Bayesian Methods for Assessing Water Quality

A new methodology is developed to analyze existing monitoring networks. This methodology incorporates different aspects of monitoring, including vulnerability/probability assessment, environmental health risk, the value of information, and redundancy reduction. A conceptual framework for groundwater quality monitoring is formulated to represent the methodology's context. Relevance vector machine ͑RVM͒ plays a basic role in this conceptual framework, and is employed to reduce redundancy and to create probability map of contaminant distribution, and accordingly to estimate the expected value of sample information. Disability adjusted life years approach of the global burden of disease is used for quantifying the health risk consequences. This is demonstrated through a case study application to nitrate contamination monitoring in the West Bank, Palestine. The results obtained from the RVM analysis showed that an overlap error of less than 30% were obtained based on using around 30% of the monitoring sites ͑170 relevance vectors͒. This reflects the importance of the RVM as a useful model for improving the efficiency of monitoring systems, both in terms of reducing redundancy and increasing the information content of the collected data. However, in this application, the results of health risk assessment and the evaluation of monitoring investments were less encouraging due to the minimal elasticity of the nitrate health effect with respect to monitoring information and uncertainty.

Deplorable quality of groundwater arising from saltwater intrusion, natural leaching and anthropogenic activities is one of the major concerns for the society. Assessment of groundwater quality is, therefore, a primary objective of scientific research. Here, we propose an artificial neural network-based method set in a Bayesian neural network (BNN) framework and employ it to assess groundwater quality. The approach is based on analyzing 36 water samples and inverting up to 85 Schlumberger vertical electrical sounding data. We constructed a priori model by suitably parameterizing geochemical and geophysical data collected from the western part of India. The posterior model (post-inversion) was estimated using the BNN learning procedure and global hybrid Monte Carlo/ Markov Chain Monte Carlo optimization scheme. By suitable parameterization of geochemical and geophysical parameters, we simulated 1,500 training samples, out of which 50 % samples were used for training and remaining 50 % were used for validation and testing. We show that the trained model is able to classify validation and test samples with 85 % and 80 % accuracy respectively. Based on crosscorrelation analysis and Gibb’s diagram of geochemical attributes, the groundwater qualities of the study area were classified into following three categories: “Very good”, “Good”, and “Unsuitable”. The BNN model-based results suggest that groundwater quality falls mostly in the range of “Good” to “Very good” except for some places near the Arabian Sea. The new modeling results powered by uncertainty and statistical analyses would provide useful constrain, which could be utilized in monitoring and assessment of the groundwater quality.

Lecture Notes in Computer Science, 2004

Modular neural networks have the possibility of overcoming common scalability and interference problems experienced by fully connected neural networks when applied to large databases. In this paper we trial an approach to constructing modular ANN's for a very large problem from CEDAR for the classification of handwritten characters. In our approach, we apply progressive task decomposition methods based upon clustering and regression techniques to find modules. We then test methods for combining the modules into ensembles and compare their structural characteristics and classification performance with that of an ANN having a fully connected topology. The results reveal improvements to classification rates as well as network topologies for this problem.

Water Science and Technology, 2012

A strong normative development in Europe, including the Nitrate Directive (1991) and the Water Framework Directive (WFD) (2000), has been promulgated. The WFD states that all water bodies have to reach a good quantitative and chemical status by 2015. It is necessary to consider different objectives, often in conflict, for tackling a suitable assessment of the impacts generated by water policies aimed to reduce nitrate pollution in groundwater. For that, an annual lumped probabilistic model based on Bayesian networks (BNs) has been designed for hydro-economic modelling of groundwater quality control under uncertain conditions. The information introduced in the BN model comes from different sources such as previous groundwater flow and mass transport simulations, hydro-economic models, stakeholders and expert opinion, etc. The methodology was applied to the El Salobral–Los Llanos aquifer unit within the ‘Easter Mancha’ groundwater body, which is one of the largest aquifers in Spain (7...

