STOCHASTIC WATER QUALITY ANALYSIS USING RELIABILITY METHOD1

ABSTRACT: This study developed a QUAL2E‐Reliability Analysis (QUAL2E‐RA) model for the stochastic water quality analysis of the downstream reach of the main Han River in Korea. The proposed model is based on the QUAL2E model and incorporates the Advanced First‐Order Second‐Moment (AFOSM) and Mean‐Value First‐Order Second‐Moment (MFOSM) methods. After the hydraulic characteristics from standard step method are identified, the optimal reaction coefficients are then estimated using the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) method. Considering variations in river discharges, pollutant loads from tributaries, and reaction coefficients, the violation probabilities of existing water quality standards at several locations in the river were computed from the AFOSM and MFOSM methods, and the results were compared with those from the Monte Carlo method. The statistics of the three uncertainty analysis methods show that the outputs from the AFOSM and MFOSM methods are similar to those from the Monte Carlo method. From a practical model selection perspective, the MFOSM method is more attractive in terms of its computational simplicity and execution time.     

Availability estimation of a multi-state wind farm in fuzzy environment

Wind is one of the fastest growing renewable energy resources in the electric power system. Availability of wind energy is volatile in nature due to the stochastic behavior of wind speed and non-linear variation of the wind power curve of wind turbine generator. Because of this impression and uncertainty, the availability estimation of wind power has become a challenging issue. In this paper, Markov Fuzzy Reward technique has been proposed for finding out the reliability of wind farm by assessing the availability of wind power. According to this technique, availability of the wind power has been estimated considering wind farm and demand both as a multi-state system. In addition to the availability, different reliability indices such as the number of absolute failures, mean time to deficiency, and probability of failures of a wind farm have been assessed in a time horizon, which can provide useful information for the power system planner at wind farm installing stage. A comparison of this study reveals the efficacy of the proposed Markov Fuzzy Reward approach over the conventional Markov Reward approach.     

ANALYSIS OF A KARSTIC AQUIFER MANAGEMENT PROBLEM BY FUZZY COMPOSITE PROGRAMMING1

ABSTRACT: A multiple objective framework for water resources problems possessing uncertain or imprecise elements is provided using distance-based concepts, fuzzy set theory, and fuzzy arithmetic. The case of regional management of a karstic aquifer in Hungary in which six conflicting objectives and six alternatives have been identified illustrates the methodology The objectives are classified into three groups of two objectives each, namely: (1) environmental (aesthetics, thermal springs temperature), (2) economic (mining, tourism), and (3) water quality (nitrates, phosphates). Both environmental objectives are formulated under fuzziness, and all objectives are scaled using the extension principle. Fuzzy compromise programming (FCP-I) is then applied; here, all six objectives are entered in a single l_p norm measuring the distance between each alternative and an ideal point. Next, fuzzy composite programming (FCP-II) is developed; here, a trade off is first made within each group of objectives, and then an upper level trade-off takes place between the three groups. The fuzzy numbers describing each alternative as a result from applying these techniques are ranked to yield an ordering of the alternatives. The results of applying FCP.I, FCP-II, and two different ordering techniques are compared. The FCP-II technique appears to provide a relatively simple approach at hierarchical or multilevel multiple objective decision-making, where uncertainty is described by fuzziness. (KEY TERMS: compromise programming; fuzzy arithmetic; fuzzy sets; hierarchical criteria; karstic aquifer; l_p, norms; mining; multiple objectives; thermal springs.)     

INCORPORATING UNCERTAINTY IN THE DESIGN OF STREAM CHMNEL MODIFICATIONS1

ABSTRACT: The designs of stream channel naturalization, rehabilitation, and restoration projects are inherently fraught with uncertainty. Although a systematic approach to design can be described, the likelihood of success or failure of the design is unknown due to uncertainties within the design and implementation process. In this paper, a method for incorporating uncertainty in decision‐making during the design phase is presented that uses a decision analysis method known as Failure Modes and Effects Analysis (FMEA). The approach is applied to a channel rehabilitation project in north‐central Pennsylvania. FMEA considers risk in terms of the likelihood of a component failure, the consequences of failure, and the level of difficulty required to detect failure. Ratings developed as part of the FMEA can provide justification for decision making in determining design components that require particular attention to prevent failure of the project and the appropriate compensating actions to be taken.     

