Groundwater modelling reports fail to comply with guideline recommendations for model reproducibility.

Computer models are routinely used to underpin critical decision-making for projects that impact groundwater systems. Modelling results are communicated through technical reports, which advise regulators and other stakeholders of groundwater impacts, thereby informing approvals, project restrictions and monitoring requirements. Several guidelines and texts are available to instruct groundwater model development and reporting. In seven of the eight guidelines/texts reviewed, it is recommended that modelling reports (or a model archive) contain sufficient information for an external party to rebuild the model. This study examined that expectation (assumed to be "best practice") by reviewing 25 groundwater modelling reports from eight countries and assessing whether the information contained therein was sufficient (or an archive was provided) to rebuild the model on which the report was based. The reports were characterised based on 18 model components (e.g., aquifer properties, boundary conditions, etc.), and the availability of sufficient information in the report to rebuild each one. The "rebuildability" of model components was classified as: (a) reproducible (from the report), (b) reproducible but assumptions needed, and (c) not reproducible. The Analytical Hierarchical Process was employed to rank the reports based on the reproducibility of the models they describe. Only one of the 25 reports provided adequate information to rebuild the model, while one other report was accompanied by a model archive, resulting in two cases of model reproducibility, contrary to guideline recommendations. This outcome reflects problems with reproducibility in the wider scientific community. We conclude that modelling reports need to provide more detailed information to be compliant with best practice or model archives ought to be made available. Addressing this issue will ensure that stakeholders have access to the information needed to properly assess whether future groundwater impacts have been reliably evaluated.

Effects of porous media thickness and its hydraulic gradient history on the formation of sand boils: Experimental investigation.

Sand boils occur where groundwater discharges to the land surface under sufficient hydraulic gradient to cause internal erosion and the upward transport of particles. A proper understanding of sand boil processes is essential in evaluating a wide range of geomechanical and sediment transport situations under which groundwater seepage occurs, such as the effects of groundwater discharge on beach stability. Although various empirical methods have been developed to estimate the critical hydraulic gradient (icr) leading to sand liquefaction, a prerequisite for sand boil occurrence, the effect of sand layer thickness and the implications of driving head fluctuations on the formation and reformation of sand boils have not been explored previously. This paper uses laboratory experiments to study sand boil formation and reformation for various sand thicknesses and hydraulic gradients to fill this knowledge gap. Sand layer thicknesses of 90 mm, 180 mm and 360 mm were adopted in evaluating sand boil reactivation, which was created by imposing hydraulic head fluctuations. While the first experiment (i.e., 90 mm sand layer) yielded a value for icr smaller (by 5%) than Terzaghi's (1922) value, the same theory underestimated icr by 12% and 4% for 180 mm and 360 mm sand layers, respectively. Moreover, icr needed for the reformation of sand boils decreased by 22%, 22% and 26% (relative to icr applicable to the initial sand boil) for the 90 mm, 180 mm and 360 mm sand layer thicknesses, respectively. We conclude that the formation of sand boils requires consideration of sand depth and the history of sand boil formation, particularly in relation to sand boils that form (and potentially reform) under oscillating pressures (e.g., tidal beaches).

Sediment mobilisation and release through groundwater discharge to the land surface: Review and theoretical development.

