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Joseph D. Hughes

Publications and source records attributed to Joseph D. Hughes.

At least 19 recordsLinked to original sources

Total uncertainty quantification in inverse solutions with deep learning surrogate models

We propose an approximate Bayesian method for quantifying the total uncertainty in inverse partial differential equation (PDE) solutions obtained with machine learning surrogate models, including operator learning models. The proposed method accounts for uncertainty in the observations, PDE, and surrogate models. First, we use the surrogate model to formulate a minimization problem in the reduced space for the maximum a posteriori (MAP) inverse solution. Then, we randomize the MAP objective function and obtain samples of the posterior distribution by minimizing different realizations of the objective function. We test the proposed framework by comparing it with the iterative ensemble smoother and deep ensembling methods for a nonlinear diffusion equation with an unknown space-dependent diffusion coefficient. Among other applications, this equation describes the flow of groundwater in an unconfined aquifer. Depending on the training dataset and ensemble sizes, the proposed method provides similar or more descriptive posteriors of the parameters and states than the iterative ensemble smoother method. Deep ensembling underestimates uncertainty and provides less-informative posteriors than the other two methods. Our results show that, despite inherent uncertainty, surrogate models can be used for parameter and state estimation as an alternative to the inverse methods relying on (more accurate) numerical PDE solvers.

Journal of Computational Physics↗

Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation

We evaluate the performance of the Karhunen–Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen–Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.

Advances in Water Resources↗

A new groundwater energy transport model for the MODFLOW hydrologic simulator

Heat transport in the subsurface is an important aspect of research related to the effects of a warming climate on ecological services (i.e., cold-water refugia); the development of geothermal resources for energy banking schemes (i.e., aquifer thermal energy storage [ATES]); and the effects of temperature on other aspects of groundwater quality, such as nutrient cycling. Historically, simulation of heat transport using the MODFLOW groundwater simulator and related codes was performed by scaling the input parameters of a solute-transport model to emulate heat transport. However, that approach required additional pre- and post-processing of input and output and could not account for the variation in effective thermal storage and transport properties during transient, unsaturated flow, for example. True heat-transport capabilities in the context of MODFLOW were first introduced in a variant called USG-Transport. More recently, a new groundwater energy-transport (GWE) model type has been added to MODFLOW 6, the core version of the MODFLOW hydrologic simulator. GWE supports the simulation of heat transport on structured or unstructured grids as well as within and between features of advanced packages that represent streams, lakes, multi-aquifer wells, and the unsaturated zone. GWE is integrated within MODFLOW 6 and is accessible through the FloPy Python package and the MODFLOW 6 application programming interface (API). An example simulation demonstrates conduction between grid cells through both the water and the solid aquifer material, including thermal bleeding from saturated overburden cells into a groundwater flow field.

Groundwater↗

Simulation of groundwater-flow dynamics in the U.S. Northern High Plains driven by multi-model estimates of surficial aquifer recharge

There is growing interest in incorporating higher-resolution groundwater modeling within the framework of large-scale land surface models (LSMs), including processes such as three-dimensional flow, variable soil saturation, and surface water/groundwater interactions. Conversely, complex groundwater models (e.g., the U.S. Geological Survey Groundwater-Flow Model, MODFLOW) often use simpler representations of land surface dynamics (e.g., surface vegetation, evapotranspiration, recharge) and may benefit from higher process fidelity and temporal resolutions in these inputs. This study investigates the potential of improving groundwater representation in LSMs and land surface dynamics in MODFLOW through forcing MODFLOW with recharge from LSMs. Groundwater simulations build on an existing and well-calibrated MODFLOW model of the U.S. Northern High Plains aquifer, a hydrologically complex basin under the dual impacts of conversion of native vegetation to intense irrigated agricultural fields and climate change. Simulated groundwater recharge from four different land models are used to drive MODFLOW groundwater simulations. Results show relatively large discrepancies between recharge estimates among simulations. Forcing MODFLOW using recharge simulated by some of the LSMs in place of a simple water balance model marginally improves MODFLOW groundwater simulation. Further, our results support the efficacy of coupling LSMs to a sophisticated groundwater model such as MODFLOW. The coupling results in notable improvements in matching the historical groundwater levels through reduction of the skewness coefficient in percent bias histogram (from 1.50 and 1.41 in original LSMs to 0.44 and 0.27, respectively, when MODFLOW is forced by groundwater recharge from LSMs) and reduction of bias. This modeling effort seeks to identify the best compromise between comprehensive land surface processes from global LSMs and advanced representation of groundwater from regional models.

