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Hydrological models play a crucial role in forecasting future water resource availability and water-related risks. It's essential that they realistically represent and simulate the processes of interest. However, which model structure is most suitable for a given task, catchment and data situation is often difficult to determine. There are only few tangible guidelines for model structure selection, and comparing multiple models simply to choose one to use in further work is a cumbersome process. It is therefore not surprising that the hydrological community has spent considerable effort on improving model parameter estimation, which can be treated as an automatized process, but the selection of a suitable model structure (i.e., the specific set of equations describing catchment function) has received comparatively little attention. To facilitate easier testing of different model structures, this thesis introduces an approach for Automatic Model Structure Identification (AMSI), which allows for the simultaneous calibration of model structural choices and model parameters. Model structural choices are treated as integer decision variables while model parameters are treated as continuous model variables in this approach. Through combining the modular modelling framework Raven with the mixed-integer optimization algorithm DDS, the testing of different structural hypotheses can thus be automated. AMSI then allows to effectively search a vast number of model structure and parameter choices to identify the most suitable model structures for a specific objective function. This thesis uses four experiments to test and benchmark AMSI's performance and capabilities. First, a synthetic experiment generates “observations” with known model structures and tests AMSI’s ability to re-identify these same structures. Second, AMSI is used in a real-world application on twelve diverse MOPEX catchments to test the feasibility of the approach. Third, a comprehensive benchmark study explores how reliably AMSI searches the available model space by comparing AMSI’s outcomes to a brute force approach that calibrates all feasible model structures in the available model search space. Fourth, the model space AMSI searches was compared to a much wider model hypothesis space, as defined by 45 diverse and commonly used model structures taken from the MARRMoT-Toolbox. This evaluation of AMSI’s performance is based on mathematical accuracy (tested via statistical metric performance) and hydrological adequacy (tested via the performance on several hydrological signatures) to assess the advantages and limitations of the method. The re-identification experiments showed that process choices that show little impact on the hydrograph are difficult to re-identify due to near equivalent diagnostic measures. The real-world experiment showed that AMSI is capable of identifying feasible and avoiding infeasible model structures for the twelve tested MOPEX catchments. The performance of the identified models was compared to that of eight other models configured for the MOPEX catchments. AMSI's performance is in the top half of the performance range found by these eight, partially more complex, models, and is therefore considered satisfactory. However, the high variance in the identified model structures with comparable objective function values reflects substantial model equifinality. This was also seen in the benchmark study. While AMSI reliably identifies the most accurate model structures in a given model hypothesis space, the equifinality in model choice as measured through an aggregated metric such as KGE is considerable. In some catchments up to 30\% of the tested model choices obtain comparable KGE scores. These models, however, show significantly different behaviour in their internal storages, showing that a wide range of simulated hydrologic conditions can lead to comparable efficiency scores and therefore a wide ensemble of different model structures may appear suitable. Using AMSI with aggregated statistical metrics therefore provides only limited insights into which models are most suitable for the given catchment. Further investigations showed that the large number of identified mathematically accurate models (as measured through good metric performance) could hardly ever also be considered hydrologically adequate models (as measured through good signature performance). In nine out of twelve catchments none of the accurate models was also considered to be adequate, while only between one (0.1\%) and 49 (0.7\%) of all tested model structures met the defined adequacy requirements in the other three catchments. This glaring disconnect between mathematical accuracy and hydrological adequacy applies to all model selection approaches tested in the benchmark experiments. Neither AMSI, nor the brute force search, nor the MARRMoT models are able to provide accurate as well as adequate model structures when calibrated for the aggregated statistical metric KGE. Therefore, no distinct advantages of commonly used, expert-developed conceptual model structures could be identified over the data-derived AMSI models, as long as model performance is assessed only with aggregated efficiency scores. This has relevant implications for all modelling studies, as despite many papers suggesting to do otherwise, assessing model performance only through mathematical accuracy (i.e., with scores such as NSE or KGE) has remained the standard practice. The great empirical evidence of the inherent constraints of aggregated metrics such as KGE provided in this thesis may help to convey the message that relying only on these scores simply cannot guarantee hydrologically adequate model structures due to the equifinality in the combined model and parameter selection problem. The results also indicate that the AMSI method is able to identify model structures that are just as mathematically accurate and hydrologically inadequate as previously developed methods for model selection yield, but at a reduced work load to the modeller. Multi-variate datasets and better model performance metrics are often mentioned as ways to reduce equifinality. If such improved methods are implemented in the calibration procedure, AMSI's ability to discriminate between more granular process equations will increase. AMSI could then be a promising way forward to reduce the subjectivity in model selection, and to explore the connections between suitable model structures and catchment characteristics.

