Multimodel Validity Assessment of Groundwater Flow Simulation Models Using Area Metric Approach

We demonstrate the application of the Area Metric developed by Ferson et al. (2008) for multimodel validity assessment. The Area Metric quantified the degree of models' replicative validity: the degree of agreement between the observed data and the corresponding simulated outputs represented as their empirical cumulative distribution functions (ECDFs). This approach was used to rank multiple representations of a case study groundwater flow model of a landfill by their Area Metric scores. A multimodel approach allows to account for uncertainties that may either be epistemic (from lack of knowledge) or aleatory (from variability inherent in the system). The Area Metric approach enables explicit incorporation of model uncertainties, epistemic as well as aleatory, into validation assessment. The proposed approach informs understanding of the collected data and that of the model domain. It avoids model overfitting to a particular system state, and in fact is a blind assessment of the models' validity: models are not adjusted, or updated, to achieve a better numerical fit. This approach assesses the degree of models' validity, in place of the typical binary model validation/invalidation process. Collectively, this increases confidence in the model's representativeness that, in turn, reduces risk to model users.     

Custom Map Projections for Regional Groundwater Models

For regional groundwater flow models (areas greater than 100,000 km²), improper choice of map projection parameters can result in model error for boundary conditions dependent on area (recharge or evapotranspiration simulated by application of a rate using cell area from model discretization) and length (rivers simulated with head‐dependent flux boundary). Smaller model areas can use local map coordinates, such as State Plane (United States) or Universal Transverse Mercator (correct zone) without introducing large errors. Map projections vary in order to preserve one or more of the following properties: area, shape, distance (length), or direction. Numerous map projections are developed for different purposes as all four properties cannot be preserved simultaneously. Preservation of area and length are most critical for groundwater models. The Albers equal‐area conic projection with custom standard parallels, selected by dividing the length north to south by 6 and selecting standard parallels 1/6th above or below the southern and northern extent, preserves both area and length for continental areas in mid latitudes oriented east‐west. Custom map projection parameters can also minimize area and length error in non‐ideal projections. Additionally, one must also use consistent vertical and horizontal datums for all geographic data. The generalized polygon for the Floridan aquifer system study area (306,247.59 km²) is used to provide quantitative examples of the effect of map projections on length and area with different projections and parameter choices. Use of improper map projection is one model construction problem easily avoided.     

Including Vertical Fault Structures in Layered Groundwater Flow Models

Accurate representation of groundwater flow and solute transport requires a sound representation of the underlying geometry of aquifers. Faults can have a significant influence on the structure and connectivity of aquifers, which may allow permeable units to connect, and aquifers to seal when juxtaposed against lower permeability units. Robust representation of groundwater flow around faults remains challenging despite the significance of faults for flow and transport. We present a methodology for the inclusion of faults utilizing the unstructured grid features of MODFLOW-USG and MODFLOW 6. The method focuses on the representation of fault geometries using non-neighbor connections between juxtaposed layers. We present an illustration of the method for a synthetic fluvial aquifer. The combined impact of the heterogeneous aquifer and fault offset is clearly visible where channel features at different depths in the aquifer were connected at the fault. These results highlight the importance of representing fault features in groundwater flow models.     

Simulation of Groundwater Level in Ephemeral Streams with an Improved Groundwater Hydraulics Model

As a component of arid ecosystems, groundwater plays an important role in plant growth; therefore, it is essential to use deterministic models to reconstruct the process of groundwater level change. Typically, the linearized solution of the one-dimensional (1-D) Boussinesq equation yields acceptable performance in simulating transient conditions over short recharge periods in ephemeral stream systems, but the ability of this solution to simulate multiyear changes in groundwater levels is limited. In this study, an improved groundwater hydraulics (GH-D2) model is built based on the groundwater hydraulics (GH) solution of the 1-D Boussinesq equation to simulate multiyear changes in the groundwater level in ephemeral stream systems. The model is validated in the lower reaches of the Tarim River to simulate groundwater level fluctuations within the scope of influence of the river (300, 500, 750, 1050 m) over a 16-year period (2000 to 2015). To evaluate the performance of the models, the bias, mean absolute error, root mean squared error, Nash-Sutcliffe efficiency (NSE), and coefficient of determination (R²) are calculated. The results show that the improved GH-D2 model, which considers ephemeral streamflow, unsteady flow theory and the delayed response effect of groundwater level changes, performs well in simulating multiyear changes in the groundwater level in the ephemeral stream system. The observed and simulated values of the groundwater level at different river distances are consistent, and the model provides a new basis for multiyear simulations of groundwater level fluctuations in ephemeral stream systems.     

