Calibrating a model of depth to water table using Fourier series and Simpson numerical integration

Depth to water table (DWT) in shallow groundwater affects land salinization, ecological system, irrigation scheduling, and agriculture output. Few researches have, however, focused on the impact of the complex transient dynamics of precipitation and evapotranspiration on the behavior of DWT in shallow groundwater. This study proposes a one-dimensional DWT model driven by complex multi-periodic precipitation and evapotranspiration, coupling the Boussinesq equation with the Averianov formula. The model is calibrated using multi-modes truncated Fourier series against 1-D data from the field experiment in Guanzhong Basin, Shaanxi Province, China. The experiment shields lateral groundwater flow effectively to ensure an accurate measurement of the effect of precipitation and evapotranspiration on DWT in the vertical direction. Results of the study show that fluctuations of DWT are driven by multi-periodic evapotranspiration and precipitation primarily in the long-wave components because the high-frequency precipitation and evapotranspiration are essentially filtered out when they propagate through unsaturated zones. This result beneficial for future studies on DWT via the Fourier series. In particular, the calibrated model can quickly determine the DWT of Guanzhong Basin site, predict DWT in the short term, and simulate the dynamic change of groundwater level, the vegetation in the study area. Besides, although the calibrated parameters cannot be directly applied to other sites, they may be useful to the prediction of the DWT fluctuations in the sites.