A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> In the preliminary analysis of environmental problems, mathematical modelling studies can sometimes aid in hypothesis development and in the integration of preliminary data. Circumstances usually require models used in this way to be simulation models closely based on traditional scientific descriptions of component processes. As a result, such models contain many ill-defined parameters, a fact which severely limits the reliance that can be placed on the outcome of any single simulation. In an attempt to overcome this difficulty, it has been proposed that parameters be assigned statistical distributions which reflect the degree of parametric uncertainty and that these distributions be used in Monte Carlo simulation analyses. The authors propose a variation on this theme in which they first stipulate the systems' problem-defining behavior and define a classification algorithm to be applied to the model's output. This algorithm results in each simulation run being classified as a behavior, B, or not a behavior, anti B. The parameters leading to the result are stored according to the behavioural outcome. Subsequently, all parameter vectors are subjected to analysis to determine the degree to which the a prior; distributions separate under the behavioral mapping. This separation, or lack thereof, forms the basis for amore » generalized sensitivity analysis in which parameters and their related processes important to the simulation of the behaviour are singled out. The procedure has been applied to a eutrophication problem in the Peel-Harvey Inlet of Western Australia with encouraging results.« less <s> BIB001 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> This paper describes a methodology for calibration and uncertainty estimation of distributed models based on generalized likelihood measures. The GLUE procedure works with multiple sets of parameter values and allows that, within the limitations of a given model structure and errors in boundary conditions and field observations, different sets of values may be equally likely as simulators of a catchment. Procedures for incorporating different types of observations into the calibration; Bayesian updating of likelihood values and evaluating the value of additional observations to the calibration process are described. The procedure is computationally intensive but has been implemented on a local parallel processing computer. <s> BIB002 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> Application of stream water-quality models in decision making has been hampered by a lack of data appropriate for minimization of model-simulation uncertainty. A method for determining data needed to reduce model-prediction uncertainty is illustrated in this paper. First-order reliability analysis is applied to determine (1) the model parameters that significantly affect model-prediction uncertainty; and (2) the constituents for which model-prediction uncertainty is unacceptable. Additional data are required to reduce uncertainty in the parameters that significantly affect constituents with high prediction uncertainty and consequently in model prediction. The method is demonstrated for multiconstituent water-quality modeling on the Passaic River in New Jersey applying QUAL2E. The model-prediction uncertainty of dissolved oxygen, biochemical oxygen demand, ammonia, and chlorphyll a is considered. For this example, only the reaeration rate and the algal maximum-specific-growth rate contribute significant un... <s> BIB003 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> 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. <s> BIB004 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> FUNDAMENTALS OF BAYESIAN INFERENCE Probability and Inference Single-Parameter Models Introduction to Multiparameter Models Asymptotics and Connections to Non-Bayesian Approaches Hierarchical Models FUNDAMENTALS OF BAYESIAN DATA ANALYSIS Model Checking Evaluating, Comparing, and Expanding Models Modeling Accounting for Data Collection Decision Analysis ADVANCED COMPUTATION Introduction to Bayesian Computation Basics of Markov Chain Simulation Computationally Efficient Markov Chain Simulation Modal and Distributional Approximations REGRESSION MODELS Introduction to Regression Models Hierarchical Linear Models Generalized Linear Models Models for Robust Inference Models for Missing Data NONLINEAR AND NONPARAMETRIC MODELS Parametric Nonlinear Models Basic Function Models Gaussian Process Models Finite Mixture Models Dirichlet Process Models APPENDICES A: Standard Probability Distributions B: Outline of Proofs of Asymptotic Theorems C: Computation in R and Stan Bibliographic Notes and Exercises appear at the end of each chapter. <s> BIB005 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> Abstract Two Monte Carlo-based approaches for assessing parameter uncertainty in complex hydrologic models are considered. The first, known as importance sampling, has been implemented in the generalised likelihood uncertainty estimation (GLUE) framework of Beven and Binley. The second, known as the Metropolis algorithm, differs from importance sampling in that it uses a random walk that adapts to the true probability distribution describing parameter uncertainty. Three case studies are used to investigate and illustrate these Monte Carlo approaches. The first considers a simple water balance model for which exact results are known. It is shown that importance sampling is inferior to Metropolis sampling. Unless a large number of random samples are drawn, importance sampling can produce seriously misleading results. The second and third case studies consider more complex catchment models to