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Computing flow-field distortion coefficients from well-construction and formation properties

Direct measurements of groundwater velocity made with borehole flowmeters in screened wells must be compensated for the effects of flow-field distortion (also known as borehole acceleration). A theoretical equation developed by Drost et al. (1968) and simple inputs describing hydraulic properties of well construction and geologic formation were programmed into an Excel workbook to facilitate computation by groundwater-flowmeter users. Tables describing the physical and hydraulic properties for well constructions and gravel pack media are provided with an example to facilitate use of the workbook. Groundwater flowlines converge or diverge as they pass from a geologic formation, through a gravel pack and well screen. The extent of flowline convergence or divergence and the value of the flow-field distortion coefficient is related to the relative changes in hydraulic conductivity of the well screen, gravel pack, and geologic formation. Convergence or divergence is accompanied by acceleration or deceleration of groundwater. Direct measurements of groundwater velocity at the center of the monitoring well can be adjusted to provide a more accurate estimate of velocity in the formation by applying a correction for flow-field distortion. Variables required to compute the flow-field distortion coefficient include the hydraulic conductivity of the gravel pack, well screen, and the geologic formation surrounding the well screen; the borehole radius, and the inside radius and outside radius of the well screen.

Groundwater

Deep groundwater total dissolved solids mapping in the Dakota Group, Williston Basin, USA

Growing concern about the quantity of available freshwater around the world has led to interest in surveying groundwater total dissolved solids (TDS) below water well depths. Deep TDS has not been systematically mapped, and there is much to learn about the distribution and controls on deeper groundwater. In sedimentary basins across the United States, groundwater resources often overlie hydrocarbon resources, providing an opportunity to use borehole geophysical data collected for hydrocarbons to characterize groundwater and pore space resources. This study adapts a recently developed subsurface geostatistical and geophysical modeling approach to continuously map groundwater TDS, porosity, and temperature in the Dakota Group of the Williston Basin—an undercharacterized regional aquifer system overlying deeper hydrocarbon reservoirs. Groundwater TDS in the Dakota Group ranges from approximately 4800 to 26,900 mg/L. TDS patterns are stratified with higher TDS in the lower and upper Dakota Group, and relatively lower TDS in the middle Dakota Group. The lower TDS in the middle zone may represent a preferential regional flow path for lower-TDS meteoric recharge from the west. The alternating pattern of TDS may also be evidence of higher-TDS inflows into the Dakota Group from underlying and potentially from overlying aquifers. Porosity is lower near the center of the Williston Basin and tends to be higher to the east, which may be related to grain size distributions. The new regional TDS and porosity modeling serves as a quantitative reference for water users and provides supporting evidence for hypotheses on Dakota Group recharge.

Montana, North Dakota, South Dakota

Multi-objective optimization of a hydro-economic model in an over-allocated agricultural basin

Groundwater depletion for agricultural irrigation poses significant environmental and economic challenges. This study introduces a proof-of-concept that combines hydro-economic modeling, scenario-based modeling, and multi-objective optimization to manage pumping curtailment in an over-allocated basin in the western United States. Three optimization scenarios were evaluated, each offering different degrees of management flexibility. Results reveal that scenarios with finer spatial resolution achieved greater environmental benefits per unit profit loss. Additionally, strategies allowing fractional reductions in curtailed wells–rather than complete shutdowns based on water rights seniority–substantially improved efficiency, highlighting the value of increased decision-making flexibility. Although scenario testing can aid stakeholder engagement and strategy exploration, multi-objective optimization provides a systematic framework to quantify tradeoffs between competing objectives. This combined approach demonstrates promise for building consensus and supporting the design of sustainable water management strategies that balance agricultural livelihoods with ecosystem preservation.

Oregon

Teach me how to pycap: A high-capacity well decision support tool using analytical solutions in Python

Regulatory agencies in humid temperate environments rely on timely evaluations of streamflow depletion and drawdown to protect aquatic ecosystems and existing water users. Numerical models offer detailed insights, but their complexity and time demands often preclude their practical use in rapid decision-making. We present pycap-dss, an open-source Python package that implements a suite of analytical solutions for estimating streamflow depletion and drawdown. The tool supports superposition of multiple wells and time-varying pumping, enabling cumulative impact assessments in situations with multiple wells and streams. The software is modular and extensible, allowing users to interchange solutions or add new analytical methods. A YAML-based configuration supports batch processing of multiple wells, and an optional AnalysisProject class facilitates integration with regulatory workflows. Rigorous unit and regression testing ensures computational reliability, and continuous integration supports ongoing development. We demonstrate deterministic examples of drawdown where multiple solutions are readily compared and streamflow depletion with multiple wells in the Central Sands region of Wisconsin. We also show the value of Monte Carlo analyses of streamflow depletion in the same Central Sands example, leveraging computational efficiency to evaluate the uncertainty of individual and cumulative streamflow depletion calculations from over 200 high-capacity wells.

