Risk-based assessment of arsenic-affected aquacultural water in blackfoot disease hyperendemic areas

This work explored a risk-based arsenic (As) regulation in farmed pond water by ingesting tilapia (Oreochromis mossambicus) in blackfoot disease hyperendemic areas and discussed a rational As regulation in pond water. Monte Carlo analysis was used to propagate the parameter uncertainty and to assess probabilistically regulation risks. A dynamic scheme of groundwater management was proposed that curves of utilization ratios against As concentrations in groundwater were established based on the risk-based regulation. The 5th to 95th percentiles of risks range from 3.5 × 10⁻⁷ to 6.0 × 10⁻⁵ via ingesting the farmed tilapia under the current As regulation in farmed pond water in Taiwan, 50 μg/L. To compare to inorganic As regulation in drinking water, the current As regulation in farmed pond water does not pose a great threat to human health, but it is unsafe. Therefore, this study suggests that the regulation of As in farmed pond water is revised to be 25 μg/L.     

Knowledge,transparency, and refutability in groundwater models,an example from the Death Valley regional groundwater flow system

This work demonstrates how available knowledge can be used to build more transparent and refutable computer models of groundwater systems. The Death Valley regional groundwater flow system, which surrounds a proposed site for a high level nuclear waste repository of the United States of America, and the Nevada National Security Site (NNSS), where nuclear weapons were tested, is used to explore model adequacy, identify parameters important to (and informed by) observations, and identify existing old and potential new observations important to predictions. Model development is pursued using a set of fundamental questions addressed with carefully designed metrics. Critical methods include using a hydrogeologic model, managing model nonlinearity by designing models that are robust while maintaining realism, using error-based weighting to combine disparate types of data, and identifying important and unimportant parameters and observations and optimizing parameter values with computationally frugal schemes. The frugal schemes employed in this study require relatively few (10–1000 s), parallelizable model runs. This is beneficial because models able to approximate the complex site geology defensibly tend to have high computational cost. The issue of model defensibility is particularly important given the contentious political issues involved.     

Stochastic modelling of groundwater flow and solute transport in aquifers

This paper presents an introductory overview of recently developed stochastic theories for tackling spatial variability problems in predicting groundwater flow and solute transport. Advantages and limitations of the theories are discussed. Lastly, strategies based on the stochastic approaches to predict solute transport in aquifers are recommended.     

Probabilistic risk and uncertainty analysis for bioremediation of four chlorinated ethenes in groundwater

Groundwater contamination risk assessment for health-threatening compounds should benefit from a stochastic environmental risk assessment which considers the effects of biological, chemical, human behavioral, and physiological processes that involve elements of biotic and abiotic aquifer uncertainty, and human population variability. This paper couples a complex model of chemical degradation and transformation with movement in an aquifer undergoing bioremediation to generate a health risk analysis for different population cohorts in the community. A two-stage Monte Carlo simulation has separate stages for population variability and aquifer uncertainty yielding a computationally efficient and conceptually attractive algorithm. A hypothetical example illustrates how risk variance analysis can be conducted to determine the distribution of risk, and the relative impact of uncertainty and variability in different sets of parameters upon the variation of risk values for adults, adolescents, and children. The groundwater example considers a community water supply contaminated with chlorinated ethenes. Biodegradation pathways are enhanced by addition of butyrate. The results showed that the contribution of uncertainty to the risk variance is comparable to that of variability. Among the uncertain parameters considered, transmissivity accounted for the major part of the output variance. Children were the most susceptible and vulnerable population cohort.     

An integrated fuzzy-stochastic modeling approach for assessing health-impact risk from air pollution

