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.

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.

FloPy Workflows for Creating Structured and Unstructured MODFLOW Models.

FloPy is a 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 simplify the process required to download MODFLOW-based and other executables for Linux, MacOS, and Windows operating systems. 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.

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.

Hydraulic-Head Formulation for Density-Dependent Flow and Transport.

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.

Impact of Local Groundwater Flow Model Errors on Transport and a Practical Solution for the Issue.

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.

MODFLOW/MT3DMS-based simulation of variable-density ground water flow and transport.

This paper presents an approach for coupling MODFLOW and MT3DMS for the simulation of variable-density ground water flow. MODFLOW routines were modified to solve a variable-density form of the ground water flow equation in which the density terms are calculated using an equation of state and the simulated MT3DMS solute concentrations. Changes to the MODFLOW and MT3DMS input files were kept to a minimum, and thus existing data files and data files created with most pre- and postprocessors can be used directly with the SEAWAT code. The approach was tested by simulating the Henry problem and two of the saltpool laboratory experiments (low- and high-density cases). For the Henry problem, the simulated results compared well with the steady-state semianalytic solution and also the transient isochlor movement as simulated by a finite-element model. For the saltpool problem, the simulated breakthrough curves compared better with the laboratory measurements for the low-density case than for the high-density case but showed good agreement with the measured salinity isosurfaces for both cases. Results from the test cases presented here indicate that the MODFLOW/MT3DMS approach provides accurate solutions for problems involving variable-density ground water flow and solute transport.

A Semi-Structured MODFLOW-USG Model to Evaluate Local Water Sources to Wells for Decision Support.

In order to better represent the configuration of the stream network and simulate local groundwater-surface water interactions, a version of MODFLOW with refined spacing in the topmost layer was applied to a Lake Michigan Basin (LMB) regional groundwater-flow model developed by the U.S. Geological. Regional MODFLOW models commonly use coarse grids over large areas; this coarse spacing precludes model application to local management issues (e.g., surface-water depletion by wells) without recourse to labor-intensive inset models. Implementation of an unstructured formulation within the MODFLOW framework (MODFLOW-USG) allows application of regional models to address local problems. A "semi-structured" approach (uniform lateral spacing within layers, different lateral spacing among layers) was tested using the LMB regional model. The parent 20-layer model with uniform 5000-foot (1524-m) lateral spacing was converted to 4 layers with 500-foot (152-m) spacing in the top glacial (Quaternary) layer, where surface water features are located, overlying coarser resolution layers representing deeper deposits. This semi-structured version of the LMB model reproduces regional flow conditions, whereas the finer resolution in the top layer improves the accuracy of the simulated response of surface water to shallow wells. One application of the semi-structured LMB model is to provide statistical measures of the correlation between modeled inputs and the simulated amount of water that wells derive from local surface water. The relations identified in this paper serve as the basis for metamodels to predict (with uncertainty) surface-water depletion in response to shallow pumping within and potentially beyond the modeled area, see Fienen et al. (2015a).

Stochastic ground water flow simulation with a fracture zone continuum model.

A method is presented for incorporating the hydraulic effects of vertical fracture zones into two-dimensional cell-based continuum models of ground water flow and particle tracking. High hydraulic conductivity features are used in the model to represent fracture zones. For fracture zones that are not coincident with model rows or columns, an adjustment is required for the hydraulic conductivity value entered into the model cells to compensate for the longer flowpath through the model grid. A similar adjustment is also required for simulated travel times through model cells. A travel time error of less than 8% can occur for particles moving through fractures with certain orientations. The fracture zone continuum model uses stochastically generated fracture zone networks and Monte Carlo analysis to quantify uncertainties with simulated advective travel times. An approach is also presented for converting an equivalent continuum model into a fracture zone continuum model by establishing the contribution of matrix block transmissivity to the bulk transmissivity of the aquifer. The methods are used for a case study in west-central Florida to quantify advective travel times from a potential wetland rehydration site to a municipal supply wellfield. Uncertainties in advective travel times are assumed to result from the presence of vertical fracture zones, commonly observed on aerial photographs as photolineaments.

Simulation of submarine ground water discharge to a marine estuary: Biscayne Bay, Florida.

Variable density ground water flow models are rarely used to estimate submarine ground water discharge because of limitations in computer speed, data availability, and availability of a simulation tool that can minimize numerical dispersion. This paper presents an application of the SEAWAT code, which is a combined version of MODFLOW and MT3D, to estimate rates of submarine ground water discharge to a coastal marine estuary. Discharge rates were estimated for Biscayne Bay, Florida, for the period from January 1989 to September 1998 using a three-dimensional, variable density ground water flow and transport model. Hydrologic stresses in the 10-layer model include recharge, evapotranspiration, ground water withdrawals from municipal wellfields, interactions with surface water (canals in urban areas and wetlands in the Everglades), boundary fluxes, and submarine ground water discharge to Biscayne Bay. The model was calibrated by matching ground water levels in monitoring wells, baseflow to canals, and the position of the 1995 salt water intrusion line. Results suggest that fresh submarine ground water discharge to Biscayne Bay may have exceeded surface water discharge during the 1989, 1990, and 1991 dry seasons, but the average discharge for the entire simulation period was only approximately 10% of the surface water discharge to the bay. Results from the model also suggest that tidal canals intercept fresh ground water that might otherwise have discharged directly to Biscayne Bay. This application demonstrates that regional scale variable density models are potentially useful tools for estimating rates of submarine ground water discharge.

Effect of sea-level rise on salt water intrusion near a coastal well field in southeastern Florida.

