Heterogeneity and thermal modeling of ground water

Heat transport in aquifers is becoming an increasingly important topic due to recent growth in the use of ground water in thermal applications. However, the effect of heterogeneity on heat transport in aquifers has yet to be examined in the same detail as it has been for solute transport, and it is unclear what effect this may have on our ability to create accurate models. This study examines this issue through stochastic modeling using the geostatistics for two aquifers with low and high degrees of heterogeneity. The results indicate that there is considerable uncertainty in the distribution of heat associated with injection of warm water into an aquifer. Heterogeneity in the permeability field was also found to slightly reduce the ability to recover this introduced heat at a later time. These simulations also reveal that hydrodynamic macrodispersion is an important consideration in some heat flow problems.     

Uncertainty estimation of pathlines in ground water models

A method is proposed to estimate the uncertainty of the location of pathlines in two-dimensional, steady-state confined or unconfined flow in aquifers due to the uncertainty of the spatially variable unconditional hydraulic conductivity or transmissivity field. The method is based on concepts of the semianalytical first-order theory given in Stauffer et al. (2002, 2004), which allows estimates of the lateral second moment (variance) of the location of a moving particle. However, this method is reformulated in order to account for nonuniform recharge and nonuniform aquifer thickness. One prominent application is the uncertainty estimation of the catchment of a pumping well by considering the boundary pathlines starting at a stagnation point. In this method, the advective transport of particles is considered, based on the velocity field. In the case of a well catchment, backtracking is applied by using the reversed velocity field. Spatial variability of hydraulic conductivity or transmissivity is considered by taking into account an isotropic exponential covariance function of log-transformed values with parameters describing the variance and correlation length. The method allows postprocessing of results from ground water models with respect to uncertainty estimation. The code PPPath, which was developed for this purpose, provides a postprocessing of pathline computations under PMWIN, which is based on MODFLOW. In order to test the methodology, it was applied to results from Monte Carlo simulations for catchments of pumping wells. The results correspond well. Practical applications illustrate the use of the method in aquifers.     

Multimodel ranking and inference in ground water modeling

Uncertainty of hydrogeologic conditions makes it important to consider alternative plausible models in an effort to evaluate the character of a ground water system, maintain parsimony, and make predictions with reasonable definition of their uncertainty. When multiple models are considered, data collection and analysis focus on evaluation of which model(s) is(are) most supported by the data. Generally, more than one model provides a similar acceptable fit to the observations; thus, inference should be made from multiple models. Kullback-Leibler (K-L) information provides a rigorous foundation for model inference that is simple to compute, is easy to interpret, selects parsimonious models, and provides a more realistic measure of precision than evaluation of any one model or evaluation based on other commonly referenced model selection criteria. These alternative criteria strive to identify the true (or quasi-true) model, assume it is represented by one of the models in the set, and given their preference for parsimony regardless of the available number of observations the selected model may be underfit. This is in sharp contrast to the K-L information approach, where models are considered to be approximations to reality, and it is expected that more details of the system will be revealed when more data are available. We provide a simple, computer-generated example to illustrate the procedure for multimodel inference based on K-L information and present arguments, based on statistical underpinnings that have been overlooked with time, that its theoretical basis renders it preferable to other approaches.     

PRO-GRADE: GIS toolkits for ground water recharge and discharge estimation

PRO-GRADE is an ESRI ArcGIS 9.2 plug-in package that consists of two separate toolkits: (1) the p attern r ecognition o rganizer for g eographic i nformation s ystem (PRO-GIS) and (2) the g round water r echarge a nd d ischarge e stimator for GIS (GRADE-GIS). PRO-GIS is a collection of several existing image-processing algorithms into one user interface to offer the flexibility to extract spatial patterns according to the user's needs. GRADE-GIS is a ground water recharge and discharge estimation interface using a mass balance method that requires only hydraulic conductivity, water table, and bedrock elevation data for simulating two-dimensional steady-state unconfined aquifers. PRO-GRADE was developed to assist ongoing assessments of the water resources in Illinois and Wisconsin, and is being used to assist several ground water resource studies in several locations in the United States. The advantage of using PRO-GRADE is to enable fast production of initial recharge and discharge maps that can be further enhanced by using a follow-up ground water flow model with parameter estimation codes. PRO-GRADE leverages ArcGIS to provide a computer-assisted framework to support expert judgment in order to efficiently select alternative recharge and discharge maps that can be used as (1) guidelines for field study planning and decision making; (2) initial conditions for numerical simulation; and (3) screening for alternative model selection and prediction/parameter uncertainty evaluation. In addition, PRO-GRADE allows for more easy and rapid correlation of those maps with other hydrologically relevant geospatial data.     

