flow to a subsurface tile drain

The goal of this paper is to develop and test a semi-analytical model for event-based transient flow to a subsurface tile drain. A sharp-front theory was used to describe redistribution of infiltrated water in the vadose zone. New approximate analytical solutions in terms of Fourier series were sought for the Boussinesq equation describing subsurface saturated flow subject to time-dependent recharge. Both one and two-term solutions of the series approximation were compared with observed tile hydrograph data from the Purdue Water Quality Field Station (WQFS) in West Lafayette, Indiana. In general, the models were able to capture the peaks of the tile-drain hydrographs, as well as the times-to-peak and the times-of-initial-response to rainfall events. The models performed particularly well for rainfall events with single-burst hyetographs, and in the prediction of the first hydrograph peak from multiple-burst hyetographs, though subsequent peaks could not be captured as well. A further comparison of results from the one-term model with those from HYDRUS 2D suggested that the one-term model is adequate for estimating transient flow to a tile drain. The solution developed here holds promise for extension to larger watersheds where the hydrology is governed by tile drains.