An approximate analytical solution of depth to water table driven by periodical precipitation and evapotranspiration in shallow groundwater zones
Xin Guo, Xu‐Sheng Wang, Jun Li, Tongke Wang, Zhi-Xue Zhao, Huiqing Hao, Hongbin Zhan, Qi Wang, Yonghong Hao
Abstract
Depth to water table (DWT) for an unconfined aquifer affects a wide range of hydrological, ecological, and agricultural problems such as soil salinization, plant type, and crop output. In a world without human impacts, DWT in shallow groundwater zones is mainly driven by evapotranspiration and precipitation. In the real-world however, human impacts on groundwater hydrological processes are ubiquitous, which hinders one to fully understand the natural groundwater hydrological rule. The purpose of this study is to derive an analytical solution of precipitation-evapotranspiration driven DWT irrespective of the human impacts. Through pretreatment of practical data to eliminate human impacts, we show that the proposed method is efficient in dealing with the real-world problems. Specifically, we establish a mathematical model describing impacts of periodic evapotranspiration and precipitation on DWT. An innovative quasi-analytical solution using the Fourier series is developed and analyzed in detail based on the model. This study indicates that the amplitude of DWT is correlated linearly with the amplitude of precipitation and quadratically with the amplitude of potential evapotranspiration. The phase position of DWT is subject to the phase lag between the precipitation and potential evapotranspiration. In arid regions, the evapotranspiration has a greater influence on the phase of DWT than the precipitation. This quasi-analytical solution is limited for a shallow groundwater situation in which DWT is less than the extinction depth of groundwater evapotranspiration.