Comparison of an algebraic multigrid algorithm to two iterative solvers used for modeling ground water flow and transport

Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling.     

An efficient approach for successively perturbed groundwater models

Global optimization methods such as simulated annealing, genetic algorithms and tabu search are being increasingly used to solve groundwater remediation design and parameter identification problems. While these methods enjoy some unique advantages over traditional gradient based methods, they typically require thousands to tens of thousands of forward simulation runs before reaching optimal or near-optimal solutions. Thus, one severe limitation associated with these global optimization methods is very long computation time. To mitigate this limitation, this paper presents a new approach for obtaining, repeatedly and efficiently, the solutions of a linear forward simulation model subject to successive perturbations. The proposed approach takes advantage of the fact that successive forward simulation runs, as required by a global optimization procedure, usually involve only slight changes in the coefficient matrices of the resultant linear equations. As a result, the new solution to a system of linear equations perturbed by the changes in aquifer properties and/or sinks/sources can be obtained as the sum of a non-perturbed base solution and the solution to the perturbed portion of the linear equations. The computational efficiency of the proposed approach arises from the fact that the perturbed solution can be derived directly without solving the linear equations again. A two-dimensional test problem with 20 by 30 nodes demonstrates that the proposed approach is much more efficient than repeatedly running the simulation model, by more than 15 times after a fixed number of model evaluations. The ratio of speedup increases with the number of model evaluations and also the size of simulation model. The main limitation of the proposed approach is the large amount of computer memory required to store the inverse matrix. Effective ways for limiting the storage requirement are briefly discussed.     

An integrated optimization algorithm for parameter structure identification in groundwater modeling

The inverse problem of parameter structure identification in a distributed parameter system remains challenging. Identifying a more complex parameter structure requires more data. There is also the problem of over-parameterization. In this study, we propose a modified Tabu search for parameter structure identification. We embed an adjoint state procedure in the search process to improve the efficiency of the Tabu search. We use Voronoi tessellation for automatic parameterization to reduce the dimension of the distributed parameter. Additionally, a coarse-fine grid technique is applied to further improve the effectiveness and efficiency of the proposed methodology. To avoid over-parameterization, at each level of parameter complexity we calculate the residual error for parameter fitting, the parameter uncertainty error and a modified Akaike Information Criterion. To demonstrate the proposed methodology, we conduct numerical experiments with synthetic data that simulate both discrete hydraulic conductivity zones and a continuous hydraulic conductivity distribution. Our results indicate that the Tabu search allied with the adjoint state method significantly improves computational efficiency and effectiveness in solving the inverse problem of parameter structure identification.     

Cluster-based fuzzy models for groundwater flow in the unsaturated zone

In this paper fuzzy models are used as an alternative to describe groundwater flow in the unsaturated zone. The core of these models consists of a fuzzy rule-based model of the Takagi–Sugeno type. Various fuzzy clustering algorithms are compared in the data-driven identification of these Takagi–Sugeno models. The performance of the resulting fuzzy models is evaluated on the training surface on which they were identified, and on time series measurements of water content values obtained through an experiment carried out by the non-vegetated terrain (NVT) workgroup of the European Microwave Signature Laboratory (EMSL) (see [Mancini M, Hoeben R, Troch PA. Multifrequency radar observations of bare surface soil moisture content: a laboratory experiment. Water Resour Res 1999;35(6):1827–38] and [Hoeben R, Troch PA. Assimilation of active microwave observation data for soil moisture profile estimation. Water Resour Res 2000;36(10):2805–19]). Despite higher errors at the borders of high water content values in the training surface, good results are obtained on the simulation of the time series.     

Comparison of machine learning models for predicting fluoride contamination in groundwater

Groundwater is an especially important freshwater source for water supplies in the Maku area of northwest Iran. The groundwater of the area contains high concentrations of fluoride and is, therefore, important in predicting the fluoride contamination of the groundwater for the purpose of planning and management. The present study aims to evaluate the ability of the extreme learning machine (ELM) model to predict the level of fluoride contamination in the groundwater in comparison to multilayer perceptron (MLP) and support vector machine (SVM) models. For this purpose, 143 water samples were collected in a five-year period, 2004–2008. The samples were measured and analyzed for electrical conductivity, pH, major chemical ions and fluoride. To develop the models, the data set—including Na⁺, K⁺, Ca²⁺ and HCO₃ ^? concentrations as the inputs and fluoride concentration as the output—was divided into two subsets; training/validation (80% of data) and testing (20% of data), based on a cross-validation technique. The radial basis-based ELM model resulted in an R ² of 0.921, an NSC of 0.9071, an RMSE of 0.5638 (mg/L) and an MABE of 0.4635 (mg/L) for the testing data. The results showed that the ELM models performed better than MLP and SVM models for prediction of fluoride contamination. It was observed that ELM models learned faster than the other models during model development trials and the SVM models had the highest computation time.     