Next Generation Computers Warrant Next Generation Groundwater Models

Modern hydrologic models have extraordinary capabilities for representing complex process in surface-subsurface systems. These capabilities have revolutionized the way we conceptualize flow systems, but how to represent uncertainty in simulated flow systems is not as well developed. Currently, characterizing model uncertainty can be computationally expensive, in part, because the techniques are appended to the numerical methods rather than seamlessly integrated. The next generation of computers, however, presents opportunities to reformulate the modeling problem so that the uncertainty components are handled more directly within the flow system simulation. Misconceptions about quantum computing abound and they will not be a “silver bullet” for solving all complex problems, but they might be leveraged for certain kinds of highly uncertain problems, such as groundwater (GW). The point of this issue paper is that the GW community could try to revise the foundations of our models so that the governing equations being solved are tailored specifically for quantum computers. The goal moving forward should not just be to accelerate the models we have, but also to address their deficiencies. Embedding uncertainty into the models by evolving distribution functions will make predictive GW modeling more complicated, but doing so places the problem into a complexity class that is highly efficient on quantum computing hardware. Next generation GW models could put uncertainty into the problem at the very beginning of a simulation and leave it there throughout, providing a completely new way of simulating subsurface flows.     

Representing the Sensitivity of Convective Cloud Systems to Tropospheric Humidity in General Circulation Models

Convective cloud variability on many times scales can be viewed as having three major components: a suppressed phase of shallow and congestus clouds, a disturbed phase of deep convective clouds, and a mature phase of transition to stratiform upper-level clouds. Cumulus parameterization development has focused primarily on the second phase until recently. Consequently, many parameterizations are not sufficiently sensitive to variations in tropospheric humidity. This shortcoming may affect global climate model simulations of climate sensitivity to external forcings, the continental diurnal cycle of clouds and precipitation, and intraseasonal precipitation variability. The lack of sensitivity can be traced in part to underestimated entrainment of environmental air into rising convective clouds and insufficient evaporation of rain into the environment. As a result, the parameterizations produce deep convection too easily while stabilizing the environment too quickly to allow the effects of convective mesoscale organization to occur. Recent versions of some models have increased their sensitivity to tropospheric humidity and improved some aspects of their variability, but a parameterization of mesoscale organization is still absent from most models. Evidence about the effect of these uncertainties on climate change projections suggests that climate modelers should make improved simulation of high and convective clouds as high a priority as better representations of low clouds.     

Representing Grounding Line Dynamics in Numerical Ice Sheet Models: Recent Advances and Outlook

Recent satellite observations of the Antarctic and Greenland ice sheets show accelerated ice flow and associated ice sheet thinning along coastal outlet glaciers in contact with the ocean. Both processes are the result of grounding line retreat due to melting at the grounding line (the grounding line is the contact of the ice sheet with the ocean, where it starts to float and forms an ice shelf or ice tongue). Such rapid ice loss is not yet included in large-scale ice sheet models used for IPCC projections, as most of the complex processes are poorly understood. Here we report on the state-of-the art of grounding line migration in marine ice sheets and address different ways in which grounding line migration can be attributed and represented in ice sheet models. Using one-dimensional ice flow models of the ice sheet/ice shelf system we carried out a number of sensitivity experiments with different spatial resolutions and stress approximations. These are verified with semi-analytical steady state solutions. Results show that, in large-scale finite-difference models, grounding line migration is dependent on the numerical treatment (e.g. staggered/non-staggered grid) and the level of physics involved (e.g. shallow-ice/shallow-shelf approximation).     

