ANALYSIS OF WASTE LOAD ALLOCATION PROCEDURES1

A study was made to analyze and modify procedures used for stream assimilation capacity and point source wasteload allocation calculations. This paper describes the sources and types of information collected and the analysis of alternative computation methods developed during the study. The calculation of stream assimilation capacity or Total Maximum Daily Load (TMDL), will depend upon assumed stream flows, quality standards, reaction rates, and modeling procedures. The “critical conditions” selected for TMDL calculations usually are low flows and warm temperatures. The complexity of water quality models used for TMDL and allocation calculations can range from simple, complete mixing to calibrated and verified mathematical models. A list of 20 wasteload allocation (WLA) methods was developed. Five of these WLA's were applied to an example stream to permit comparisons based on cost, equity, efficient use of stream assimilation capacity, and sensitivity to fundamental stream quality data. Based on insensitivity to data errors and current use by several states, the WLA method of “equal percent treatment” was preferable in the example stream.     

USE OF FIRST-ORDER UNCERTAINTY ANALYSIS TO OPTIMIZE SUCCESSFUL STREAM WATER QUALITY SIMULATION1

ABSTRACT: A first-order uncertainty technique is developed to quantify the relationship between field data collection and a modeling exercise involving both calibration and subsequent verification. A simple statistic (LTOTAL) is used to quantify the total likelihood (probability) of successfully calibrating and verifying the model. Results from the first-order technique are compared with those from a traditional Monte Carlo simulation approach using a simple Streeter-Phelps dissolved oxygen model. The largest single difference is caused by the filtering or removal of unrealistic outcomes within the Monte Carlo framework. The amount of bias inherent in the first-order approach is also a function of the magnitude of input variability and sampling location. The minimum bias of the first-order technique is approximately 20 percent for a case involving relatively large uncertainties. However the bias is well behaved (consistent) so as to allow for correct decision making regarding the relative efficacy of various sampling strategies. The utility of the first-order technique is demonstrated by linking data collection costs with modeling performance. For a simple and inexpensive project, a wise and informed selection resulted in an LTOTAL value of 86 percent, while an uninformed selection could result in an LTOTAL value of only 55 percent.     

MODELING THE BIG BLACK RIVER: A COMPARISON OF WATER QUALITY MODELS1

ABSTRACT: The Mississippi Department of Environmental Quality uses the Steady Riverine Environmental Assessment Model (STREAM) to establish effluent limitations. While the U.S. Environmental Protection Agency has approved of its use, questions arise regarding the model's simplicity. The objective of this research was to compare STREAM with the more commonly utilized Enhanced Stream Water Quality Model (QUAL2E). The comparison involved a statistical evaluation procedure based on sensitivity analyses, input probability distribution functions, and Monte Carlo simulation with site‐specific data from a 46‐mile (74‐km) reach of the Big Black River in central Mississippi. Site specific probability distribution functions were derived from measured rates of reaeration, sediment oxygen demand, photosynthesis, and respiration. Both STREAM and QUAL2E reasonably predicted daily average dissolved oxygen (DO) based on a comparison of output probability distributions with observed DO. Observed DO was consistently within 90 percent confidence intervals of model predictions. The STREAM approach generally overpredicted while QUAL2E generally matched observed DO. Using the more commonly assumed lognormal distribution as opposed to a Weibull distribution for two of the sensitive input parameters resulted in minimal differences in the statistical evaluations. The QUAL2E approach had distinct advantages over STREAM in simulating the growth cycle of algae.     

AN EVALUATION OF EIGHT WASTELOAD ALLOCATION METHODS1

Evidence suggests that there is no superior wasteload allocation method. Eight allocation strategies have been evaluated based on: total cost of implementation, equity in distributing costs and loads among dischargers, effectiveness in use of available waste assimilative capacity, and sensitivity to changes in water-quality-related variables. One method, which allocated equal percentages of the maximum allowable dissolved oxygen deficit, was eliminated as a feasible strategy because it led to excessive costs and overly conservative load estimates. The other seven methods remained viable alternatives. Two methods proved to be insensitive to changes in the water-quality-related variables tested, which may be advantageous in certain applications. This report presents seven workable alternatives that may be used in wasteload allocation and demonstrates a procedure to determine the practicability of other methods.     