A real-time, interactive steering environment for integrated ground water modeling

We present in this note an innovative software environment, called Interactive Ground Water (IGW), for unified deterministic and stochastic ground water modeling. Based on efficient computational algorithms, IGW allows simulating three-dimensional (3D) unsteady flow and transport in saturated media subject to systematic and "random" stresses and geological and chemical heterogeneity. Adopting a new computing paradigm, IGW eliminates the fragmentation in the traditional modeling schemes and allows fully utilizing today's dramatically increased computing power. For many problems, IGW enables real-time modeling, visualization, mapping, and analysis. The software environment functions as a "numerical laboratory" in which an investigator may freely explore the following: creating visually an aquifer system of desired configurations, interactively applying stresses and boundary conditions, and then investigating and visualizing on the fly the geology and flow and transport dynamics. At any time, a researcher can pause to interact dynamically with virtually any aspects of the modeling process and then resume the integrated visual exploration; he or she can initiate, pause, or resume particle tracking, plume modeling, subscale modeling, stochastic modeling, monitoring, and budget analyses. IGW continually provides results that are dynamically processed, overlaid, and displayed. It dynamically merges modeling inputs and outputs into composite two-dimensional/3D images-integrating related data to provide a more complete view of the complex interplay among the geology, hydrology, flow system, and transport. These unique capabilities of real-time modeling, steering, analysis, and mapping expand the utility of models as tools for research, education, and professional investigations.     

A combinatorial optimization scheme for parameter structure identification in ground water modeling

This research develops a methodology for parameter structure identification in ground water modeling. For a given set of observations, parameter structure identification seeks to identify the parameter dimension, its corresponding parameter pattern and values. Voronoi tessellation is used to parameterize the unknown distributed parameter into a number of zones. Accordingly, the parameter structure identification problem is equivalent to finding the number and locations as well as the values of the basis points associated with the Voronoi tessellation. A genetic algorithm (GA) is allied with a grid search method and a quasi-Newton algorithm to solve the inverse problem. GA is first used to search for the near-optimal parameter pattern and values. Next, a grid search method and a quasi-Newton algorithm iteratively improve the GA's estimates. Sensitivities of state variables to parameters are calculated by the sensitivity-equation method. MODFLOW and MT3DMS are employed to solve the coupled flow and transport model as well as the derived sensitivity equations. The optimal parameter dimension is determined using criteria based on parameter uncertainty and parameter structure discrimination. Numerical experiments are conducted to demonstrate the proposed methodology, in which the true transmissivity field is characterized by either a continuous distribution or a distribution that can be characterized by zones. We conclude that the optimized transmissivity zones capture the trend and distribution of the true transmissivity field.     

Transboundary impacts on regional ground water modeling in Texas

Recent legislation required regional grassroots water resources planning across the entire state of Texas. The Texas Water Development Board (TWDB), the state's primary water resource planning agency, divided the state into 16 planning regions. Each planning group developed plans to manage both ground water and surface water sources and to meet future demands of various combinations of domestic, agricultural, municipal, and industrial water consumers. This presentation describes the challenges in developing a ground water model for the Llano Estacado Regional Water Planning Group (LERWPG), whose region includes 21 counties in the Southern High Plains of Texas. While surface water is supplied to several cities in this region, the vast majority of the regional water use comes from the High Plains aquifer system, often locally referred to as the Ogallala Aquifer. Over 95% of the ground water demand is for irrigated agriculture. The LERWPG had to predict the impact of future TWDB-projected water demands, as provided by the TWDB, on the aquifer for the period 2000 to 2050. If detrimental impacts were noted, alternative management strategies must be proposed. While much effort was spent on evaluating the current status of the ground water reserves, an appropriate numerical model of the aquifer system was necessary to demonstrate future impacts of the predicted withdrawals as well as the effects of the alternative strategies. The modeling effort was completed in the summer of 2000. This presentation concentrates on the political, scientific, and nontechnical issues in this planning process that complicated the modeling effort. Uncertainties in data, most significantly in distribution and intensity of recharge and withdrawals, significantly impacted the calibration and predictive modeling efforts. Four predictive scenarios, including baseline projections, recurrence of the drought of record, precipitation enhancement, and reduced irrigation demand, were simulated to identify counties at risk of low final ground water storage volume or low levels of satisfied demand by 2050.     

