UNCERTAINTY OF EXTREME FLOOD ESTIMATES INCORPRATING HISTORICAL DATA1

ABSTRACT: The ability to predict extreme floods is an important part of the planning process for any water project for which failure will be very costly. The length of a gage record available for use in estimating extreme flows is generally much shorter than the recurrence interval of the desired flows, resulting in estimates having a high degree of uncertainty. Maximum likelihood estimators of the parameters of the three parameter lognormal (3PLN) distribution, which make use of historical data, are presented. A Monte Carlo study of extreme flows estimated from samples drawn from three hypothetical 3PLN populations showed that inclusion of historical flows with the gage record reduced the bias and variance of extreme flow estimates. Asymptotic theory approximations of parameter variances and covariances calculated using the second and mixed partial derivatives of the log likelihood function agreed well with Monte Carlo results. First order approximations of the standard deviations of the extreme flow estimates did not agree with the Monte Carlo results. An alternative method for calculating those standard deviations, the “asymptotic simulation” method, is described. The standard deviations calculated by asymptotic simulation agree well with the Monte Carlo results.     

Environmental Integrated Assessment via Monte Carlo Simulation with a Case Study of the Mid-Atlantic Region,USA

Environmental integrated assessments are often carried out via the aggregation of a set of environmental indicators. Aggregated indices derived from the same data set can differ substantially depending upon how the indicators are weighted and aggregated, which is often a subjective matter. This article presents a method of generating aggregated environmental indices in an objective manner via Monte Carlo simulation. Rankings derived from the aggregated indices within and between three Monte Carlo simulations were used to evaluate the overall environmental condition of the study area. Other insights, such as the distribution of good or bad values of indicators at a watershed and/or a subregion, were observed in the study.     

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.     

AN ILLUSTRATION OF MODEL STRUCTURE IDENTIFICATION1

ABSTRACT: The purpose of this article is to discuss the importance of uncertainty analysis in water quality modeling, with an emphasis on the identification of the correct model specification. A wetland phosphorus retention model is used as an example to illustrate the procedure of using a filtering technique for model structure identification. Model structure identification is typically done through model parameter estimation. However, due to many sources of error in both model parameterization and observed variables and data, error-in-variable is often a problem. Therefore, it is not appropriate to use the least squares method for parameter estimation. Two alternative methods for parameter estimation are presented. The first method is the maximum likelihood estimator, which assumes independence of the observed response variable values. In anticipating the possible violation of the independence assumption, a second method, which coupled a maximum likelihood estimator and Kalman filter model, was presented. Furthermore, a Monte Carlo simulation algorithm is presented as a preliminary method for judging whether the model structure is appropriate or not.     

An approach to optimise nutrient management in environmental sanitation systems despite limited data

The material flow analysis method can be used to assess the impact of environmental sanitation systems on resource consumption and environmental pollution. However, given the limited access to reliable data, application of this data-intensive method in developing countries may be difficult. This paper presents an approach allowing to develop material flow models despite limited data availability. Application of an iterative procedure is of key importance: model parameter values should first be assessed on the basis of a literature review and by eliciting expert judgement. If model outputs are not plausible, sensitive input parameters should be reassessed more accurately. Moreover, model parameters can be expressed as probability distributions and variable uncertainty estimated by using Monte Carlo simulation. The impact of environmental sanitation systems on the phosphorus load discharged into surface water in Hanoi, Vietnam, is simulated by applying the proposed approach.     

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.     

微生物法和微生物生态法的评价和选用

微生物法和微生物生态法作为生物治理方案的两大类型，已日益受到环保工作者的重视。这两种类型的治理方法各有特点，各有利弊。如何选择使用？主要取决于污染场所中污染形成的时间长短、污染程度、污染物浓度、污染物中是否含有污水、是否需要快速治理等。应明确指出的是，采用生物治理法虽可在多种情况下大大降低污染物的浓度，但从长远来看，还不能单纯依靠降低污染物的排放浓度，而是应从低浓度污染物对人和环境产生的长期影响着眼，制定出一套治理标准，这样才能准确评价生物治理技术在环境保护中所起的真正作用。     

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.     

MODIFIED WATER QUANTITY RECEIVING MODEL FOR FLORIDA CONSERVATION AREAS1

ABSTRACT: The Conservation Areas in South Florida have been considered as one of the major water storage areas to provide a water supply for the Everglades National Park and Lower East Coast (LEC). Due to the increasing water demands of the area, additional backpumping of the surplus runoff from the LEC area into the Conservation Areas has been considered as one of several alternative plans. The Receiving Water Quantity (EPA, 1971) model has been adapted and modified to be applicable in the Conservation Areas to investigate the possible impact of additional inflow under various backpumping cases. The modification of the model included Manning's roughness coefficient, depth of flow, width of hypothetical channels through marsh areas, rainfall input, seepage rate, etc. The use of the Monte Carlo technique for area computations was found to be easy and time saving both in area and weighting rainfall input to each node. Comparison of results generated by this modified model with the recorded values in Conservation Areas 1 and 2A indicated that the model not only can be a very good evaluation tool to simulate the hydraulic regime of the Conservation Areas system but also a proper tool for investigating the impact of additional inflow resulting from the backpumping related to the water use planning and management.     