Simulations and modeling of large-scale systems are vital to understanding real world phenomena. However, even advanced numerical models can only approximate the true physics. The discrepancy between model results and nature can be attributed to different sources of uncertainty including the parameters of the model, input data, or some missing physics that is not included in the model due to a lack of knowledge or high computational costs. Uncertainty reduction approaches seek to improve the model accuracy by decreasing the overall uncertainties in models. Aiming to contribute to this area, this study explores uncertainty quantification and reduction approaches for complex physical problems. This study proposes several novel probabilistic and statistical approaches for identifying the sources of uncertainty, modeling the errors, and reducing uncertainty to improve the model predictions for large-scale simulations. We explore different computational models. The first class of models studied herein are inherently stochastic, and numerical approximations suffer from stability and accuracy issues. The second class of models are partial differential equations, which capture the laws of mathematical physics; however, they only approximate a more complex reality, and have uncertainties due to missing dynamics which is not captured by the models. The third class are low-fidelity models, which are fast approximations of very expensive high-fidelity models. The reduced-order models have uncertainty due to loss of information in the dimension reduction process. We also consider uncertainty analysis in the data assimilation framework, specifically for ensemble based methods where the effect of sampling errors is alleviated by localization. Finally, we study the uncertainty in numerical weather prediction models coming from approximate descriptions of physical processes. / Ph. D. / Computational models are used to understand the behavior of the natural phenomenon. Models are used to approximate the evolution of the true phenomenon or reality in time. We obtain more accurate forecast for the future by combining the model approximation together with the observation from reality. Weather forecast models, oceanography, geoscience, etc. are some examples of the forecasting models. However, models can only approximate the true reality to some extent and model approximation of reality is not perfect due to several sources of error or uncertainty. The noise in measurements or in observations from nature, the uncertainty in some model components, some missing components in models, the interaction between different components of the model, all cause model forecast to be different from reality. The aim of this study is to explore the techniques and approaches of modeling the error and uncertainty of computational models, provide solution and remedies to reduce the error of model forecast and ultimately improve the model forecast. Taking the discrepancy or error between model forecast and reality in time and mining that error provide valuable information about the origin of uncertainty in models as well as the hidden dynamics that is not considered in the model. Statistical and machine learning based solutions are proposed in this study to identify the source of uncertainty, capturing the uncertainty and using that information to reduce the error and enhancing the model forecast. We studied the error modeling, error or uncertainty quantification and reduction techniques in several frameworks from chemical models to weather forecast models. In each of the models, we tried to provide proper solution to detect the origin of uncertainty, model the error and reduce the uncertainty to improve the model forecast.

Response of flexible structures — such as cable-supported bridges and aircraft wings — is associated with a number of uncertainties in structural and flow parameters. This thesis is aimed at efficient uncertainty quantification in a few such flow and flow-induced structural response problems. First, the uncertainty quantification in the lift force exerted on a submerged body in a potential flow is considered. To this end, a new method — termed here as semi-intrusive stochastic perturbation (SISP) — is proposed. A sensitivity analysis is also performed, where for the global sensitivity analysis (GSA) the Sobol’ indices are used. The polynomial chaos expansion (PCE) is used for estimating these indices. Next, two stability problems —divergence and flutter — in the aeroelasticity are studied in the context of reliability based design optimization (RBDO). Two modifications are proposed to an existing PCE-based metamodel to reduce the computational cost, where the chaos coefficients are estimated using Gauss quadrature to gain computational speed and GSA is used to create nonuniform grid to reduce the cost even further. The proposed method is applied on a rectangular unswept cantilever wing model. Next, reliability computation in limit cycle oscillations (LCOs) is considered. While the metamodel performs poorly in this case due to bimodality in the distribution, a new simulation-based scheme proposed to this end. Accordingly, first a reduced-order model (ROM) is used to identify the critical region in the random parameter space. Then the full-scale expensive model is run only over a this critical region. This is applied to the rectangular unswept cantilever wing with cubic and fifth order stiffness terms in its equation of motion. Next, the wind speed is modeled as a spatio-temporal process, and accordingly new representations of spatio-temporal random processes are proposed based on tensor decompositions of the covariance kernel. These are applied to three problems: a heat equation, a vibration, and a readily available covariance model for wind speed. Finally, to assimilate available field measurement data on wind speed and to predict based on this assimilation, a new framework based on the tensor decompositions is proposed. The framework is successfully applied to a set of measured data on wind speed in Ireland, where the prediction based on simulation is found to be consistent with the observed data.