Journal of Hydrology↗

An agricultural package for MODFLOW 6 using the Application Programming Interface

An agricultural water use package has been developed for MODFLOW 6 using the MODFLOW Application Programming Interface (API). The MODFLOW API Agricultural Water Use Package (API-Ag) was based on the approach to simulate irrigation demand in the MODFLOW-NWT and GSFLOW Agricultural Water Use (AG) Package. The API-Ag Package differs from the previous approach by implementing new features and support for additional irrigation providers. New features include representation of deficit and over-irrigation, Multi-Aquifer Well and Lake Package irrigation providers, and support for structured, vertex, and unstructured grid models. Three example problems are presented that demonstrate how the API-Ag Package improves representation of highly managed systems and are further used to validate the irrigation demand and delivery formulations. Irrigation volumes simulated in the three example problems show excellent agreement with the MODFLOW-NWT AG Package.

Groundwater↗

MODFLOW as a configurable multi-model hydrologic simulator

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.

Groundwater↗

FloPy workflows for creating structured and unstructured MODFLOW models

FloPy is a popular Python package for creating, running, and post-processing MODFLOW-based groundwater flow and transport models. FloPy functionality has expanded to support the latest version of MODFLOW (MODFLOW 6) including support for unstructured grids. FloPy can be used to download MODFLOW-based and other executables for Linux, MacOS, and Windows operating systems, which simplifies the process required to download and use these executables. Expanded FloPy capabilities include (1) full support for structured and unstructured spatial discretizations; (2) geoprocessing of spatial features and raster data to develop model input for supported discretization types; (3) the addition of functionality to provide direct access to simulated output data; (4) extension of plotting capabilities to unstructured MODFLOW 6 discretization types; and (5) the ability to export model data to shapefiles, NetCDF, and VTK formats for processing, analysis, and visualization by other software products. Examples of using expanded FloPy capabilities are presented for a hypothetical watershed. An unstructured groundwater flow and transport model, with several advanced stress packages, is presented to demonstrate how FloPy can be used to develop complicated unstructured model datasets from original source data (shapefiles and rasters), post-process model results, and plot simulated results.

Groundwater↗

Hydrogeology, land-surface subsidence, and documentation of the Gulf Coast Land Subsidence and Groundwater-Flow (GULF) model, southeast Texas, 1897–2018

