A methodology for validating numerical ground water models

Ground water validation is one of the most challenging issues facing modelers and hydrogeologists. Increased complexity in ground water models has created a gap between model predictions and the ability to validate or build confidence in predictions. Specific procedures and tests that can be easily adapted and applied to determine the validity of site-specific ground water models do not exist. This is true for both deterministic and stochastic models, with stochastic models posing the more difficult validation problem. The objective of this paper is to propose a general validation approach that addresses important issues recognized in previous validation studies, conferences, and symposia. The proposed method links the processes for building, calibrating, evaluating, and validating models in an iterative loop. The approach focuses on using collected validation data to reduce uncertainty in the model and narrow the range of possible outcomes. This method is designed for stochastic numerical models utilizing Monte Carlo simulation approaches, but it can be easily adapted for deterministic models. The proposed methodology relies on the premise that absolute validity is not theoretically possible, nor is it a regulatory requirement. Rather, the proposed methodology highlights the importance of testing various aspects of the model and using diverse statistical tools for rigorous checking and confidence building in the model and its predictions. It is this confidence that will encourage regulators and the public to accept decisions based on the model predictions. This validation approach will be applied to a model, described in this paper, dealing with an underground nuclear test site in rural Nevada.     

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.     

Stochastic-fuzzy multi criteria decision making for robust water resources management

All realistic Multi Criteria Decision Making (MCDM) problems in water resources management face various kinds of uncertainty. In this study the evaluations of the alternatives with respect to the criteria will be assumed to be stochastic. Fuzzy linguistic quantifiers will be used to obtain the uncertain optimism degree of the Decision Maker (DM). A new approach for stochastic-fuzzy modeling of MCDM problems will be then introduced by merging the stochastic and fuzzy approaches into the Ordered Weighted Averaging (OWA) operator. The results of the new approach, entitled SFOWA, give the expected value and the variance of the combined goodness measure for each alternative, which are essential for robust decision making. In order to combine these two characteristics, a composite goodness measure will be defined. By using this measure the model will give more sensitive decisions to the stakeholders whose optimism degrees are different than that of the decision maker. The methodology will be illustrated by using a water resources management problem in the Central Tisza River in Hungary. Finally, SFOWA will be compared to other methods known from the literature to show its suitability for MCDM problems under uncertainty.     

Determining extreme parameter correlation in ground water models

In ground water flow system models with hydraulic-head observations but without significant imposed or observed flows, extreme parameter correlation generally exists. As a result, hydraulic conductivity and recharge parameters cannot be uniquely estimated. In complicated problems, such correlation can go undetected even by experienced modelers. Extreme parameter correlation can be detected using parameter correlation coefficients, but their utility depends on the presence of sufficient, but not excessive, numerical imprecision of the sensitivities, such as round-off error. This work investigates the information that can be obtained from parameter correlation coefficients in the presence of different levels of numerical imprecision, and compares it to the information provided by an alternative method called the singular value decomposition (SVD). Results suggest that (1) calculated correlation coefficients with absolute values that round to 1.00 were good indicators of extreme parameter correlation, but smaller values were not necessarily good indicators of lack of correlation and resulting unique parameter estimates; (2) the SVD may be more difficult to interpret than parameter correlation coefficients, but it required sensitivities that were one to two significant digits less accurate than those that required using parameter correlation coefficients; and (3) both the SVD and parameter correlation coefficients identified extremely correlated parameters better when the parameters were more equally sensitive. When the statistical measures fail, parameter correlation can be identified only by the tedious process of executing regression using different sets of starting values, or, in some circumstances, through graphs of the objective function.     

Adaptive underrelaxation of Picard iterations in ground water models

This methods note examines the use of adaptive underrelaxation of Picard iterations to accelerate the solution convergence for nonlinear ground water flow problems. Ground water problems are nonlinear when drains, phreatophytes, stream aquifer, and similar features are simulated. Typically, simple Picard iterations are used to address such nonlinear problems. Nevertheless, the convergence rate can be slow, or convergence cannot be obtained. However, convergence often can be accelerated using Picard iterations with adaptive underrelaxation, and convergence often can be obtained where it otherwise would not occur.     

A new methodology for water resources multicriteria decision making under uncertainty

A multiciteria decision making problem in water resource is addressed through the generation of fuzzy Pareto optimal set. Methodology is using positive and negative ideal solutions (Lai, Y.-J., Liu, T.-Y., Hwang, C.L. (1994). TOPSIS for MODM. European Journal of Operational Research 76, 486-500) and a set of weights assigned to the objective functions in fuzzy triangular form. Solution of the problem is obtained by transforming each objective function into a set of three objective functions. A planning problem of multicriteria waste water treatment from the literature is used as an illustrative example to demonstrate the utility of the proposed methodology. The obtained fuzzy Pareto solution set has been compared with the deterministic solution set. It is shown that the proposed approach can: (a) capture the uncertainty associated with the assignment of weights; and (b) provide the decision makers with a wider range of solutions to select from.     