Parameter Estimation for Groundwater Models under Uncertain Irrigation Data

The success of modeling groundwater is strongly influenced by the accuracy of the model parameters that are used to characterize the subsurface system. However, the presence of uncertainty and possibly bias in groundwater model source/sink terms may lead to biased estimates of model parameters and model predictions when the standard regression‐based inverse modeling techniques are used. This study first quantifies the levels of bias in groundwater model parameters and predictions due to the presence of errors in irrigation data. Then, a new inverse modeling technique called input uncertainty weighted least‐squares (IUWLS) is presented for unbiased estimation of the parameters when pumping and other source/sink data are uncertain. The approach uses the concept of generalized least‐squares method with the weight of the objective function depending on the level of pumping uncertainty and iteratively adjusted during the parameter optimization process. We have conducted both analytical and numerical experiments, using irrigation pumping data from the Republican River Basin in Nebraska, to evaluate the performance of ordinary least‐squares (OLS) and IUWLS calibration methods under different levels of uncertainty of irrigation data and calibration conditions. The result from the OLS method shows the presence of statistically significant (p < 0.05) bias in estimated parameters and model predictions that persist despite calibrating the models to different calibration data and sample sizes. However, by directly accounting for the irrigation pumping uncertainties during the calibration procedures, the proposed IUWLS is able to minimize the bias effectively without adding significant computational burden to the calibration processes.     

On Integrating Groundwater Transport Models with Wireless Sensor Networks

The emerging technology of wireless sensor networks (WSNs) is an integrated, distributed, wireless network of sensing devices. It has the potential to monitor dynamic hydrological and environmental processes more effectively than traditional monitoring and data acquisition techniques by providing environmental information at greater spatial and temporal resolutions. Furthermore, due to continuing high-performance computing development, these data may be introduced into increasingly robust and complex numerical models; for instance, the parameters of subsurface transport simulators may be automatically updated. Early field deployments and laboratory experiments conducted using in situ sensor technology and WSNs indicated significant fundamental issues concerning sensor and network hardware reliability—suggesting that investigations should first be conducted in controlled environments before field deployment. A first step in this validation process involves evaluating the predictive capability of a computational advection-dispersion transport model when incorporating concentration data from a WSN simulation. Data quality is a major concern, especially when sensor readings are automatically fed into data assimilation procedures. The appropriate employment of an independent WSN fault detection service can ensure that erroneous data (e.g., missing or anomalous values) do not mislead the model. Parameter estimation regularization techniques may then deal with remaining data noise. The primary purpose of this study is to determine the suitability of WSNs (and other in situ data delivery technologies) for use in contaminant transport modeling applications by conducting research in a realistic simulative environment.     

A Correction on Coastal Heads for Groundwater Flow Models

We introduce a simple correction to coastal heads for constant‐density groundwater flow models that contain a coastal boundary, based on previous analytical solutions for interface flow. The results demonstrate that accurate discharge to the sea in confined aquifers can be obtained by direct application of Darcy's law (for constant‐density flow) if the coastal heads are corrected to ((α + 1)/α)h_s ? B/2α, in which h_s is the mean sea level above the aquifer base, B is the aquifer thickness, and α is the density factor. For unconfined aquifers, the coastal head should be assigned the value . The accuracy of using these corrections is demonstrated by consistency between constant‐density Darcy's solution and variable‐density flow numerical simulations. The errors introduced by adopting two previous approaches (i.e., no correction and using the equivalent fresh water head at the middle position of the aquifer to represent the hydraulic head at the coastal boundary) are evaluated. Sensitivity analysis shows that errors in discharge to the sea could be larger than 100% for typical coastal aquifer parameter ranges. The location of observation wells relative to the toe is a key factor controlling the estimation error, as it determines the relative aquifer length of constant‐density flow relative to variable‐density flow. The coastal head correction method introduced in this study facilitates the rapid and accurate estimation of the fresh water flux from a given hydraulic head measurement and allows for an improved representation of the coastal boundary condition in regional constant‐density groundwater flow models.     

Direct Conservative Domain in the Continuous Galerkin Method for Groundwater Models

The continuous Galerkin finite element method is commonly considered locally nonconservative because a single element with fluxes computed directly from its potential distribution is unable to conserve its mass and fluxes across edges that are discontinuous. Some literature sources have demonstrated that the continuous Galerkin method can be locally conservative with postprocessed fluxes. This paper proposes the concept of a direct conservative domain (DCD), which could conserve mass when fluxes are computed directly from the potential distribution. Also presented here is a method for modifying the advection fluxes to obtain different conservative domains from the DCDs. Furthermore, DCDs are used to analyze the local conservation of several postprocessing algorithms, for which DCDs provide the theoretical basis. The local conservation of DCDs and the proposed method are illustrated and verified by using a hypothetical 2‐D model.     

