Water Quality Model Uncertainty Research Articles

The uncertainity in stormwater quality modelling for temperate and tropical catchments

More research has been done on the uncertainty of stormwater quantity as compared to quality modelling. Although the washoff model has been in use for decades, there is a general lack of studies on the uncertainty associated with washoff modelling and how this uncertainty varies between catchments in different climate zones due to differences in rainfall conditions. This study investigated model structure uncertainty, in addition to gaining knowledge on model parameter uncertainty in water quality modelling of urban catchments located in two climate zones. Such a study not only adds to the body of knowledge but highlights the importance of distinguishing the difference in washoff behaviour, and their results, between catchments in different climate zones. Following an exhaustive search and assessment of data quality, the rainfall, discharge and water quality data sourced from 11 residential catchments, which include 72 events from temperate catchments and 59 from tropical catchments were analysed. Comparison of uncertainty between buildup-washoff model (BW) and washoff model (WO) results for particulate (Total Suspended Solids (TSS)), mixed (Total Phosphorus (TP), Total Nitrogen (TN)) and dissolved (ortho-Phosphate (OP), Ammonium (NH4-N)) phase water quality parameters were carried by using the Generalized Likelihood Uncertainty Estimation (GLUE) method. Higher Average Relative Interval Length (ARIL) values obtained for tropical catchments showed that uncertainty in model prediction is higher than temperate catchments. This result is confirmed for both the BW and WO modelling approaches. The threshold criteria for obtaining behavioural set chosen as likelihood measure of Tr = 0.7 (based on the Nash-Sutcliffe coefficient) and η ≥ 70 % (proportion of observed data falling within the 90 % uncertainty band of the simulated data distribution over the total number of observations) are mostly satisfied for the particulate phase and least by the dissolved phase water quality parameters, providing further evidence that the structure of the models are not universally applicable, and that model results should be understood in the light of this difference. Comparisons between the BW and WO approaches showed similar levels of uncertainty, irrespective of climate. Although this is consistent with other studies reported in the literature, the antecedent dry period (ADP), a key parameter in the buildup process, was not significantly (p =.07) different between the temperate and tropical datasets. This is likely an artifact of sampling, especially for temperate catchments, where field data is collected during the rainy season, when ADP is limited and similar with catchment in the tropics.

Effects of quality controlled measured and re-analysed meteorological data on the performance of water temperature simulations

One of the most prominent sources of error and uncertainty in water quality modeling results is the input data. In this study, data from three meteorological databases were used to test the performance of a water temperature model of Lake Diefenbaker: the data from the Environment and Climate Change Canada (ECCC) had long-term quality control history (>20 years); the data from the AccuWeather had short-term quality control history (<10 years), and the data from the MeteoBlue database were modeled values. The CE-QUAL-W2 hydrodynamic and water quality model was used for this study. The models were calibrated by adjusting model coefficients controlling the amount of measured solar radiation and wind that reach the surface of the water. The sensitivity results showed very similar performances with slightly better performances (root mean square root difference of ±0.1) with the ECCC data followed by the MeteoBlue data and thereafter by the AccuWeather data respectively.

Improving In-Stream Nutrient Routines in Water Quality Models Using Stable Isotope Tracers: A Review and Synthesis

Abstract. Water quality models serve as an economically feasible alternative to quantify fluxes of nutrient pollution and to simulate effective mitigation strategies; however, their applicability is often questioned due to broad uncertainties in model structure and parameterization, leading to uncertain outputs. We argue that reduction of uncertainty is partially achieved by integrating stable isotope data streams within the water quality model architecture. This article outlines the use of stable isotopes as a response variable within water quality models to improve the model boundary conditions associated with nutrient source provenance, constrain model parameterization, and elucidate shortcomings in the model structure. To assist researchers in future modeling efforts, we provide an overview of stable isotope theory; review isotopic signatures and applications for relevant carbon, nitrogen, and phosphorus pools; identify biotic and abiotic processes that impact isotope transfer between pools; review existing models that have incorporated stable isotope signatures; and highlight recommendations based on synthesis of existing knowledge. Broadly, we find existing applications that use isotopes have high efficacy for reducing water quality model uncertainty. We make recommendations toward the future use of sediment stable isotope signatures, given their integrative capacity and practical analytical process. We also detail a method to incorporate stable isotopes into multi-objective modeling frameworks. Finally, we encourage watershed modelers to work closely with isotope geochemists to ensure proper integration of stable isotopes into in-stream nutrient fate and transport routines in water quality models. Keywords: Isotopes, Nutrients, Uncertainty analysis, Water quality modeling, Watershed.