Executive Summary As a part of the Texas Water Development Board groundwater availability modeling program, the U.S. Geological Survey developed the Gulf Coast Land Subsidence and Groundwater-Flow model (hereinafter, the “GULF model”) and ensemble to simulate groundwater flow and land-surface subsidence in the northern part of the Gulf Coast aquifer system (the study area) in Texas from predevelopment (1897) through 2018. Since the publication of a previous groundwater model for the greater Houston area in 2012, there have been changes to the distribution of groundwater withdrawals and advances in modeling tools. To reflect these changes and to simulate more recent conditions, the GULF model was developed in cooperation with the Harris-Galveston and Fort Bend Subsidence Districts to provide an updated Groundwater Availability Model. Since the early 1900s, most of the groundwater withdrawals in the study area have been from three of the hydrogeologic units that compose the Gulf Coast aquifer system—the Chicot, Evangeline, and Jasper aquifers and, more recently, from the Catahoula confining unit. Withdrawals from these hydrogeologic units are used for municipal supply, commercial and industrial use, and irrigation purposes. Withdrawals of large quantities of groundwater in the greater Houston area have caused widespread groundwater-level declines in the Chicot, Evangeline, and Jasper aquifers of more than 300 feet (ft). Early development of the aquifer system, which began before 1900, resulted in nearly 50 percent of the eventual historical groundwater-level minimums having been reached as early as 1946 in some areas. These groundwater-level declines led to more than 9 ft of land-surface subsidence—historically in central and southeastern Harris County and Galveston County, but more recently in northern, northwestern, and western Harris County, Montgomery County, and northern Fort Bend County—from depressurization and compaction of clay and silt layers interbedded in the aquifer sediments. In a generalized conceptual model of the Gulf Coast aquifer system, water enters the groundwater system in topographically high outcrops of the hydrogeologic units in the northwestern part of the aquifer system. Groundwater that does not discharge to streams flows to intermediate and deep zones of the aquifer system southeastward of the outcrop areas where it is discharged by wells and by upward leakage in topographically low areas near the coast. The uppermost parts of the aquifer system, which include outcrop areas, are under water-table (unconfined) conditions where the groundwater is not confined under pressure. As depth increases in the aquifer system and interbedded clay and silt layers accumulate, water-table conditions evolve into confined conditions where the groundwater is under pressure. Groundwater flow and land-surface subsidence in the GULF model and ensemble were simulated by using MODFLOW 6 with the Skeletal Storage, Compaction, and Subsidence package. The model consists of six layers, one for each of the five hydrogeologic units in the northern part of the Gulf Coast aquifer system and a surficial top layer that includes part of each hydrogeologic unit. Transient groundwater flow was simulated during 1897–2018 by using a combination of multiyear, annual, and monthly stress periods. An initial steady-state stress period was configured to represent predevelopment mean annual inflows and outflows. The subsidence package used in the GULF model and ensemble uses a head-based subsidence formulation that simulates the delayed drainage response from clay and silt sediment to changes in groundwater levels. The GULF model and ensemble were history matched to groundwater-level observations at selected wells, land-surface subsidence at benchmarks, aquifer compaction at borehole extensometers, and vertical displacement from Global Positioning System stations. A Bayesian framework was used to represent uncertainty in modeled parameters and simulated outputs of interest. History matching and uncertainty quantification were performed by using a Monte Carlo approach enabled through iterative ensemble smoother software to produce an ensemble of models fit to historical data. The iterative ensemble smoother substantially reduced the computational demand of parameter estimation by approximating the first-order relation between model inputs and outputs, thereby allowing 183,207 adjustable parameters to be used for history matching at a relatively low computational and time cost. The history-matched parameter values are within the ranges of previously published values and agree with the current understanding of the spatial and temporal patterns of parameter uncertainty for the Gulf Coast aquifer system. A good agreement between the observed (or estimated) and simulated groundwater levels, land-surface subsidence, compaction, and vertical displacement was obtained across the modeled area based on qualitative and quantitative comparisons. Ensemble mean annual groundwater-flow rates to the Chicot, Evangeline, Jasper aquifers and Catahoula confining unit were 0.0–0.49 inch (in.), 0.09–0.33 in., 0.01–0.07 in., and 0.01–0.05 in., respectively. GULF model mean annual groundwater-flow rates to the Chicot, Evangeline, and Jasper aquifers and Catahoula confining unit were 0.31 in., 0.19 in., 0.03 in., and 0.03 in., respectively. The GULF-model-simulated recharge to the outcrop area was the largest inflow (75 percent), and recharge to other areas was 25 percent of the model inflow. The simulated outflows included (1) net surface-water/groundwater exchange with study area streams (50 percent), (2) groundwater use (49 percent), and (3) net surface-water/groundwater exchange with the Gulf of Mexico (1 percent). The sum of the simulated values of the outflows (1,041,973 acre-feet per year [acre-ft/yr]) and the elastic expansion of the fine-grained sediment and numerical solver error (339 acre-ft/yr) minus the inflows (654,172 acre-ft/yr) represents the reduction of storage from the Gulf Coast aquifer system (388,140 acre-ft/yr). Most of the storage depletion is caused by the long-term groundwater-level declines that have resulted primarily in inelastic compaction. The GULF model was used to estimate Jasper aquifer compaction at selected benchmarks in Montgomery County and northern Harris County, which are the primary locations of Jasper aquifer groundwater use. Simulated Jasper aquifer compaction in northern Harris County was between 0.2 and 0.5 ft, or between about 5 and 16 percent of simulated subsidence at the benchmark locations. Simulated Jasper aquifer compaction in Montgomery County was between 0.8 and 1.2 ft, or between about 33 and 57 percent of simulated subsidence at the benchmark locations.

