A hybrid artificial neural network-numerical model for ground water problems

Numerical models constitute the most advanced physical-based methods for modeling complex ground water systems. Spatial and/or temporal variability of aquifer parameters, boundary conditions, and initial conditions (for transient simulations) can be assigned across the numerical model domain. While this constitutes a powerful modeling advantage, it also presents the formidable challenge of overcoming parameter uncertainty, which, to date, has not been satisfactorily resolved, inevitably producing model prediction errors. In previous research, artificial neural networks (ANNs), developed with more accessible field data, have achieved excellent predictive accuracy over discrete stress periods at site-specific field locations in complex ground water systems. In an effort to combine the relative advantages of numerical models and ANNs, a new modeling paradigm is presented. The ANN models generate accurate predictions for a limited number of field locations. Appending them to a numerical model produces an overdetermined system of equations, which can be solved using a variety of mathematical techniques, potentially yielding more accurate numerical predictions. Mathematical theory and a simple two-dimensional example are presented to overview relevant mathematical and modeling issues. Two of the three methods for solving the overdetermined system achieved an overall improvement in numerical model accuracy for various levels of synthetic ANN errors using relatively few constrained head values (i.e., cells), which, while demonstrating promise, requires further research. This hybrid approach is not limited to ANN technology; it can be used with other approaches for improving numerical model predictions, such as regression or support vector machines (SVMs).     

Optimal sequencing for a multipurpose water supply system

The optimal sequencing of a multipurpose water supply system in the Hajduhátság region of Hungary is determined by dynamic programming. The goal function minimizes the present value of capital costs, operation costs, and economic losses due to water shortages. Future water requirements are considered to be random variables because of natural and forecasting uncertainties. The nonlinear optimization problem at each stage is equivalent to a readily solved game theoretical problem, the solution of which is straightforward. Sensitivity analysis performed with respect to economic losses, water requirements and discount rate, showed that optimal development and sequencing depend largely on the economic losses and the discount rate.     

Kriging without negative weights

Under a constant drift, the linear kriging estimator is considered as a weighted average ofn available sample values. Kriging weights are determined such that the estimator is unbiased and optimal. To meet these requirements, negative kriging weights are sometimes found. Use of negative weights can produce negative block grades, which makes no practical sense. In some applications, all kriging weights may be required to be nonnegative. In this paper, a derivation of a set of nonlinear equations with the nonnegative constraint is presented. A numerical algorithm also is developed for the solution of the new set of kriging equations.     

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.     

Multiobjective analysis of a public wellfield using artificial neural networks

As competition for increasingly scarce ground water resources grows, many decision makers may come to rely upon rigorous multiobjective techniques to help identify appropriate and defensible policies, particularly when disparate stakeholder groups are involved. In this study, decision analysis was conducted on a public water supply wellfield to balance water supply needs with well vulnerability to contamination from a nearby ground water contaminant plume. With few alternative water sources, decision makers must balance the conflicting objectives of maximizing water supply volume from noncontaminated wells while minimizing their vulnerability to contamination from the plume. Artificial neural networks (ANNs) were developed with simulation data from a numerical ground water flow model developed for the study area. The ANN-derived state transition equations were embedded into a multiobjective optimization model, from which the Pareto frontier or trade-off curve between water supply and wellfield vulnerability was identified. Relative preference values and power factors were assigned to the three stakeholders, namely the company whose waste contaminated the aquifer, the community supplied by the wells, and the water utility company that owns and operates the wells. A compromise pumping policy that effectively balances the two conflicting objectives in accordance with the preferences of the three stakeholder groups was then identified using various distance-based methods.     

