Evaluating Groundwater Interbasin Flow Using Multiple Models and Multiple Types of Data

The groundwater interbasin flow, Q_y, from the north of Yucca Flat into Yucca Flat simulated using the Death Valley Regional Flow System (DVRFS) model greatly exceeds assessments obtained using other approaches. This study aimed to understand the reasons for the overestimation and to examine whether the Q_y estimate can be reduced. The two problems were tackled from the angle of model uncertainty by considering six models revised from the DVRFS model with different recharge components and hydrogeological frameworks. The two problems were also tackled from the angle of parametric uncertainty for each model by first conducting Morris sensitivity analysis to identify important parameters and then conducting Monte Carlo simulations for the important parameters. The uncertainty analysis is general and suitable for tackling similar problems; the Morris sensitivity analysis has been utilized to date in only a limited number of regional groundwater modeling. The simulated Q_y values were evaluated by using three kinds of calibration data (i.e., hydraulic head observations, discharge estimates, and constant‐head boundary flow estimates). The evaluation results indicate that, within the current DVRFS modeling framework, the Q_y estimate can only be reduced to about half of the original estimate without severely deteriorating the goodness‐of‐fit to the calibration data. The evaluation results also indicate that it is necessary to develop a new hydrogeological framework to produce new flow patterns in the DVRFS model. The issues of hydrogeology and boundary flow are being addressed in a new version of the DVRFS model planned for release by the U.S. Geological Survey.     

Multimodel Validity Assessment of Groundwater Flow Simulation Models Using Area Metric Approach

We demonstrate the application of the Area Metric developed by Ferson et al. (2008) for multimodel validity assessment. The Area Metric quantified the degree of models' replicative validity: the degree of agreement between the observed data and the corresponding simulated outputs represented as their empirical cumulative distribution functions (ECDFs). This approach was used to rank multiple representations of a case study groundwater flow model of a landfill by their Area Metric scores. A multimodel approach allows to account for uncertainties that may either be epistemic (from lack of knowledge) or aleatory (from variability inherent in the system). The Area Metric approach enables explicit incorporation of model uncertainties, epistemic as well as aleatory, into validation assessment. The proposed approach informs understanding of the collected data and that of the model domain. It avoids model overfitting to a particular system state, and in fact is a blind assessment of the models' validity: models are not adjusted, or updated, to achieve a better numerical fit. This approach assesses the degree of models' validity, in place of the typical binary model validation/invalidation process. Collectively, this increases confidence in the model's representativeness that, in turn, reduces risk to model users.     

A Correction on Coastal Heads for Groundwater Flow Models

We introduce a simple correction to coastal heads for constant‐density groundwater flow models that contain a coastal boundary, based on previous analytical solutions for interface flow. The results demonstrate that accurate discharge to the sea in confined aquifers can be obtained by direct application of Darcy's law (for constant‐density flow) if the coastal heads are corrected to ((α + 1)/α)h_s ? B/2α, in which h_s is the mean sea level above the aquifer base, B is the aquifer thickness, and α is the density factor. For unconfined aquifers, the coastal head should be assigned the value . The accuracy of using these corrections is demonstrated by consistency between constant‐density Darcy's solution and variable‐density flow numerical simulations. The errors introduced by adopting two previous approaches (i.e., no correction and using the equivalent fresh water head at the middle position of the aquifer to represent the hydraulic head at the coastal boundary) are evaluated. Sensitivity analysis shows that errors in discharge to the sea could be larger than 100% for typical coastal aquifer parameter ranges. The location of observation wells relative to the toe is a key factor controlling the estimation error, as it determines the relative aquifer length of constant‐density flow relative to variable‐density flow. The coastal head correction method introduced in this study facilitates the rapid and accurate estimation of the fresh water flux from a given hydraulic head measurement and allows for an improved representation of the coastal boundary condition in regional constant‐density groundwater flow models.     

Re-Purposing Groundwater Flow Models for Age Assessments: Important Characteristics

Groundwater flow model construction is often time-consuming and costly, with development ideally focused on a specific purpose, such as quantifying well capture from water bodies or providing flow fields for simulating advective transport. As environmental challenges evolve, the incentive to re-purpose existing groundwater flow models may increase. However, few studies have evaluated which characteristics of groundwater flow models deserve greatest consideration when re-purposing models for groundwater age and advective transport simulations. In this paper, we compare simulated age metrics produced by three MODFLOW-MODPATH models of the same area but with differing levels of complexity (layering and heterogeneity). Comparisons are made at three watershed scales (HUC 8 to HUC 12). Groundwater age metrics, specifically the young fraction and median age of the young and old fractions, are used for evaluation because they relate to intrinsic susceptibility of aquifers and are simpler to interpret than full age distributions used for advective transport. Results indicate that: (1) the young fraction is less sensitive to model layering than the median age of young and old fractions, suggesting that simple models may suffice for basic intrinsic susceptibility assessments; (2) water table mounding and associated discharge into partially penetrating boundaries, such as head-water streams, is important for simulating both the young fraction and the median age of the young fraction; and (3) the influence of partially penetrating head-water streams is maintained regardless of the porosity distribution. Results of this work should aid modelers with evaluating the appropriateness of re-purposing existing groundwater flow models for age simulations.     