Analysis of incorporating groundwater exchanges in hydrological models

In many catchments, the geographical demarcation does not coincide with the limits of the aquifers, so groundwater may be exchanged beyond their topographic boundaries. By studying groundwater exchanges, the natural resources of a catchment can be better assessed, and the divergences between hydrological models and measurements can be explained. The aim of this work is to reveal the importance of including groundwater exchanges in the hydrological modelling of some catchments, using a water balance model. For this purpose, a simple example is conducted. The so‐called parent model scheme is modified to only allow groundwater exchanges, and it is applied to the headwater of the Segura River Basin District, located in the southeast of Spain. This area is selected because groundwater plays an important role in surface hydrology. The results reveal that groundwater exchanges cannot be neglected in some catchments when assessing water resources because their integration in the hydrological model corrects errors in the water balance. Moreover, this paper proves that water balance models are a useful tool for estimating groundwater exchanges between catchments, which can be contrasted with more complex distributed models or isotopic tracers if there is enough information available. Copyright © 2015 John Wiley & Sons, Ltd.     

Alternative split-operator approach for solving chemical reaction/groundwater transport models

Various schemes are available to solve coupled transport/reaction mathematical models, one of the most efficient and easy to apply being the two-step split-operator method in which the transport and reaction steps are performed separately. Operator splitting, however, does not solve exactly the fully coupled numerical model derived from the governing partial differential and algebraic equations describing the transport and reaction processes. An error, proportional to Δt (the time step used in the numerical solution) is introduced. Thus, small time steps must be used to ensure that accurate solutions result. An alternative scheme is presented, which iterates to the exact solution of the fully coupled numerical model. The new scheme enables accurate solutions to be calculated more efficiently than the two-step method, while maintaining separation of the transport and reaction steps in the calculations. As in the two-step method, the reaction calculations are performed node-wise throughout the computation grid. However, because the scheme relies on LU factorisation of the coefficient matrix in the transport equation solution, the reaction calculations must be performed in sequence, the sequence order being determined by the ordering of the nodes in the grid. Also, because LU factorisation is used, the scheme is limited to solute transport problems for which LU factorisation is a practical solution method.     

A simple overland flow calculation method for distributed groundwater recharge models

A method to improve the calculation of overland flow in distributed groundwater recharge models is presented and applied to two sub‐catchments in the Thames Basin, UK. Recharge calculation studies tend to simulate the runoff flow component of river flow in a simplistic way, often as a fraction of rainfall over a particular period. The method outlined in this study intends to improve the calculation of groundwater recharge estimates in distributed recharge models but does not present an alternative to complex overland flow simulators. This method uses seasonally varying coefficients to calculate runoff for specified hydrogeological classes or runoff zones, which are used to model baseflow index variations across the basin. It employs a transfer function model to represent catchment storage. Monte Carlo simulation was applied to refine the runoff values. Decoupling the runoff zones between the two sub‐catchments produces a better match between the simulated and observed values; however, the difference between observed runoff and the simulated output indicates other factors, such as landuse and topographical characteristics that affect the generation of runoff flow, need to be taken into account when classifying runoff zones. British Geological Survey © NERC 2011. Hydrological Processes © 2011 John Wiley & Sons, Ltd.     