Texas↗

Documentation for the MODFLOW 6 Groundwater Transport Model

This report documents a new Groundwater Transport (GWT) Model for MODFLOW 6. The GWT Model simulates three-dimensional transport of a single chemical species in fowing groundwater based on a generalized control-volume fnite-difference approach. Although each GWT Model is only able to represent a single chemical species, multiple GWT Models may be invoked within a single MODFLOW 6 simulation to represent solute transport of multiple non-interacting chemical species. The GWT Model is designed to work with the Groundwater Flow (GWF) Model for MODFLOW 6, which simulates transient, three-dimensional groundwater fow. The version of the GWT model documented here must use the same spatial discretization used by the GWF Model; however, that spatial discretization can be represented by regular MODFLOW grids consisting of layers, rows, and columns, or by more general unstructured grids. The GWT Model simulates (1) advective transport, (2) the combined hydrodynamic dispersion processes of velocity-dependent mechanical dispersion and molecular diffusion, (3) adsorption and absorption (collectively referred to as sorption) of solutes by the aquifer matrix, (4) transfer between the mobile domain and one or more immobile domains, (5) frst-or zero-order solute decay or production, (6) mixing from groundwater sources and sinks, and (7) direct addition of solute mass. The GWT Model can also represent advective solute transport through advanced package features, such as streams, lakes, multi-aquifer wells, and the unsaturated zone. If the GWF Model application uses the Water Mover (MVR) Package to connect fow packages, then solute transport between these packages can also be represented. The transport processes described in this report have been implemented in a fully implicit manner and are solved in a system of equations using iterative numerical methods. The present version of the GWT Model for MODFLOW 6 does not have an option to calculate steady-state transport solutions; if a steady-state solution is required, then transient evolution of the solute must be represented using multiple time steps until no further changes in solute concentrations are detected.

Techniques and Methods↗

Documentation for the Skeletal Storage, Compaction, and Subsidence (CSUB) Package of MODFLOW 6

This report describes the skeletal storage, compaction and subsidence (CSUB) package of MODFLOW 6. The CSUB package simulates the vertical compaction of compressible sediments and land subsidence. The package simulates groundwater storage changes and elastic compaction in coarse-grained aquifer sediments. The CSUB package also simulates groundwater storage changes and elastic and inelastic compaction in fne-grained, compressible interbeds, or in extensive confning units. The package can account for effective stress-dependent changes in storage properties. The CSUB package can also explicitly account for the contribution of water compressibility to groundwater storage changes. Compaction of compressible sediments is formulated using Terzaghi’s elastoplastic model and assumes the total compaction is a small fraction of the total initial thickness of compressible sediments. Compaction is controlled by head or pore-pressure changes and overburden stress changes associated with water-table changes, and thus by effective stress changes within coarse-and fne-grained compressible sediments. If the stress in a compressible unit is less than the preconsolidation stress, compaction is elastic (recoverable). If the stress in a compressible sediment is greater than the preconsolidation stress, compaction is inelastic (irrecoverable) and permanent land subsidence occurs. The propagation of head changes within fne-grained, compressible interbeds is represented numerically using a transient, one-dimensional (vertical) groundwater fow equation. This equation accounts for delayed release of water from storage or uptake of water into storage in the interbeds. Vertical hydraulic conductivity, elastic and inelastic skeletal specifc storage, and interbed thickness control the timing of interbed storage changes. Interbeds that are thin, have a relatively large vertical hydraulic conductivity, or relatively small specifc-storage values equilibrate quickly with heads/pore pressures in surrounding coarse-grained sediments and can be represented as no-delay interbeds that use the simulated groundwater head in a cell to calculate interbed compaction and do not need to be solved numerically using a vertically discretized interbed and the vertical groundwater fow equation. In addition to the applicability to confned groundwater fow systems, several features of the CSUB package make it applicable to shallow, unconfned groundwater fow systems. Geostatic stress can be treated as a function of water-table elevation, and compaction is a function of computed changes in effective stress. The porosity, void ratio, and thickness of shallow and deep coarse-grained aquifer sediments, fne-grained interbeds, and extensive confning units can vary in time based on calculated strain.