GEOLOGIC INFERENCE FROM “FLOW NET” TRANSMISSIVITY DETERMINATION: THREE CASE STUDIES1

A graphical inverse method for determining the regional transmissivity distribution was applied to three field problems. The study areas were the Hanford Site, Washington; the Rocky Mountain Arsenal, Colorado; and the Nevada Test Site, Nevada. This method can aid in flow system conceptualization by revealing the location of bedrock controls for groundwater flow. It is a valuable tool for aiding the hydrogeologist in asking questions about the nature of trends in the pattern of transmissivity values. Quantitative estimates of regional transmissivities can be used as starting points for further parameter refinement. Sensitivity analysis using Monte Carlo simulation shows that quantitative estimates of transmissivity can be obtained when measurement error in the hydraulic head does not cause a large error in the hydraulic gradient.     

PARAMETER UNCERTAINTY IN RAINFALL-RUNOFF MODELING FOR POLDER SYSTEM DESIGN1

ABSTRACT: An approach is developed for incorporating the uncertainty of parameters for estimating runoff in the design of polder systems in ungaged watersheds. Monte Carlo Simulation is used to derive a set of realizations of streamflow hydrographs for a given design rainstorm using the U. S. Soil Conservation Service (SCS) unit hydrograph model. The inverse of the SCS curve number, which is a function of the antecedent runoff condition in the SCS model, is the random input in the Monte Carlo Simulation. Monte Carlo realizations of streamfiow hydrographs are used to simulate the performance of a polder flood protection system. From this simulation the probability of occurrence of flood levels for a particular hydraulic design may be used to evaluate its effectiveness. This approach is demonstrated for the Pluit Polder flood protection system for the City of Jakarta, Indonesia. While the results of the application indicate that uncertainty in the antecedent runoff condition is important, the effects of uncertainty in rainfall data, in additional runoff parameters, such as time to peak, in the hydraulic design, and in the rainfall-runoff model selected should also be considered. Although, the SCS model is limited to agricultural conditions, the approach presented herein may be applied to other flood control systems if appropriate storm runoff models are selected.     

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.     

A COMPARISON OF METHODS FOR ESTIMATING LOW FLOW CHARACTERISTICS OF STREAMS1

ABSTRACT: Four methods for estimating the 7-day, 10-year and 7-day, 20-year low flows for streams are compared by the bootstrap method. The bootstrap method is a Monte Carlo technique in which random samples are drawn from an unspecified sampling distribution defined from observed data. The nonparametric nature of the bootstrap makes it suitable for comparing methods based on a flow series for which the true distribution is unknown. Results show that the two methods based on hypothetical distributions (Log-Pearson III and Weibull) had lower mean square errors than did the Box-Cox transformation method or the Log-Boughton method which is based on a fit of plotting positions.     

COMPUTING THE RISKS ASSOCIATED WITH WASTELOAD) ALLOCATION MODELING1

ABSTRACT: The risks associated with a traditional wasteload allocation (WLA) analysis were quantified with data from a recent study of the Upper Trinity River (Texas). Risk is define here as the probability of failing to meet an established in-stream water quality standard. The QUAL-TX dissolved oxygen (DO) water quality model was modified to a Monte Carlo framework. Flow augmentation coding was also modified to allow an exact match to be computed between the predicted and an established DO concentration standard, thereby providing an avenue for linking input parameter uncertainty to the assignment of a wasteload permit (allowable mass loading rate). Monte Carlo simulation techniques were employed to propagate input parameter uncertainties, typically encountered during WLA analysis, to the computed effluent five-day carbonaceous biochemical oxygen demand requirements for a single major wastewater treatment plant (WWTP). The risk of failing to meet an established in-stream DO criterion may be as high as 96 percent. The uncertainty associated with estimation of the future total Kjeldahl nitrogen concentration for a single tributary was found to have the greatest impact on the determination of allowable WWTP loadings.     