INTERPLAY BETWEEN PARAMETER UNCERTAINTY AND MODEL AGGREGATION ERROR1

ABSTRACTS: Modeling error can be divided into two basic components: use of an incorrect model and input parameter uncertainty. Incorrect model usage can be further subdivided into inappropriate model selection and inherent modeling error due to process aggregation. Total modeling error is a culmination of these various modeling error components, with overall optimization requiring reductions in all. A technique, utilizing Monte Carlo analysis, is employed to investigate the relative importance of input parameter uncertainty versus process aggregation error. An expanded form of the Streeter-Phelps dissolved oxygen equation is used to demonstrate the application of this technique. A variety of scenarios are analyzed to illustrate the relative obfuscation of each modeling error component. Under certain circumstances an aggregated model performs better than a more complex model, which perfectly simulates the real system. Alternately, process aggregation error dominates total modeling error for other situations. The ability to differentiate modeling error impact is a function of the desired or imposed model performance level (accuracy tolerance).     

A WATERSHED-LEVEL ECOLOGICAL RISK ASSESSMENT METHODOLOGY1

ABSTRACT: We present an ecological risk assessment methodology at the watershed level for freshwater ecosystems. The major component is a pollutant transport and fate model (a modified EUTROMOD) with an integrated uncertainty analysis utilizing a two-phase Monte Carlo procedure. The uncertainty analysis methodology distinguishes between knowledge uncertainty and stochastic variability. The model assesses the ecological risk of lentic (lake) ecosystems in response to the stress of excess phosphorus resulting in eutrophication. The methodology and model were tested on the Wister Lake watershed in Oklahoma with the lake and its trophic state as the endpoint for ecological risk assessment. A geographic information system was used to store, manage, and manipulate spatially referenced data for model input.     

A FRAMEWORK FOR PHOSPHORUS TRANSPORT MODELING IN THE LAKE OKEECHOBEE WATERSHED1

ABSTRACT: A modeling framework was developed to determine phosphorus loadings to Lake Okeechobee from watersheds located north of the lake. This framework consists of the land-based model CREAMS-WT, the in-stream transport model QUAL2E, and an interface procedure to format the land-based model output for use by the in-stream model. QUAL2E hydraulics and water quality routines were modified to account for flow routing and phosphorus retention in both wetlands and stream channels. Phosphorus loadings obtained from previous applications of CREAMS-WT were used by QUAL2E, and calibration and verification showed that QUAL2E accurately simulated seasonal and annual phosphorus loadings from a watershed. Sensitivity and uncertainty analyses indicated that the accuracy of monthly loadings can be improved by using better estimates of in-stream phosphorus decay rates, ground water phosphorus concentrations, and runoff phosphorus concentrations as input to QUAL2E.     

ESTIMATING THE PROBABILITY OF EXCEEDING GROUNDWATER QUALITY STANDARDS1

ABSTRACT: A model for estimating the probability of exceeding groundwater quality standards at environmental receptors based on a simple contaminant transport model is described. The model is intended for locations where knowledge about site-specific hydrogeologic conditions is limited. An efficient implementation methodology using numerical Monte Carlo simulation is presented. The uncertainty in the contaminant transport system due to uncertainty in the hydraulic conductivity is directly calculated in the Monte Carlo simulations. Numerous variations of the deterministic parameters of the model provide an indication of the change in exceedance probability with change in parameter value. The results of these variations for a generic example are presented in a concise graphical form which provides insight into the topology of the exceedance probability surface. This surface can be used to assess the impact of the various parameters on exceedance probability.     