Including Vertical Fault Structures in Layered Groundwater Flow Models

Accurate representation of groundwater flow and solute transport requires a sound representation of the underlying geometry of aquifers. Faults can have a significant influence on the structure and connectivity of aquifers, which may allow permeable units to connect, and aquifers to seal when juxtaposed against lower permeability units. Robust representation of groundwater flow around faults remains challenging despite the significance of faults for flow and transport. We present a methodology for the inclusion of faults utilizing the unstructured grid features of MODFLOW-USG and MODFLOW 6. The method focuses on the representation of fault geometries using non-neighbor connections between juxtaposed layers. We present an illustration of the method for a synthetic fluvial aquifer. The combined impact of the heterogeneous aquifer and fault offset is clearly visible where channel features at different depths in the aquifer were connected at the fault. These results highlight the importance of representing fault features in groundwater flow models.     

On Solving Groundwater Flow and Transport Models with Algebraic Multigrid Preconditioning

Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual delineation approach. This involves a single groundwater flow linear solution and a pure advective transport solution with different right-hand sides. The new solver was compared with other preconditioned iterative methods, the MODFLOW's GMG solver, and direct sparse solvers. Test problems include two- and three-dimensional benchmarks spanning homogeneous and highly heterogeneous and anisotropic formations. For the groundwater flow problems, using the algebraic multigrid preconditioning speeds up the numerical solution by one to two orders of magnitude. The algebraic multigrid preconditioner efficiency was preserved for the three dimensional heterogeneous and anisotropic problem unlike for the MODFLOW's GMG solver. Contrarily, a sparse direct solver was the most efficient for the pure advective transport processes such as the forward travel time simulations. Hence, the best sparse solver for the more general advection-dispersion transport equation is likely to be Péclet number dependent. When equipped with the best solvers, processing multimillion grid blocks by the dual delineation approach is a matter of seconds. This paves the way for its routine application to large geological models. The paper gives practical hints on the strategies and conditions under which algebraic multigrid preconditioning would remain competitive for the class of nonlinear and/or transient problems.     

Unstructured Gridding for MODFLOW from Prior Groundwater Flow Models: A New Paradigm

This work introduces a new unstructured gridding approach relying on feedback from a previous groundwater flow model. All cells in a relatively coarse model using a rectilinear grid are recursively subdivided following a cell wise specific discharge-based indicator to generate quadtree, octree or Voronoï grids. This technique leverages the full potential of the latest MODFLOW engines. The suitability of this approach is demonstrated on challenging single and multilayered heterogeneous formations. The proposed method is straightforward to implement in existing software packages. It supports iterative updating of groundwater flow models from the legacy rectilinear to unstructured grids.     

Tangent Vectors of Isochron Rays and Velocity Rays Expressed in Global Cartesian Coordinates

This paper provides Cartesian expressions for tangent vectors of isochron rays and velocity rays previously derived in so-called isochron-orthonormal coordinates. The Cartesian expressions are simpler and easier to implement than the expressions in isochron-orthonormal coordinates. It is shown that the expressions in both coordinate systems are equivalent.     

Estimating Preferential Flow in Karstic Aquifers Using Statistical Mixed Models

Karst aquifers are highly productive groundwater systems often associated with conduit flow. These systems can be highly vulnerable to contamination, resulting in a high potential for contaminant exposure to humans and ecosystems. This work develops statistical models to spatially characterize flow and transport patterns in karstified limestone and determines the effect of aquifer flow rates on these patterns. A laboratory‐scale Geo‐HydroBed model is used to simulate flow and transport processes in a karstic limestone unit. The model consists of stainless steel tanks containing a karstified limestone block collected from a karst aquifer formation in northern Puerto Rico. Experimental work involves making a series of flow and tracer injections, while monitoring hydraulic and tracer response spatially and temporally. Statistical mixed models (SMMs) are applied to hydraulic data to determine likely pathways of preferential flow in the limestone units. The models indicate a highly heterogeneous system with dominant, flow‐dependent preferential flow regions. Results indicate that regions of preferential flow tend to expand at higher groundwater flow rates, suggesting a greater volume of the system being flushed by flowing water at higher rates. Spatial and temporal distribution of tracer concentrations indicates the presence of conduit‐like and diffuse flow transport in the system, supporting the notion of both combined transport mechanisms in the limestone unit. The temporal response of tracer concentrations at different locations in the model coincide with, and confirms the preferential flow distribution generated with the SMMs used in the study.     

