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The performance of time series models is assessed using synthetic head series simulated with a numerical model that solves Richards' equation for variably saturated flow. Heads were simulated in a homogeneous unconfined aquifer between two parallel canals; measured daily precipitation and potential evaporation are specified at the land surface and root water uptake is simulated. The head response to a precipitation event is nonlinear and depends on the saturation degree and rainfall before and after the precipitation event while evaporation reduction occurs during summers. Synthetic series were generated for 27 years and three different soil types; the unsaturated zone thickness varies between 0 and >5 m. The synthetic head series were simulated with a linear and nonlinear time series model. Performance of a linear time series model with four parameters, using a scaled Gamma response, gave R 2 values ranging from 0.67 to 0.96. The nonlinear time series model with five parameters simulates recharge using a root zone reservoir after which the head response to recharge is simulated with a scaled Gamma response function. The nonlinear time series model was able to simulate all synthetic head series very well with R 2 values above 0.9 for almost all models. The head response of the nonlinear model to a single precipitation event compares well to the response of the variably saturated groundwater model. The provided scripts may be used to simulate synthetic head series for other climates or for systems with additional complexity to assess the performance of other data-driven models., (© 2024 The Authors. Groundwater published by Wiley Periodicals LLC on behalf of National Ground Water Association.)

Managed aquifer recharge has become a standard water resources management practice to promote the development of locally sustainable water supplies and combat water scarcity. However, installation of injection wells for replenishment purposes in urban areas with complex hydrogeology faces many challenges, such as limited land availability, potential impacts on municipal production wells and known subsurface contamination plumes, and complex spatially variable hydraulic connections between aquifer units. To assess the feasibility and cost-effectiveness of injecting advanced treated water (ATW) into a complex urban aquifer system, a Simulation-Optimization (SO) model was developed to automate a systematic search for the most cost-effective locations to install new wells for injecting various quantities of ATW, if feasible. The generalized workflow presented here uses an existing MODFLOW groundwater model-along with advanced optimization routines that are publicly available-to flexibly accommodate a multiobjective function, complex constraints, and specific project requirements. The model successfully placed wells for injection of 1 to 4 MGD of ATW in aquifers underlying the study area. The injection well placement was primarily constrained by avoiding excessive impact on environmental sites with underlying groundwater plumes. The largest costs were for well installation and piping to the wells from the existing ATW pipes. This workflow is readily adaptable to other sites with different complexities, decision variables, or constraints., (© 2023 National Ground Water Association.)

MODFLOW 6 is the latest in a line of six "core" versions of MODFLOW released by the U.S. Geological Survey. The MODFLOW 6 architecture supports incorporation of additional hydrologic processes, in addition to groundwater flow, and allows interaction between processes. The architecture supports multiple model instances and multiple types of models within a single simulation, a flexible approach to formulating and solving the equations that represent hydrologic processes, and recent advances in interoperability, which allow MODFLOW to be accessed and controlled by external programs. The present version of MODFLOW 6 consolidates popular capabilities available in MODFLOW variants, such as the unstructured grid support in MODFLOW-USG, the Newton-Raphson formulation in MODFLOW-NWT, and the support for partitioned stress boundaries in MODFLOW-CDSS. The flexible multi-model capability allows users to configure MODFLOW 6 simulations to represent the local-grid refinement (LGR) capabilities available in MODFLOW-LGR, the multi-species transport capabilities in MT3DMS, and the coupled variable-density capabilities available in SEAWAT. This paper provides a new, holistic and integrated overview of simulation capabilities made possible by the MODFLOW 6 architecture, and describes how ongoing and future development can take advantage of the program architecture to integrate new capabilities in a way that is minimally invasive and automatically compatible with the existing MODFLOW 6 code., (© 2023 Deltares and The Authors. Groundwater published by Wiley Periodicals LLC on behalf of National Ground Water Association. This article has been contributed to by U.S. Government employees and their work is in the public domain in the USA.)

Simulating the interaction of groundwater with surface water networks using traditional boundary packages available with MODFLOW-USG can be challenging for complex systems. Often several package types are required as they are typically purpose built. Moreover, these packages generally do not interact with one another which complicates accounting of groundwater discharge at different points within the system. Here, we demonstrate that the connected linear network (CLN) package of MODFLOW-USG, and advances therein in USG-Transport, can be used to simulate groundwater interaction with a complex surface water network comprised of creeks, ponds, wetlands, and springs, in a manner that is comparable with these other packages, but with additional benefits, including explicit routing of water between the features., (© 2022 National Ground Water Association.)