Techniques and Methods↗

The MODFLOW Application Programming Interface for simulationcontrol and software interoperability

The MODFLOW API allows other programs to control MODFLOW and interactively change variables without having to modify the source code. The MODFLOW API is based on the Basic Model Interface (BMI), which is a set of conventions that define how to initialize a simulation, update the model state by advancing in time, and finalize the run. For many existing MODFLOW coupling applications, the information provided to MODFLOW must be updated multiple times in a time step. As this capability to modify variables within a time step is not defined by the BMI, an extension to BMI was developed. This eXtended Model Interface is part of the MODFLOW API and allows such a tight coupling to other models. Examples are included for a variety of use cases, including new flexibility for users to develop custom packages without modifying the MODFLOW source code and coupling MODFLOW with other models and optimization libraries.

Environmental Modelling & Software↗

Use of the MODFLOW 6 water mover package to represent natural and managed hydrologic connections

The latest release of MODFLOW 6, the current core version of the MODFLOW groundwater modeling software, debuted a new package dubbed the “mover” (MVR). Using a generalized approach, MVR facilitates the transfer of water among any arbitrary combination of simulated features (i.e., pumping wells, stream, drains, lakes, etc.) within a MODFLOW 6 simulation. Four “rules” controlling the amount of water transferred from a providing feature to a receiving feature are currently available. In this way, MVR can represent natural connections between features, for example streams entering or exiting lakes, and perhaps more interestingly, it also can transfer water among simulated features to more accurately simulate water management. An example model representative of an agricultural setting demonstrates some of the available MVR connections. For example, an irrigation event that transfers surface water from an irrigation delivery ditch to multiple cropped areas demonstrates a “one-to-many” connection that is possible within MVR. Conversely, irrigation or precipitation runoff from multiple fields may be routed to a particular stream segment using “many-to-one” MVR connections. MVR supports many additional connection types, several of which are demonstrated by the included example problem.

Groundwater↗

Distributed memory parallel groundwater modeling for the Netherlands Hydrological Instrument

Worldwide, billions of people rely on fresh groundwater reserves for their domestic, agricultural and industrial water use. Extreme droughts and excessive groundwater pumping put pressure on water authorities in maintaining sustainable water usage. High-resolution integrated models are valuable assets in supporting them. The Netherlands Hydrological Instrument (NHI) provides the Dutch water authorities with open source modeling software and data. However, NHI integrated groundwater models often require long run times and large memory usage, therefore strongly limiting their application. As a solution, we present a distributed memory parallelization, focusing on the National Hydrological Model. Depending on the level of integration, we show that significant speedups can be obtained up to two orders of magnitude. As far as we know, this is the first reported integrated groundwater parallelization of an operational hydrological model used for national-scale integrated water management and policy making. The parallel model code and data are freely available.

Environmental Software & Modelling↗

Integrated hydro-terrestrial modeling: Development of a national capability

Water is one of our most important natural resources and is essential to our national economy and security. Multiple federal government agencies have mission elements that address national needs related to water. Each water-related agency champions a unique science and/or operational mission focused on advancing a portion of the nation’s ability to meet our water-related challenges, often in close collaboration with scientists from the academic community. These diverse mission needs have engendered a rich and extensive base of water-related data and modeling capabilities. While useful for their intended purposes, these capabilities are not well integrated to address complex regional problems and overarching national problems. These major investments by several federal agencies and their scientific partners, however, lay the foundation for an integrated hydro-terrestrial modeling and data infrastructure that will enhance knowledge, understanding, prediction, and management of the nation’s diverse water challenges.