A variable-density groundwater flow and dispersive solute transport model was developed for the shallow coastal aquifer system near a municipal supply well field in southeastern Florida. The model was calibrated for a 105-year period (1900 to 2005). An analysis with the model suggests that well-field withdrawals were the dominant cause of salt water intrusion near the well field, and that historical sea-level rise, which is similar to lower-bound projections of future sea-level rise, exacerbated the extent of salt water intrusion. Average 2005 hydrologic conditions were used for 100-year sensitivity simulations aimed at quantifying the effect of projected rises in sea level on fresh coastal groundwater resources near the well field. Use of average 2005 hydrologic conditions and a constant sea level result in total dissolved solids (TDS) concentration of the well field exceeding drinking water standards after 70 years. When sea-level rise is included in the simulations, drinking water standards are exceeded 10 to 21 years earlier, depending on the specified rate of sea-level rise.

Modeling variably saturated subsurface solute transport with MODFLOW-UZF and MT3DMS.

The MT3DMS groundwater solute transport model was modified to simulate solute transport in the unsaturated zone by incorporating the unsaturated-zone flow (UZF1) package developed for MODFLOW. The modified MT3DMS code uses a volume-averaged approach in which Lagrangian-based UZF1 fluid fluxes and storage changes are mapped onto a fixed grid. Referred to as UZF-MT3DMS, the linked model was tested against published benchmarks solved analytically as well as against other published codes, most frequently the U.S. Geological Survey's Variably-Saturated Two-Dimensional Flow and Transport Model. Results from a suite of test cases demonstrate that the modified code accurately simulates solute advection, dispersion, and reaction in the unsaturated zone. Two- and three-dimensional simulations also were investigated to ensure unsaturated-saturated zone interaction was simulated correctly. Because the UZF1 solution is analytical, large-scale flow and transport investigations can be performed free from the computational and data burdens required by numerical solutions to Richards' equation. Results demonstrate that significant simulation runtime savings can be achieved with UZF-MT3DMS, an important development when hundreds or thousands of model runs are required during parameter estimation and uncertainty analysis. Three-dimensional variably saturated flow and transport simulations revealed UZF-MT3DMS to have runtimes that are less than one tenth of the time required by models that rely on Richards' equation. Given its accuracy and efficiency, and the wide-spread use of both MODFLOW and MT3DMS, the added capability of unsaturated-zone transport in this familiar modeling framework stands to benefit a broad user-ship.

Solute and heat transport model of the Henry and hilleke laboratory experiment.

SEAWAT is a coupled version of MODFLOW and MT3DMS designed to simulate variable-density ground water flow and solute transport. The most recent version of SEAWAT, called SEAWAT Version 4, includes new capabilities to represent simultaneous multispecies solute and heat transport. To test the new features in SEAWAT, the laboratory experiment of Henry and Hilleke (1972) was simulated. Henry and Hilleke used warm fresh water to recharge a large sand-filled glass tank. A cold salt water boundary was represented on one side. Adjustable heating pads were used to heat the bottom and left sides of the tank. In the laboratory experiment, Henry and Hilleke observed both salt water and fresh water flow systems separated by a narrow transition zone. After minor tuning of several input parameters with a parameter estimation program, results from the SEAWAT simulation show good agreement with the experiment. SEAWAT results suggest that heat loss to the room was more than expected by Henry and Hilleke, and that multiple thermal convection cells are the likely cause of the widened transition zone near the hot end of the tank. Other computer programs with similar capabilities may benefit from benchmark testing with the Henry and Hilleke laboratory experiment.

Quantifying data worth toward reducing predictive uncertainty.

The present study demonstrates a methodology for optimization of environmental data acquisition. Based on the premise that the worth of data increases in proportion to its ability to reduce the uncertainty of key model predictions, the methodology can be used to compare the worth of different data types, gathered at different locations within study areas of arbitrary complexity. The method is applied to a hypothetical nonlinear, variable density numerical model of salt and heat transport. The relative utilities of temperature and concentration measurements at different locations within the model domain are assessed in terms of their ability to reduce the uncertainty associated with predictions of movement of the salt water interface in response to a decrease in fresh water recharge. In order to test the sensitivity of the method to nonlinear model behavior, analyses were repeated for multiple realizations of system properties. Rankings of observation worth were similar for all realizations, indicating robust performance of the methodology when employed in conjunction with a highly nonlinear model. The analysis showed that while concentration and temperature measurements can both aid in the prediction of interface movement, concentration measurements, especially when taken in proximity to the interface at locations where the interface is expected to move, are of greater worth than temperature measurements. Nevertheless, it was also demonstrated that pairs of temperature measurements, taken in strategic locations with respect to the interface, can also lead to more precise predictions of interface movement.

Modeling axisymmetric flow and transport.

Unmodified versions of common computer programs such as MODFLOW, MT3DMS, and SEAWAT that use Cartesian geometry can accurately simulate axially symmetric ground water flow and solute transport. Axisymmetric flow and transport are simulated by adjusting several input parameters to account for the increase in flow area with radial distance from the injection or extraction well. Logarithmic weighting of interblock transmissivity, a standard option in MODFLOW, can be used for axisymmetric models to represent the linear change in hydraulic conductance within a single finite-difference cell. Results from three test problems (ground water extraction, an aquifer push-pull test, and upconing of saline water into an extraction well) show good agreement with analytical solutions or with results from other numerical models designed specifically to simulate the axisymmetric geometry. Axisymmetric models are not commonly used but can offer an efficient alternative to full three-dimensional models, provided the assumption of axial symmetry can be justified. For the upconing problem, the axisymmetric model was more than 1000 times faster than an equivalent three-dimensional model. Computational gains with the axisymmetric models may be useful for quickly determining appropriate levels of grid resolution for three-dimensional models and for estimating aquifer parameters from field tests.