Practical Precautionary Resource Management Using Robust Optimization

Uncertainties inherent in fisheries motivate a precautionary approach to management, meaning an approach specifically intended to avoid bad outcomes. Stochastic dynamic optimization models, which have been in the fisheries literature for decades, provide a framework for decision making when uncertain outcomes have known probabilities. However, most such models incorporate population dynamics models for which the parameters are assumed known. In this paper, we apply a robust optimization approach to capture a form of uncertainty nearly universal in fisheries, uncertainty regarding the values of model parameters. Our approach, developed by Nilim and El Ghaoui (Oper Res 53(5):780–798, 2005), establishes bounds on parameter values based on the available data and the degree of precaution that the decision maker chooses. To demonstrate the applicability of the method to fisheries management problems, we use a simple example, the Skeena River sockeye salmon fishery. We show that robust optimization offers a structured and computationally tractable approach to formulating precautionary harvest policies. Moreover, as better information about the resource becomes available, less conservative management is possible without reducing the level of precaution.     

DESIGN OF SEWER SYSTEMS1

In order to cope with the ever increasing problems of the urban environment, new approaches are being sought to their solution. The objective of this paper is to review and evaluate the merits of certain new methods aimed at finding optimal solutions in sewer design. Based on principles similar to the ones advanced by Deininger [1966] and Holland [1968] the authors propose an integer programming algorithm for optimizing pipe sizes and slopes. The new algorithm is applied to an actual situation and compared with a solution arrived at by a traditional design approach.     

EVALUATION OF THE WORTH OF ADDITIONAL DATA1

ABSTRACT .Inherent in every decision process is a certain amount of uncertainty, which is reduced with information. Perfect knowledge yields no uncertainty for a process, but perfect knowledge for hydrologic and water resource systems would require a highly excessive investment. Therefore, it is the aim of this paper to delineate a procedure that places a value on this uncertainty so that it may be compared to a cost of further investment, which would provide a basis for deciding the time at which the value of additional data does not exceed the cost of that data. A decision theory approach is employed on a hydrologic problem to formalize the steps in making a decision. Examples are given.     

A decision model for selecting sustainable drinking water supply and greywater reuse systems for developing communities with a case study in Cimahi, Indonesia

Capacity Factor Analysis is a decision support system for selection of appropriate technologies for municipal sanitation services in developing communities. Developing communities are those that lack the capability to provide adequate access to one or more essential services, such as water and sanitation, to their residents. This research developed two elements of Capacity Factor Analysis: a capacity factor based classification for technologies using requirements analysis, and a matching policy for choosing technology options. First, requirements analysis is used to develop a ranking for drinking water supply and greywater reuse technologies. Second, using the Capacity Factor Analysis approach, a matching policy is developed to guide decision makers in selecting the appropriate drinking water supply or greywater reuse technology option for their community. Finally, a scenario-based informal hypothesis test is developed to assist in qualitative model validation through case study. Capacity Factor Analysis is then applied in Cimahi Indonesia as a form of validation. The completed Capacity Factor Analysis model will allow developing communities to select drinking water supply and greywater reuse systems that are safe, affordable, able to be built and managed by the community using local resources, and are amenable to expansion as the community's management capacity increases.     

PROBABILISTIC METHODS IN STREAM QUALITY MANAGEMENT1

ABSTRACT. Recent advances in water quality modelling have pointed out the need for stochastic models to simulate the probabilistic nature of water quality. However, often all that is needed is an estimate of the uncertainty in predicting water quality variables. First order analysis is a simple method of providing an estimate in the uncertainty in a deterministic model due to uncertain parameters. The method is applied to the simplified Streeter-Phelps equations for DO and BOD; a more complete Monte Carlo simulation is used to check the accuracy of the results. The first order analysis is found to give accurate estimates of means and variances of DO and BOD up to travel times exceeding the critical time. Uncertainty in travel time and the BOD decay constant are found to be most important for small travel times; uncertainty in the reaeration coefficient dominates near the critical time. Uncertainty in temperature was found to be a negligible source of uncertainty in DO for all travel times.     