Parameter uncertainty-based pattern identification and optimization for robust decision making on watershed load reduction

Nutrients loading reduction in watershed is essential for lake restoration from eutrophication. The efficient and optimal decision-making on loading reduction is generally based on water quality modeling and the quantitative identification of nutrient sources at the watershed scale. The modeling process is influenced inevitably by inherent uncertainties, especially by uncertain parameters due to equifinality. Therefore, the emerging question is: if there is parameter uncertainty, how to ensure the robustness of the optimal decisions? Based on simulation-optimization models, an integrated approach of pattern identification and analysis of robustness was proposed in this study that focuses on the impact of parameter uncertainty in water quality modeling. Here the pattern represents the discernable regularity of solutions for load reduction under multiple parameter sets. Pattern identification is achieved by using a hybrid clustering analysis (i.e., Ward-Hierarchical and K-means), which was flexible and efficient in analyzing Lake Bali near the Yangtze River in China. The results demonstrated that urban domestic nutrient load is the most potential source that should be reduced, and there are two patterns for Total Nitrogen (TN) reduction and three patterns for Total Phosphorus (TP) reduction. The patterns indicated different total reduction of nutrient loads, which reflect diverse decision preferences. The robust solution was identified by the highest accomplishment with the water quality at monitoring stations that were improved uniformly with this solution. We conducted a process analysis of robust decision-making that was based on pattern identification and uncertainty, which provides effective support for decision-making with preference under uncertainty.

Catchment‐scale sensitivity and uncertainty in water quality modelling

AbstractIn this paper, we assess the performance of the catchment model SIMulated CATchment model (SIMCAT), to predict nitrate and soluble reactive phosphorus concentrations against four monitoring regimes with different spatial and temporal sampling frequencies. The Generalised Likelihood Uncertainty Estimation (GLUE) uncertainty framework is used, along with a general sensitivity analysis to understand relative parameter sensitivity. Improvements to model calibration are explored by introducing more detailed process representation using the Integrated Catchments model (INCA) water quality model, driven by the European hydrological predictions for the environment model. The results show how targeted sampling of headwater watercourses upstream of point discharges is essential for calibrating diffuse loads and can exert a strong influence on the whole‐catchment model performance. Further downstream, if the point discharges and loads are accurately represented, then the improvement in the catchment‐scale model performance is relatively small as more calibration points are added or frequency is increased.The higher‐order, dynamic model integrated catchments model of phosphorus dynamics, which incorporates sediment and biotic interaction, resulted in improved whole‐catchment performance over SIMCAT, although there are still large epistemic uncertainties from land‐phase export coefficients and runoff. However, the very large sampling errors in routine monitoring make it difficult to invest confidence in the modelling, especially because we know phosphorous transport to be very episodic and driven by high flow conditions for which there are few samples. The environmental modelling community seems to have been stuck in this position for some time, and whilst it is useful to use an uncertainty framework to highlight these issues, it has not widely been adopted, perhaps because there is no clear mechanism to allow uncertainties to influence investment decisions. This raises the question as to whether it might better place a cost on uncertainty and use this to drive more data collection or improved models, before making investment decisions concerning, for example, mitigation strategies. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Uncertainty assessment of water quality modeling for a small-scale urban catchment using the GLUE methodology: a case study in Shanghai, China.

There is often great uncertainty in water quality modeling for urban drainage systems because water quality variation in systems is complex and affected by many factors. The stormwater management model (SWMM) was applied to a small-scale urban catchment with a simple and well-maintained stormwater drainage system without illicit connections. This was done to assess uncertainty in build-up and wash-off modeling of pollutants within the generalized likelihood uncertainty estimation (GLUE) methodology, based on a well-calibrated water quantity model. The results indicated great uncertainty of water quality modeling within the GLUE methodology. Comparison of uncertainties in various pollutant build-up and wash-off models that were available in SWMM indicated that those uncertainties varied slightly. This may be a consequence of the specific characteristics of rainfall events and experimental sites used in the study. The uncertainty analysis of water quality parameters in SWMM is conducive to effectively evaluating model reliability, and provides an experience base for similar research and applications.

