Redistribution of groundwater evapotranspiration and water table around a well field in an unconfined aquifer: A simplified analytical model

Groundwater evapotranspiration (GE) is an essential component for regional water balance in areas with shallow water table. When the depth to water table (DWT) falls due to pumping in a well field, GE will decrease, which also influence the redistribution of water table. A mathematical model of steady radial flow is developed to investigate the problem. The well field is simplified by a circular area with uniformly distributed pumpage. Relationship between GE and DWT is described with a commonly used linear formula when DWT is less than an extinction depth. Analytical solutions for three cases with or without a zero-GE zone (no GE occurs in the zone) are obtained. The redistributions of GE and water table are controlled by three lumped parameters. The analytical model is applied in a case study of the Ordos well field in China, with 55 pumping wells. It sufficiently agrees with a numerical model based on MODFLOW except in the vicinity of individual wells where cones of water table falling appear. The result of GE is not influenced by the discrepancy in water table due to existing of the zero-GE zone. Runge–Kutta solutions of using nonlinear GE formulas are presented and also applied in the case study to compare with the analytical model. They predict almost the same water table distribution and similar redistribution patterns of GE. The analytical model can be applied to determine the protection zone of well fields located in places without strong heterogeneous in topography and initial water table.