Analysis and integrated modelling of groundwater infiltration to sewer networks

Infiltration of groundwater to sewer systems is a problem for the capacity of the system as well as for treatment processes at waste water treatment plants. This paper quantifies the infiltration of groundwater to a sewer system in Frederikshavn Municipality, Denmark, by measurements of sewer flow and novel model set‐up, which simulates the interaction between groundwater and sewer flow. The study area has a separate waste water sewer system, but the discharged volumes from the system are approximately twice the volumes from a tight system without infiltration. The model set‐up makes use of two commercial models: mike she for simulation of groundwater transport and mike urban (mouse ) [DHI, Hørsholm, Denmark] for simulation of sewer flow. By simulating the groundwater level and calibrating infiltration coefficients against sewer flow measurements, it has been possible to estimate the average infiltration to the sewer system with satisfying results. The infiltration processes are indeed complicated and to a large degree heterogeneous throughout the sewer system. The paper shows contribution from both saturated and unsaturated groundwater zones, which makes the modelling process complex. Copyright © 2016 John Wiley & Sons, Ltd.     

An iterative technique to delineate protection buffers for wetlands in regions subject to intensive groundwater pumping

Wetlands are vulnerable to groundwater extraction, which has proven detrimental to aquatic ecosystems around the planet. As wetlands rank among the world’s most endangered ecosystems, versatile strategies are required to protect them. This paper provides a modelling-based method to delineate protection buffers in wetlands subject to groundwater extraction. The technique is sufficiently flexible to cater to a wide variety of conditions, and simple enough to underpin management decisions on a daily basis. A numerical model is used to obtain a map of the critical rate of groundwater abstraction, based on the distance between wetlands and suitable discharge thresholds. The outcomes determine the allowed pumping rate at any point under steady and transient-state conditions. A new iteration is developed every time a new pumping allowance is made. This procedure is demonstrated by means of hypothetical scenarios, as well as by a case study application in the Valle del Cauca region, Colombia.     

Testing linear models of sea-floor topography

Stochastic models can generate profiles that resemble topography by taking uncorrelated, zero-average noise as input, introducing some correlation in the time series of noise, and integrating the resulting correlated noise. The output profile will depict a nonstationary, randomly rough surface. Two models have been chosen for comparison: a fractal model, in which the noise is correlated even at large distances, and an autoregressive model of order 1, in which the correlation of the noise decays rapidly. Both models have as an end-member a random walk, which is the integration of uncorrelated noise. The models have been fitted to profiles of submarine topography, and the sample autocorrelation, power spectrum and variogram have been compared to the theoretical predictions. The results suggest that a linear system approach is a viable method to model and classify sea-floor topography. The comparison does not show substantial disagreement of the data with either the autoregressive or the fractal model, although a fractal model seems to give a better fit. However, the amplitudes predicted by a nonstationary fractal model for long wavelengths (of the order of 1000 km) are unreasonably large. When viewed through a large window, ocean floor topography is likely to have an expected value determined by isostasy, and to be stationary. Nonstationary models are best applied to wavelengths of the order of 100 km or less.     

A re-evaluation of equivalent linear models for simple yielding systems

Commonly used equivalent linear models for simple yielding systems subjected to harmonic and earthquake excitations are re-evaluated. It is shown that with respect to damping, these models contain the same basic information. Reported differences in the literature are simply due to scaling: since the product of the equivalent stiffness and equivalent damping is a constant, smaller damping values would be obtained by the use of the small amplitude equivalent stiffnesses. It is argued that for harmonic excitation, the secant stiffness is an appropriate representation of equivalent stiffness, leading to large equivalent damping values that increase with ductility. For earthquake excitation the Iwan proposal is shown to be the preferred model leading to larger damping values than previously reported. A comparison of the models for harmonic and earthquake excitations shows that, in general, and at comparable ductilities, damping values due to harmonic excitation are about five times those due to earthquake excitation, and the period changes due to harmonic excitation are about twice those due to earthquake excitation.     

Optimal control algorithm and neural network for dynamic groundwater management

Researchers have found that obtaining optimal solutions for groundwater resource‐planning problems, while simultaneously considering time‐varying pumping rates, is a challenging task. This study integrates an artificial neural network (ANN) and constrained differential dynamic programming (CDDP) as simulation‐optimization model, called ANN‐CDDP. Optimal solutions for a groundwater resource‐planning problem are determined while simultaneously considering time‐varying pumping rates. A trained ANN is used as the transition function to predict ground water table under variable pumping conditions. The results show that the ANN‐CDDP reduces computational time by as much as 94·5% when compared to the time required by the conventional model. The proposed optimization model saves a considerable amount of computational time for solving large‐scale problems. Copyright © 2009 John Wiley & Sons, Ltd.     