Report↗

Potential for increased inundation in flood-prone regions of southeast Florida in response to climate and sea-level changes in Broward County, Florida, 2060–69

The U.S. Geological Survey, in cooperation with Broward County Environmental Planning and Resilience Division, has developed county-scale and local-scale groundwater/surface-water models to study the potential for increased inundation and flooding in eastern Broward County that are due to changes in future climate and sea-level rise. These models were constructed by using MODFLOW 2005, with the surface-water system represented by using the Surface-Water Routing process and a new Urban Runoff process. The local-scale model allowed the use of finer grid resolution in a selected area of the county, whereas the county-scale model provided boundary conditions for the local-scale model and insight into the hydrologic behavior of the larger system. The aquifer layering, properties, and boundaries relied heavily on a previous three-dimensional variable-density solute-transport model of the same area developed by the U.S. Geological Survey. The surface-water system within these new models actively simulates a part of the extensive canal network by using level-pool routing and active structure operations within the Surface-Water Routing process. These models were used to simulate a historical base-case period (1990–99) by using measured data and regional climate model rainfall and potential evapotranspiration output. The simulated flow and water-level results generally captured the behavior of the hydrologic system. A future period (2060–69) was simulated by using regional climate model rainfall and potential evapotranspiration output representing a wetter and drier future and low, intermediate, and high sea-level rise projections. The results were used to evaluate the potential effects on the surface-water drainage system, coastal-structure operation, and wet-season groundwater levels. Future period simulations using the county-scale model indicate that (1) the effects of the changing climate and sea level are much more evident in eastern and coastal areas of Broward County compared to western areas, with increases in groundwater level nearly equivalent to sea-level rise; (2) coastal groundwater-level increases are distributed farther inland in the wetter future scenarios than in the drier future scenarios; (3) water levels at the westernmost groundwater station locations exhibited little change caused by sea-level rise and showed more dependence on changes in precipitation; (4) there was a reduced west-to-east groundwater gradient with increasing sea-level rise; and (5) increased downstream tidal stage at the S–13 structure resulted in increased reliance on the pump to control upstream inland canal stages. Future simulations using the local-scale model indicate similar behavior as seen in the county-scale model: (1) the coastal areas exhibited the largest impacts in groundwater levels in the future scenarios; (2) the westernmost, interior areas exhibited little change during the future scenarios; and (3) there was an increased reliance on the pump at the S–13 coastal structure but to a lesser extent than indicated in the county-scale model because of the reduced temporal scale of the local-scale model. Possible adaptation and mitigation strategies were simulated to evaluate the county-scale and local-scale models’ ability to simulate hydrologic changes. Alterations to S–13 pump operations within the county-scale model were tested, and results indicate a reduced effect of sea-level rise inland of the control structure, but the affected area is spatially limited. The concept of using pumps to reduce the local groundwater levels in two neighborhood-sized areas was tested by using the local-scale model. The MODFLOW 2005 Drain package was used to remove groundwater by using drainage elevations set to zero, 1 foot, and 2 feet above average wet-season groundwater levels. Area 1 was well connected to coastal boundaries, and a high rate of groundwater removal was required, whereas the rate of groundwater removal required was greatly reduced in Area 2, which is less connected to tidal boundaries. Water for these scenarios was assumed to be pumped to tide with no downstream effects.

Florida↗

Documentation for the MODFLOW 6 Groundwater Flow Model

This report documents the Groundwater Flow (GWF) Model for a new version of MODFLOW called MODFLOW 6. The GWF Model for MODFLOW 6 is based on a generalized control-volume finite-difference approach in which a cell can be hydraulically connected to any number of surrounding cells. Users can define the model grid using one of three discretization packages, including (1) a structured discretization package for defining regular MODFLOW grids consisting of layers, rows, and columns, (2) a discretization by ver­tices package for defining layered unstructured grids consisting of layers and cells, and (3) a general unstruc­tured discretization package for defining flexible grids comprised of cells and their connection properties. For layered grids, a new capability is available for removing thin cells and vertically connecting cells overlying and underlying the thin cells. For complex problems involving water-table conditions, an optional Newton-Raphson formulation, based on the formulations in MODFLOW-NWT and MODFLOW-USG, can be acti­vated. Use of the Newton-Raphson formulation will often improve model convergence and allow solutions to be obtained for difficult problems that cannot be solved using the traditional wetting and drying approach. The GWF Model is divided into “packages,” as was done in previous MODFLOW versions. A package is the part of the model that deals with a single aspect of simulation. Packages included with the GWF Model include those related to internal calculations of groundwater flow (discretization, initial conditions, hydraulic conduc­tance, and storage), stress packages (constant heads, wells, recharge, rivers, general head boundaries, drains, and evapotranspiration), and advanced stress packages (streamflow routing, lakes, multi-aquifer wells, and unsaturated zone flow). An additional package is also available for moving water available in one package into the individual features of the advanced stress packages. The GWF Model also has packages for obtaining and controlling output from the model. This report includes detailed explanations of physical and mathematical concepts on which the GWF Model and its packages are based. Like its predecessors, MODFLOW 6 is based on a highly modular structure; however, this structure has been extended into an object-oriented framework. The framework includes a robust and generalized numeri­cal solution object, which can be used to solve many different types of models. The numerical solution object has several different matrix preconditioning options as well as several methods for solving the linear system of equations. In this new framework, the GWF Model itself is an object as are each of the GWF Model packages. A benefit of the object-oriented structure is that multiple objects of the same type can be used in a single sim­ulation. Thus, a single forward run with MODFLOW 6 may contain multiple GWF Models. GWF Models can be hydraulically connected using GWF-GWF Exchange objects. Connecting GWF models in different ways permits the user to utilize a local grid refinement strategy consisting of parent and child models or to couple adjacent GWF Models. An advantage of the approach implemented in MODFLOW 6 is that multiple models and their exchanges can be incorporated into a single numerical solution object. With this design, models can be tightly coupled at the matrix level.

