Stagnation and pseudostagnation lines for separating 3D groundwater flow systems in Tothian basins

Stagnation points have been found to be useful in characterizing groundwater flow regimes in 2D or 3D domains. However, in 3D basins with complicated water table undulation and/or fluctuation, knowledge on stagnation points is limited. In this study, we first derived transient solution of basinal flow under spatially undulating and periodically changing water table in 3D Tóthian basins and examined the occurrence of stagnation points. Based on the analysis of groundwater flow systems distribution in simple 3D basins, we extend the method of delineating groundwater flow systems in 2D profiles using stagnation points to delineating 3D groundwater flow systems using stagnation or pseudostagnation lines, which consist of a series of stagnation or pseudostagnation points. This novel approach was successfully applied to 3D synthetic basins with more complex water table configuration (with undulations in all directions). Based on the transient hydraulic head solution in 3D Tóthian basins with a periodically fluctuating water table, it was found that the evolution of (pseudo)stagnation lines are controlled by the combination of hydraulic diffusivity and the period of the water table fluctuation, both of which determine the dimensionless response time. The change in shape of (pseudo)stagnation lines, induced by spatial undulations and/or temporal fluctuations of the water table, also reflects the variation of groundwater flow systems in penetration depth and horizontal range. The method proposed here improves the efficiency of partitioning groundwater flow systems in 3D domains, and our analytical study of (pseudo)stagnation lines partially fills the knowledge gap between stagnation points and stagnation zones.