A Generic Closed-Loop Contaminant Treatment System Package for MODFLOW 6.

We present a contaminant treatment system (CTS) package for MODFLOW 6 that facilitates the simulation of pump-and-treat systems for groundwater remediation. Using the "nonintrusive" MODFLOW 6 application programming interface (API) capability, the CTS package can balance flows between extraction and injection wells within the outer flow solution loop and applies blended concentration/mass treatment efficiency within the outer transport solution loop. The former can be important when the requested extraction rate cannot be satisfied by the current simulated groundwater system conditions, while the latter can be important for simulating incomplete/imperfect treatment schemes. Furthermore, the CTS package allows users to temporally vary all aspects of a simulated CTS system, including the configuration and location of injection and extraction wells, and the CTS efficiency. This flexibility combined with the API-based implementation provide a generic and general CTS package that can be applied across the wide range of MODFLOW 6 simulation options and that evolves in step with MODFLOW 6 code modifications and advancements without needing to update the CTS package itself.

Risk-Based Wellhead Protection Decision Support: A Repeatable Workflow Approach.

Environmental water management often benefits from a risk-based approach where information on the area of interest is characterized, assembled, and incorporated into a decision model considering uncertainty. This includes prior information from literature, field measurements, professional interpretation, and data assimilation resulting in a decision tool with a posterior uncertainty assessment accounting for prior understanding and what is learned through model development and data assimilation. Model construction and data assimilation are time consuming and prone to errors, which motivates a repeatable workflow where revisions resulting from new interpretations or discovery of errors can be addressed and the analyses repeated efficiently and rigorously. In this work, motivated by the real world application of delineating risk-based (probabilistic) sources of water to supply wells in a humid temperate climate, a scripted workflow was generated for groundwater model construction, data assimilation, particle-tracking and post-processing. The workflow leverages existing datasets describing hydrogeology, hydrography, water use, recharge, and lateral boundaries. These specific data are available in the United States but the tools can be applied to similar datasets worldwide. The workflow builds the model, performs ensemble-based history matching, and uses a posterior Monte Carlo approach to provide probabilistic capture zones describing source water to wells in a risk-based framework. The water managers can then select areas of varying levels of protection based on their tolerance for risk of potential wrongness of the underlying models. All the tools in this workflow are open-source and free, which facilitates testing of this repeatable and transparent approach to other environmental problems.

Evaluating Lower Computational Burden Approaches for Calibration of Large Environmental Models.

Realistic environmental models used for decision making typically require a highly parameterized approach. Calibration of such models is computationally intensive because widely used parameter estimation approaches require individual forward runs for each parameter adjusted. These runs construct a parameter-to-observation sensitivity, or Jacobian, matrix used to develop candidate parameter upgrades. Parameter estimation algorithms are also commonly adversely affected by numerical noise in the calculated sensitivities within the Jacobian matrix, which can result in unnecessary parameter estimation iterations and less model-to-measurement fit. Ideally, approaches to reduce the computational burden of parameter estimation will also increase the signal-to-noise ratio related to observations influential to the parameter estimation even as the number of forward runs decrease. In this work a simultaneous increments, an iterative ensemble smoother (IES), and a randomized Jacobian approach were compared to a traditional approach that uses a full Jacobian matrix. All approaches were applied to the same model developed for decision making in the Mississippi Alluvial Plain, USA. Both the IES and randomized Jacobian approach achieved a desirable fit and similar parameter fields in many fewer forward runs than the traditional approach; in both cases the fit was obtained in fewer runs than the number of adjustable parameters. The simultaneous increments approach did not perform as well as the other methods due to inability to overcome suboptimal dropping of parameter sensitivities. This work indicates that use of highly efficient algorithms can greatly speed parameter estimation, which in turn increases calibration vetting and utility of realistic models used for decision making.

Risk-Based Decision-Support Groundwater Modeling for the Lower San Antonio River Basin, Texas, USA.

A numerical surface-water/groundwater model was developed for the lower San Antonio River Basin to evaluate the responses of low base flows and groundwater levels within the basin under conditions of reduced recharge and increased groundwater withdrawals. Batch data assimilation through history matching used a simulation of historical conditions (2006-2013); this process included history-matching to groundwater levels and base-flow estimates at several gages, and was completed in a high-dimensional (highly parameterized) framework. The model was developed in an uncertainty framework such that parameters, observations, and scenarios of interest are envisioned stochastically as distributions of potential values. Results indicate that groundwater contributions to surface water during periods of low flow may be reduced from 6% to 25% with a corresponding 25% reduction in recharge and a 25% increase in groundwater pumping over an 8-year planning period. Furthermore, results indicate groundwater-level reductions in some hydrostratigraphic units are more likely than in other hydrostratigraphic units over an 8-year period under drought conditions with the higher groundwater withdrawal scenario.

Extending the Capture Map Concept to Estimate Discrete and Risk-Based Streamflow Depletion Potential.