Comparison of several approaches representing terrestrial and in-stream nutrient retention and decomposition in watershed modelling

Retention and transformation of nutrients within a river catchment are important mechanisms influencing water quality measured at the watershed outlet. Nutrient storage and reduction can occur in soils as well as in the river and should be considered in water quality modelling. Consideration is possible using various methods at several points during modelling cascade. The study compares the effects of five different equation sets implemented into the Soil and Water Integrated Model (SWIM), one describing terrestrial and four in-stream retention with a rising complexity (including algal growth and death at the highest complexity level). The influences of the different methods alone and in combinations on water quality model outputs (NO3-N, NH4-N, PO4-P) were analyzed for the outlet of the large-scale Saale basin in Germany. Experiments revealed that nutrient forms coming primarily from diffuse sources are mostly influenced by retention processes in the soils of the catchment, and river processes are less important. Nutrients introduced to the river mainly by point sources are more subject to retention by in-stream processes, but both nutrient retention and transformation processes in soils and rivers have to be included. Although the best overall results could be achieved at the highest complexity level, the calibration efforts for this case are extremely high, and only minor improvements of overall model performance with the highest complexity were detected. Therefore, it could be reasoned that for some research questions also less complex model approaches would be sufficient, which could help to reduce unnecessary complexity and diminish high uncertainty in water quality modelling at the catchment scale.

Bayesian Framework for Water Quality Model Uncertainty Estimation and Risk Management

AbstractA formal Bayesian methodology is presented for integrated model calibration and risk-based water quality management using Bayesian Monte Carlo simulation and maximum likelihood estimation (BMCML). The primary focus is on lucid integration of model calibration with risk-based water quality management and total maximum daily load (TMDL) estimation under conditions of uncertainty. The sources of uncertainty considered in the analysis are modeling errors, observational data errors and fuzziness of the water quality standard. The difference between observed data or transformation thereof and corresponding model response is assumed to follow first-order Markov process, a specific case of which is statistically independent Gaussian errors. The BMCML method starts with sampling parameter sets from prior probability distributions of the model parameters and uses Bayes theorem and the maximum likelihood technique to estimate the triplicate (variance of residual errors, bias and autocorrelation coefficient o...

Water Quality Model Uncertainty Analysis of a Point-Point Source Phosphorus Trading Program1

Kardos, Josef S. and Christopher C. Obropta, 2011. Water Quality Model Uncertainty Analysis of a Point-Point Source Phosphorus Trading Program. Journal of the American Water Resources Association (JAWRA) 47(6):1317–1337. DOI: 10.1111/j.1752-1688.2011.00591.x Abstract: Water quality modeling is a major source of scientific uncertainty in the Total Maximum Daily Load (TMDL) process. The effects of these uncertainties extend to water quality trading programs designed to implement TMDLs. This study examines the effects of water quality model uncertainty on a nutrient trading program. The study builds on previous work to design a phosphorus trading program for the Nontidal Passaic River Basin in New Jersey that would implement the watershed TMDL for total phosphorus (TP). The study identified how water quality model uncertainty affects outcomes of potential trades of TP between wastewater treatment plants. The uncertainty analysis found no evidence to suggest that the outcome of trades between wastewater treatment plants, as compared with command and control regulation, will significantly increase uncertainty in the attainment of dissolved oxygen surface water quality standards, site-specific chlorophyll a criteria, and reduction targets for diverted TP load at potential hot spots in the watershed. Each simulated trading scenario demonstrated parity with or improvement from the command and control approach at the TMDL critical locations, and low risk of hot spots elsewhere.

Input data resolution-induced uncertainty in watershed modelling

The temporal-spatial resolution of input data-induced uncertainty in a watershed-based water quality model, Hydrologic Simulation Program-FORTRAN (HSPF), is investigated in this study. The temporal resolution-induced uncertainty is described using the coefficient of variation (CV). The CV is found to decrease with decreasing temporal resolution and follow a log-normal relation with time interval for temperature data while it exhibits a power-law relation for rainfall data. The temporal-scale uncertainties in the temperature and rainfall data follow a general extreme value distribution and a Weibull distribution, respectively. The Nash-Sutcliffe coefficient (NSC) is employed to represent the spatial resolution induced uncertainty. The spatial resolution uncertainty in the dissolved oxygen and nitrate-nitrogen concentrations simulated using HSPF is observed to follow a general extreme value distribution and a log-normal distribution, respectively. The probability density functions (PDF) provide new insights into the effect of temporal-scale and spatial resolution of input data on uncertainties involved in watershed modelling and total maximum daily load calculations. This study exhibits non-symmetric distributions of uncertainty in water quality modelling, which simplify weather and water quality monitoring and reducing the cost involved in flow and water quality monitoring. Copyright © 2011 John Wiley & Sons, Ltd.