An imprecise fuzzy risk approach for water quality management of a river system

Uncertainty plays an important role in water quality management problems. The major sources of uncertainty in a water quality management problem are the random nature of hydrologic variables and imprecision (fuzziness) associated with goals of the dischargers and pollution control agencies (PCA). Many Waste Load Allocation (WLA) problems are solved by considering these two sources of uncertainty. Apart from randomness and fuzziness, missing data in the time series of a hydrologic variable may result in additional uncertainty due to partial ignorance. These uncertainties render the input parameters as imprecise parameters in water quality decision making. In this paper an Imprecise Fuzzy Waste Load Allocation Model (IFWLAM) is developed for water quality management of a river system subject to uncertainty arising from partial ignorance. In a WLA problem, both randomness and imprecision can be addressed simultaneously by fuzzy risk of low water quality. A methodology is developed for the computation of imprecise fuzzy risk of low water quality, when the parameters are characterized by uncertainty due to partial ignorance. A Monte-Carlo simulation is performed to evaluate the imprecise fuzzy risk of low water quality by considering the input variables as imprecise. Fuzzy multiobjective optimization is used to formulate the multiobjective model. The model developed is based on a fuzzy multiobjective optimization problem with max–min as the operator. This usually does not result in a unique solution but gives multiple solutions. Two optimization models are developed to capture all the decision alternatives or multiple solutions. The objective of the two optimization models is to obtain a range of fractional removal levels for the dischargers, such that the resultant fuzzy risk will be within acceptable limits. Specification of a range for fractional removal levels enhances flexibility in decision making. The methodology is demonstrated with a case study of the Tunga–Bhadra river system in India.     

Exploring red deer culling strategies using a population-specific calibrated management model

Wildlife management is generally carried out under conditions of uncertainty. The exact population size is unknown, its future dynamics are uncertain and clear management objectives are often not formulated. In order to provide management advice in this situation, a framework is presented for combining different sources of information using a Bayesian approach for calibrating a management model. Harvesting strategies can then be explored based on predictions of future populations size and structure which incorporate parameter uncertainty. This method makes it possible to evaluate the probability of achieving certain objectives with different management strategies. The advantage of the approach presented in this paper lies in that both the model and the harvesting strategies are adaptable to any particular population of interest. The approach is illustrated for two Scottish red deer populations for which culling strategies corresponding to different management objectives are explored and their benefits evaluated. It is found that each population requires different culling rates for keeping population number stable, demonstrating the benefits of the population specific calibration of the management model.     

Uncertainty characterization approaches for risk assessment of DBPs in drinking water: A review

The management of risk from disinfection by-products (DBPs) in drinking water has become a critical issue over the last three decades. The areas of concern for risk management studies include (i) human health risk from DBPs, (ii) disinfection performance, (iii) technical feasibility (maintenance, management and operation) of treatment and disinfection approaches, and (iv) cost. Human health risk assessment is typically considered to be the most important phase of the risk-based decision-making or risk management studies. The factors associated with health risk assessment and other attributes are generally prone to considerable uncertainty. Probabilistic and non-probabilistic approaches have both been employed to characterize uncertainties associated with risk assessment. The probabilistic approaches include sampling-based methods (typically Monte Carlo simulation and stratified sampling) and asymptotic (approximate) reliability analysis (first- and second-order reliability methods). Non-probabilistic approaches include interval analysis, fuzzy set theory and possibility theory. However, it is generally accepted that no single method is suitable for the entire spectrum of problems encountered in uncertainty analyses for risk assessment. Each method has its own set of advantages and limitations. In this paper, the feasibility and limitations of different uncertainty analysis approaches are outlined for risk management studies of drinking water supply systems. The findings assist in the selection of suitable approaches for uncertainty analysis in risk management studies associated with DBPs and human health risk.     

AGRICULTURAL NITRATE CONTAMINATION OF GROUND WATER: AN EVALUATION OF ENVIRONMENTAL POLICY1

ABSTRACT: The contribution of agriculture to nitrate pollution of 8Urface and ground water is a growing concern throughout the world. The objective of this article is to evaluate the current environmental policy governing nitrate contamination of ground water in the South Platte alluvial aquifer. In particular, the “best management practice” approach is assessed in its relationship to optimal policy design. First, the current physical environmental problem and existing institutional arrangements are described. Second, legal and economic criteria are brought to bear on the question of appropriate policy design. Finally, the strengths and weaknesses of the existing policy are evaluated in this context and changes in policy that would increase effectiveness are recommended. Considerable justification is found for state-initiated control because victims of ground water pollution are dispersed and risk assessment is technically demanding. However, ex post elements of existing policy must be improved, perhaps through targeting and some devolution in monitoring and enforcement responsibilities.     