Techniques and Methods↗

Documentation for the “XT3D” option in the Node Property Flow (NPF) Package of MODFLOW 6

This report describes the “XT3D” option in the Node Property Flow (NPF) Package of MODFLOW 6. The XT3D option extends the capabilities of MODFLOW by enabling simulation of fully three-dimensional anisotropy on regular or irregular grids in a way that properly takes into account the full, three-dimensional conductivity tensor. It can also improve the accuracy of groundwater-flow simulations in cases in which the model grid violates certain geometric requirements. Three example problems demonstrate the use of the XT3D option to simulate groundwater flow on irregular grids and through three-dimensional porous media with anisotropic hydraulic conductivity. Conceptually, the XT3D method of estimating flow between two MODFLOW 6 model cells can be viewed in terms of three main mathematical steps: construction of head-gradient estimates by interpolation; construction of fluid-flux estimates by application of the full, three-dimensional form of Darcy’s Law, in which the conductivity tensor can be heterogeneous and anisotropic; and construction of the flow expression by enforcement of continuity of flow across the cell interface. The resulting XT3D flow expression, which relates the flow across the cell interface to the values of heads computed at neighboring nodes, is the sum of terms in which conductance-like coefficients multiply head differences, as in the conductance-based flow expression the NPF Package uses by default. However, the XT3D flow expression contains terms that involve “neighbors of neighbors” of the two cells for which the flow is being calculated. These additional terms have no analog in the conductance-based formulation. When assembled into matrix form, the XT3D formulation results in a larger stencil than the conductance-based formulation; that is, each row of the coefficient matrix generally contains more nonzero elements. The “RHS” suboption can be used to avoid expanding the stencil by placing the additional terms on the right-hand side of the matrix equation and evaluating them at the previous iteration or time step. The XT3D option can be an alternative to the Ghost-Node Correction (GNC) Package. However, the XT3D formulation is typically more computationally intensive than the conductance-based formulation the NPF Package uses by default, either with or without ghost nodes. Before deciding whether to use the GNC Package or XT3D option for production runs, the user should consider whether the conductance-based formulation alone can provide acceptable accuracy for the particular problem being solved.

Techniques and Methods↗

Documentation for the MODFLOW 6 framework

MODFLOW is a popular open-source groundwater flow model distributed by the U.S. Geological Survey. Growing interest in surface and groundwater interactions, local refinement with nested and unstructured grids, karst groundwater flow, solute transport, and saltwater intrusion, has led to the development of numerous MODFLOW versions. Often times, there are incompatibilities between these different MODFLOW versions. The report describes a new MODFLOW framework called MODFLOW 6 that is designed to support multiple models and multiple types of models. The framework is written in Fortran using a modular object-oriented design. The primary framework components include the simulation (or main program), Timing Module, Solutions, Models, Exchanges, and Utilities. The first version of the framework focuses on numerical solutions, numerical models, and numerical exchanges. This focus on numerical models allows multiple numerical models to be tightly coupled at the matrix level.

Techniques and Methods↗