A strategy for modeling ground water rebound in abandoned deep mine systems

Discharges of polluted water from abandoned mines are a major cause of degradation of water resources worldwide. Pollution arises after abandoned workings flood up to surface level, by the process termed ground water rebound. As flow in large, open mine voids is often turbulent, standard techniques for modeling ground water flow (which assume laminar flow) are inappropriate for predicting ground water rebound. More physically realistic models are therefore desirable, yet these are often expensive to apply to all but the smallest of systems. An overall strategy for ground water rebound modeling is proposed, with models of decreasing complexity applied as the temporal and spatial scales of the systems under analysis increase. For relatively modest systems (area < 200 km2), a physically based modeling approach has been developed, in which 3-D pipe networks (representing major mine roadways, etc.) are routed through a variably saturated, 3-D porous medium (representing the country rock). For systems extending more than 100 to 3000 km2, a semidistributed model (GRAM) has been developed, which conceptualizes extensively interconnected volumes of workings as ponds, which are connected to other ponds only at discrete overflow points, such as major inter-mine roadways, through which flow can be efficiently modeled using the Prandtl-Nikuradse pipe-flow formulation. At the very largest scales, simple water-balance calculations are probably as useful as any other approach, and a variety of proprietary codes may be used for the purpose.     

Regional estimation of total recharge to ground water in Nebraska

Naturally occurring long-term mean annual recharge to ground water in Nebraska was estimated by a novel water-balance approach. This approach uses geographic information systems (GIS) layers of land cover, elevation of land and ground water surfaces, base recharge, and the recharge potential in combination with monthly climatic data. Long-term mean recharge > 140 mm per year was estimated in eastern Nebraska, having the highest annual precipitation rates within the state, along the Elkhorn, Platte, Missouri, and Big Nemaha River valleys where ground water is very close to the surface. Similarly high recharge values were obtained for the Sand Hills sections of the North and Middle Loup, as well as Cedar River and Beaver Creek valleys due to high infiltration rates of the sandy soil in the area. The westernmost and southwesternmost parts of the state were estimated to typically receive < 30 mm of recharge a year.     

The role of hand calculations in ground water flow modeling

Most ground water modeling courses focus on the use of computer models and pay little or no attention to traditional analytic solutions to ground water flow problems. This shift in education seems logical. Why waste time to learn about the method of images, or why study analytic solutions to one-dimensional or radial flow problems? Computer models solve much more realistic problems and offer sophisticated graphical output, such as contour plots of potentiometric levels and ground water path lines. However, analytic solutions to elementary ground water flow problems do have something to offer over computer models: insight. For instance, an analytic one-dimensional or radial flow solution, in terms of a mathematical expression, may reveal which parameters affect the success of calibrating a computer model and what to expect when changing parameter values. Similarly, solutions for periodic forcing of one-dimensional or radial flow systems have resulted in a simple decision criterion to assess whether or not transient flow modeling is needed. Basic water balance calculations may offer a useful check on computer-generated capture zones for wellhead protection or aquifer remediation. An easily calculated "characteristic leakage length" provides critical insight into surface water and ground water interactions and flow in multi-aquifer systems. The list goes on. Familiarity with elementary analytic solutions and the capability of performing some simple hand calculations can promote appropriate (computer) modeling techniques, avoids unnecessary complexity, improves reliability, and is likely to save time and money. Training in basic hand calculations should be an important part of the curriculum of ground water modeling courses.     

