Parameter ESTimation With the Gauss-Levenberg-Marquardt Algorithm: An Intuitive Guide.

In this paper, we review the derivation of the Gauss-Levenberg-Marquardt (GLM) algorithm and its extension to ensemble parameter estimation. We explore the use of graphical methods to provide insights into how the algorithm works in practice and discuss the implications of both algorithm tuning parameters and objective function construction in performance. Some insights include understanding the control of both parameter trajectory and step size for GLM as a function of tuning parameters. Furthermore, for the iterative Ensemble Smoother (iES), we discuss the importance of noise on observations and show how iES can cope with non-unique outcomes based on objective function construction. These insights are valuable for modelers using PEST, PEST++, or similar parameter estimation tools.

Evaluation of an Impulse-Response Emulator for Groundwater Contaminant Transport Modeling.

There is a significant need to develop decision support tools capable of delivering accurate representations of environmental conditions, such as ground and surface water solute concentrations, in a timely and computationally efficient manner. Such tools can be leveraged to assess a large number of potential management strategies for mitigating non-point source pollutants. Here, we assess the effectiveness of the impulse-response emulation approach to approximate process-based groundwater model estimates of solute transport from MODFLOW and MT3D over a wide range of model inputs and parameters, with the goal of assessing where in parameter space the assumptions underlying this emulation approach are valid. The impulse-response emulator was developed using the sensitivity analysis utilities in the PEST++ software suite and is capable of approximating MODFLOW/MT3D estimates of solute transport over a large portion of the parameter space tested, except in cases where the Courant number is above 0.5. Across all runs tested, the highest percent errors were at the plume fronts. These results suggest that the impulse-response approach may be suitable for emulation of solute transport models for a wide range of cases, except when high-resolution outputs are needed, or when very low concentrations at plume edges are of particular interest.

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.

SFRmaker and Linesink-Maker: Rapid Construction of Streamflow Routing Networks from Hydrography Data.

Groundwater models have evolved to encompass more aspects of the water cycle, but the incorporation of realistic boundary conditions representing surface water remains time-consuming and error-prone. We present two Python packages that robustly automate this process using readily available hydrography data as the primary input. SFRmaker creates input for the MODFLOW SFR package, while Linesink-maker creates linesink string input for the GFLOW analytic element program. These programs can reduce weeks or even months of manual effort to a few minutes of execution time, and carry the added advantages of reduced potential for error, improved reproducibility and facilitation of step-wise modeling through reduced dependency on a particular conceptual model or discretization. Two real-world examples at the county to multi-state scales are presented.

Multi-Constrained Catchment Scale Optimization of Groundwater Abstraction Using Linear Programming.

Due to increasing water demands globally, freshwater ecosystems are under constant pressure. Groundwater resources, as the main source of accessible freshwater, are crucially important for irrigation worldwide. Over-abstraction of groundwater leads to declines in groundwater levels; consequently, the groundwater inflow to streams decreases. The reduction in baseflow and alteration of the streamflow regime can potentially have an adverse effect on groundwater-dependent ecosystems. A spatially distributed, coupled groundwater-surface water model can simulate the impacts of groundwater abstraction on aquatic ecosystems. A constrained optimization algorithm and a simulation model in combination can provide an objective tool for the water practitioner to evaluate the interplay between economic benefits of groundwater abstractions and requirements to environmental flow. In this study, a holistic catchment-scale groundwater abstraction optimization framework has been developed that allows for a spatially explicit optimization of groundwater abstraction, while fulfilling a predefined maximum allowed reduction of streamflow (baseflow [Q95] or median flow [Q50]) as constraint criteria for 1484 stream locations across the catchment. A balanced K-Means clustering method was implemented to reduce the computational burden of the optimization. The model parameters and observation uncertainties calculated based on Bayesian linear theory allow for a risk assessment on the optimized groundwater abstraction values. The results from different optimization scenarios indicated that using the linear programming optimization algorithm in conjunction with integrated models provides valuable information for guiding the water practitioners in designing an effective groundwater abstraction plan with the consideration of environmental flow criteria important for the ecological status of the entire system.