Journal of Hydrologic Engineering, 2013

A formal Bayesian methodology is presented for integrated model calibration and risk-based water quality management using Bayesian Monte Carlo simulation and maximum likelihood estimation (BMCML). The primary focus is on lucid integration of model calibration with risk-based water quality management and total maximum daily load (TMDL) estimation under conditions of uncertainty. The sources of uncertainty considered in the analysis are modeling errors, observational data errors and fuzziness of the water quality standard. The difference between observed data or transformation thereof and corresponding model response is assumed to follow first-order Markov process, a specific case of which is statistically independent Gaussian errors. The BMCML method starts with sampling parameter sets from prior probability distributions of the model parameters and uses Bayes theorem and the maximum likelihood technique to estimate the triplicate (variance of residual errors, bias and autocorrelation coefficient of total errors) for each parameter set and the corresponding likelihood value. By approximating integration over the entire parameter space discretely, analytical expressions are derived for the cumulative probability distributions of model outputs and probability of violating water quality standards. The solution of the TMDL problem and related margin of safety (MOS) is then framed in the context of the developed Bayesian framework. Three example applications of varying complexities are utilized to demonstrate the versatility of the Bayesian methodology for water quality management. The BMCML methodology is validated using a hypothetical lake-phosphorus model and familiar statistical benchmarks. It is shown that the risk-based framework can estimate the reliability of an arbitrarily selected MOS as demonstrated in the Fork Creek bacteria and Shunganunga Creek dissolved oxygen TMDL case-studies. It is also shown that neglecting covariation among model parameters (i.e., by sampling parameter values from their posterior marginal distributions) influences the estimation of probability of exceedance and could potentially lead to the overestimation of the MOS at low risk levels.

1990

In this paper an alternative Bayesian estimation procedure is described. This Bayesian method uses what Omre (1987) called "qualified guesses" as prior information. A new type of semi-variogra m, that proved to be very useful in the analysis of groundwater levels, is discussed. The procedure is applied to water levels in the Dewetsdorp aquifer with very promising results.

Journal of Water Resource and Protection, 2012

Groundwater contamination by nitrate within an unconfined sandy aquifer was mapped using a Bayesian Data Fusion (BDF) framework. Groundwater monitoring data was therefore combined with a statistical groundwater contamination model. In a first step, nitrate concentrations, measured at 99 monitoring stations irregularly distributed within the study area, were spatialized using ordinary kriging. Secondly, a statistical regression tree model of nitrate contamination in groundwater was constructed using land use, depth to the water table, altitude and slope as predictor variables. This allowed the construction of a regression tree based contamination map. In a third step, BDF was used to combine optimally the kriged nitrate contamination map with the regression tree based model into one single map, thereby weighing the kriged and regression tree based contamination maps in terms of their estimation uncertainty. It is shown that BDF allows integrating different sources of information about contamination in a final map, allowing quantifying the expected value and variance of the nitrate contamination estimation. It is also shown that the uncertainty in the final map is smaller than the uncertainty from the kriged or regression tree based contamination map.

International Journal of Computational Intelligence Research, 2007

Development and rapid population growth have impacted Oman's water resources significantly. Increasing the degradation of groundwater quality by salinization and chemical contaminants threaten primary sources of drinking water, especially in the coastal agricultural areas. Hence, there is a substantial demand in the country for water conservation technology. This work elaborates the quality deterioration of groundwater due to chemical contaminants, which are the prime environmental issue of the Salalah region to the south of Oman. First, we describe the development and application of Dynamic Bayesian Networks (DBNs) combine with a preprocessing Bayesian technique to determine the impact of these contaminants on groundwater quality. These paradigm address the probabilistic and dynamic characteristics that are significant in the understanding of pollution generation from various information sources, but in a fashion which manages the uncertainties in these sources. Second, we discuss and compare the results produced by these methods with that produced by the application of classical time series models.

Iranian Journal of Science and Technology-Transactions of Civil Engineering, 2016

Pollution source identification in groundwater resources is a challenging task due to existing uncertainties in both pollutant source characteristics and mass transport in porous media. To obtain a robust and cost-effective groundwater monitoring configuration, this paper presents a new regret-based optimization model which minimizes the number of monitoring wells and average regret in estimating undetected polluted area. A Monte Carlo analysis is used to consider existing uncertainties in both pollution source characteristics and parameters of groundwater quality simulation model. MODFLOW and MT3D, groundwater quantity and quality simulation models, are used to simulate the spatial and temporal variations of a water quality indicator in groundwater. For each non-dominated solution provided by a bi-objective optimization model, the optimal positions of monitoring wells are also determined by minimizing the corresponding regret in undetected polluted area. Furthermore, a Bayesian network (BN) is trained and validated based on results of the Monte Carlo analysis. The trained BN is capable of accurately determining an unknown pollution source using monitoring data in real-time operation of monitoring system. To demonstrate the efficiency and applicability of the proposed methodology, it is applied to the Tehran Aquifer in the Tehran refinery region, which is highly polluted due to leakage from several tanks of petroleum products.