High concentrations of air pollutants in the ambient environment can result in breathing problems with human communities. Effective assessment of health-impact risk from air pollution is important for supporting decisions of the related detection, prevention, and correction efforts. However, the quality of information available for environmental/health risk assessment is often not satisfactory enough to be presented as deterministic numbers. Stochastic method is one of the methods for tackling those uncertainties, by which uncertain information can be presented as probability distributions. However, if the uncertainties can not be presented as probabilities, they can then be handled through fuzzy membership functions. In this study, an integrated fuzzy-stochastic modeling (IFSM) approach is developed for assessing air pollution impacts towards asthma susceptibility. This development is based on Monte Carlo simulation for the fate of SO₂ in the ambient environment, examination of SO₂ concentrations based on the simulation results, quantification of evaluation criteria using fuzzy membership functions, and risk assessment based on the combined fuzzy-stochastic information. The IFSM entails (a) simulation for the fate of pollutants in ambient environment, with the consideration of source/medium uncertainties, (b) formulation of fuzzy air quality management criteria under uncertain human-exposure pathways, exposure dynamics, and SPG-response variations, and (c) integrated risk assessment under complexities of the combined fuzzy/stochastic inputs of contamination level and health effect (i.e., asthma susceptibility). The developed IFSM is applied to a study of regional air quality management. Reasonable results have been generated, which are useful for evaluating health risks from air pollution. They also provide support for regional environmental management and urban planning.     

Modeling of transport in groundwater for environmental risk assessment

This paper presents the principles underlying a recently developed numerical technique for modeling transport in heterogeneous porous media. The method is then applied to derive the concentration mean and variance, the concentration CDF, exceedance probabilities and exposure time CDF, which are required by various regulatory agencies for risk and performance assessment calculations. The dependence of the various statistics on elapsed travel time, location in space, the dimension of the detection volume, natural variability and pore-scale dispersion is investigated and discussed.     

Contamination of groundwater under cultivated fields in an arid environment, central Arava Valley, Israel

The purpose of this study is to obtain a better understanding of groundwater contamination processes in an arid environment (precipitation of 50 mm/year) due to cultivation. Additional aims were to study the fate of N, K, and other ions along the whole hydrological system including the soil and vadose zone, and to compare groundwater in its natural state with contaminated groundwater (through the drilling of several wells).

A combination of physical, chemical, and isotopic analyses was used to describe the hydrogeological system and the recharge trends of water and salts to the aquifers. The results indicate that intensive irrigation and fertilization substantially affected the quantity and quality of groundwater recharge. Low irrigation efficiency of about 50% contributes approximately 3.5–4 million m³/year to the hydrological system, which corresponds to 0.65 m per year of recharge in the irrigated area, by far the most significant recharge mechanism.

Two main contamination processes were identified, both linked to human activity: (1) salinization due to circulation of dissolved salts in the irrigation water itself, mainly chloride, sulfate, sodium and calcium, and (2) direct input of nitrate and potassium mainly from fertilizers.

The nitrate concentrations in a local shallow groundwater lens range between 100 and 300 mg/l and in the upper sub-aquifer are over 50 mg/l. A major source of nitrate is fertilizer N in the excess irrigation water. The isotopic compositions of δ¹⁵N–NO₃ (range of 4.9–14.8‰) imply also possible contributions from nearby sewage ponds and/or manure. Other evidence of contamination of the local groundwater lens includes high concentrations of K (20–120 mg/l) and total organic carbon (about 10 mg/l).     

Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations

In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions.     

Simulation-based risk assessment of contaminated sites under remediation scenarios, planning periods, and land-use patterns—a Canadian case study

Risk assessment of contaminated sites is crucial for quantifying adverse impacts on human health and the environment. It also provides effective decision support for remediation and management of such sites. This study presents an integrated approach for environmental and health risk assessment of subsurface contamination through the incorporation of a multiphase multicomponent modeling system within a general risk assessment framework. The method is applied to a petroleum-contaminated site in western Canada. Three remediation scenarios with different efficiencies (0, 60, and 90%) and planning periods (10, 20, 40, 60, and 80 years later) are examined for each of the five potential land-use plans of the study site. Then three risky zones with different temporal and spatial distributions are identified based on the local environmental guidelines and the excess lifetime cancer risk criteria. The obtained results are useful for assessing potential human health effects when the groundwater is used for drinking water supply. They are also critical for evaluating environmental impacts when the groundwater is used for irrigation, stockbreeding, fish culture, or when the site remains the status quo. Moreover, the results indicate that the proposed method can effectively identify risky zones with different risk levels under various remediation actions, planning periods, and land-use patterns.     

