Analytical expressions of specific yield for shallow groundwater estimation and modeling

Specific yield (S_y) is an essential hydrogeological parameter in groundwater-related modeling and estimation. In this study, we proposed several new analytical expressions of S_y to characterize the nonlinear variations of S_y under shallow groundwater environments, encompassing S_y for three-layered soil, transition zone S_y, and flux-dependent S_y (in Boussinesq-type equation). The proposed S_y expression for three-layered soils expanded the applicability of previous expressions for homogeneous soil. The result indicated that different from the trend for homogeneous soil, S_y for three-layered soils may also decrease with the increase of water table depth. Besides, S_y corresponding to the transition zone (S_y,tz) was analytically quantized to improve the previous empirical method, and we found that S_y,tz was not dependent on initial water table depth but the increment of depth. Moreover, flux-dependent S_y in the Boussinesq-type equation was proposed by considering the vertical fluxes in the unsaturated zone, which effectively improved the modeling behavior of the previous Boussinesq-type equation with S_y under the hydrostatic assumption. Sensitivity analysis of analytical expressions showed that saturated moisture content, shape parameter α, and water table depth were the three most important variables for S_y expressions. Overall, our study expanded the applicability of the previous analytical expressions of S_y and offered valuable analytical approaches for sustainable groundwater management.