Approaches to Evaluate Water Quality Model Parameter Uncertainty for Adaptive TMDL Implementation1

Abstract: The National Research Council recommended Adaptive Total Maximum Daily Load implementation with the recognition that the predictive uncertainty of water quality models can be high. Quantifying predictive uncertainty provides important information for model selection and decision‐making. We review five methods that have been used with water quality models to evaluate model parameter and predictive uncertainty. These methods (1) Regionalized Sensitivity Analysis, (2) Generalized Likelihood Uncertainty Estimation, (3) Bayesian Monte Carlo, (4) Importance Sampling, and (5) Markov Chain Monte Carlo (MCMC) are based on similar concepts; their development over time was facilitated by the increasing availability of fast, cheap computers. Using a Streeter‐Phelps model as an example we show that, applied consistently, these methods give compatible results. Thus, all of these methods can, in principle, provide useful sets of parameter values that can be used to evaluate model predictive uncertainty, though, in practice, some are quickly limited by the “curse of dimensionality” or may have difficulty evaluating irregularly shaped parameter spaces. Adaptive implementation invites model updating, as new data become available reflecting water‐body responses to pollutant load reductions, and a Bayesian approach using MCMC is particularly handy for that task.     

WATER QUALITY MODEL CALIBRATION: A COMPARISON OF INPUT AND OUTPUT ERROR CRITERIA1

ABSTRACT: A common framework for the analysis of water resources systems is the input-parameter-output representation. The system, described by its parameters, is driven by inputs and responds with outputs. To calibrate (estimate the parameters) models of these systems requires data on both inputs and outputs, both of which are subject to random errors. When one is uncertain as to whether the predominant source of error is associated with inputs or outputs, uncertainty also exists as to the correct specification of a calibration criterion. This paper develops and analyzes two alternative least squares criteria for calibrating a numerical water quality model. The first criterion assumes that errors are associated with inputs while the second assumes output errors. Statistical properties of the resulting estimators are examined under conditions of pure input or output error and mixed error conditions from a theoretical perspective and then using simulated results from a series of Monte Carlo experiments.     

Propagation of uncertainties in soil and pesticide properties to pesticide leaching

In the new Dutch decision tree for the evaluation of pesticide leaching to groundwater, spatially distributed soil data are used by the GeoPEARL model to calculate the 90th percentile of the spatial cumulative distribution function of the leaching concentration in the area of potential usage (SP90). Until now it was not known to what extent uncertainties in soil and pesticide properties propagate to spatially aggregated parameters like the SP90. A study was performed to quantify the uncertainties in soil and pesticide properties and to analyze their contribution to the uncertainty in SP90. First, uncertainties in the soil and pesticide properties were quantified. Next, a regular grid sample of points covering the whole of the agricultural area in the Netherlands was randomly selected. At the grid nodes, realizations from the probability distributions of the uncertain inputs were generated and used as input to a Monte Carlo uncertainty propagation analysis. The analysis showed that the uncertainty concerning the SP90 is 10 times smaller than the uncertainty about the leaching concentration at individual point locations. The parameters that contribute most to the uncertainty about the SP90 are, however, the same as the parameters that contribute most to uncertainty about the leaching concentration at individual point locations (e.g., the transformation half-life in soil and the coefficient of sorption on organic matter). Taking uncertainties in soil and pesticide properties into account further leads to a systematic increase of the predicted SP90. The important implication for pesticide regulation is that the leaching concentration is systematically underestimated when these uncertainties are ignored.     

Simulating solute transport in a structured field soil: uncertainty in parameter identification and predictions

Dual-permeability models have been developed to account for the significant effects of macropore flow on contaminant transport, but their use is hampered by difficulties in estimating the additional parameters required. Therefore, our objective was to evaluate data requirements for parameter identification for predictive modeling with the dual-permeability model MACRO. Two different approaches were compared: sequential uncertainty fitting (SUFI) and generalized likelihood uncertainty estimation (GLUE). We investigated six parameters controlling macropore flow and pesticide sorption and degradation, applying MACRO to a comprehensive field data set of bromide andbentazone [3-isopropyl-1H-2,1,3-benzothiadiazin-4(3H)-one-2,2dioxide] transport in a structured soil. The GLUE analyses of parameter conditioning for different combinations of observations showed that both resident and flux concentrations were needed to obtain highly conditioned and unbiased parameters and that observations of tracer transport generally improved the conditioning of macropore flow parameters. The GLUE "behavioral" parameter sets covered wider parameter ranges than the SUFI posterior uncertainty domains. Nevertheless, estimation uncertainty ranges defined by the 5th and 95th percentiles were similar and many simulations randomly sampled from the SUFI posterior uncertainty domains had negative model efficiencies (minimum of -3.2). This is because parameter correlations are neglected in SUFI and the posterior uncertainty domains were not always determined correctly. For the same reasons, uncertainty ranges for predictions of bentazone losses through drainflow for good agricultural practice in southern Sweden were 27% larger for SUFI compared with GLUE. Although SUFI proved to be an efficient parameter estimation tool, GLUE seems better suited as a method of uncertainty estimation for predictions.     