Re-Purposing Groundwater Flow Models for Age Assessments: Important Characteristics

Groundwater flow model construction is often time-consuming and costly, with development ideally focused on a specific purpose, such as quantifying well capture from water bodies or providing flow fields for simulating advective transport. As environmental challenges evolve, the incentive to re-purpose existing groundwater flow models may increase. However, few studies have evaluated which characteristics of groundwater flow models deserve greatest consideration when re-purposing models for groundwater age and advective transport simulations. In this paper, we compare simulated age metrics produced by three MODFLOW-MODPATH models of the same area but with differing levels of complexity (layering and heterogeneity). Comparisons are made at three watershed scales (HUC 8 to HUC 12). Groundwater age metrics, specifically the young fraction and median age of the young and old fractions, are used for evaluation because they relate to intrinsic susceptibility of aquifers and are simpler to interpret than full age distributions used for advective transport. Results indicate that: (1) the young fraction is less sensitive to model layering than the median age of young and old fractions, suggesting that simple models may suffice for basic intrinsic susceptibility assessments; (2) water table mounding and associated discharge into partially penetrating boundaries, such as head-water streams, is important for simulating both the young fraction and the median age of the young fraction; and (3) the influence of partially penetrating head-water streams is maintained regardless of the porosity distribution. Results of this work should aid modelers with evaluating the appropriateness of re-purposing existing groundwater flow models for age simulations.     

A Simple Relation to Constrain Groundwater Models Using Surface Deformation

A simple relation between pore pressure change and one-dimensional surface deformation is presented. The relation is for pore pressure change in a confined aquifer that causes surface deformation. It can be applied to groundwater models of any discretization and is computationally efficient. The estimated surface deformation from model results can be compared to observed surface deformation through geodetic techniques such as Differential Interferometric Synthetic Aperture Radar. Model parameters then are constrained using the observed surface deformation. The validity of this relation is shown through constraint of model parameters for surface uplift due to pore pressure increase caused by wastewater disposal injection.     

Forecasting Groundwater Temperature with Linear Regression Models Using Historical Data

Although temperature is an important determinant of many biogeochemical processes in groundwater, very few studies have attempted to forecast the response of groundwater temperature to future climate warming. Using a composite linear regression model based on the lagged relationship between historical groundwater and regional air temperature data, empirical forecasts were made of groundwater temperature in several aquifers in Switzerland up to the end of the current century. The model was fed with regional air temperature projections calculated for greenhouse‐gas emissions scenarios A2, A1B, and RCP3PD. Model evaluation revealed that the approach taken is adequate only when the data used to calibrate the models are sufficiently long and contain sufficient variability. These conditions were satisfied for three aquifers, all fed by riverbank infiltration. The forecasts suggest that with respect to the reference period 1980 to 2009, groundwater temperature in these aquifers will most likely increase by 1.1 to 3.8 K by the end of the current century, depending on the greenhouse‐gas emissions scenario employed.     

On Solving Groundwater Flow and Transport Models with Algebraic Multigrid Preconditioning

Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual delineation approach. This involves a single groundwater flow linear solution and a pure advective transport solution with different right-hand sides. The new solver was compared with other preconditioned iterative methods, the MODFLOW's GMG solver, and direct sparse solvers. Test problems include two- and three-dimensional benchmarks spanning homogeneous and highly heterogeneous and anisotropic formations. For the groundwater flow problems, using the algebraic multigrid preconditioning speeds up the numerical solution by one to two orders of magnitude. The algebraic multigrid preconditioner efficiency was preserved for the three dimensional heterogeneous and anisotropic problem unlike for the MODFLOW's GMG solver. Contrarily, a sparse direct solver was the most efficient for the pure advective transport processes such as the forward travel time simulations. Hence, the best sparse solver for the more general advection-dispersion transport equation is likely to be Péclet number dependent. When equipped with the best solvers, processing multimillion grid blocks by the dual delineation approach is a matter of seconds. This paves the way for its routine application to large geological models. The paper gives practical hints on the strategies and conditions under which algebraic multigrid preconditioning would remain competitive for the class of nonlinear and/or transient problems.     