Direct Conservative Domain in the Continuous Galerkin Method for Groundwater Models

The continuous Galerkin finite element method is commonly considered locally nonconservative because a single element with fluxes computed directly from its potential distribution is unable to conserve its mass and fluxes across edges that are discontinuous. Some literature sources have demonstrated that the continuous Galerkin method can be locally conservative with postprocessed fluxes. This paper proposes the concept of a direct conservative domain (DCD), which could conserve mass when fluxes are computed directly from the potential distribution. Also presented here is a method for modifying the advection fluxes to obtain different conservative domains from the DCDs. Furthermore, DCDs are used to analyze the local conservation of several postprocessing algorithms, for which DCDs provide the theoretical basis. The local conservation of DCDs and the proposed method are illustrated and verified by using a hypothetical 2‐D model.     

Accelerating Groundwater Flow Simulation in MODFLOW Using JASMIN‐Based Parallel Computing

To accelerate the groundwater flow simulation process, this paper reports our work on developing an efficient parallel simulator through rebuilding the well‐known software MODFLOW on JASMIN (J Adaptive Structured Meshes applications Infrastructure). The rebuilding process is achieved by designing patch‐based data structure and parallel algorithms as well as adding slight modifications to the compute flow and subroutines in MODFLOW. Both the memory requirements and computing efforts are distributed among all processors; and to reduce communication cost, data transfers are batched and conveniently handled by adding ghost nodes to each patch. To further improve performance, constant‐head/inactive cells are tagged and neglected during the linear solving process and an efficient load balancing strategy is presented. The accuracy and efficiency are demonstrated through modeling three scenarios: The first application is a field flow problem located at Yanming Lake in China to help design reasonable quantity of groundwater exploitation. Desirable numerical accuracy and significant performance enhancement are obtained. Typically, the tagged program with load balancing strategy running on 40 cores is six times faster than the fastest MICCG‐based MODFLOW program. The second test is simulating flow in a highly heterogeneous aquifer. The AMG‐based JASMIN program running on 40 cores is nine times faster than the GMG‐based MODFLOW program. The third test is a simplified transient flow problem with the order of tens of millions of cells to examine the scalability. Compared to 32 cores, parallel efficiency of 77 and 68% are obtained on 512 and 1024 cores, respectively, which indicates impressive scalability.     

Calculating Groundwater Response Times for Flow in Heterogeneous Porous Media

Predicting the amount of time required for a transient groundwater response to take place is a practical question that is of interest in many situations. This time scale is often called the response time. In the groundwater hydrology literature, there are two main methods used to calculate the response time: (1) both the transient and steady‐state groundwater flow equations are solved, and the response time is taken to be amount of time required for the transient solution to approach the steady solution within some tolerance; and (2) simple scaling arguments are adopted. Certain limitations restrict both of these approaches. In this study, we outline a third method, based on the theory of mean action time. We derive the governing boundary value problem for both the mean and variance of action time for confined flow in two‐dimensional heterogeneous porous media. Importantly, we show that these boundary value problems can be solved using widely available software. Applying these methods to a test case reveals the advantages of the theory of mean action time relative to standard methods.     

Lattice Boltzmann Models for Flow and Transport in Saturated Karst

Flow and transport simulation in karst aquifers remains a significant challenge for the ground water modeling community. Darcy's law–based models cannot simulate the inertial flows characteristic of many karst aquifers. Eddies in these flows can strongly affect solute transport. The simple two-region conduit/matrix paradigm is inadequate for many purposes because it considers only a capacitance rather than a physical domain. Relatively new lattice Boltzmann methods (LBMs) are capable of solving inertial flows and associated solute transport in geometrically complex domains involving karst conduits and heterogeneous matrix rock. LBMs for flow and transport in heterogeneous porous media, which are needed to make the models applicable to large-scale problems, are still under development. Here we explore aspects of these future LBMs, present simple examples illustrating some of the processes that can be simulated, and compare the results with available analytical solutions. Simulations are contrived to mimic simple capacitance-based two-region models involving conduit (mobile) and matrix (immobile) regions and are compared against the analytical solution. There is a high correlation between LBM simulations and the analytical solution for two different mobile region fractions. In more realistic conduit/matrix simulation, the breakthrough curve showed classic features and the two-region model fit slightly better than the advection-dispersion equation (ADE). An LBM-based anisotropic dispersion solver is applied to simulate breakthrough curves from a heterogeneous porous medium, which fit the ADE solution. Finally, breakthrough from a karst-like system consisting of a conduit with inertial regime flow in a heterogeneous aquifer is compared with the advection-dispersion and two-region analytical solutions.