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.     

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.     

Multiple pollutant discharge permit markets,a challenge for wastewater treatment plants

This study focuses on the challenge of using a multiple pollutant transferable discharge permit market for operating wastewater treatment plants. It uses an analytical case of Sefidrud River in Iran with two checkpoints. It shows that the operating limitations for simultaneous biochemical oxidation demand (BOD) and total nitrogen (TN) removal may convert the economically optimal waste load allocation (WLA) to a framework with lack of incentives. Therefore, water quality trading (WQT) may lose its economical advantages. In this case, a third parameter, such as dissolved oxygen is recommended as an index for assigning market interactions. In spite of economical and practical success, this approach made WLA become a more complicated and uncertain policy. It was totally concluded that using single parameter WQT is only recommended for areas with small agricultural activities or lakes. Otherwise, the integrated discharged permit and reclaimed water market is proposed instead for simultaneous BOD and TN management.     

NPS MODEL PARAMETER UNCERTAINTY ANALYSIS FOR AN OFF-STREAM RESERVOIR1

ABSTRACT: Parameter uncertainties exert a significant effect on nonpoint source pollution (NPS) modeling results. A decision made on the basis of such results may thereby be inappropriate. In this work, the parameter uncertainty is analyzed to explore an improved modeling procedure. Drainage patterns generated from digital elevation data and rainfall are the major parameters examined. A case study for the watershed of the Posan off-stream reservoir is implemented. A significant spatial variation of NPS distribution simulated with a drainage pattern generated from varied methods is observed. The effects of rainfall randomness on the spatial loading distribution are assessed and computed based on a Monte Carlo simulation. The proposed procedure is capable of improving the quality of modeling results and the decision for an appropriate control strategy.     

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.     

Water quality modelling of the river Yamuna (India) using QUAL2E-UNCAS

This paper describes the utility of QUAL2E as a modelling package in the evaluation of a water quality improvement programme. In this study, QUAL2E was applied to determine the pollution loads in the river Yamuna during its course through the national capital territory of Delhi, India. The study aimed at examining the influence of different scenarios on river water quality. Four different pollution scenarios were analysed besides the 'business as usual' situation. The study revealed that it was necessary to treat the discharge from drains to the river Yamuna and diversion of a substantial load to the Agra canal for further treatment was also essential. It was also established through this study that maintaining a flow rate of more than 10 m(3)/s in the river could also help preserve the river's water quality. To clearly display the model outcomes and demarcate polluted zones in the river stretch, model results were interfaced with a Geographical Information System (GIS) to produce cartographic outputs. In addition, uncertainty analysis in the form of first-order error analysis and Monte Carlo analysis was performed, to realise the effect of each model parameter on DO and BOD predictions. The uncertainty analysis gave satisfactory results on simulated data.     

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 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.     

MODELING THE IMPACT OF SUBSURFACE NUTRIENT FLUX ON WATER QUALITY IN THE LOWER TRUCKEE RWER,NEVADA1

ABSTRACT: The impacts of regional groundwater quality and local agricultural activities on in-stream water quality in the Lower Truckee River, Nevada, were assessed through a detailed program of monitoring and computer simulation. An agricultural diversion and return-flow were monitored in great detail to determine mass loading rates of nutrients from agriculture in the area. Once characterized, the cumulative impacts of agricultural diversions and return-flows were evaluated using the Water Quality Assessment Program (WASP) to model nitrogen, phosphorus, periphyton, and dissolved oxygen. Monitoring showed that a significant proportion of the water diverted for agricultural purposes returned to the river as surface point return-flow (estimated at 13.9 percent $ 0.1 percent), and as groundwater diffuse return-flow (estimated at 27 percent $ 6 percent). Modeling efforts demonstrated the significant effect of assumed regional groundwater quality (nitrate) upon predicted periphyton growth and associated diel fluctuations of dissolved oxygen.     

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.     

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.