The discharge of groundwater to the land surface and to lakes and streams may express subsurface particles. This may lead to preferential pathways and increased fluxes of groundwater, sediment and contaminants, and modified subsurface structures. The current review attempts to describe and categorise the various forms through which sediment may be liberated in areas of groundwater discharge. Forces acting on subsurface particles in areas of groundwater discharge include seepage (drag), buoyancy and particle weight, amongst other, more complex forces. Equations for these can be combined to create formulae for approximating the conditions under which groundwater discharge will transport particles to the surface. Two forms of subsurface sediment transport are considered: (1) flow through an immobile granular matrix (suffusion and suffosion), and (2) flow through preferential pathways (i.e., often treated as pipes). Suffusion involves sediment movement that does not impact the soil's stability, whereas suffosion creates changes to soil stability and, consequently, soil volume. Preferential flow may arise from cracks in cohesive materials or through localised fluidization of non-cohesive soils, leading in some situations to sand boils. Guidance is presented on the minimum theoretical hydraulic gradient required for grains of various sizes to start to rise. New simple formulae are developed that build on existing theory, and these are compared to previous laboratory data, showing that suffusion is more or less predictable using the new simple method. However, experimental sand boils require larger hydraulic gradients compared to theory. The current analysis summarises the state of knowledge and persistent knowledge gaps associated with sediment ejection through groundwater discharge, which we expect has wide-ranging applications in terms of sediment transport in coastal regions and to surface water bodies, and where strong groundwater discharge is known to occur.

Modelling size constraints on carbonate platform formation in groundwater upwelling zones.

Carbonate depositional systems related to groundwater upwelling are ubiquitous around the world and form ecologically and culturally important features of many landscapes. Spring carbonate deposits record past climatic and hydrological conditions. The reconstruction of past processes using spring carbonate proxies requires fundamental understanding of the factors that control their geometry. In this work, we show that the spatial extent of spring carbonate platforms is amenable to quantitative prediction by simulating the early growth stage of their formation for the iconic mound springs in the central Australian outback. We exploit their well-defined, circular geometry to demonstrate the existence of two size-limiting regimes: one controlled by the spring flow rate and the other by the concentration of lattice ions. Deviations between modelled and observed size metrics are attributable to diminishing spring flow rates since formation, enabling assessment of the relative vulnerability of springs to further hydrological change.

Transient Recharge Estimability Through Field-Scale Groundwater Model Calibration.

The estimation of recharge through groundwater model calibration is hampered by the nonuniqueness of recharge and aquifer parameter values. It has been shown recently that the estimability of spatially distributed recharge through calibration of steady-state models for practical situations (i.e., real-world, field-scale aquifer settings) is limited by the need for excessive amounts of hydraulic-parameter and groundwater-level data. However, the extent to which temporal recharge variability can be informed through transient model calibration, which involves larger water-level datasets, but requires the additional consideration of storage parameters, is presently unknown for practical situations. In this study, time-varying recharge estimates, inferred through calibration of a field-scale highly parameterized groundwater model, are systematically investigated subject to changes in (1) the degree to which hydraulic parameters including hydraulic conductivity (K) and specific yield (Sy ) are constrained, (2) the number of water-level calibration targets, and (3) the temporal resolution (up to monthly time steps) at which recharge is estimated. The analysis involves the use of a synthetic reality (a reference model) based on a groundwater model of Uley South Basin, South Australia. Identifiability statistics are used to evaluate the ability of recharge and hydraulic parameters to be estimated uniquely. Results show that reasonable estimates of monthly recharge (<30% recharge root-mean-squared error) require a considerable amount of transient water-level data, and that the spatial distribution of K is known. Joint estimation of recharge, Sy and K, however, precludes reasonable inference of recharge and hydraulic parameter values. We conclude that the estimation of temporal recharge variability through calibration may be impractical for real-world settings.

A Spatially Periodic Solute Boundary for MT3DMS and PHT3D.

The assumption of spatial repetition is commonly made when producing bedform scale models of the hyporheic zone. Two popular solute transport codes, MT3DMS and PHT3D, do not currently provide the necessary boundary condition required to simulate spatial periodicity in hyporheic zone transport problems. In this study, we develop a spatially periodic boundary (SPB) for solutes that is compatible with a SPB that was previously developed for MODFLOW to simulate the flow component of spatially periodic problems. The approach is ideal for simulating groundwater flow and transport patterns under repeating surface features, such as ripples or dunes on the bottom of a lake or stream. The appropriate block-centered finite-difference approach to implement the boundary is presented and the necessary source code modifications are discussed. The performance of the solute SPB, operating in conjunction with the groundwater flow SPB, is explored through comparison of a multi-bedform hyporheic-zone model with a single bedform variant. The new boundary conditions perform well in situations where both dispersive effects and lateral seepage flux in the underflow regime beneath the hyporheic zone are minimal.