Wisconsin

Groundwater salinity: Applying the specific conductance and water type proxy

Groundwater is increasingly needed for water supplies but may have limited utility in some locations because of its salinity. Salinity, often expressed as total dissolved solid (TDS), is frequently estimated using specific conductance (SC) measurements. However, the commonly used proxy (0.65 multiplied by SC to indicate TDS, common in many handheld meters) can result in inaccurate TDS estimates. First, the TDS–SC relationship is not linear over the entire concentration range of groundwater. Furthermore, the TDS (and salinity)–SC relationships vary substantially depending on the major-ion composition. Here we develop a proxy method utilizing SC and major-ion water type to estimate TDS and salinity specifically for groundwaters. Compared to most surface waters, groundwater tends to have a wider range of salinity (fresh to highly saline) and higher concentrations of bedrock-derived solutes such as carbonate ions, silica, and many other ions. The dataset used to develop the proxies includes water chemistry data from 149,059 discrete groundwater samples. The groundwater proxies, which employ nonlinear log–log relations, utilize five water types (HCO 3 , Cl, Ca-Mg-SO 4 , Na-K-SO 4 , and mixed waters), are accurate (median percent difference between TDS and salinity determined using the proxy compared to discrete measurements was <±0.8%) over a wide range of SC (up to 200 mS/cm), rapid, cost-effective, and can be measured on-site.

Groundwater

A regional model comparison between MODPATH and MT3D of groundwater travel time distributions

Groundwater quality changes in wells and streams lag behind changes to land use due to groundwater travel times. Two contaminant transport methods were compared to assess differences in their simulated travel time distributions (TTDs) to streams and wells in the Wisconsin Central Sands. MODPATH simulates advective groundwater flow with particle tracking, while MT3D simulates age-mass using a finite difference solution without dispersion to allow for direct comparison of the two methods. MODPATH appropriately simulates groundwater TTDs from the water table to surface discharge but is subject to inaccuracies at weak-sink well cells due to the flow-model grid discretization and imprecise location of well discharge within well cells. MT3D better represents weak-sink well cells since it removes mass in proportion to the prescribed pumping rate, although travel time within well cells is neglected. Conversely, MT3D's treatment of surface water boundary cells is not as accurate as MODPATH because mass should be removed from the water table rather than the full cell volume. MT3D simulations of TTDs can also be confounded by the instantaneous vertical distribution of mass introduced throughout recharge cells instead of at the water table, which initiates mass along deeper flow paths. We evaluated 9 MODPATH and 13 MT3D implementations, generating differences in median travel times of up to 18 years. Both methods have strengths and weaknesses, with MT3D better representing weak-sink well cell behavior and MODPATH better representing surficial recharge and discharge. The effect of these characteristics on simulated TTDs, along with ideas for ameliorating method weaknesses, is discussed.

Wisconsin

PEST++IES how many iterations & realizations, finding the point of diminishing returns

PEST++IES (White 2018; White et al. 2020) is widely used in the groundwater modeling community for its ability to perform computationally efficient history matching and uncertainty analysis in a highly parameterized context. One primary advantage of using an iterative ensemble smoother is that the number of model runs required per iteration depends on the number of realizations in an ensemble, not the number of parameters in each realization. However, this raises the question: what is the optimal number of realizations and iterations to use for any one model before the point of diminishing returns? Using a modified version of the Freyberg model (Freyberg 1988; Hunt et al. 2020), different parameter and observation scenarios were evaluated for four iterations and ensembles of 10, 25, 50, 100, 250, 500, 1000, and 2000 realizations. To match observations, PEST++IES altered hydraulic conductivity ( k ), both globally across the model and locally at three different pilot point densities, as well as global recharge (via a single multiplier), global river conductance, and individual well flow rates. Risk-based well capture zone results (Fienen et al. 2022a) and estimated hydraulic conductivity fields from each scenario were quantitatively and qualitatively compared against the “truth” model and its outputs. Across the cases examined, ensemble sizes of 100 to 250 realizations and two PEST++IES iterations were generally sufficient to achieve good results.