illustrate the insights the Metropolis algorithm can offer. They demonstrate assessment of parameter uncertainty in the presence of bimodality, evaluation of the significance of split-sample tests, use of prior information and the assessment of confidence limits on hydrologic responses not used in calibration. When compared with the capabilities of traditional inference based on first-order approximation, the Metropolis algorithm provides a quantum advance in our capability to deal with parameter uncertainty in hydrologic models. <s> BIB006 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> A Bayesian procedure is presented for parameter estimation in nonlinear flood event models. We derive a pooling diagnostic using Bayes factors to identify when it is reasonable to pool model parameters across storm events. A case study involving a quasi-distributed, nonlinear flood event model and five watersheds in the southwest of Western Australia is presented to illustrate the capabilities and utility of the procedure. The results indicate that Markov chain Monte Carlo methods based on the Metropolis-Hastings algorithm are useful tools for parameter estimation. We find that pooling is not justified for the model and data at hand. This suggests that current practices in nonlinear flood event modeling may be in need of urgent review. <s> BIB007 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> A fully Bayesian approach to parameter estimation and inference in conceptual rainfall-runoff models (CRRMs) is presented. Computations are performed using a Markov chain Monte Carlo (MCMC) method based on the Metropolis-Hastings algorithm. Single-site and block updating schemes are used for model parameters subject to nonnegativity restrictions as well as interval, equality, and order constraints. Diagnostics for the convergence of the Markov chain and CRRM assessment are also considered. The MCMC approach produces samples from the joint posterior distribution of the model parameters. This provides more information than single-point estimates and avoids the need to use a normal approximation to the posterior as the basis for inference. The methodology is demonstrated using an eight-parameter conceptual rainfall-runoff model and two case studies from southeastern Australia. The first case study considers a watershed with high runoff yield over a 12-year period. The second case study considers a watershed with low yield over a 17-year period. The results indicate that (1) Bayesian methods provide an objective framework for model criticism and choice, (2) the proposed strategies for handling constraints on model parameters are effective, (3) the model parameters are sensitive to likelihood function selection, (4) the conventional approach of using a power transformation and an autoregressive process to stabilize error variance and model dependence in the residuals may have limited success, and (5) some care is required in the implementation of the MCMC approach and reliable results will be difficult to obtain when CRRM complexity exceeds the limitations of the rainfall-runoff data at hand. A key finding is that the MCMC scheme presented herein provides a powerful means of identifying specific inadequacies in the structure of CRRMs. <s> BIB008 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> Abstract There are many sources of uncertainty in modelling systems including uncertainty due to parameter estimations, input data and structure of the system. In this paper, modelling system structure is understood to be the algorithms and equations used to describe and calculate processes. Specific attention is given to the uncertainty in the equations, which link models interactively in a modelling system and algorithms, which pass information between the models. This paper places emphasis on structural uncertainty in modelling systems since this topic has received very little attention in research compared to the wealth of literature on parameter and input data uncertainty. This imbalance is partly due to the difficulty in quantifying structural uncertainty and an example is given showing how this may be done. The modelling system used for this study incorporates the coupling of three models from the WASP5 package (Water quality Analysis Simulation Program) developed by the US Environmental Protection Agency: DYNHYD (hydrodynamics), EUTRO (dissolved oxygen, nutrient and phytoplankton dynamics) and TOXI (transport and transformation of sediments and micro-pollutants). The three models were coupled in the high level architecture (HLA) platform to enable interactions between the models during simulations. This platform allowed ease of implementing Monte Carlo simulation runs, which were used for the uncertainty analyses. The modelling system structure focuses on the exchange of data between EUTRO and TOXI in simulating two processes: (i) sorption of heavy metals to suspended solids as a function of the fraction of organic carbon constituting the solids and (ii) phytoplankton growth limitation by light extinction through the water column as a function of the concentration of suspended solids and chlorophyll a in the water. Both processes are described by empirical relationships using regression curves derived from field data. The variance in the y -axis interceptions of the curves (also called regression uncertainty) is taken to be the uncertainty bounds for the Monte Carlo simulations used for the uncertainty analyses. The results show that structural uncertainty can be more significant than parameter and input data uncertainty, especially if the processes are very sensitive to the state variables. <s> BIB009 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> Where numerical models are employed as an aid to environmental management, the uncertainty associated with predictions made by such models must be assessed. A number of different methods are available to make such an assessment. This paper explores the use of three such methods, and compares their performance when used in conjunction with a lumped parameter model for surface water flow (HSPF) in a large watershed. Linear (or first-order) uncertainty analysis has the advantage that it can be implemented with virtually no computational burden. While the results of such an analysis can be extremely useful for assessing parameter uncertainty in a relative sense, and ascertaining the degree of correlation between model parameters, its use in analyzing predictive uncertainty is often limited. Markov Chain Monte Carlo (MCMC) methods are far more robust, and can produce reliable estimates of parameter and predictive uncertainty. As well as this, they can provide the modeler with valuable qualitative information on the shape of parameter and predictive probability distributions; these shapes can be quite complex, especially where local objective function optima lie within those parts of parameter space that are considered probable after calibration has been undertaken. Nonlinear calibration-constrained optimization can also provide good estimates of parameter and predictive uncertainty, even in situations where the objective function surface is complex. Furthermore, they can achieve these estimates using far fewer model runs than MCMC methods. However, they do not provide the same amount of qualitative information on the probability structure of parameter space as do MCMC methods, a situation that can be partially rectified by combining their use with an efficient gradient-based search method that is specifically designed to locate different local optima. All methods of parameter and predictive uncertainty analysis discussed herein are implemented using freely-available software. Hence similar studies, or extensions of the present study, can be easily undertaken in other modeling contexts by other modelers. <s> BIB010 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> Abstract An uncertainty assessment method for evaluating models, the Sources of UNcertainty GLobal Assessment using Split SamplES (SUNGLASSES), is presented, which assesses predictive uncertainty that is not captured by parameter or other input uncertainties. The method uses the split sample approach to generate a quantitative estimate of the fit-for-purpose of the model, thus focusing on the purpose for which the model is used. It operates by comparing the output to be used for decision making to its observed counterpart and the associated uncertainty. The described method is applied on a Soil Water Assessment Tool (SWAT) model of Honey Creek, a tributary of the Sandusky catchment in Ohio, USA. Water flow and sediment loads are analysed. In this case study the uncertainty estimated by the proposed method is much larger than the typically estimated parameter uncertainty. <s> BIB011 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> The generation and formation of non-point source pollution involves great uncertainty, and this uncertainty makes monitoring and controlling pollution very difficult. Understanding the main parameters that affect non-point source pollution uncertainty is necessary to provide the basis for the planning and design of control measures. In this study, three methods were adopted to do the parameter uncertainty analysis with the Soil and Water Assessment Tool (SWAT). Based on the results of parameter sensitivity analysis by the Morris screening method, the ten parameters that most affect runoff, sediment, organic N, nitrate, and total phosphorous (TP) were chosen for further uncertainty analysis. First-order error analysis (FOEA) and the Monte Carlo method (MC) were used to analyze the effect of parameter uncertainty on model outputs. FOEA results showed that only a few parameters had significantly affected the uncertainty of the final simulation results, and many parameters had little or no effect. The SCS curve number was the parameter with significant uncertainty impact on runoff, sediment, organic N, nitrate and TP, and it showed that the runoff process was mainly responsible for the uncertainty of non-point source pollution load. The uncertainty of sediment was the biggest among the five model output results described above. MC results indicated that neglecting the parameter uncertainty of the model would underestimate the non-point source pollution load, and that the relationship between model input and output was non-linear. The uncertainty of non-point source pollution exhibited a temporal pattern: It was greater in summer than in winter. The uncertainty of runoff was smaller compared to that of sediment, organic N, nitrate, and TP, and the source of uncertainty was mainly affected by parameters associated with runoff. <s> BIB012 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> Abstract In the last few decades hydrologists have made tremendous progress in using dynamic simulation models for the analysis and understanding of hydrologic systems. However, predictions with these models are often deterministic and as such they focus on the most probable forecast, without an explicit estimate of the associated uncertainty. This uncertainty arises from incomplete process representation, uncertainty in initial conditions, input, output and parameter error. The generalized likelihood uncertainty estimation (GLUE) framework was one of the first attempts to represent prediction uncertainty within the context of Monte Carlo (MC) analysis coupled with Bayesian estimation and propagation of uncertainty. Because of its flexibility, ease of implementation and its suitability for parallel implementation on distributed computer systems, the GLUE method has been used in a wide variety of applications. However, the MC based sampling strategy of the prior parameter space typically utilized in GLUE is not particularly efficient in finding behavioral simulations. This becomes especially problematic for high-dimensional parameter estimation problems, and in the case of complex simulation models that require significant computational time to run and produce the desired output. In this paper we improve the computational efficiency of GLUE by sampling the prior parameter space using an adaptive Markov Chain Monte Carlo scheme (the Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm). Moreover, we propose an alternative strategy to determine the value of the cutoff threshold based on the appropriate coverage of the resulting uncertainty bounds. We demonstrate the superiority of this revised GLUE method with three different conceptual watershed models of increasing complexity, using both synthetic and real-world streamflow data from two catchments with different hydrologic regimes. <s> BIB013 </s> A REVIEW ON ACCURACY AND UNCERTAINTY OF SPATIAL DATA AND ANALYSES WITH SPECIAL REFERENCE TO URBAN AND HYDROLOGICAL MODELLING <s> SWAT Model Uncertainties <s> In this paper, the issue of nonlinear sensitivity analysis for dimensionality reduction in hydrologic model calibration is discussed, and a novel method to quantify the sensitivity of each parameter that considers the nonlinear relationship in the model is presented. The method is based on computing the absolute variation of the nonlinear function represented by the model in its parameter space. The paper discusses the theoretical background of the method and presents the algorithm. The algorithm employs neural network as a pseudo simulator to reduce the computational burden of the analysis. The proposed approach of sensitivity analysis is illustrated through a case study on a physically based distributed hydrologic model. The results indicate that the method is able to rank the parameters effectively, and the ranking can be interpreted in the context of the physical processes being considered by the model. <s> BIB014
Much attention has been paid to uncertainty issues in hydrological modelling due to their great effects on prediction and further on decision making BIB011 BIB014 . Usually, the uncertainty in hydrological modelling is from model structures, input data and parameters BIB009 . Currently, parameter uncertainty is a hot topic in the uncertainty research field BIB012 BIB014 . Several calibration and uncertainty analysis techniques have been applied in previous research work, such as the first order error analysis [FOEA] BIB003 , the Monte Carlo method BIB004 and the Generalized Likelihood Uncertainty Estimation Method [GLUE] BIB002 . The GLUE method can also handle the parameter interactions and non-linearity implicitly through the likelihood measure (Vazquz et al., 2009 ). In addition, GLUE is a simple concept and is relatively easy to implement. The GLUE method  ) is an uncertainty analysis technique inspired by importance sampling and regional sensitivity analysis BIB001 . In GLUE, parameter uncertainty accounts for all sources of uncertainty; i.e., input, structural, parameter and response uncertainties. Hence, this method is widely used in many areas as an effective and general strategy for model calibration and uncertainty estimation associated with complex models. With the advances in computing technology, Monte Carlo based methods are popular , with strengths in dealing with the nonlinearity and interdependency of parameters in complex hydrological models. Two Monte Carlo based approaches are commonly seen in literatures: importance sampling and Markov Chain Monte Carlo (MCMC) simulation (e.g. BIB002  BIB006 BIB008 BIB010 . Importance sampling is a technique for randomly sampling from a probability distribution and was implemented in Generalised Likelihood Uncertainty Estimation (GLUE) by BIB002 . The efficiency of this algorithm depends strongly on the choice of the importance distribution. If one or more importance weights dominate, the algorithm can produce unreliable inferences BIB005 . MCMC is one of the most important numerical technique for creating a sample from the posterior distribution, which has been widely used in hydrological modelling to quantify parameter uncertainties (e.g. BIB006 BIB007   . Its underlying rationale is to set up a Markov chain to simulate the true posterior distribution by generating samples from a random walk. An obvious advantage of this method is that it does not require linearity assumptions in model or even that model outputs do not need to be differentiable with respect to parameter values BIB010 . Because of its robust performance, MCMC is often used to assess parameter uncertainties in combination with GLUE or Bayesian inference by estimating a probability density for model parameters conditioned on observations. BIB013 recently found that using a MCMC sampling scheme coupled with GLUE significantly improves the efficiency and effectiveness of the methodology of GLUE. Another widely used method for parameter estimation and uncertainty analysis is the Bayesian method which provide more information than single-point estimates BIB008  BIB010  . The posterior distribution could be obtained by applying Bayes' theorem based on a prior distribution and observed data BIB005 . The Monte Carlo based approaches are often used to generate a large-enough sample from the posterior distribution so that desired features of the posterior distribution may be summarized.