Is Decoupling GDP Growth from Environmental Impact Possible?

The argument that human society can decouple economic growth-defined as growth in Gross Domestic Product (GDP)-from growth in environmental impacts is appealing. If such decoupling is possible, it means that GDP growth is a sustainable societal goal. Here we show that the decoupling concept can be interpreted using an easily understood model of economic growth and environmental impact. The simple model is compared to historical data and modelled projections to demonstrate that growth in GDP ultimately cannot be decoupled from growth in material and energy use. It is therefore misleading to develop growth-oriented policy around the expectation that decoupling is possible. We also note that GDP is increasingly seen as a poor proxy for societal wellbeing. GDP growth is therefore a questionable societal goal. Society can sustainably improve wellbeing, including the wellbeing of its natural assets, but only by discarding GDP growth as the goal in favor of more comprehensive measures of societal wellbeing.

Application of an Analytical Solution as a Screening Tool for Sea Water Intrusion.

Sea water intrusion into aquifers is problematic in many coastal areas. The physics and chemistry of this issue are complex, and sea water intrusion remains challenging to quantify. Simple assessment tools like analytical models offer advantages of rapid application, but their applicability to field situations is unclear. This study examines the reliability of a popular sharp-interface analytical approach for estimating the extent of sea water in a homogeneous coastal aquifer subjected to pumping and regional flow effects and under steady-state conditions. The analytical model is tested against observations from Canada, the United States, and Australia to assess its utility as an initial approximation of sea water extent for the purposes of rapid groundwater management decision making. The occurrence of sea water intrusion resulting in increased salinity at pumping wells was correctly predicted in approximately 60% of cases. Application of a correction to account for dispersion did not markedly improve the results. Failure of the analytical model to provide correct predictions can be attributed to mismatches between its simplifying assumptions and more complex field settings. The best results occurred where the toe of the salt water wedge is expected to be the closest to the coast under predevelopment conditions. Predictions were the poorest for aquifers where the salt water wedge was expected to extend further inland under predevelopment conditions and was therefore more dispersive prior to pumping. Sharp-interface solutions remain useful tools to screen for the vulnerability of coastal aquifers to sea water intrusion, although the significant sources of uncertainty identified in this study require careful consideration to avoid misinterpreting sharp-interface results.

Heat and solute tracers: how do they compare in heterogeneous aquifers?

A comparison of groundwater velocity in heterogeneous aquifers estimated from hydraulic methods, heat and solute tracers was made using numerical simulations. Aquifer heterogeneity was described by geostatistical properties of the Borden, Cape Cod, North Bay, and MADE aquifers. Both heat and solute tracers displayed little systematic under- or over-estimation in velocity relative to a hydraulic control. The worst cases were under-estimates of 6.63% for solute and 2.13% for the heat tracer. Both under- and over-estimation of velocity from the heat tracer relative to the solute tracer occurred. Differences between the estimates from the tracer methods increased as the mean velocity decreased, owing to differences in rates of molecular diffusion and thermal conduction. The variance in estimated velocity using all methods increased as the variance in log-hydraulic conductivity (K) and correlation length scales increased. The variance in velocity for each scenario was remarkably small when compared to σ2 ln(K) for all methods tested. The largest variability identified was for the solute tracer where 95% of velocity estimates ranged by a factor of 19 in simulations where 95% of the K values varied by almost four orders of magnitude. For the same K-fields, this range was a factor of 11 for the heat tracer. The variance in estimated velocity was always lowest when using heat as a tracer. The study results suggest that a solute tracer will provide more understanding about the variance in velocity caused by aquifer heterogeneity and a heat tracer provides a better approximation of the mean velocity.