A digital procedure for ground water recharge and discharge pattern recognition and rate estimation

A digital procedure to estimate recharge/discharge rates that requires relatively short preparation time and uses readily available data was applied to a setting in central Wisconsin. The method requires only measurements of the water table, fluxes such as stream baseflows, bottom of the system, and hydraulic conductivity to delineate approximate recharge/discharge zones and to estimate rates. The method uses interpolation of the water table surface, recharge/discharge mapping, pattern recognition, and a parameter estimation model. The surface interpolator used is based on the theory of radial basis functions with thin-plate splines. The recharge/discharge mapping is based on a mass-balance calculation performed using MODFLOW. The results of the recharge/discharge mapping are critically dependent on the accuracy of the water table interpolation and the accuracy and number of water table measurements. The recharge pattern recognition is performed with the help of a graphical user interface (GUI) program based on several algorithms used in image processing. Pattern recognition is needed to identify the recharge/discharge zonations and zone the results of the mapping method. The parameter estimation program UCODE calculates the parameter values that provide a best fit between simulated heads and flows and calibration head-and-flow targets. A model of the Buena Vista Ground Water Basin in the Central Sand Plains of Wisconsin is used to demonstrate the procedure.     

Stochastic modeling of Iranian earthquakes and estimation of ground motion for future earthquakes in Greater Tehran

Strong-motion data from eight significant well-documented earthquakes in Iran have been simulated using a stochastic modeling technique for finite faults proposed by Beresnev and Atkinson [Bull Seismol Soc Am 87 (1997) 67–84; Seism Res Lett 69 (1998) 27–32]. The database consists of 61 three-component records from eight earthquakes of magnitude ranging from M 6.3 to M 7.4, recorded at hypocentral distances up to 200 km. The model predictions are in good agreement with available Iranian strong-motion data as evidenced by near-zero average of differences between logarithms of the observed and predicted values for all frequencies. The strength factor, sfact, a quantity that controls the high-frequency radiation from the source is determined, on an event-by-event basis, by fitting simulated to observed response spectra.     

Regional estimation of base recharge to ground water using water balance and a base-flow index

Naturally occurring long-term mean annual base recharge to ground water in Nebraska was estimated with the help of a water-balance approach and an objective automated technique for base-flow separation involving minimal parameter-optimization requirements. Base recharge is equal to total recharge minus the amount of evapotranspiration coming directly from ground water. The estimation of evapotranspiration in the water-balance equation avoids the need to specify a contributing drainage area for ground water, which in certain cases may be considerably different from the drainage area for surface runoff. Evapotranspiration was calculated by the WREVAP model at the Solar and Meteorological Surface Observation Network (SAMSON) sites. Long-term mean annual base recharge was derived by determining the product of estimated long-term mean annual runoff (the difference between precipitation and evapotranspiration) and the base-flow index (BFI). The BFI was calculated from discharge data obtained from the U.S. Geological Survey's gauging stations in Nebraska. Mapping was achieved by using geographic information systems (GIS) and geostatistics. This approach is best suited for regional-scale applications. It does not require complex hydrogeologic modeling nor detailed knowledge of soil characteristics, vegetation cover, or land-use practices. Long-term mean annual base recharge rates in excess of 110 mm/year resulted in the extreme eastern part of Nebraska. The western portion of the state expressed rates of only 15 to 20 mm annually, while the Sandhills region of north-central Nebraska was estimated to receive twice as much base recharge (40 to 50 mm/year) as areas south of it.     

Three-dimensional numerical modeling of full-space transient electromagnetic responses of water in goaf

The full-space transient electromagnetic response of water-filled goaves in coal mines were numerically modeled. Traditional numerical modeling methods cannot be used to simulate the underground full-space transient electromagnetic field. We used multiple transmitting loops instead of the traditional single transmitting loop to load the transmitting loop into Cartesian grids. We improved the method for calculating the z-component of the magnetic field based on the characteristics of full space. Then, we established the fullspace 3D geoelectrical model using geological data for coalmines. In addition, the transient electromagnetic responses of water-filled goaves of variable shape at different locations were simulated by using the finite-difference time-domain (FDTD) method. Moreover, we evaluated the apparent resistivity results. The numerical modeling results suggested that the resistivity differences between the coal seam and its roof and floor greatly affect the distribution of apparent resistivity, resulting in nearly circular contours with the roadway head at the center. The actual distribution of apparent resistivity for different geoelectrical models of water in goaves was consistent with the models. However, when the goaf water was located in one side, a false low-resistivity anomaly would appear on the other side owing to the full-space effect but the response was much weaker. Finally, the modeling results were subsequently confirmed by drilling, suggesting that the proposed method was effective.     