Benchmarking of two three-dimensional numerical models in time/space domain to predict railway-induced ground vibrations

In the last 30 years,the scientific community has developed and proposed different models and numerical approaches for the study of vibrations induced by railway traffic.Most of them are formulated in the frequency/wave number domain and with a 2.5D approach.Three-dimensional numerical models formulated in the time/space domain are less frequently used,mainly due to their high computational cost.Notwithstanding,these models present very attractive characteristics,such as the possibility of considering nonlinear behaviors or the modelling of excess pore pressure and non-homogeneous and non-periodic geometries in the longitudinal direction of the track.In this study,two 3D numerical approaches formulated in the time/space domain are compared and experimentally validated.The first one consists of a finite element approach and the second one of a finite difference approach.The experimental validation in an actual case situated in Carregado(Portugal)shows an acceptable fitting between the numerical results and the actual measurements for both models.However,there are some differences among them.This study therefore includes some recommendations for their use in practical soil dynamics and geotechnical engineering.     

The practical use of simplicity in developing ground water models

The advantages of starting with simple models and building complexity slowly can be significant in the development of ground water models. In many circumstances, simpler models are characterized by fewer defined parameters and shorter execution times. In this work, the number of parameters is used as the primary measure of simplicity and complexity; the advantages of shorter execution times also are considered. The ideas are presented in the context of constructing ground water models but are applicable to many fields. Simplicity first is put in perspective as part of the entire modeling process using 14 guidelines for effective model calibration. It is noted that neither very simple nor very complex models generally produce the most accurate predictions and that determining the appropriate level of complexity is an ill-defined process. It is suggested that a thorough evaluation of observation errors is essential to model development. Finally, specific ways are discussed to design useful ground water models that have fewer parameters and shorter execution times.     

Analyzing hydrologic uncertainty and its impact upon decision making in water resources

Bayesian Inference and Decision Theory tools are applied to the problem of synthetic hydrology when model and parameter uncertainty exist. Issues such as optimal parameter estimation, use of synthetic generation in design problems, and the effects of parameter uncertainty on statistical estimation are discussed and applied to the problem of reservoir slorage-yield analysis.     

Testing alternative ground water models using cross-validation and other methods

Many methods can be used to test alternative ground water models. Of concern in this work are methods able to (1) rank alternative models (also called model discrimination) and (2) identify observations important to parameter estimates and predictions (equivalent to the purpose served by some types of sensitivity analysis). Some of the measures investigated are computationally efficient; others are computationally demanding. The latter are generally needed to account for model nonlinearity. The efficient model discrimination methods investigated include the information criteria: the corrected Akaike information criterion, Bayesian information criterion, and generalized cross-validation. The efficient sensitivity analysis measures used are dimensionless scaled sensitivity (DSS), composite scaled sensitivity, and parameter correlation coefficient (PCC); the other statistics are DFBETAS, Cook's D, and observation-prediction statistic. Acronyms are explained in the introduction. Cross-validation (CV) is a computationally intensive nonlinear method that is used for both model discrimination and sensitivity analysis. The methods are tested using up to five alternative parsimoniously constructed models of the ground water system of the Maggia Valley in southern Switzerland. The alternative models differ in their representation of hydraulic conductivity. A new method for graphically representing CV and sensitivity analysis results for complex models is presented and used to evaluate the utility of the efficient statistics. The results indicate that for model selection, the information criteria produce similar results at much smaller computational cost than CV. For identifying important observations, the only obviously inferior linear measure is DSS; the poor performance was expected because DSS does not include the effects of parameter correlation and PCC reveals large parameter correlations.     

An assessment of aquifer storage recovery using ground water flow models

Owing to increased demands on ground water accompanied by increased drawdowns, technologies that use recharge options, such as aquifer storage recovery (ASR), are being used to optimize available water resources and reduce adverse effects of pumping. In this paper, three representative ground water flow models were created to assess the impact of hydrogeologic and operational parameters/factors on recovery efficiency of ASR systems. Flow/particle tracking and solute transport models were used to track the movement of water during injection, storage, and recovery. Results from particle tracking models consistently produced higher recovery efficiency than the solute transport models for the parameters/properties examined because the particle tracking models neglected mixing of the injected and ambient water. Mixing between injected and ambient water affected recovery efficiency. Results from this study demonstrate the interactions between hydrogeologic and operational parameters on predictions of recovery efficiency. These interactions are best simulated using coupled numerical ground water flow and transport models that include the effects of mixing of injected water and ambient ground water.     