Data-worth analysis for multiobjective optimal design of pump-and-treat remediation systems

The design and the management of pump-and-treat (PAT) remediation systems for contaminated aquifers under uncertain hydrogeological settings and parameters often involve decisions that trade off cost optimality against reliability. Both design objectives can be improved by planning site characterization programs that reduce subsurface parameter uncertainty. However, the cost for subsurface investigation often weighs heavily upon the budget of the remedial action and must thus be taken into account in the trade-off analysis. In this paper, we develop a stochastic data-worth framework with the purpose of estimating the economic opportunity of subsurface investigation programs. Since the spatial distribution of hydraulic conductivity is most often the major source of uncertainty, we focus on the direct sampling of hydraulic conductivity at prescribed locations of the aquifer. The data worth of hydraulic conductivity measurements is estimated from the reduction of the overall management cost ensuing from the reduction in parameter uncertainty obtained from sampling. The overall cost is estimated as the expected value of the cost of installing and operating the PAT system plus penalties incurred due to violations of cleanup goals and constraints. The crucial point of the data-worth framework is represented by the so-called pre-posterior analysis. Here, the tradeoff between decreasing overall costs and increasing site-investigation budgets is assessed to determine a management strategy proposed on the basis of the information available at the start of remediation. The goal of the pre-posterior analysis is to indicate whether the proposed management strategy should be implemented as is, or re-designed on the basis of additional data collected with a particular site-investigation program. The study indicates that the value of information is ultimately related to the estimates of cleanup target violations and decision makers’ degree of risk-aversion.     

A BME solution of the inverse problem for saturated groundwater flow

In most real-world hydrogeologic situations, natural heterogeneity and measurement errors introduce major sources of uncertainty in the solution of the inverse problem. The Bayesian Maximum Entropy (BME) method of modern geostatistics offers an efficient solution to the inverse problem by first assimilating various physical knowledge bases (hydrologic laws, water table elevation data, uncertain hydraulic resistivity measurements, etc.) and then producing robust estimates of the subsurface variables across space. We present specific methods for implementing the BME conceptual framework to solve an inverse problem involving Darcys law for subsurface flow. We illustrate one of these methods in the case of a synthetic one-dimensional case study concerned with the estimation of hydraulic resistivity conditioned on soft data and hydraulic head measurements. The BME framework processes the physical knowledge contained in Darcys law and generates accurate estimates of hydraulic resistivity across space. The optimal distribution of hard and soft data needed to minimize the associated estimation error at a specified sampling cost is determined. This work was supported by grants from the National Institute of Environmental Health Sciences (Grant no. 5 P42 ES05948 and P30ES10126), the National Aeronautics and Space Administration (Grant no. 60-00RFQ041), the Army Research Office (Grant no. DAAG55-98-1-0289), and the National Science Foundation under Agreement No. DMS-0112069.     

Stochastic modelling and risk analysis of groundwater pollution using FORM coupled with automatic differentiation

The first order reliability method (FORM) has been widely used in probabilistic modelling of groundwater problems. The FORM approach requires an iterative optimization procedure to find out the system failure point (the most probable point).The advantages of this approach are that it does not require many computations in comparison with other methods when applied to simple problems, and it produces reasonably accurate results. However, it has been found that the computations of FORM can equal or exceed that of other methods in case of large number of variables.In this paper, a new implementation of FORM was proposed with more efficiency and accuracy than the traditional FORM method. In the proposed approach, automatic differentiation is used to obtain the gradient vector of the limit state function, which is required by FORM, instead of using finite difference estimation. This way, the first order derivative was obtained with a very good accuracy, and with less computational effort. Based on the obtained results, it is found that the proposed implementation of FORM is a very good tool for probabilistic risk assessment and uncertainty analysis in groundwater problems.     