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.

Prioritizing river basins for intensive monitoring and assessment by the US Geological Survey.

The US Geological Survey (USGS) is currently (2020) integrating its water science programs to better address the nation's greatest water resource challenges now and into the future. This integration will rely, in part, on data from 10 or more intensively monitored river basins from across the USA. A team of USGS scientists was convened to develop a systematic, quantitative approach to prioritize candidate basins for this monitoring investment to ensure that, as a group, the 10 basins will support the assessment and forecasting objectives of the major USGS water science programs. Candidate basins were the level-4 hydrologic units (HUC04) with some of the smaller HUC04s being combined; median candidate-basin area is 46,600 km2. Candidate basins for the contiguous United States (CONUS) were grouped into 18 hydrologic regions. Ten geospatial variables representing land use, climate change, water use, water-balance components, streamflow alteration, fire risk, and ecosystem sensitivity were selected to rank candidate basins within each of the 18 hydrologic regions. The two highest ranking candidate basins in each of the 18 regions were identified as finalists for selection as "Integrated Water Science Basins"; final selection will consider input from a variety of stakeholders. The regional framework, with only one basin selected per region, ensures that as a group, the basins represent the range in major drivers of the hydrologic cycle. Ranking within each region, primarily based on anthropogenic stressors of water resources, ensures that settings representing important water-resource challenges for the nation will be studied.

Groundwater Model Simulations of Stakeholder-Identified Scenarios in a High-Conflict Irrigated Area.

This study investigated collaborative groundwater-flow modeling and scenario analysis in the Little Plover River basin, Wisconsin, USA where an unconfined aquifer supplies groundwater for agricultural irrigation, industrial processing, municipal water supply, and stream baseflow. We recruited stakeholders with diverse interests to identify, prioritize, and evaluate scenarios defined as management changes to the landscape. Using a groundwater flow model, we simulated the top 10 stakeholder-ranked scenarios under historically informed dry, average, and wet weather conditions and evaluated the ability of scenarios to meet government-defined stream flow performance measures. Results show that multiple changes to the landscape are necessary to maintain optimum stream flow, particularly during dry years. Yet, when landscape changes from three scenarios-transferring water from the local waste water treatment plant to basin headwaters, moving municipal wells further from the river and downstream, and converting 240 acre (97 ha) of irrigated land to unirrigated land-were simulated in combination, the probability of meeting or exceeding optimum flows rose to 75, 65, and 34% at upper, mid, and lower stream gages, respectively, in dry climate conditions. Discussions with stakeholders reveal that the collaborative model and scenario analysis process resulted in social learning that built upon the existing complex and dynamic institutional landscape. The approach provided a forum for solution-based discussions, and the model served as an important mediation tool for the development and evaluation of community-defined scenarios in a high conflict environment. Today, stakeholders continue to work collaboratively to overcome challenges and implement voluntary solutions in the basin.

A Simple Method for Simulating Groundwater Interactions with Fens to Forecast Development Effects.

Protection of fens-wetlands dependent on groundwater discharge-requires characterization of groundwater sources and stresses. Because instrumentation and numerical modeling of fens is labor intensive, easy-to-apply methods that model fen distribution and their vulnerability to development are desirable. Here we demonstrate that fen areas can be simulated using existing steady-state MODFLOW models when the unsaturated zone flow (UZF) package is included. In cells where the water table is near land surface, the UZF package calculates a head difference and scaled conductance at these "seepage drain" cells to generate average rates of vertical seepage to the land. This formulation, which represents an alternative to blanketing the MODFLOW domain with drains, requires very little input from the user because unsaturated flow-routing is inactive and results are primarily driven by easily obtained topographic information. Like the drain approach, it has the advantage that the distribution of seepage areas is not predetermined by the modeler, but rather emerges from simulated heads. Beyond the drain approach, it takes account of intracell land surface variation to explicitly quantify multiple surficial flows corresponding to infiltration, rejected recharge, recharge and land-surface seepage. Application of the method to a basin in southeastern Wisconsin demonstrates how it can be used as a decision-support tool to first, reproduce fen distribution and, second, forecast drawdown and reduced seepage at fens in response to shallow pumping.