Application of the integrated NMR-TDEM method in groundwater exploration in Israel

The Nuclear Magnetic Resonance (NMR) method is the only physical tool currently available which is able to detect directly the presence of fresh water in the subsurface. The Time Domain Electromagnetic (TDEM) method, in turn, has been proven highly efficient in detecting saline groundwater. The combined application of these two methods is the most promising way to delineate accurately groundwater-bearing aquifers and to evaluate the quality of the water. This idea was tested during the feasibility study carried out under different hydrogeological conditions throughout Israel during August–September 1992. The Russian Hydroscope and Geonics PROTEM-IV instruments were used for the NMR and TDEM measurements, respectively.A total of 36 NMR and 12 TDEM stations was established, mostly in close proximity to existing observation wells. Among these only 19 NMR measurements showed reasonable signal-to-noise characteristics, while the rest were obviously distorted by ambient noise. The number of distorted measurements could have been even greater had they been carried out at all points planned. However, a significant number of the NMR stations were cancelled due to their proximity (less than 1–1.5 km) to electric power lines. As a result almost the entire Mediterranean coast of Israel, which was originally chosen as the main test site for this survey, turned out to be unsuitable owing to the low ambient noise protection of the Hydroscope. Another serious limitation of NMR measurements is the maximum penetration depth. The deepest information obtained during the feasibility study was from a depth of 74 m.Nevertheless, within the framework of its applicability, the NMR measurements proved to be sufficiently accurate and to have a high resolving capability. A comparison with the borehole data shows that, in most cases, NMR is able not only to detect the presence of water, but also to delineate different subaquifers. At the same time, however, the transmissivity and aquifer texture are much less reliably detected. The combined application of the NMR and TDEM methods may essentially improve the reliability of the interpretation. In all cases where the NMR anomaly fits the drop in TDEM resistivity, water of a different salinity is found at approximately the same depth. A reasonable correlation between the interpreted resistivities and water salinities is obtained for these horizons. However, if only one method indicates the presence of water, this, in many cases, was not confirmed by the borehole data. The TDEM anomalies were obviously caused by low-resistivity lithologies, while some of the false NMR signals could be explained by a low signal-to-noise ratio.As regards the freshwater/seawater interface, this was, in all cases, accurately detected by the TDEM measurements alone. It is interesting to note that at the same depth, NMR measurements indicated a drastically increasing anomaly followed by the absence of water at greater depths. The latter can most likely be explained by the very low resistivity of the sea water, which is not taken into account by the existing NMR interpretation.     

Mathematical models of groundwater flow with a horizontal drain

An analytical review is given to drainage theory, the foundation of which was laid down by researchers in our country in the first half of the 20th century. Later the author of this paper developed and thoroughly studied a complex of mathematical models describing two-dimensional groundwater flow in drained soils based on the boundary problems of the theory of analytical functions. These models were used to provide a hydrodynamic substantiation for the regularities in subsoil water dynamics that were established by ameliorators in relation to the leaching of salts from soils; to identify the specific features of groundwater flow with drainage in the presence in the flow of one or two unknown free boundaries; and to develop approaches to the analysis of such flows in a direct formulation.     

积分安培离子色谱法测定地下水中碘化物的不确定度评定

本文对积分安培离子色谱法测定地下水中碘化物含量的不确定度进行了评定,标准曲线采用双误差拟合法,建立了不确定度评定模型,得出几种影响测定结果的因素。     

Non‐iterative time integration scheme for non‐linear dynamic FEM analysis

This paper proposes a non‐iterative time integration (NITI) scheme for non‐linear dynamic FEM analysis. The NITI scheme is constructed by combining explicit and implicit schemes, taking advantage of their merits, and enables stable computation without an iteration process for convergence even when used for non‐linear dynamic problems. Formulation of the NITI scheme is presented and its stability is studied. Although the NITI scheme is not unconditionally stable when applied to non‐linear problems, it is stable in most cases unless stiffness hardening occurs or the problem has a large velocity‐dependent term. The NITI scheme is applied to dynamic analysis of the non‐linear soil–structure system and computation results are compared with those by the central difference method (CDM). Comparison shows that the stability of the NITI scheme is superior to that of the CDM. Accuracy of the NITI scheme is verified because its results are identical with those by the CDM in which the time step is set as 1/10 of that for the NITI scheme. The application of the NITI scheme to the mesh‐partitioned FEM is also proposed. It is applied to dynamic analysis of the linear soil–structure system. It yields the same results as a conventional single‐domain FEM analysis using the Newmark β method. This result verifies the usability of mesh‐partitioned FEM analysis using the NITI scheme. Copyright © 2003 John Wiley& Sons, Ltd.     

