Seepage boundary conditions are commonly used in groundwater simulations to allow groundwater to discharge at the upper surface of the model when groundwater head exceeds atmospheric pressure. However, the extent and transient behavior of the seepage zone is often unknown a priori and is difficult to predict. A mathematical description of the boundary condition is straightforward, such that head is equivalent to elevation only when groundwater flow indicates a seepage condition, which is a mixed conditional Dirichlet and Neumann boundary condition. This standard representation of the boundary condition has been successfully implemented and applied in a real-world context by most groundwater models. However, it is rarely reported that convergence is only guaranteed when both the efflux and zero pressure conditions are simultaneously satisfied, often requiring unnecessarily small timestep sizes, which results in low computational efficiency. This study suggests a continuous differentiable equation as an alternative to model the seepage boundary. The new formulation is derived by analogy to the first-order exchange equation, which is commonly used to represent the interactions between surface water and groundwater flow in integrated hydrologic simulations. The results of this study suggest that mixed Dirichlet and Neumann boundary conditions can be effectively converted into a Robin boundary condition, which is a head-dependent flux condition that incorporates appropriate physical considerations. This new approach has the potential to significantly improve the accuracy and efficiency of groundwater flow simulations and can help to advance the understanding of subsurface hydrology.

Computing aquitard depletion, which is often overlooked, is of great significance for the assessment of groundwater resources and land subsidence. The issue is viewed as troublesome because of the additional computational burden, the poorly known hydrogeological parameters of the aquitard, and the lack of drawdown history in pumped aquifers. In this study, an analytical solution is derived to describe the drawdown variation in a nonlinear-consolidated aquitard under the condition of variable drawdowns in adjacent aquifers. Based on the analytical solution, we study the characteristics of groundwater dynamics and water balance under the conditions of linearly increasing drawdown of aquifers in adjacent aquifers. In addition, we put forward a method to calculate the depletion and hydrogeological parameters of an aquitard corresponding to variable drawdowns in adjacent aquifers, applicable even when historical drawdown data are lacking. The accuracy of the method is generally very good, but results improve when the drawdown history of pumped aquifers is divided into more periods for estimation. Under the condition of linear drawdown in adjacent aquifers, groundwater depletion and maximum water release rate of the aquitard increases with increasing compression index, coefficient of consolidation, aquitard thickness, rate of drawdown change in the adjacent aquifer, while decreasing with initial void ratio, and initial effective stress. The proposed approach is demonstrated at a field site in Shanghai City of China, and it would help for the effective management of groundwater resources and estimation of the global transfer from groundwater to surface water.

Hydraulic tomography (HT) has been proven to be an effective approach in mapping the heterogeneity of hydraulic parameters. The travel-time based inversion (TTI) and geostatistical inversion (GI) approaches are two of several HT methods. In particular, the GI approach is used to compute heterogeneous hydraulic conductivity (K) and specific storage (Ss) tomograms, while the TTI approach yields diffusivity (D = K/Ss) tomograms. The main objective of this paper is to evaluate these two methods through a synthetic study. Two cases are designed based on different monitoring configurations. Two independent scenarios are designed by: providing the same data sets and providing all available data for calibration, while data selection follows recommended strategies utilized by the two approaches. Then, the estimated tomograms are evaluated by visual comparison of estimated parameter distributions and assessments of model calibration and validation results. Results show that the advantages of TTI are: (1) imaging of structural features representing high D zones; (2) requirement of less data for inverse modeling; and (3) rapid computational times. In contrast, the advantages of the GI approach are: (1) the direct characterization of both K and Ss distributions; (2) better drawdown predictions; and (3) a larger estimated area. Our study suggests that the TTI approach is suitable for rapid, coarse characterization of heterogeneity that could potentially be utilized for providing hydrogeological structures for an initial model for the GI approach. The GI approach, although significantly more computationally intensive, is more robust and preferable to applications that require higher accuracy in parameter estimation.

This study proposes the utilization of municipal well records as an alternative dataset for large-scale heterogeneity characterization of hydraulic conductivity () and specific storage () using hydraulic tomography (HT). To investigate the performance of HT and the feasibility of utilizing municipal well records, a three-dimensional aquifer/aquitard system is constructed and synthetic groundwater flow and solute transport experiments are conducted to generate data for inverse modeling and validation of results. In particular, we simultaneously calibrate four groundwater models with varying parameterization complexity using five datasets consisting of different time durations and periods. Calibration and validation results are qualitatively and quantitatively assessed to evaluate the performance of investigated models. The estimated and tomograms from different model cases are also validated through the simulation of independently conducted pumping tests and conservative solute transport. Our study reveals that: 1) the HT analysis of municipal well records is feasible and yields reliable heterogeneous and distributions where drawdown records are available; 2) accurate geological information is of critical importance when data density is low and should be incorporated for geostatistical inversions; 3) the estimated and tomograms from the geostatistical model with geological information are capable in providing robust predictions of both groundwater flow and solute transport. Overall, this synthetic study provides a general framework for large-scale heterogeneity characterization using HT through the interpretation of municipal well records, and provides guidance for applying this concept to field problems.