Analytical solutions for two-dimensional groundwater flow with subsurface drainage tiles

•We proposed new analytical solutions for groundwater flow with drainage tile.•Groundwater discharge to river was increased significantly with drainage tile.•Drainage tile can result in increased nitrate loads in baseflow of a river.

SummaryThe tile drainage problem in an unconfined aquifer was investigated. A mathematical model was established that describes two-dimensional groundwater flow in an unconfined aquifer near a river with a linearized Boussinesq equation, time-dependent sources and a sloped tile. Analytical solutions for groundwater level and discharge were derived and used to compare hydrologic conditions in a system with and without tile (natural drainage). We found that the spatial and temporal variations of groundwater level and discharge were significantly altered by the presence of drainage tile. In an aquifer with tile drainage, the groundwater level was lower and total groundwater discharge to the river increased compared to an aquifer with no tile. Application of the solutions to a synthetic case demonstrates that the analytical solutions derived can be used to quantify effect of tiles on nitrate loads in the baseflow of a river and assess the effectiveness of various conservation practices.