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)hs - B/2α, in which hs 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 hs1+α/α. 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.

Influence of boundary condition types on unstable density-dependent flow.

Boundary conditions are required to close the mathematical formulation of unstable density-dependent flow systems. Proper implementation of boundary conditions, for both flow and transport equations, in numerical simulation are critical. In this paper, numerical simulations using the FEFLOW model are employed to study the influence of the different boundary conditions for unstable density-dependent flow systems. A similar set up to the Elder problem is studied. It is well known that the numerical simulation results of the standard Elder problem are strongly dependent on spatial discretization. This work shows that for the cases where a solute mass flux boundary condition is employed instead of a specified concentration boundary condition at the solute source, the numerical simulation results do not vary between different convective solution modes (i.e., plume configurations) due to the spatial discretization. Also, the influence of various boundary condition types for nonsource boundaries was studied. It is shown that in addition to other factors such as spatial and temporal discretization, the forms of the solute transport equation such as divergent and convective forms as well as the type of boundary condition employed in the nonsource boundary conditions influence the convective solution mode in coarser meshes. On basis of the numerical experiments performed here, higher sensitivities regarding the numerical solution stability are observed for the Adams-Bashford/Backward Trapezoidal time integration approach in comparison to the Euler-Backward/Euler-Forward time marching approach. The results of this study emphasize the significant consequences of boundary condition choice in the numerical modeling of unstable density-dependent flow.

Spatial periodic boundary condition for MODFLOW.

Small-scale hyporheic zone (HZ) models often use a spatial periodic boundary (SPB) pair to simulate an infinite repetition of bedforms. SPB's are common features of commercially available multiphysics modeling packages. MODFLOW's lack of this boundary type has precluded it from being effectively utilized in this area of HZ research. We present a method to implement the SPB in MODFLOW by development of the appropriate block-centered finite-difference expressions. The implementation is analogous to MODFLOW's general head boundary package. The difference is that the terms on the right hand side of the solution equations must be updated with each iteration. Consequently, models that implement the SPB converge best with solvers that perform both inner and outer iterations. The correct functioning of the SPB condition in MODFLOW is verified by two examples. This boundary condition allows users to build HZ-bedform models in MODFLOW, facilitating further research using related codes such as MT3DMS and PHT3D.

Bias of apparent tracer ages in heterogeneous environments.

The interpretation of apparent ages often assumes that a water sample is composed of a single age. In heterogeneous aquifers, apparent ages estimated with environmental tracer methods do not reflect mean water ages because of the mixing of waters from many flow paths with different ages. This is due to nonlinear variations in atmospheric concentrations of the tracer with time resulting in biases of mixed concentrations used to determine apparent ages. The bias of these methods is rarely reported and has not been systematically evaluated in heterogeneous settings. We simulate residence time distributions (RTDs) and environmental tracers CFCs, SF6 , (85) Kr, and (39) Ar in synthetic heterogeneous confined aquifers and compare apparent ages to mean ages. Heterogeneity was simulated as both K-field variance (σ(2) ) and structure. We demonstrate that an increase in heterogeneity (increase in σ(2) or structure) results in an increase in the width of the RTD. In low heterogeneity cases, widths were generally on the order of 10 years and biases generally less than 10%. In high heterogeneity cases, widths can reach 100 s of years and biases can reach up to 100%. In cases where the temporal variations of atmospheric concentration of individual tracers vary, different patterns of bias are observed for the same mean age. We show that CFC-12 and CFC-113 ages may be used to correct for the mean age if analytical errors are small.

Maximizing net extraction using an injection-extraction well pair in a coastal aquifer.