Application of Artificial Neural Networks to Complex Groundwater Management Problems

As water quantity and quality problems become increasingly severe, accurate prediction and effective management of scarcer water resources will become critical. In this paper, the successful application of artificial neural network (ANN) technology is described for three types of groundwater prediction and management problems. In the first example, an ANN was trained with simulation data from a physically based numerical model to predict head (groundwater elevation) at locations of interest under variable pumping and climate conditions. The ANN achieved a high degree of predictive accuracy, and its derived state-transition equations were embedded into a multiobjective optimization formulation and solved to generate a trade-off curve depicting water supply in relation to contamination risk. In the second and third examples, ANNs were developed with real-world hydrologic and climate data for different hydrogeologic environments. For the second problem, an ANN was developed using data collected for a 5-year, 8-month period to predict heads in a multilayered surficial and limestone aquifer system under variable pumping, state, and climate conditions. Using weekly stress periods, the ANN substantially outperformed a well-calibrated numerical flow model for the 71-day validation period, and provided insights into the effects of climate and pumping on water levels. For the third problem, an ANN was developed with data collected automatically over a 6-week period to predict hourly heads in 11 high-capacity public supply wells tapping a semiconfined bedrock aquifer and subject to large well-interference effects. Using hourly stress periods, the ANN accurately predicted heads for 24-hour periods in all public supply wells. These test cases demonstrate that the ANN technology can solve a variety of complex groundwater management problems and overcome many of the problems and limitations associated with traditional physically based flow models.     

Predicting conductance due to upconing using neural networks

Artificial neural networks (ANNs) were developed to accurately predict highly time-variable specific conductance values in an unconfined coastal aquifer. Conductance values in the fresh water lens aquifer change in response to vertical displacements of the brackish zone and fresh water-salt water interface, which are caused by variable pumping and climate conditions. Unlike physical-based models, which require hydrologic parameter inputs, such as horizontal and vertical hydraulic conductivities, porosity, and fluid densities, ANNs can "learn" system behavior from easily measurable variables. In this study, the ANN input predictor variables were initial conductance, total precipitation, mean daily temperature, and total pumping extraction. The ANNs were used to predict salinity (specific conductance) at a single monitoring well located near a high-capacity municipal-supply well over time periods ranging from 30 d to several years. Model accuracy was compared against both measured/interpolated values and predictions were made with linear regression, and in general, excellent prediction accuracy was achieved. For example, although the average percent change of conductance over 90-d periods was 39%, the absolute mean prediction error achieved with the ANN was only 1.1%. The ANNs were also used to conduct a sensitivity analysis that quantified the importance of each of the four predictor variables on final conductance values, providing valuable insights into the dynamics of the system. The results demonstrate that the ANN technology can serve as a powerful and accurate prediction and management tool, minimizing degradation of ground water quality to the extent possible by identifying appropriate pumping policies under variable and/or changing climate conditions.     

A neural network model for predicting aquifer water level elevations

Artificial neural networks (ANNs) were developed for accurately predicting potentiometric surface elevations (monitoring well water level elevations) in a semiconfined glacial sand and gravel aquifer under variable state, pumping extraction, and climate conditions. ANNs "learn" the system behavior of interest by processing representative data patterns through a mathematical structure analogous to the human brain. In this study, the ANNs used the initial water level measurements, production well extractions, and climate conditions to predict the final water level elevations 30 d into the future at two monitoring wells. A sensitivity analysis was conducted with the ANNs that quantified the importance of the various input predictor variables on final water level elevations. Unlike traditional physical-based models, ANNs do not require explicit characterization of the physical system and related physical data. Accordingly, ANN predictions were made on the basis of more easily quantifiable, measured variables, rather than physical model input parameters and conditions. This study demonstrates that ANNs can provide both excellent prediction capability and valuable sensitivity analyses, which can result in more appropriate ground water management strategies.     

Stochastic forecasting of mine water inrushes

An event-based stochastic forecasting approach is used to model water inrushes into underground works under karstic water hazard. The stochastic properties of inrushes are related to the statistical properties of fissures in the karstic rock. The probability distributions (DF) of five random variables of interest in design are estimated; namely, inrush yield q, number N of inrushes per unit area, distance L between inrushes, maximum q_max in N events and total yield Q. The phenomenological hypotheses of log normal DF of q and Poisson DF of N are reinforced by observation data. On the basis of these DF, a Monte Carlo simulation of a spatial Poisson process of inrushes is run to estimate the DF of q_max and Q. The derivation of Bayesian DF to account for parameter uncertainty is discussed. The stochastic model is used for design and operation of minewater control facilities in the Transdanubian karstic region of Hungary.