全极化探地雷达正演模拟

全极化探地雷达不但能获取当前探地雷达使用的共极化信息,而且能使用交叉极化信息,进而更好地分析目标属性.本文在时域有限差分法的基础上,构建了全极化探地雷达的正演模拟方法,通过水平正交双方向同时接收获取全极化信息.标准目标体金属板和角反射器的正演模拟与实验室物理模型测试一致的共极化和交叉极化响应信息,证实了该正演模拟方法的有效性.同时还模拟了典型目标(随机表面和斜裂缝)的响应.正演模拟和实验结果均反映出结合交叉极化响应和共极化响应信息有助于识别和判断目标的方向、结构组成等属性.     

Cooperative modeling: linking science, communication, and ground water planning

Equitable allocation of ground water resources is a growing challenge due to both the increasing demand for water and the competing values placed on its use. While scientists can contribute to a technically defensible basis for water resource planning, this framework must be cast in a broader societal and environmental context. Given the complexity and often contentious nature of resource allocation, success requires a process for inclusive and transparent sharing of ideas complemented by tools to structure, quantify, and visualize the collective understanding and data, providing an informed basis of dialogue, exploration, and decision making. Ideally, a process that promotes shared learning leading to cooperative and adaptive planning decisions. While variously named, mediated modeling, group modeling, cooperative modeling, shared vision planning, or computer-mediated collaborative decision making are similar approaches aimed at meeting these objectives. In this paper, we frame "cooperative modeling" in the context of ground water planning and illustrate the process with two brief examples.     

Recharge,upflux and water table response for shallow water table conditions in southwest Florida

A disproportionate increase or decrease in water table in response to minor water input or drainage is observed in shallow water table conditions inside drainage lysimeters. This increase happens because the capillary fringe of the shallow water table reaches up to or near the surface (Wieringermeer effect). The correlations between water table level changes and rainfall, seepage irrigation, drip irrigation, and drainage were analysed. Correlations with rainfall, seepage irrigation, and drainage were high (R² ranged from 0·46 to 0·97). Drip irrigation had low correlations due to the low rates of application (R² ranged from 0·26 to 0·44). Conventional methods of calculating recharge, such as multiplying the specific yield with the water table fluctuations, cannot be used for Wieringermeer effect situations. A method using water balance data and soil moisture at different depths in the lysimeters was developed to estimate recharge and upflux. The recharge results were used to develop the apparent specific yield S_ya, which could be used to calculate consequent recharge events from water table fluctuation data. Combining the water table fluctuation relationships developed with the S_ya value will allow the prediction of recharge from rainfall and irrigation events without the need for soil moisture equipment. Copyright © 2005 John Wiley & Sons, Ltd.     

Analytic element ground water modeling as a research program (1980 to 2006)

Scientists and engineers who use the analytic element method (AEM) for solving problems of regional ground water flow may be considered a community, and this community can be studied from the perspective of history and philosophy of science. Applying the methods of the Hungarian philosopher of science Imre Lakatos (1922 to 1974), the AEM "research program" is distinguished by its hard core (theoretical basis), protective belt (auxiliary assumptions), and heuristic (problem solving machinery). AEM has emerged relatively recently in the scientific literature and has a relatively modest number of developers and practitioners compared to the more established finite-element and finite-difference methods. Nonetheless, there is evidence to support the assertion that the AEM research program remains in a progressive phase. The evidence includes an expanding publication record, a growing research strand following Professor Otto Strack's book Groundwater Mechanics (1989), the continued placement of AEM researchers in academia, and the further development of innovative analytical solutions and computational solvers/models.     

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.     

General database for ground water site information

In most cases, analysis and modeling of flow and transport dynamics in ground water systems require long-term, high-quality, and multisource data sets. This paper discusses the structure of a multisite database (the H+ database) developed within the scope of the ERO program (French Environmental Research Observatory, http://www.ore.fr). The database provides an interface between field experimentalists and modelers, which can be used on a daily basis. The database structure enables the storage of a large number of data and data types collected from a given site or multiple-site network. The database is well suited to the integration, backup, and retrieval of data for flow and transport modeling in heterogeneous aquifers. It relies on the definition of standards and uses a templated structure, such that any type of geolocalized data obtained from wells, hydrological stations, and meteorological stations can be handled. New types of platforms other than wells, hydrological stations, and meteorological stations, and new types of experiments and/or parameters could easily be added without modifying the database structure. Thus, we propose that the database structure could be used as a template for designing databases for complex sites. An example application is the H+ database, which gathers data collected from a network of hydrogeological sites associated with the French Environmental Research Observatory.