Towards an Integrated Approach to Natural Hazards Risk Assessment Using GIS: With Reference to Bushfires

This paper develops a GIS-based integrated approach to risk assessment in natural hazards, with reference to bushfires. The challenges for undertaking this approach have three components: data integration, risk assessment tasks, and risk decision-making. First, data integration in GIS is a fundamental step for subsequent risk assessment tasks and risk decision-making. A series of spatial data integration issues within GIS such as geographical scales and data models are addressed. Particularly, the integration of both physical environmental data and socioeconomic data is examined with an example linking remotely sensed data and areal census data in GIS. Second, specific risk assessment tasks, such as hazard behavior simulation and vulnerability assessment, should be undertaken in order to understand complex hazard risks and provide support for risk decision-making. For risk assessment tasks involving heterogeneous data sources, the selection of spatial analysis units is important. Third, risk decision-making concerns spatial preferences and/or patterns, and a multicriteria evaluation (MCE)-GIS typology for risk decision-making is presented that incorporates three perspectives: spatial data types, data models, and methods development. Both conventional MCE methods and artificial intelligence-based methods with GIS are identified to facilitate spatial risk decision-making in a rational and interpretable way. Finally, the paper concludes that the integrated approach can be used to assist risk management of natural hazards, in theory and in practice.     

Relationship Between Tourism Development and Vegetated Landscapes in Luya Mountain Nature Reserve, Shanxi, China

The relationship between tourism development and vegetated landscapes is analyzed for the Luya Mountain Nature Reserve (LMNR), Shanxi, China, in this study. Indices such as Sensitive Level (SL), Landscape Importance Value (LIV), information index of biodiversity (H’), Shade-tolerant Species Proportion (SSP), and Tourism Influencing Index (TII) are used to characterize vegetated landscapes, the impact of tourism, and their relationship. Their relationship is studied by Two-Way Indicator Species Analysis (TWINSPAN) and Detrended Correspondence Analysis (DCA). TWINSPAN gives correct and rapid partition to the classification, and DCA ordination shows the changing tendency of all vegetation types based on tourism development. These results reflect the ecological relationship between tourism development and vegetated landscapes. In Luya Mountain Nature Reserve, most plant communities are in good or medium condition, which shows that these vegetated landscapes can support more tourism. However, the occurrence of the bad condition shows that there is a severe contradiction between tourism development and vegetated landscapes.     

Hospital site selection using fuzzy AHP and its derivatives

Environmental managers are commonly faced with sophisticated decisions, such as choosing the location of a new facility subject to multiple conflicting criteria. This paper considers the specific problem of creating a well-distributed network of hospitals that delivers its services to the target population with minimal time, pollution and cost. We develop a Multi-Criteria Decision Analysis process that combines Geographical Information System (GIS) analysis with the Fuzzy Analytical Hierarchy Process (FAHP), and use this process to determine the optimum site for a new hospital in the Tehran urban area. The GIS was used to calculate and classify governing criteria, while FAHP was used to evaluate the decision factors and their impacts on alternative sites. Three methods were used to estimate the total weights and priorities of the candidate sites: fuzzy extent analysis, center-of-area defuzzification, and the α-cut method. The three methods yield identical priorities for the five alternatives considered. Fuzzy extent analysis provides less discriminating power, but is simpler to implement and compute than the other two methods. The α-cut method is more complicated, but integrates the uncertainty and overall attitude of the decision-maker. The usefulness of the new hospital site is evaluated by computing an accessibility index for each pixel in the GIS, defined as the ratio of population density to travel time. With the addition of a new hospital at the optimum site, this index improved over about 6.5 percent of the geographical area.