The χMD matrix solver package is incorporated into USGS groundwater modeling software, such as MODFLOW-NWT, MODFLOW-USG, and MT3D. The solver is used to solve matrices assembled through numerical discretization of the groundwater flow equation, and solute transport equations. χMD has demonstrated its higher robustness, faster execution speed, and more efficient memory usage compared to the existing solvers for many types of groundwater flow problems. χMD uses preconditioned iterative Krylov-subspace methods and consists of preconditioning and acceleration modules. Because the solver package uses a variety of preconditioning features including level-based incomplete lower-upper (ILU) factorization method with a drop tolerance scheme, users must choose optimal preconditioning parameters to improve execution speed and robustness. In order to examine how the preconditioning parameters, ILU factorization level, and drop tolerance values affect the overall performance of the matrix solver, we evaluated five different groundwater model applications using MODFLOW-USG that include different numerical complexities. For those five cases, the number of discretization nodes varied from 10,000 cells to 730,300 cells. From the analysis, we found that the preconditioning parameters greatly affect execution times and memory usage of the preconditioning and acceleration procedures. In addition, a combination of the ILU level between five to seven and the drop tolerance value between 10 -2 and 10 -3 usually resulted in shorter overall execution time. Our study suggests that the users can elicit higher performance and robustness of the χMD matrix solver using this combination of the parameters and enhance computational efficiency of solving groundwater and solute transport problems., (© 2021 National Ground Water Association.)

Density-dependent flow and transport solutions for coastal saltwater intrusion investigations, analyses of fluid injection into deep brines, and studies of convective fingering and instabilities of denser fluids moving through less dense fluids typically formulate the groundwater flow equation in terms of pressure or equivalent freshwater head. A formulation of the flow equation in terms of hydraulic head is presented here as an alternative. The hydraulic-head formulation can facilitate adaptation of existing constant-density groundwater flow codes to include density-driven flow by avoiding the need to convert between freshwater head and hydraulic head within the code and by incorporating density-dependent terms as a compartmentalized "correction" to constant-density calculations already performed by the code. The hydraulic-head formulation also accommodates complexities such as unconfined groundwater flow and Newton-Raphson solution schemes more readily than the freshwater-head formulation. Simulation results are presented for four example problems solved using an implementation of the hydraulic-head formulation in MODFLOW., (© 2019, National Ground Water Association.)

Axisymmetric groundwater models are used for simulating radially symmetric conditions. Groundwater simulators built specifically to model axisymmetric conditions are most commonly used for simulating aquifer tests. Although some numerical models capable of simulating flow and solute transport that are developed in the cartesian coordinate system framework offer flexibility to simulate axisymmetric conditions, most of the numerical groundwater models, such as the MODFLOW family of codes, are based on structured grids in which axisymmetric flows cannot be directly simulated. Researchers in the past have provided methods to manipulate aquifer properties to mimic axisymmetric conditions. This study presents a methodology that takes advantage of the unstructured grids of MODFLOW-USG to simulate axisymmetric models within the MODFLOW framework. To develop axisymmetric models, the intercell interface area arrays of MODFLOW-USG were calculated to accurately represent coaxial cylindrical model cells. Three examples are presented to demonstrate the application of MODFLOW-USG for axisymmetric modeling: a pumping well with delayed yield effects, a vadose zone flow model simulating an infiltration basin, and a density-dependent saltwater intrusion problem for a circular island. Results were verified against analytical solutions and published numerical codes., (© 2019, National Ground Water Association.)

A groundwater flow model is typically used to provide the flow field for conducting groundwater solute transport simulations. The advection term of the mass conserved formulation for groundwater transport assumes that the flow field is perfectly balanced and that all water flowing into a numerical grid cell is exactly balanced by outflows after accounting for sources/sinks or internal storage. However, in many complicated regional or site-scale models, there may be localized flow balance errors that may be difficult to eliminate through tighter flow convergence tolerances due to simulation time constraints or numerical limits on convergence tolerances. Thus, if water is erroneously gained or lost within a grid cell during the flow computation, the solutes within it will also be numerically affected in the associated transport simulation. Transport solutions neglect this error in groundwater flow as the transport equations that are solved assume no error in flow. This flow imbalance error can however have consequences on the transport solution ranging from unnoticeable errors in the resulting concentrations to spurious oscillations that can grow in time and hinder further solution. An approach has been suggested here, to explicitly handle these flow imbalances during mass conserved advective transport computations and report them in the corresponding transport mass balance output, as corrections that are needed to handle errors originating in the flow solution. Example problems are provided to explain the concepts and demonstrate the impacts., (© 2017, National Ground Water Association.)

Various approaches have been proposed to manage the nonlinearities associated with the unconfined flow equation and to simulate perched groundwater conditions using the MODFLOW family of codes. The approaches comprise a variety of numerical techniques to prevent dry cells from becoming inactive and to achieve a stable solution focused on formulations of the unconfined, partially-saturated, groundwater flow equation. Keeping dry cells active avoids a discontinuous head solution which in turn improves the effectiveness of parameter estimation software that relies on continuous derivatives. Most approaches implement an upstream weighting of intercell conductance and Newton-Raphson linearization to obtain robust convergence. In this study, several published approaches were implemented in a stepwise manner into MODFLOW for comparative analysis. First, a comparative analysis of the methods is presented using synthetic examples that create convergence issues or difficulty in handling perched conditions with the more common dry-cell simulation capabilities of MODFLOW. Next, a field-scale three-dimensional simulation is presented to examine the stability and performance of the discussed approaches in larger, practical, simulation settings., (© 2011, The Author(s). Ground Water © 2011, National Ground Water Association.)