Groundwater

ARCHI: A new R package for automated imputation of regionally correlated hydrologic records

Missing data in hydrological records can limit resource assessment, process understanding, and predictive modeling. Here, we present ARCHI (Automated Regional Correlation Analysis for Hydrologic Record Imputation), a new, open-source software package in R designed to aggregate, impute, cluster, and visualize regionally correlated hydrologic records. ARCHI imputes missing data in “target” records by linear regression using more complete “reference” records as predictors. Automated imputation is implemented using a novel, iterative algorithm that allows each site to be considered a target or reference for regression, growing the pool of complete references with each imputed record until viable gap-filling ceases. Users can limit artifacts from spurious correlations by specifying model-acceptance criteria and applying geospatial, correlation, and group-based filters to control reference selection. ARCHI provides additional functions for visualizing results, clustering records with similar correlation structures, evaluating holdout data, and interactive parameterization with an accessible and intuitive graphical user interface (GUI). This methods brief provides an overview of the ARCHI package, modeling guidelines, and benchmarking on two regional groundwater-level datasets from the Central Valley, CA and Long Island, NY. We evaluate ARCHI alongside widely used multivariate imputation software to highlight and contextualize its computational efficiency, imputation accuracy, and model transparency when applied to large, groundwater-level datasets.

California, New York

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

Accurate simulation of flow through dipping aquifers with MODFLOW 6 using enhanced cell connectivity

In simulations of groundwater flow through dipping aquifers, layers of model cells are often “deformed” to follow the top and bottom elevations of the aquifers. When this approach is used in MODFLOW, adjacent cells within the same model layer are vertically offset from one another, and the standard conductance-based (two-point) formulation for flow between cells does not rigorously account for these offsets. The XT3D multi-point flow formulation in MODFLOW 6 is designed to account for geometric irregularities in the grid, including vertical offsets, and to provide accurate results for both isotropic and anisotropic groundwater flow. A recent study evaluated the performance of the standard formulation and XT3D using a simple, synthetic benchmark model of a steeply dipping aquifer. Although XT3D generally improved the accuracy of flow simulations relative to the standard formulation as expected, neither formulation produced accurate flows in cases that involved large vertical offsets. In this paper, we explain that the inability of XT3D to produce accurate flows in the steeply dipping aquifer benchmark was not due to an inherent limitation of the flow formulation, but rather to the limited cell connectivity inherent in the most commonly used discretization packages in MODFLOW 6. Furthermore, we demonstrate that XT3D is able to produce the expected accuracy when adequate cell connectivity is introduced using MODFLOW's unstructured grid type and the aquifer is discretized vertically using at least two model layers.

Groundwater

Utility of an instantaneous salt dilution method for measuring streamflow in headwater streams

Streamflow records are biased toward large streams and rivers, yet small headwater streams are often the focus of ecological research in response to climate change. Conventional flow measurement instruments such as acoustic Doppler velocimeters (ADVs) do not perform well during low-flow conditions in small streams, truncating the development of rating curves during critical baseflow conditions dominated by groundwater inflow. We revisited an instantaneous solute tracer injection method as an alternative to ADVs based on paired measurements to compare their precision, efficiency, and feasibility within headwater streams across a range of flow conditions. We show that the precision of discharge measurements using salt dilution by slug injection and ADV methods were comparable overall, but salt dilution was more precise during the lowest flows and required less time to implement. Often, headwater streams were at or below the depth threshold where ADV measurements could even be attempted and transects were complicated by coarse bed material and cobbles. We discuss the methodological benefits and limitations of salt dilution by slug injection and conclude that the method could facilitate a proliferation of streamflow observation across headwater stream networks that are highly undersampled compared to larger streams.

Virginia

Evaluation of models for estimating hydraulic conductivity in glacial aquifers from NMR logging

Nuclear magnetic resonance (NMR) logging is a promising method for estimating hydraulic conductivity ( K ). During the past ∼60 years, NMR logging has been used for petroleum applications, and different models have been developed for deriving estimates of permeability. These models involve calibration parameters whose values were determined through decades of research on sandstones and carbonates. We assessed the use of five models to derive estimates of K in glacial aquifers from NMR logging data acquired in two wells at each of two field sites in central Wisconsin, USA. Measurements of K , obtained with a direct push permeameter (DPP), K DPP , were used to obtain the calibration parameters in the Schlumberger-Doll Research, Seevers, Timur-Coates, Kozeny-Godefroy, and sum-of-echoes (SOE) models so as to predict K from the NMR data; and were also used to assess the ability of the models to predict K DPP . We obtained four well-scale calibration parameter values for each model using the NMR and DPP measurements in each well; and one study-scale parameter value for each model by using all data. The SOE model achieved an agreement with K DPP that matched or exceeded that of the other models. The Timur-Coates estimates of K were found to be substantially different from K DPP . Although the well-scale parameter values for the Schlumberger-Doll, Seevers, and SOE models were found to vary by less than a factor of 2, more research is needed to confirm their general applicability so that site-specific calibration is not required to obtain accurate estimates of K from NMR logging data.

Wisconsin