Conceptual and numerical models for groundwater flow in an arid inland river basin

The Heihe River Basin (HRB) is an inland watershed in northwest China with a total area of approximately 130,000 km², stretching from the Qilian Mountains in the south to the oases and agricultural fields in the middle and further to the Gobi desert in the north bordering Mongolia. As part of a major ecohydrological research initiative to provide a stronger scientific underpinning for sustainable water management in arid ecosystems, a regional‐scale integrated ecological and hydrological model is being developed, incorporating the knowledge based on the results of environmental isotope tracer analysis and the multiscale observation datasets. The first step in the model development effort is to construct and calibrate a groundwater flow model for the middle and lower HRB where the oases and vegetation along the Heihe river corridor are highly dependent on groundwater. In this study, the software tool ‘Arc Hydro Groundwater’ is used to build and visualize a hydrogeological data model for the HRB that links all relevant spatiotemporal hydrogeological data in a unified geodatabase within the ArcGIS environment. From the conceptual model, a regional‐scale groundwater flow model has been developed using MODFLOW‐2005. Critical considerations in developing the flow model include the representation of mountainous terrains and fluvial valleys by individual model layers, treatment of aquifer heterogeneities across multiple scales and selection of proper observation data and boundary conditions for model calibration. This paper discusses these issues in the context of the Heihe River Basin, but the results and insights from this study will have important implications for other large, regional groundwater modelling studies, especially in arid and semiarid inland river basins. Copyright © 2014 John Wiley & Sons, Ltd.     

Stochastic environmental risk analysis: an integrated methodology for predicting cancer risk from contaminated groundwater

Stochastic environmental risk assessment considers the effects of numerous biological, chemical, physical, behavioral and physiological processes that involve elements of uncertainty and variability. A methodology for predicting health risks to individuals from contaminated groundwater is presented that incorporates the elements of uncertainty and variability in geological heterogeneity, physiological exposure parameters, and in cancer potency. An idealized groundwater basin is used to perform a parametric sensitivity study to assess the relative impact of (a) geologic uncertainty, (b) behavioral and physiological variability in human exposure and (c) uncertainty in cancer potency on the prediction of increased cancer risk to individuals in a population exposed to contaminants in household water supplied from groundwater. A two-dimensional distribution (or surface) of human health risk was generated as a result of the simulations. Cuts in this surface (fractiles of variability and percentiles of uncertainty) are then used as a measure of relative importance of various model components on total uncertainty and variability. A case study for perchloroethylene or PCE, shows that uncertainty and variability in hydraulic conductivity play an important role in predicting human health risk that is on the same order of influence as uncertainty of cancer potency.     

The application of ecohydrological groundwater indicators to hydrogeological conceptual models

This article reviews the application of ecohydrological indicators to hydrogeological conceptual models for earth-scientists with little or no botanical training. Ecohydrological indicators are plants whose presence or morphology can provide data about the hydrogeological setting. By examining the literature from the fields of ecohydrology, hydrogeology, geobotany, and ecology, this article summarizes what is known about groundwater indicator plants, their potential for providing information about the aquifer, and how this data can be a cost-effective addition to hydrogeological conceptual models. We conclude that the distribution and morphology of ecohydrological groundwater indicator plants can be useful to hydrogeologists in certain circumstances. They are easiest to evaluate in arid and semiarid climates. Ecohydrological groundwater indicators can provide information about the absolute depth to the water table, patterns of groundwater fluctuation, and the mineralization of the aquifer. It is shown that an understanding of the meteorological conditions of a region is often necessary to accurately interpret groundwater indicator plants and that useful data is usually obtained by observing patterns of vegetation behavior rather than interpreting individual plants. The most serious limitations to applying this source of information to hydrogeological conceptual models are the limited data in the literature and the regional nature of many indicator plants. The physical and physiological indications of the plants exist, but little effort has been made to interpret them. This article concludes by outlining several potential lines of research that could further the usefulness of ecohydrological groundwater indicators to the hydrogeological community.