Analytic modeling of groundwater dynamics with an approximate impulse response function for areal recharge

An analytic approach is presented for the simulation of variations in the groundwater level due to temporal variations of recharge in surficial aquifers. Such variations, called groundwater dynamics, are computed through convolution of the response function due to an impulse of recharge with a measured time series of recharge. It is proposed to approximate the impulse response function with an exponential function of time which has two parameters that are functions of space only. These parameters are computed by setting the zeroth and first temporal moments of the approximate impulse response function equal to the corresponding moments of the true impulse response function. The zeroth and first moments are modeled with the analytic element method. The zeroth moment may be modeled with existing analytic elements, while new analytic elements are derived for the modeling of the first moment. Moment matching may be applied in the same fashion with other approximate impulse response functions. It is shown that the proposed approach gives accurate results for a circular island through comparison with an exact solution; both a step recharge function and a measured series of 10 years of recharge were used. The presented approach is specifically useful for modeling groundwater dynamics in aquifers with shallow groundwater tables as is demonstrated in a practical application. The analytic element method is a gridless method that allows for the precise placement of ditches and streams that regulate groundwater levels in such aquifers; heads may be computed analytically at any point and at any time. The presented approach may be extended to simulate the effect of other transient stresses (such as fluctuating surface water levels or pumping rates), and to simulate transient effects in multi-aquifer systems.     

Bias and uncertainty in regression-calibrated models of groundwater flow in heterogeneous media

Groundwater models need to account for detailed but generally unknown spatial variability (heterogeneity) of the hydrogeologic model inputs. To address this problem we replace the large, m-dimensional stochastic vector β that reflects both small and large scales of heterogeneity in the inputs by a lumped or smoothed m-dimensional approximation γθ_∗, where γ is an interpolation matrix and θ_∗ is a stochastic vector of parameters. Vector θ_∗ has small enough dimension to allow its estimation with the available data. The consequence of the replacement is that model function f(γθ_∗) written in terms of the approximate inputs is in error with respect to the same model function written in terms of β, f(β), which is assumed to be nearly exact. The difference f(β) − f(γθ_∗), termed model error, is spatially correlated, generates prediction biases, and causes standard confidence and prediction intervals to be too small. Model error is accounted for in the weighted nonlinear regression methodology developed to estimate θ_∗ and assess model uncertainties by incorporating the second-moment matrix of the model errors into the weight matrix. Techniques developed by statisticians to analyze classical nonlinear regression methods are extended to analyze the revised method. The analysis develops analytical expressions for bias terms reflecting the interaction of model nonlinearity and model error, for correction factors needed to adjust the sizes of confidence and prediction intervals for this interaction, and for correction factors needed to adjust the sizes of confidence and prediction intervals for possible use of a diagonal weight matrix in place of the correct one. If terms expressing the degree of intrinsic nonlinearity for f(β) and f(γθ_∗) are small, then most of the biases are small and the correction factors are reduced in magnitude. Biases, correction factors, and confidence and prediction intervals were obtained for a test problem for which model error is large to test robustness of the methodology. Numerical results conform with the theoretical analysis.     

Modeling groundwater velocity uncertainty in nonstationary composite porous media

Despite the intensive research over the past decades in the field of stochastic subsurface hydrology, our ability to analyze and model heterogeneous groundwater systems remains limited. Most existing theories are either too restrictive to handle practical complexity or too expensive to be applied to realistic problem sizes. In this paper we present approximate, closed-form equations that allow modeling 2D nonstationary flows in statistically inhomogeneous aquifers, including composite aquifers containing multiple zones characterized by different statistical models. The composite representation has the effect of decreasing the variance of deviations from the mean, relaxing the limitation of the small-perturbation assumption. The simple formulas are illustrated with a number of examples and compared with a corresponding first-order nonstationary numerical analysis and Monte Carlo simulation. The results show that, despite the gross simplifications, the closed-form equations are robust and able to capture complex variance dynamics, reproducing surprisingly well the first-order numerical solutions and the Monte Carlo simulation even in highly nonstationary, variable situations.     

On the optimal risk based design of highway drainage structures

For a proposed highway bridge or culvert, the total cost to the public during its expected service life includes capital investment on the structures, regular operation and maintenance costs, and various flood related costs. The flood related damage costs include items such as replacement and repair costs of the highway bridge or culvert, flood plain property damage costs, users costs from traffic interruptions and detours, and others. As the design discharge increases, the required capital investment increases but the corresponding flood related damage costs decrease. Hydraulic design of a bridge or culvert using a riskbased approach is to choose among the alternatives the one associated with the least total expected cost.In this paper, the risk-based design procedure is applied to pipe culvert design. The effect of the hydrologic uncertainties such as sample size and type of flood distribution model on the optimal culvert design parameters including design return period and total expected cost are examined in this paper.     