Estimating ground water recharge using flow models of perched karstic aquifers

The fraction of rain that is annually recharged to ground water is a function of the transient quantities of precipitation (wet vs. dry years) as well as other meteorological and geologic factors, and thus it is very difficult to estimate. In this study, we have used long records (20 to 30 years) of precipitation and spring discharge to reconstruct the transient character of yearly recharge. These data sets were used to calibrate numerical ground water flow models on the less than 3 km(2) scale for four separate perched karstic aquifers in the Judean and Samarian Mountains of Israel. The stratification and karstic character of the local carbonate rock aquifers cause ground water to flow through discrete dissolution channels and to discharge at isolated springs. An innovative, dual-porosity approach was used where a finite-difference solution simulates flow in the rock matrix, while the karstic channels are simulated using computationally simple drains. Perched conditions are also simulated innovatively using MODFLOW by treating the bottom unsaturated layer as if it is saturated, but by assuming zero pressure head throughout the "unsaturated" layer. Best fitting between measured and computed spring hydrograph data has allowed us to develop a set of empirical functions relating measured precipitation to recharge to the aquifer. The generic methodology presented gives insight into the suspected changes in aquifer recharge rates between particularly wet or dry years.     

太湖流域高度城镇化地区畅流活水多目标调度决策研究

随着城市化进程的加快,高污染负荷、弱水动力条件、强人工干预导致的平原河网地区河道水质恶化、生态衰退已成为制约城市高质量发展的瓶颈之一。结合太湖流域高度城镇化地区水文水动力特性,构建了水动力-水质耦合模型,模拟了不同情景下河网水动力与水质情况。统筹考虑水质改善、水动力提升、经济成本等多目标,建立了活水调度多目标决策体系,基于模糊层次分析法确定评价体系水质改善、水动力提升与经济成本指标层权重分别为0.390、0.345、0.265,为各指标层设计对应的要素层,并利用模糊综合评价法进行评价。结果表明,针对不同调度情景下水质改善、水动力提升及经济成本等多目标的决策,利用多目标调度决策方法可有效确定效果最佳的工程调度情形。太湖流域高度城镇化地区区域性控制工程对畅流活水效果的影响要远大于锡山区控制工程,运东大包围城市防洪工程调度模式对研究区活水效果的影响最大。比选出的最优活水方案实现的研究区活水效果为水质达标率82%,水质平均提升率31%,Ⅲ类水断面占比61%,平均流速0.10 m/s,较优流速占比39%,滞水率32%。相较于传统的单指标或多指标简单比较的决策方法,多目标调度决策方法更具有综合性、...     

Using fuzzy operators to address the complexity in decision making of water resources redistribution in two neighboring river basins

This paper emphasizes the use of fuzzy sets for incorporating objective and subjective uncertainties to address coevolutionary alignment of a suite of water resources redistribution alternatives in a transboundary channel–reservoir system. The highlighted decision making complexity arises from the interactions between two neighboring water systems (i.e., the Tseng-Wen and Kao-Ping River Basins, South Taiwan) where a pending diversion plan has been under intensive debate for over a decade. While the local stakeholders make uncertain science linked with uncertain politics resulting in endless delay of the diversion plan, the environmental advocacy groups stress the increasing concern of loss of biological integrity due to changes of land use when sharing water resources across the boundary. Consequently, there is a need to generate a novel integration that enables us to consider a vast number of internal weirs, water intakes, reservoirs, drainage ditches, and transfer pipelines within the basin and bring out the connectivity via diversion between these two neighboring river basins under uncertainty. To explore the managerial implications with varying risk perception and risk attitude, four types of fuzzy operators tailored for the fuzzy multi-objective decision analysis depict greater flexibility in representing the complexity of possible trade-offs among those alternatives. These trade-offs in the multi-objective evaluation context are constrained by physical, chemical, socioeconomic, managerial, and technical factors reflecting the needs for adaptive water resources management. Findings indicates that the use of fuzzy operators is instructive, which could provide unique guidance for enlightening the potential barriers in sustainable water resources management at the regional scale.     

AHP-based group decision making approach to supplier selection of irrigation equipment

Supplier selection is a complex task which assumes decision making in presence of many conflicting criteria and various parameters. If there are more than one decision maker, the problem shifts into a group context and it requires proper approach in mediating the decision making process and use of supporting multi-criteria methods and tools. This paper proposes group decision making approach for supplier selection based on analytic hierarchy process (AHP) that is combined with consensus convergence model, and two voting methods, non-preferential approval voting and preferential Borda count. Proposed approach utilized strengths of these methods thus enabling their adaption to the specific decision problem of supplier selection. An example of selecting a supplier of irrigation equipment in the company engaged in projecting, installing and maintenance of irrigation systems is used to explain and demonstrate how proposed approach can be implemented. Furthermore, this approach is viable as sufficiently general in supporting different selection processes in a field of water planning, management, and development and it can be adapted and applied on various group decision making problems.     

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.     

A numerical method to index the risk of conflict around the transboundary water resources. Validation by a studied case

The world-wide crisis of water will make that the transboundary water resources will be the object of tensions and litigations increasingly marked. Also, the transboundary conflicts on fresh water intended to the categories of traditional uses are subjected to a growing attention on behalf of national and international organizations. Each case of conflict, related as well to surface water as groundwater, has its accurate characteristics and to appreciate its relative importance, it is necessary to consult a broad documentation based on reports of commissions, organizations or groups of research. According to criteria and data taken into account, the situation is some times appreciated differently.