A popular and contemporary use of numerical groundwater models is to estimate the discrete relation between groundwater extraction and surface-water/groundwater exchange. Previously, the concept of a "capture map" has been put forward as a means to effectively summarize this relation for decision-making consumption. While capture maps have enjoyed success in the environmental simulation industry, they are deterministic, ignoring uncertainty in the underlying model. Furthermore, capture maps are not typically calculated in a manner that facilitates analysis of varying combinations of extraction locations and/or reaches. That is, they are typically constructed with focus on a single reach or group of reaches. The former of these limitations is important for conveying risk to decision makers and stakeholders, while the latter is important for decision-making support related to surface-water management, where future foci may include reaches that were not the focus of the original capture analysis. Herein, we use the concept of a response matrix to generalize the theory of the capture-map approach to estimate spatially discrete streamflow depletion potential. We also use first-order, second-moment uncertainty estimation techniques with the concept of "risk shifting" to place capture maps and streamflow depletion potential in a stochastic, risk-based framework. Our approach is demonstrated for an integrated groundwater/surface-water model of the lower San Antonio River, Texas, USA.

Revisiting "An Exercise in Groundwater Model Calibration and Prediction" After 30 Years: Insights and New Directions.

In 1988, an important publication moved model calibration and forecasting beyond case studies and theoretical analysis. It reported on a somewhat idyllic graduate student modeling exercise where many of the system properties were known; the primary forecasts of interest were heads in pumping wells after a river was modified. The model was calibrated using manual trial-and-error approaches where a model's forecast quality was not related to how well it was calibrated. Here, we investigate whether tools widely available today obviate the shortcomings identified 30 years ago. A reconstructed version of the 1988 true model was tested using increasing parameter estimation sophistication. The parameter estimation demonstrated the inverse problem was non-unique because only head data were available for calibration. When a flux observation was included, current parameter estimation approaches were able to overcome all calibration and forecast issues noted in 1988. The best forecasts were obtained from a highly parameterized model that used pilot points for hydraulic conductivity and was constrained with soft knowledge. Like the 1988 results, however, the best calibrated model did not produce the best forecasts due to parameter overfitting. Finally, a computationally frugal linear uncertainty analysis demonstrated that the single-zone model was oversimplified, with only half of the forecasts falling within the calculated uncertainty bounds. Uncertainties from the highly parameterized models had all six forecasts within the calculated uncertainty. The current results outperformed those of the 1988 effort, demonstrating the value of quantitative parameter estimation and uncertainty analysis methods.

Consequences of Groundwater-Model Vertical Discretization in Risk-Based Decision-Making.

One of the first and most important decisions facing practitioners when constructing a numerical groundwater model is vertical discretization. Several factors will influence this decision, such as the conceptual model of the system and hydrostratigraphy, data availability, resulting computational burden, and the purpose of the modeling analysis. Using a coarse vertical discretization is an attractive option for practitioners because it reduces data requirements and model construction efforts, can increase model stability, and can reduce computational demand. However, using a coarse vertical discretization as a form of model simplification is not without consequence; this may give rise to unwanted side-effects such as biases in decision-relevant simulated outputs. Given its foundational role in the modeled representation of the aquifer system, herein we investigate how vertical discretization may affect decision-relevant simulated outputs using a paired complex-simple model analysis. A Bayesian framework and decision analysis approach are adopted. Two case studies are considered, one of a synthetic, linked unsaturated-zone/surface-water/groundwater hydrologic model and one of a real-world linked surface-water/groundwater hydrologic-nitrate transport model. With these models, we analyze decisions related to abstraction-induced changes in ecologically important streamflow characteristics and differences in groundwater and surface-water nitrate concentrations and mass loads following potential land-use change. We show that for some decision-relevant simulated outputs, coarse vertical discretization induces bias in important simulated outputs, and can lead to incorrect resource management action. For others, a coarse vertical discretization has little or no consequence for resource management decision-making.

Use of general purpose graphics processing units with MODFLOW.

To evaluate the use of general-purpose graphics processing units (GPGPUs) to improve the performance of MODFLOW, an unstructured preconditioned conjugate gradient (UPCG) solver has been developed. The UPCG solver uses a compressed sparse row storage scheme and includes Jacobi, zero fill-in incomplete, and modified-incomplete lower-upper (LU) factorization, and generalized least-squares polynomial preconditioners. The UPCG solver also includes options for sequential and parallel solution on the central processing unit (CPU) using OpenMP. For simulations utilizing the GPGPU, all basic linear algebra operations are performed on the GPGPU; memory copies between the central processing unit CPU and GPCPU occur prior to the first iteration of the UPCG solver and after satisfying head and flow criteria or exceeding a maximum number of iterations. The efficiency of the UPCG solver for GPGPU and CPU solutions is benchmarked using simulations of a synthetic, heterogeneous unconfined aquifer with tens of thousands to millions of active grid cells. Testing indicates GPGPU speedups on the order of 2 to 8, relative to the standard MODFLOW preconditioned conjugate gradient (PCG) solver, can be achieved when (1) memory copies between the CPU and GPGPU are optimized, (2) the percentage of time performing memory copies between the CPU and GPGPU is small relative to the calculation time, (3) high-performance GPGPU cards are utilized, and (4) CPU-GPGPU combinations are used to execute sequential operations that are difficult to parallelize. Furthermore, UPCG solver testing indicates GPGPU speedups exceed parallel CPU speedups achieved using OpenMP on multicore CPUs for preconditioners that can be easily parallelized.