Estimating the role of a ditch network in groundwater recharge in a Mediterranean catchment using a water balance approach

Water balance variables were monitored in a farmed Mediterranean catchment characterized by a dense ditch network to allow for the separate estimation of the diffuse and concentrated recharge terms during flood events. The 27 ha central part of the catchment was equipped with (i) rain gauges, (ii) ditch gauge stations, (iii) piezometers, (iv) neutron probes, and (v) an eddy covariance mast including a 3D sonic anemometer and a fast hygrometer. The water balance was calculated for two autumnal rain and flood events. We also estimated the uncertainty of this approach with Monte Carlo simulations. Results show, that although ditch area represents only 6% of the total study area, concentrated recharge appeared to be the main source of groundwater recharge. Indeed, it was 40–50% of the total groundwater recharge for autumnal events, which are the major annual recharge events. This indicate that both, concentrated and diffuse recharge should be taken into account in any hydrological modeling approach for Mediterranean catchments. This also means that, since they collect overland flow that is often largely contaminated by chemicals, ditches may be a place where groundwater contamination is likely to occur. The uncertainty analysis indicates that recharge estimates based on water balance exhibit large uncertainty ranges. Nevertheless, Monte Carlo simulations showed that concentrated recharge was higher than expected based on their area.     

Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion

Nonlocal moment equations allow one to render deterministically optimum predictions of flow in randomly heterogeneous media and to assess predictive uncertainty conditional on measured values of medium properties. We present a geostatistical inverse algorithm for steady-state flow that makes it possible to further condition such predictions and assessments on measured values of hydraulic head (and/or flux). Our algorithm is based on recursive finite-element approximations of exact first and second conditional moment equations. Hydraulic conductivity is parameterized via universal kriging based on unknown values at pilot points and (optionally) measured values at other discrete locations. Optimum unbiased inverse estimates of natural log hydraulic conductivity, head and flux are obtained by minimizing a residual criterion using the Levenberg-Marquardt algorithm. We illustrate the method for superimposed mean uniform and convergent flows in a bounded two-dimensional domain. Our examples illustrate how conductivity and head data act separately or jointly to reduce parameter estimation errors and model predictive uncertainty.This work is supported in part by NSF/ITR Grant EAR-0110289. The first author was additionally supported by scholarships from CONACYT and Instituto de Investigaciones Electricas of Mexico. Additional support was provided by the European Commission under Contract EVK1-CT-1999-00041 (W-SAHaRA-Stochastic Analysis of Well Head Protection and Risk Assessment).     

Impact of log-transmissivity variogram structure on groundwater flow and transport predictions

We analyze the impact of the choice of the variogram model adopted to characterize the spatial variability of natural log-transmissivity on the evaluation of leading (statistical) moments of hydraulic heads and contaminant travel times and trajectories within mildly (randomly) heterogeneous two-dimensional porous systems. The study is motivated by the fact that in several practical situations the differences between various variogram types and a typical noisy sample variogram are small enough to suggest that one would often have a hard time deciding which of the tested models provides the best fit. Likewise, choosing amongst a set of seemingly likely variogram models estimated by means of geostatistical inverse models of flow equations can be difficult due to lack of sensitivity of available model discrimination criteria. We tackle the problem within the framework of numerical Monte Carlo simulations for mean uniform and radial flow scenarios. The effect of three commonly used isotropic variogram models, i.e., Gaussian, Exponential and Spherical, is analyzed. Our analysis clearly shows that (ensemble) mean values of the quantities of interest are not considerably influenced by the variogram shape for the range of parameters examined. Contrariwise, prediction variances of the quantities examined are significantly affected by the choice of the variogram model of the log-transmissivity field. The spatial distribution of the largest/lowest values of the relative differences observed amongst the tested models depends on a combination of variogram shape and parameters and relative distance from internal sources and the outer domain boundary. Our findings suggest the need of developing robust techniques to discriminate amongst a set of seemingly equally likely alternative variogram models in order to provide reliable uncertainty estimates of state variables.