Uncertainty in water quality modelling: The applicability of Variance Decomposition Approach

Quantification of uncertainty is of paramount interest in integrated urban drainage water quality modelling. Indeed, the assessment of the reliability of the results of complex water quality models is crucial in understanding their significance. However, the state of knowledge regarding uncertainties in urban drainage models is poor. In the case of integrated urban drainage water quality models, due to the fact that integrated approaches are basically a cascade of sub-models (simulating the sewer system, wastewater treatment plant and receiving water body), uncertainty produced in one sub-model propagates to the following ones in a manner dependent on the model structure, the estimation of parameters and the availability and uncertainty of measurements in the different parts of the system. Uncertainty basically propagates throughout a chain of models in which the simulation output from upstream models is transferred to the downstream ones as input. The Variance Decomposition Approach tracks uncertainty propagation commonly assuming that the correlation among error sources is negligible. In complex environmental models, the overall uncertainty can differ significantly from the simple sum of uncertainties generated in each sub-model, showing the well-known uncertainty accumulation problems due to non-linearity in the model and correlation among the sources of uncertainty. This work discusses the importance of such issues in the application of a complex integrated urban drainage model with the aim of evaluating the applicability of Variance Decomposition Approach. The integrated model and the methodology for the uncertainty decomposition were then applied to a complex integrated catchment: the Nocella basin (Italy). The results showed that the Variance Decomposition Approach can be a powerful tool for uncertainty analysis, but a possible correlation among uncertainty sources should be considered because it can greatly affect the analysis.

Predictive Uncertainty in Water-Quality Modeling

A general and integrated approach to parameter identification, model calibration, and estimation of predictive uncertainty in water-quality models is proposed and validated. The proposed approach determines the maximal conditional likelihood functions of each of the model parameters using a transformation that forces the model errors to be normally distributed, with predictive uncertainty characterized by random normally distributed and homoscedastic model errors in the transform space. The proposed approach is demonstrated using a watershed-scale model to predict the fecal coliform levels in a third-order stream within the Little River Experimental Watershed in Georgia. Maximal conditional likelihood functions were identified for all parameters in the log, square root, and no-transformation cases. The key results are: (1) the number of sensitive parameters and the optimal parameter values can depend on the transformation; (2) only in the case of the log-transformation are the errors normally distributed and consistent with the assumed Gaussian likelihood function; (3) the standard error in the model is least for the no-transform case and highest for the log-transform case; and (4) the observed model errors are most predictable using the log-transform and least predictable using the no-transform approach.

Effect of Water Quality Model Uncertainty on the Passaic TMDL and Water Quality Trading Program for Total Phosphorus

Water quality modeling is a major source of scientific uncertainty in the Total Maximum Daily Load (TMDL) process. The effects of these uncertainties extend to water quality trading programs designed to implement TMDLs. This study identified how water quality model uncertainty affects outcomes related to the Non-Tidal Passaic River Basin TMDL for total phosphorus (TP) and potential trades of TP between point sources. Although the TMDL scenario showed greater than 10% probability of exceeding TMDL targets for chlorophyll-a (chl-a) at Dundee Lake and TP load diverted to the Wanaque Reservoir, the efficacy of TMDL measures was clearly demonstrated when compared directly to actual conditions in Water Year (WY) 2002. Trading scenario simulations suggest that trading ratios have been well designed. Each scenario demonstrated parity with or improvement from the baseline at the TMDL critical locations of Dundee Lake and the Wanaque South intake, and low risk of hot spots elsewhere.