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.

Wrangling distributed computing for high-throughput environmental science: An introduction to HTCondor.

Biologists and environmental scientists now routinely solve computational problems that were unimaginable a generation ago. Examples include processing geospatial data, analyzing -omics data, and running large-scale simulations. Conventional desktop computing cannot handle these tasks when they are large, and high-performance computing is not always available nor the most appropriate solution for all computationally intense problems. High-throughput computing (HTC) is one method for handling computationally intense research. In contrast to high-performance computing, which uses a single "supercomputer," HTC can distribute tasks over many computers (e.g., idle desktop computers, dedicated servers, or cloud-based resources). HTC facilities exist at many academic and government institutes and are relatively easy to create from commodity hardware. Additionally, consortia such as Open Science Grid facilitate HTC, and commercial entities sell cloud-based solutions for researchers who lack HTC at their institution. We provide an introduction to HTC for biologists and environmental scientists. Our examples from biology and the environmental sciences use HTCondor, an open source HTC system.

Capture Versus Capture Zones: Clarifying Terminology Related to Sources of Water to Wells.

The term capture, related to the source of water derived from wells, has been used in two distinct yet related contexts by the hydrologic community. The first is a water-budget context, in which capture refers to decreases in the rates of groundwater outflow and (or) increases in the rates of recharge along head-dependent boundaries of an aquifer in response to pumping. The second is a transport context, in which capture zone refers to the specific flowpaths that define the three-dimensional, volumetric portion of a groundwater flow field that discharges to a well. A closely related issue that has become associated with the source of water to wells is streamflow depletion, which refers to the reduction in streamflow caused by pumping, and is a type of capture. Rates of capture and streamflow depletion are calculated by use of water-budget analyses, most often with groundwater-flow models. Transport models, particularly particle-tracking methods, are used to determine capture zones to wells. In general, however, transport methods are not useful for quantifying actual or potential streamflow depletion or other types of capture along aquifer boundaries. To clarify the sometimes subtle differences among these terms, we describe the processes and relations among capture, capture zones, and streamflow depletion, and provide proposed terminology to distinguish among them.

Depletion Mapping and Constrained Optimization to Support Managing Groundwater Extraction.

Groundwater models often serve as management tools to evaluate competing water uses including ecosystems, irrigated agriculture, industry, municipal supply, and others. Depletion potential mapping-showing the model-calculated potential impacts that wells have on stream baseflow-can form the basis for multiple potential management approaches in an oversubscribed basin. Specific management approaches can include scenarios proposed by stakeholders, systematic changes in well pumping based on depletion potential, and formal constrained optimization, which can be used to quantify the tradeoff between water use and stream baseflow. Variables such as the maximum amount of reduction allowed in each well and various groupings of wells using, for example, K-means clustering considering spatial proximity and depletion potential are considered. These approaches provide a potential starting point and guidance for resource managers and stakeholders to make decisions about groundwater management in a basin, spreading responsibility in different ways. We illustrate these approaches in the Little Plover River basin in central Wisconsin, United States-home to a rich agricultural tradition, with farmland and urban areas both in close proximity to a groundwater-dependent trout stream. Groundwater withdrawals have reduced baseflow supplying the Little Plover River below a legally established minimum. The techniques in this work were developed in response to engaged stakeholders with various interests and goals for the basin. They sought to develop a collaborative management plan at a watershed scale that restores the flow rate in the river in a manner that incorporates principles of shared governance and results in effective and minimally disruptive changes in groundwater extraction practices.

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).