Sustainable Water Quality Management Framework and a Strategy Planning System for a River Basin

In Taiwan, the authorities have spent years working on remedying polluted rivers. Generally, the remediation planning works are divided into two phases. During the first phase, the allowed pollution discharge quantity and abatement quantity of each drainage zone, including the assimilative capacity, are generated based on the total river basin. In the second phase, the abatement action plans for each pollution source in each drainage zone are respectively devised by the related organizations based on the strategies generated during the first phase. However, the effectiveness of linking the two phases is usually poor. Highly integrated performances are not always achieved because the separate two-phase method does not take system and management thinking into consideration in the planning stage. This study pioneers the use of the Managing for Results (MFR) method in planning strategies and action plans for river water quality management. A sustainable management framework is proposed based on the concept and method of MFR, Management Thinking, and System Analysis. The framework, consisting of planning, implementation, and controlling stages, systematically considers the relationships and interactions among four factors: environment, society, economy, and institution, based on the principles of sustainable development. Based on the framework, the Modified Bounded Implicit Enumeration algorithm, which is used as a solving method, is combined with Visual Basic software and MS Excel to develop a computer system for strategy planning. The Shetzu River, located in northern Taiwan, is applied as a case study. According to the theoretical, practical, and regulatory considerations, the result-oriented objectives are defined to first improve the pollution length of the Shetzu River in specific remediation periods to finally meet regulated water quality standards. The objectives are then addressed as some of the constraints for the strategy planning model. The model objective is to pursue the maximum assimilative capacity (environmental phase) subjected to the constraints of water quality standards (institutional phase), social equity (social phase), and proper available technology (economic phase). The pollution quantity abatement and allocation, which are named the top strategies, of each drainage zone for different scenarios can be obtained based on each water quality standard. The middle as well as lower strategies and action plans, which consist of pollution quantity abatement and allocation of each class (domestic, industrial, livestock, and non-point pollution sources) and their individual pollution sources in each drainage zone, are then generated based on the top strategies. The performance indicators and measure plans are proposed based on the action plans to promote the comprehensive effectiveness of river water quality management. The authorities have begun to develop a budget based on the strategies and action plans developed in this study. The analytical results indicate that the objectives, strategies, and action plans developed based on the sustainable management framework and strategy planning system can effectively help the related authorities to fulfill the tasks of water quality management for a river basin.     

CALCULATION OF NONLINEAR CONFIDENCE AND PREDICTION INTERVALS FOR GROUND-WATER FLOW MODELS1

ABSTRACT: A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that includsion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.     

A Comparison of Bayesian Methods for Uncertainty Analysis in Hydraulic and Hydrodynamic Modeling

We evaluate and compare the performance of Bayesian Monte Carlo (BMC), Markov chain Monte Carlo (MCMC), and the Generalized Likelihood Uncertainty Estimation (GLUE) for uncertainty analysis in hydraulic and hydrodynamic modeling (HHM) studies. The methods are evaluated in a synthetic 1D wave routing exercise based on the diffusion wave model, and in a multidimensional hydrodynamic study based on the Environmental Fluid Dynamics Code to simulate estuarine circulation processes in Weeks Bay, Alabama. Results show that BMC and MCMC provide similar estimates of uncertainty. The posterior parameter densities computed by both methods are highly consistent, as well as the calibrated parameter estimates and uncertainty bounds. Although some studies suggest that MCMC is more efficient than BMC, our results did not show a clear difference between the performance of the two methods. This seems to be due to the low number of model parameters typically involved in HHM studies, and the use of the same likelihood function. In fact, for these studies, the implementation of BMC results simpler and provides similar results to MCMC. The results of GLUE are, on the other hand, less consistent to the results of BMC and MCMC in both applications. The posterior probability densities tend to be flat and similar to the uniform priors, which can result in calibrated parameter estimates centered in the parametric space.     

A TECHNIQUE USED TO DETERMINE RANDOM POINT POSITION1

ABSTRACT: The Monte Carlo method is a procedure which takes advantage of the high speed of electronic computer in solving complex problems in physical and mathematical fields. A rigid technique to determine whether a random point falls within an arbitrary-shaped boundary is not available. This study is to present a new technique which can be used to determine whether a random point falls within any shape of boundary, together with its range of application. A modified fixed random walk procedure is also developed to solve the problems of groundwater movement. A flowchart and computer program are also demonstrated. Comparisons of this newly developed method are made with other approximate solutions. The results indicates that the new technique is more applicable and powerful than other methods.     

Understanding communicational behavior among rangelands’ stakeholders: application of social network analysis

Understanding communicational behavior of rangelands’ stakeholders is fundamental for effective development of rangeland management plans. This study aimed to understand differences between stakeholders’ relations among various actors involved in rangeland management using social network analysis (SNA). A survey was conducted on 334 stakeholders (89 extension agents, 110 researchers and 135 executive agents) in the Tehran province, Iran. Results showed that all the three groups of stakeholders are interested in making contact mainly within their own group. Furthermore, while the executive agents have shared the strongest technical and friendship relations with the two other groups, the extension agents established the strongest administrative interactions. The researchers, however, made a poor link especially with the extension agents. The study concluded that SNA could be an efficient tool to assess communicational behavior in rangeland management.