Uncertainty and risk in water quality modelling and management

The case is presented for increasing attention to the evaluation of uncertainty in water quality modelling practice, and for this evaluation to be extended to risk management applications. A framework for risk-based modelling of water quality is outlined and presented as a potentially valuable component of a broader risk assessment methodology. Technical considerations for the successful implementation of the modelling framework are discussed. The primary arguments presented are as follows. (1) For a large number of practical applications, deterministic use of complex water quality models is not supported by the available data and/or human resources, and is not warranted by the limited information contained in the results. Modelling tools should be flexible enough to be employed at levels of complexities which suit the modelling task, data and available resources. (2) Monte Carlo simulation has largely untapped potential for the evaluation of model performance, estimation of model uncertainty and identification of factors (including pollution sources, environmental influences and ill-defined objectives) contributing to the risk of failing water quality objectives. (3) For practical application of Monte Carlo methods, attention needs to be given to numerical efficiency, and for successful communication of results, effective interfaces are required. A risk-based modelling tool developed by the authors is introduced.

Neural Network Embedded Monte Carlo Approach for Water Quality Modeling under Input Information Uncertainty

This paper proposes a neural network embedded Monte Carlo ~NNMC! approach to account for uncertainty in water quality modeling. The framework of the proposed method has three major parts: a numerical water quality model, a neural network technique, and Monte Carlo simulation. The numerical model is used to generate desirable output for training and testing sets, and the neural network is used as a universal functional mapping tool to approximate the input-output response of the numerical model. The Monte Carlo simulation then uses the neural network to generate numerical realizations based on a probabilistic distribution of parameters, thus obtaining a probabilistic distribution of the simulated state variables. By embedding a neural network into the conventional Monte Carlo simulation, the proposed approach significantly improves upon the conventional method in computational efficiency. The proposed approach has been applied to uncertainty and risk analyses of a phosphorus model for Triadelphia Reservoir in Maryland. The results of this research show that the NNMC approach has potential for efficient uncertainty analysis of water quality modeling.

Development of Bayesian Monte Carlo techniques for water quality model uncertainty

A new technique, Bayesian Monte Carlo (BMC), is used to quantify errors in water quality models caused by uncertain parameters. BMC also provides estimates of parameter uncertainty as a function of observed data on model state variables. The use of Bayesian inference generates uncertainty estimates that combine prior information on parameter uncertainty with observed variation in water quality data to provide an improved estimate of model parameter and output uncertainty. It also combines Monte Carlo analysis with Bayesian inference to determine the ability of random selected parameter sets to simulate observed data. BMC expands upon previous studies by providing a quantitative estimate of parameter acceptability using the statistical likelihood function. The likelihood of each parameter set is employed to generate an n-dimensional hypercube describing a probability distribution of each parameter and the covariance among parameters. These distributions are utilized to estimate uncertainty in model predictions. Application of BMC to a dissolved oxygen model reduced the estimated uncertainty in model output by 72% compared with standard Monte Carlo techniques. Sixty percent of this reduction was directly attributed to consideration of covariance between model parameters. A significant benefit of the technique is the ability to compare the reduction in total model output uncertainty corresponding to: (1) collection of more data on model state variables, and (2) laboratory or field studies to better define model processes. Limitations of the technique include computational requirements and accurate estimation of the joint probability distribution of model errors. This analysis was conducted assuming that model error is normally and independently distributed.

Water quality modeling: A review of the analysis of uncertainty

This paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction. More specifically, four problem areas are examined in detail: uncertainty about model structure, uncertainty in the estimated model parameter values, the propagation of prediction errors, and the design of experiments in order to reduce the critical uncertainties associated with a model. The review is rather lengthy, and it has therefore been prepared in effect as two papers. There is a shorter, largely nontechnical version, which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling. Enclosed by this shorter discussion is the main body of the review dealing in turn with (1) identifiability and experimental design, (2) the generation of preliminary model hypotheses under conditions of sparse, grossly uncertain field data, (3) the selection and evaluation of model structure, (4) parameter estimation (model calibration), (5) checks and balances on the identified model, i.e., model “verification” and model discrimination, and (6) prediction error propagation. Much time is spent in discussing the algorithms of system identification, in particular, the methods of recursive estimation, and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first‐order error analysis. There are two obvious omissions from the review. It is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty, although clearly some reference must be made to these topics. In brief, the review concludes (not surprisingly) that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality, and much remains to be done. A lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior, and there is ample evidence to show that the “larger,” more “comprehensive” models are easily capable of generating highly uncertain predictions of future behavior. For the future of the subject, it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification, a need for new questions to be posed in the problem of prediction, and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence.