Uncertainty analysis in hydrodynamic modeling is useful to identify and report the limitations of a model caused by different sources of error. In the practice, the main sources of errors are divided into model structure errors, errors in the input data due to measurement imprecision among other, and parametric errors resulting from the difficulty of identifying physically representative parameter values valid at the temporal and spatial scale of the models. This investigation identifies, implements, evaluates, and recommends a set of methods for the evaluation of model structure uncertainty, parametric uncertainty, and input data uncertainty in hydrodynamic modeling studies. A comprehensive review of uncertainty analysis methods is provided and a set of widely applied methods is selected and implemented in real case studies identifying the main limitations and benefits of their use in hydrodynamic studies. In particular, the following methods are investigated: the First Order Variance Analysis (FOVA) method, the Monte Carlo Uncertainty Analysis (MCUA) method, the Bayesian Monte Carlo (BMC) method, the Markov Chain Monte Carlo (MCMC) method and the Generalized Likelihood Uncertainty Estimation (GLUE) method. The results of this investigation indicate that the uncertainty estimates computed with FOVA are consistent with the results obtained by MCUA. In addition, the comparison of BMC, MCMC and GLUE indicates that BMC and MCMC provide similar estimations of the posterior parameter probability distributions, single-point parameter values, and uncertainty bounds mainly due to the use of the same likelihood function, and the low number of parameters involved in the inference process. However, the implementation of MCMC is substantially more complex than the implementation of BMC given that its sampling algorithm requires a careful definition of auxiliary proposal probability distributions along with their variances to obtain parameter samples that effectively belong to the posterior parameter distribution. The analysis also suggest that the results of GLUE are inconsistent with the results of BMC and MCMC. It is concluded that BMC is a powerful and parsimonious strategy for evaluation of all the sources of uncertainty in hydrodynamic modeling. Despites of the computational requirements of BMC, the method can be easily implemented in most practical applications.

To propose a methodology for the uncertainty estimation in water quality modeling as related to TMDL development, four Monte Carlo (MC) based techniques—single-phase MC, two-phase MC, Generalized Likelihood Uncertainty Estimation (GLUE), and Markov Chain Monte Carlo (MCMC) —were applied to a Hydrological Simulation Program–FORTRAN (HSPF) model developed for the Mossy Creek bacterial TMDL in Virginia. Predictive uncertainty in percent violations of instantaneous fecal coliform concentration criteria for the prediction period under two TMDL pollutant allocation scenarios was estimated. The average percent violations of the applicable water quality criteria were less than 2% for all the evaluated techniques. Single-phase MC reported greater uncertainty in percent violations than the two-phase MC for one of the allocation scenarios. With the two-phase MC, it is computationally expensive to sample the complete parameter space, and with increased simulations, the estimates of single and two-phase MC may be similar. Two-phase MC reported significantly greater effect of knowledge uncertainty than stochastic variability on uncertainty estimates. Single and two-phase MC require manual model calibration as opposed to GLUE and MCMC that provide a framework to obtain posterior or calibrated parameter distributions based on a comparison between observed and simulated data and prior parameter distributions. Uncertainty estimates using GLUE and MCMC were similar when GLUE was applied following the log-transformation of observed and simulated FC concentrations. GLUE provides flexibility in selecting any model goodness of fit criteria for calculating the likelihood function and does not make any assumption about the distribution of residuals, but this flexibility is also a controversial aspect of GLUE. MCMC has a robust formulation that utilizes a statistical likelihood function, and requires normal distribution of model errors. However, MCMC is computationally expensive to apply in a watershed modeling application compared to GLUE. Overall, GLUE is the preferred approach among all the evaluated uncertainty estimation techniques, for the application of watershed modeling as related to bacterial TMDL development. However, the application of GLUE in watershed-scale water quality modeling requires further research to evaluate the effect of different likelihood functions, and different parameter set acceptance/rejection criteria. / Ph. D.

A distributed approach can improve functionality of H/WQ (Hydrology and Water Quality) modeling by facilitating a way to explicitly incorporate spatial characteristics of a watershed into the model. The time-area approach, with its intuitive and inherently distributed concept, provides a simple method to simulate runoff mechanisms. This study developed a distributed model based on the time-area approach with the goal of improved utility and efficiency in H/WQ modeling. Uncertainty is always introduced into watershed modeling because of imperfect knowledge and scale dependant spatial heterogeneity and temporal variability. Uncertainty analysis can provide a modeler, policy maker, and stakeholder with reliability information, better understanding, and better communication about the modeling results. This study quantified uncertainty of the model parameter and output through uncertainty analysis in order to assess risk in watershed management. The main goal of this study was to develop a hydrology and sediment transport model capable of routing overland flow using a time-area concept and providing reliability of the modeling results in a probabilistic manner through uncertainty analysis. The HYSTAR (HYdrology and Sediment transport simulation using Time-ARea method) model incorporates a modified Curve Number (CN) method and the newly devised time-area routing method to estimate runoff. HYSTAR is capable of simulating direct runoff, base flow, soil moisture, and sediment load in a distributed manner and in an hourly time step. In the model, the modified CN and a continuity equation are used to calculate infiltration of the routed runoff as well as rainfall on every overland cell. The effective direct runoff volume is distributed over downstream areas using the newly developed routing method. A direct runoff hydrograph is constructed directly through the discrete convolution of the time-area histogram and the effective direct runoff volume map without employing a unit hydrograph. In addition, sediment transport is simulated using the routing method and the sediment transport capacity approach without using a delivery ratio. The sensitivity analysis found that the CN and root zone depth were the most critical parameters for runoff simulation with HYSTAR. The model provided acceptable performance in predicting runoff and sediment load of a subwatershed of the Owl Run Watershed (ORD) with the Nash-Sutcliffe efficiency coefficient and coefficient of determination greater than 0.5. However, it failed to reproduce runoff for a subwatershed of Polecat Creek Watershed (PCA), where data show that runoff is not immediately responsive to rainfall. Uncertainty analysis revealed that the confidence intervals of the simulated monthly runoff and sediment load corresponded to 9.7 % and 10.2 % of their averages, respectively, at a significance level of 0.05. In addition, the average ranges of variation created by the Digital Elevation Model (DEM) and National Land Cover Data (NLCD) errors in the simulated monthly runoff and sediment load were equivalent to 7.5 % and 15.9 % of the average of their calibrated values, respectively. Based on the uncertainty analysis results, the Margin of Safety (MOS) of Total Maximum Daily Load (TMDL) were explicitly quantified as corresponding to 7.0 % and 21.3 % of the average of the simulated runoff and sediment load for ORD at significance level of 0.05. In conclusion, the HYSTAR model provided a new way to explicitly simulate runoff and sediment load of a watershed in a distributed manner. The approach developed here retains the simplicity of a unit hydrograph approach without employing numerical methods. Uncertainty analysis found that parameter uncertainty had greater impact on the model output than did expected Geographic Information System (GIS) data errors. In addition, the impact of the topographic data error on the model output was greater than was that of the land cover data error. Finally, this study provided a proof that a 5 to 10 % MOS that many TMDL studies consider underestimates modeling uncertainty. / Ph. D.

Electric vehicles (EVs) are increasing in popularity and play an important role in decarbonizing the transport sector. However, a growing EV fleet can cause problems for power grids as the grids are not initially designed for EV charging. The potential of a power grid to accommodate EV loads can be assessed through hosting capacity (HC) analysis. The HC is grid specific and varies, therefore it is necessary to conduct analysis that reflects local conditions and covers uncertainties and correlations over time. This theses aims to investigate the HC for EVs in existing residential power grids, and to gain a better understanding of how it varies based on how the EVs are implemented and charged. The work is in collaboration with a distribution system operator (DSO) and is based on two case studies using real-life data reflecting conditions in Swedish grids. Combinations of different HC assessment methods have been used and the HC is evaluated based on cable loading, transformer loading and voltage deviation. Additionally, the study investigated three distinct charging strategies: charging on arrival, evenly spread charging over whole connection period, and charging at the lowest spot price.  The results show that decisions on acceptable voltage deviation limit can have a large influence on the HC as well as the charging strategy used. A charging strategy based on energy prices resulted in the lowest HC, as numerous EVs charging simultaneously caused high power peaks during low spot price periods. Charging on arrival was the second worst strategy, as the peak power coincided with household demand. The best strategy was to evenly spread out the charging, resulting in fewer violations for 100% EV implementation compared to the other two strategies for 25% EV implementation.  The findings underscore the necessity for coordinated charging controls for EV fleets or diversified power tariffs to balance power on a large scale in order to use the grids efficiently.

Electric vehicles (EVs) are increasing in popularity and play an important role in decarbonizing the transport sector. However, a growing EV fleet can cause problems for power grids as the grids are not initially designed for EV charging. The potential of a power grid to accommodate EV loads can be assessed through hosting capacity (HC) analysis. The HC is grid specific and varies, therefore it is necessary to conduct analysis that reflects local conditions and covers uncertainties and correlations over time. This theses aims to investigate the HC for EVs in existing residential power grids, and to gain a better understanding of how it varies based on how the EVs are implemented and charged. The work is in collaboration with a distribution system operator (DSO) and is based on two case studies using real-life data reflecting conditions in Swedish grids. Combinations of different HC assessment methods have been used and the HC is evaluated based on cable loading, transformer loading and voltage deviation. Additionally, the study investigated three distinct charging strategies: charging on arrival, evenly spread charging over whole connection period, and charging at the lowest spot price.  The results show that decisions on acceptable voltage deviation limit can have a large influence on the HC as well as the charging strategy used. A charging strategy based on energy prices resulted in the lowest HC, as numerous EVs charging simultaneously caused high power peaks during low spot price periods. Charging on arrival was the second worst strategy, as the peak power coincided with household demand. The best strategy was to evenly spread out the charging, resulting in fewer violations for 100% EV implementation compared to the other two strategies for 25% EV implementation.  The findings underscore the necessity for coordinated charging controls for EV fleets or diversified power tariffs to balance power on a large scale in order to use the grids efficiently.

This research aims to integrate mathematical water quality models with Bayesian inference techniques for obtaining effective model calibration and rigorous assessment of the uncertainty underlying model predictions. The first part of my work combines a Bayesian calibration framework with a complex biogeochemical model to reproduce oligo-, meso- and eutrophic lake conditions. The model accurately describes the observed patterns and also provides realistic estimates of predictive uncertainty for water quality variables. The Bayesian estimations are also used for appraising the exceedance frequency and confidence of compliance of different water quality criteria. The second part introduces a Bayesian hierarchical framework (BHF) for calibrating eutrophication models at multiple systems (or sites of the same system). The models calibrated under the BHF provided accurate system representations for all the scenarios examined. The BHF allows overcoming problems of insufficient local data by “borrowing strength” from well-studied sites. Both frameworks can facilitate environmental management decisions.

Neste trabalho foi proposta uma estratégia de modelagem hidrológica para a transformação chuva vazão da Bacia do Ribeirão da Onça (B.R.O) utilizando-se técnicas de auto calibração com análise de incertezas e de ponderação de modelos. Foi utilizado o modelo hidrológico Soil and Water Assessment Tool (SWAT), por ser um modelo que possui uma descrição física e de maneira distribuída dos processos hidrológicos da bacia. Foram propostas cinco diferentes séries de precipitação e esquemas de interpolação espacial a serem utilizados como dados de entrada para o modelo SWAT. Em seguida, utilizou-se o método semiautomático Sequential Uncertainty Fitting ver.-2 (SUFI-2) para a auto calibração e análise de incertezas dos parâmetros do modelo e produção de respostas com intervalos de incerteza para cada uma das séries de precipitação utilizadas. Por fim, foi utilizado o método de ponderação bayesiana de modelos (BMA) para o pós-processamento estocástico das respostas. Os resultados da análise de incerteza dos parâmetros do modelo SWAT indicam uma não adequação do método Soil Conservation Service (SCS) para simulação da geração do escoamento superficial, juntamente com uma necessidade de maior investigação das propriedades físicas do solo da bacia. A análise da precisão e acurácia dos resultados das séries de precipitação em comparação com a resposta combinada pelo método BMA sugerem a última como a mais adequada para a simulação chuva-vazão na B.R.O. / This study proposed an approach to the hydrological modeling of the Ribeirão da Onças Basin (B.R.O) based on automatic calibration and uncertainty analysis methods, together with model averaging. The Soil and Water Assessment Tool (SWAT) was used due to its distributed nature and physical description of hydrologic processes. An ensemble, composed by five different precipitation schemes, based on different sources and spatial interpolation methods was used. The Sequential Uncertainty Fitting ver-2 (SUFI-2) procedure was used for automatic calibration and uncertainty analysis of the SWAT model parameters, together with generation of streamflow simulations with uncertainty intervals. Following, the Bayesian Model Averaging (BMA) was used to merge the different responses into a single probabilistic forecast. The results of the uncertainty analysis for the SWAT parameters show that the Soil Conservation Service (SCS) model for surface runoff prediction may not be suitable for the B.R.O, and that more investigations about the soil physical properties at the Basin are recommended. An analysis of the accuracy and precision of the simulations produced by the precipitation ensemble members against the BMA simulation supports the use of the latter as a suitable framework for streamflow simulations at the B.R.O.

Over the past decade vehicle judder caused by Disc Thickness Variation (DTV) has become of major concern to automobile manufacturers worldwide. Judder is usually perceived by the driver as minor to severe vibrations transferred through the chassis during braking [1-9]. In this research, DTV is investigated via the use of a Smart Brake Pad (SBP). The SBP is a tool that will enable engineers to better understand the processes which occur in the harsh and confined environment that exists between the brake pad and disc whilst braking. It is also a tool that will enable engineers to better understand the causes of DTV and stick-slip the initiators of low and high frequency vibration in motor vehicle brakes. Furthermore, the technology can equally be used to solve many other still remaining mysteries in automotive, aerospace, rail or anywhere where two surfaces may come in contact. The SBP consists of sensors embedded into an automotive brake pad enabling it to measure pressure between the brake pad and disc whilst braking. The two sensor technologies investigated were Thick Film (TF) and Fibre Optic (FO) technologies. Each type was tested individually using a Material Testing System (MTS) at room and elevated temperatures. The chosen SBP was then successfully tested in simulated driving conditions. A preliminary mathematical model was developed and tested for the TF sensor and a novel Finite Element Analysis (FEA) model for the FO sensor. A new method called the Total Expected Error (TEE) method was also developed to simplify the sensor specification process to ensure consistent comparisons are made between sensors. Most importantly, our achievement will lead to improved comfort levels for the motorist.

Engineering directly impacts current and future regulatory policy decisions. The foundation of air pollution control and air pollution dispersion modeling lies in the math, chemistry, and physics of the environment. Therefore, regulatory decision making must rely upon sound science and engineering as the core of appropriate policy making (objective analysis in lieu of subjective opinion). This research evaluated particulate matter and ammonia concentration data as well as two modeling methods, a backward Lagrangian stochastic model and a Gaussian plume dispersion model. This analysis assessed the uncertainty surrounding each sampling procedure in order to gain a better understanding of the uncertainty in the final emission rate calculation (a basis for federal regulation), and it assessed the differences between emission rates generated using two different dispersion models. First, this research evaluated the uncertainty encompassing the gravimetric sampling of particulate matter and the passive ammonia sampling technique at an animal feeding operation. Future research will be to further determine the wind velocity profile as well as determining the vertical temperature gradient during the modeling time period. This information will help quantify the uncertainty of the meteorological model inputs into the dispersion model, which will aid in understanding the propagated uncertainty in the dispersion modeling outputs. Next, an evaluation of the emission rates generated by both the Industrial Source Complex (Gaussian) model and the WindTrax (backward-Lagrangian stochastic) model revealed that the calculated emission concentrations from each model using the average emission rate generated by the model are extremely close in value. However, the average emission rates calculated by the models vary by a factor of 10. This is extremely troubling. In conclusion, current and future sources are regulated based on emission rate data from previous time periods. Emission factors are published for regulation of various sources, and these emission factors are derived based upon back-calculated model emission rates and site management practices. Thus, this factor of 10 ratio in the emission rates could prove troubling in terms of regulation if the model that the emission rate is back-calculated from is not used as the model to predict a future downwind pollutant concentration.

Uncertainties are pervasive in the Earth System modelling. This is not just due to a lack of knowledge about physical processes but has its seeds in intrinsic, i.e. inevitable and irreducible, uncertainties concerning the process of modelling as well. Therefore, it is indispensable to quantify uncertainty in order to determine, which are robust results under this inherent uncertainty. The central goal of this thesis is to explore how uncertainties map on the properties of interest such as phase space topology and qualitative dynamics of the system. We will address several types of uncertainty and apply methods of dynamical systems theory on a trendsetting field of climate research, i.e. the Indian monsoon.<br><br> For the systematic analysis concerning the different facets of uncertainty, a box model of the Indian monsoon is investigated, which shows a saddle node bifurcation against those parameters that influence the heat budget of the system and that goes along with a regime shift from a wet to a dry summer monsoon. As some of these parameters are crucially influenced by anthropogenic perturbations, the question is whether the occurrence of this bifurcation is robust against uncertainties in parameters and in the number of considered processes and secondly, whether the bifurcation can be reached under climate change. Results indicate, for example, the robustness of the bifurcation point against all considered parameter uncertainties. The possibility of reaching the critical point under climate change seems rather improbable. <br><br> A novel method is applied for the analysis of the occurrence and the position of the bifurcation point in the monsoon model against parameter uncertainties. This method combines two standard approaches: a bifurcation analysis with multi-parameter ensemble simulations. As a model-independent and therefore universal procedure, this method allows investigating the uncertainty referring to a bifurcation in a high dimensional parameter space in many other models. <br><br> With the monsoon model the uncertainty about the external influence of El Niño / Southern Oscillation (ENSO) is determined. There is evidence that ENSO influences the variability of the Indian monsoon, but the underlying physical mechanism is discussed controversially. As a contribution to the debate three different hypotheses are tested of how ENSO and the Indian summer monsoon are linked. In this thesis the coupling through the trade winds is identified as key in linking these two key climate constituents. On the basis of this physical mechanism the observed monsoon rainfall data can be reproduced to a great extent. Moreover, this mechanism can be identified in two general circulation models (GCMs) for the present day situation and for future projections under climate change. <br><br> Furthermore, uncertainties in the process of coupling models are investigated, where the focus is on a comparison of forced dynamics as opposed to fully coupled dynamics. The former describes a particular type of coupling, where the dynamics from one sub-module is substituted by data. Intrinsic uncertainties and constraints are identified that prevent the consistency of a forced model with its fully coupled counterpart. Qualitative discrepancies between the two modelling approaches are highlighted, which lead to an overestimation of predictability and produce artificial predictability in the forced system. The results suggest that bistability and intermittent predictability, when found in a forced model set-up, should always be cross-validated with alternative coupling designs before being taken for granted. <br><br> All in this, this thesis contributes to the fundamental issue of dealing with uncertainties the climate modelling community is confronted with. Although some uncertainties allow for including them in the interpretation of the model results, intrinsic uncertainties could be identified, which are inevitable within a certain modelling paradigm and are provoked by the specific modelling approach. / Die vorliegende