In this study, we examine the maximum net extraction rate from the novel arrangement of an injection-extraction well pair in a coastal aquifer, where fresh groundwater is reinjected through the injection well located between the interface toe and extraction well. Complex potential theory is employed to derive a new analytical solution for the maximum net extraction rate and corresponding stagnation-point locations and recirculation ratio, assuming steady-state, sharp-interface conditions. The injection-extraction well-pair system outperforms a traditional single extraction well in terms of net extraction rate for a broad range of well placement and pumping rates, which is up to 50% higher for an aquifer with a thickness of 20 m, hydraulic conductivity of 10 m/d, and fresh water influx of 0.24 m(2) /d. Sensitivity analyses show that for a given fresh water discharge from an inland aquifer, a larger maximum net extraction is expected in cases with a smaller hydraulic conductivity or a smaller aquifer thickness, notwithstanding physical limits to drawdown at the pumping well that are not considered here. For an extraction well with a fixed location, the optimal net extraction rate linearly increases with the distance between the injection well and the sea, and the corresponding injection rate and recirculation ratio also increase. The analytical analysis in this study provides initial guidance for the design of well-pair systems in coastal aquifers, and is therefore an extension beyond previous applications of analytical solutions of coastal pumping that apply only to extraction or injection wells.

Vulnerability indicators of sea water intrusion.

In this paper, simple indicators of the propensity for sea water intrusion (SWI) to occur (referred to as "SWI vulnerability indicators") are devised. The analysis is based on an existing analytical solution for the steady-state position of a sharp fresh water-salt water interface. Interface characteristics, that is, the wedge toe location and sea water volume, are used in quantifying SWI in both confined and unconfined aquifers. Rates-of-change (partial derivatives of the analytical solution) in the wedge toe or sea water volume are used to quantify the aquifer vulnerability to various stress situations, including (1) sea-level rise; (2) change in recharge (e.g., due to climate change); and (3) change in seaward discharge. A selection of coastal aquifer cases is used to apply the SWI vulnerability indicators, and the proposed methodology produces interpretations of SWI vulnerability that are broadly consistent with more comprehensive investigations. Several inferences regarding SWI vulnerability arise from the analysis, including: (1) sea-level rise impacts are more extensive in aquifers with head-controlled rather than flux-controlled inland boundaries, whereas the opposite is true for recharge change impacts; (2) sea-level rise does not induce SWI in constant-discharge confined aquifers; (3) SWI vulnerability varies depending on the causal factor, and therefore vulnerability composites are needed that differentiate vulnerability to such threats as sea-level rise, climate change, and changes in seaward groundwater discharge. We contend that the approach is an improvement over existing methods for characterizing SWI vulnerability, because the method has theoretical underpinnings and yet calculations are simple, although the coastal aquifer conceptualization is highly idealized.

Impact of sea-level rise on sea water intrusion in coastal aquifers.

Despite its purported importance, previous studies of the influence of sea-level rise on coastal aquifers have focused on specific sites, and a generalized systematic analysis of the general case of the sea water intrusion response to sea-level rise has not been reported. In this study, a simple conceptual framework is used to provide a first-order assessment of sea water intrusion changes in coastal unconfined aquifers in response to sea-level rise. Two conceptual models are tested: (1) flux-controlled systems, in which ground water discharge to the sea is persistent despite changes in sea level, and (2) head-controlled systems, whereby ground water abstractions or surface features maintain the head condition in the aquifer despite sea-level changes. The conceptualization assumes steady-state conditions, a sharp interface sea water-fresh water transition zone, homogeneous and isotropic aquifer properties, and constant recharge. In the case of constant flux conditions, the upper limit for sea water intrusion due to sea-level rise (up to 1.5 m is tested) is no greater than 50 m for typical values of recharge, hydraulic conductivity, and aquifer depth. This is in striking contrast to the constant head cases, in which the magnitude of salt water toe migration is on the order of hundreds of meters to several kilometers for the same sea-level rise. This study has highlighted the importance of inland boundary conditions on the sea-level rise impact. It identifies combinations of hydrogeologic parameters that control whether large or small salt water toe migration will occur for any given change in a hydrogeologic variable.