Evaluation of Hydraulic Conductivity Estimates from Various Approaches with Groundwater Flow Models

Significant efforts have been expended for improved characterization of hydraulic conductivity (K) and specific storage (S_s) to better understand groundwater flow and contaminant transport processes. Conventional methods including grain size analyses (GSA), permeameter, slug, and pumping tests have been utilized extensively, while Direct Push-based Hydraulic Profiling Tool (HPT) surveys have been developed to obtain high-resolution K estimates. Moreover, inverse modeling approaches based on geology-based zonations, and highly parameterized Hydraulic Tomography (HT) have also been advanced to map spatial variations of K and S_s between and beyond boreholes. While different methods are available, it is unclear which one yields K estimates that are most useful for high resolution predictions of groundwater flow. Therefore, the main objective of this study is to evaluate various K estimates at a highly heterogeneous field site obtained with three categories of characterization techniques including: (1) conventional methods (GSA, permeameter, and slug tests); (2) HPT surveys; and (3) inverse modeling based on geology-based zonations and highly parameterized approaches. The performance of each approach is first qualitatively analyzed by comparing K estimates to site geology. Then, steady-state and transient groundwater flow models are employed to quantitatively assess various K estimates by simulating pumping tests not used for parameter estimation. Results reveal that inverse modeling approaches yield the best drawdown predictions under both steady and transient conditions. In contrast, conventional methods and HPT surveys yield biased predictions. Based on our research, it appears that inverse modeling and data fusion are necessary steps in predicting accurate groundwater flow behavior.     

Evaluating Groundwater Interbasin Flow Using Multiple Models and Multiple Types of Data

The groundwater interbasin flow, Q_y, from the north of Yucca Flat into Yucca Flat simulated using the Death Valley Regional Flow System (DVRFS) model greatly exceeds assessments obtained using other approaches. This study aimed to understand the reasons for the overestimation and to examine whether the Q_y estimate can be reduced. The two problems were tackled from the angle of model uncertainty by considering six models revised from the DVRFS model with different recharge components and hydrogeological frameworks. The two problems were also tackled from the angle of parametric uncertainty for each model by first conducting Morris sensitivity analysis to identify important parameters and then conducting Monte Carlo simulations for the important parameters. The uncertainty analysis is general and suitable for tackling similar problems; the Morris sensitivity analysis has been utilized to date in only a limited number of regional groundwater modeling. The simulated Q_y values were evaluated by using three kinds of calibration data (i.e., hydraulic head observations, discharge estimates, and constant‐head boundary flow estimates). The evaluation results indicate that, within the current DVRFS modeling framework, the Q_y estimate can only be reduced to about half of the original estimate without severely deteriorating the goodness‐of‐fit to the calibration data. The evaluation results also indicate that it is necessary to develop a new hydrogeological framework to produce new flow patterns in the DVRFS model. The issues of hydrogeology and boundary flow are being addressed in a new version of the DVRFS model planned for release by the U.S. Geological Survey.     

Use of Machine Learning Methods to Reduce Predictive Error of Groundwater Models

Quantitative analyses of groundwater flow and transport typically rely on a physically‐based model, which is inherently subject to error. Errors in model structure, parameter and data lead to both random and systematic error even in the output of a calibrated model. We develop complementary data‐driven models (DDMs) to reduce the predictive error of physically‐based groundwater models. Two machine learning techniques, the instance‐based weighting and support vector regression, are used to build the DDMs. This approach is illustrated using two real‐world case studies of the Republican River Compact Administration model and the Spokane Valley‐Rathdrum Prairie model. The two groundwater models have different hydrogeologic settings, parameterization, and calibration methods. In the first case study, cluster analysis is introduced for data preprocessing to make the DDMs more robust and computationally efficient. The DDMs reduce the root‐mean‐square error (RMSE) of the temporal, spatial, and spatiotemporal prediction of piezometric head of the groundwater model by 82%, 60%, and 48%, respectively. In the second case study, the DDMs reduce the RMSE of the temporal prediction of piezometric head of the groundwater model by 77%. It is further demonstrated that the effectiveness of the DDMs depends on the existence and extent of the structure in the error of the physically‐based model.     

Diffusion in Landscape Development Models: On The Nature of Basic Transport Relations

In constructing large-scale landscape development models, processes must be appropriately represented. The diffusion equation is rewritten with separate coefficients for slow, continuous mass movements and rapid, episodic mass movements. Using available transport data, transport/gradient relations are assessed and estimates of diffusivities are given. Diffusivities estimated in this study are compared with values derived in scarp studies and values adopted in landscape development models. The relation between transport and gradient may be non-linear, which would require modification of the simple diffusion equation normally accepted in modelling. New approaches are required to place these essential relations on a firmer foundation. © 1997 by John Wiley & Sons, Ltd.