Arbeit untersucht, auf welche Weise Unsicherheiten, wie sie in der integrierten Klima(folgen)forschung allgegenwärtig sind, die Stabilität und die Struktur dynamischer Systeme beeinflussen. <br> Im Rahmen der Erdsystemmodellierung wird der Unsicherheitsanalyse zunehmend eine zentrale Bedeutung beigemessen. Einerseits können mit ihrer Hilfe disziplinäre Qualitäts-standards verbessert werden, andererseits ergibt sich die Chance, im Zuge von "Integrated Assessment" robuste entscheidungsrelevante Aussagen abzuleiten. <br><br> Zur systematischen Untersuchung verschiedener Arten von Unsicherheit wird ein konzeptionelles Modell des Indischen Monsuns eingesetzt, das einen übergang von einem feuchten in ein trockenes Regime aufgrund einer Sattel-Knoten-Bifurkation in Abhängigkeit derjenigen Parameter zeigt, die die Wärmebilanz des Systems beeinflussen. Da einige dieser Parameter anthropogenen Einflüssen und Veränderungen unterworfen sind, werden zwei zentrale Punkte untersucht: zum einen, ob der Bifurkationspunkt robust gegenüber Unsicherheiten in Parametern und in Bezug auf die Anzahl und die Art der im Modell implementierten Prozesse ist und zum anderen, ob durch anthropogenen Einfluss der Bifurkationspunkt erreicht werden kann. Es zeigt sich unter anderem, dass das Auftreten der Bifurkation überaus robust, die Lage des Bifurkationspunktes im Phasenraum ist hingegen sehr sensitiv gegenüber Parameterunsicherheiten ist. <br><br> Für diese Untersuchung wird eine neuartige Methode zur Untersuchung des Auftretens und der Lage einer Bifurkation gegenüber Unsicherheiten im hochdimensionalen Parameterraum entwickelt, die auf der Kombination einer Bifurkationsanalyse mit einer multi parametrischen Ensemble Simulation basiert. <br><br> Mit dem Monsunmodell wird des weiteren die Unsicherheit bezüglich des externen Einflusses von El Niño / Southern Oscillation (ENSO) untersucht. Es ist bekannt, dass durch ENSO die Variabilität des Indischen Monsun beeinflußt wird, wohingegen der zu Grunde liegende Mechanismus kontrovers diskutiert wird. In dieser Arbeit werden drei verschiedene Hypothesen zur Kopplung zwischen diesen beiden Phänomenen untersucht. Es kann gezeigt werden, dass die Passat Winde einen Schlüsselmechanismus für den Einfluß von ENSO auf den Indischen Monsun darstellen.<br> Mit Hilfe dieses Mechanismus können die beobachteten Niederschlagsdaten des Monsuns zu einem großen Anteil reproduziert werden. Zudem kann dieser Mechanismus kann auch in zwei globalen Zirkulationsmodellen (GCMs) für den heutigen Zustand und für ein Emissionsszenario unter Klimawandel identifiziert werden. <br><br> Im weiteren Teil der Arbeit werden intrinsische Unsicherheiten identifiziert, die den Unterschied zwischen der Kopplung von Teilmodulen und dem Vorschreiben von einzelnen dieser Module durch Daten betreffen. Untersucht werden dazu ein getriebenes GCM-Ensemble und ein konzeptionelles Ozean-Atmosphären-Modell, das eine strukturierte Analyse anhand von Methoden der Theorie dynamischer Systeme ermöglicht.<br> In den meisten Fällen kann die getriebene Version, in der ein Teil der Dynamik als externer Antrieb vorschrieben wird, das voll gekoppelte Pendant nachbilden. Es wird gezeigt, dass es jedoch auch Regionen im Phasen- und Parameterraum gibt, in dem sich die zwei Modellierungsansätze signifikant unterscheiden und unter anderem zu einer überschätzung der Vorhersagbarkeit und zu künstlichen Zuständen im getriebenen System führen. Die Ergebnisse legen den Schluss nahe, dass immer auch alternative Kopplungsmechanismen getestet werden müssen bevor das getriebene System als adäquate Beschreibung des gekoppelten Gesamtsystems betrachtet werden kann. <br><br> Anhand der verschiedenen Anwendungen der Unsicherheitsanalyse macht die Arbeit deutlich, dass zum einen Unsicherheiten intrinsisch durch bestimmte Arten der Modellierung entstehen und somit unvermeidbar innerhalb eines Modellierungsansatzes sind, dass es zum anderen aber auch geeignete Methoden gibt, Unsicherheiten in die Modellierung und in die Bewertung von Modellergebnissen einzubeziehen.