Integrated sensitivity analysis, calibration, and uncertainty propagation analysis approaches for supporting hydrological modeling

The successful performance of a hydrological model is usually challenged by the quality of the sensitivity analysis, calibration and uncertainty analysis carried out in the modeling exercise and subsequent simulation results. This is especially important under changing climatic conditions where there are more uncertainties associated with climate models and downscaling processes that increase the complexities of the hydrological modeling system. In response to these challenges and to improve the performance of the hydrological models under changing climatic conditions, this research proposed five new methods for supporting hydrological modeling. First, a design of experiment aided sensitivity analysis and parameterization (DOE-SAP) method was proposed to investigate the significant parameters and provide more reliable sensitivity analysis for improving parameterization during hydrological modeling. The better calibration results along with the advanced sensitivity analysis for significant parameters and their interactions were achieved in the case study. Second, a comprehensive uncertainty evaluation scheme was developed to evaluate three uncertainty analysis methods, the sequential uncertainty fitting version 2 (SUFI-2), generalized likelihood uncertainty estimation (GLUE) and Parameter solution (ParaSol) methods. The results showed that the SUFI-2 performed better than the other two methods based on calibration and uncertainty analysis results. The proposed evaluation scheme demonstrated that it is capable of selecting the most suitable uncertainty method for case studies. Third, a novel sequential multi-criteria based calibration and uncertainty analysis (SMC-CUA) method was proposed to improve the efficiency of calibration and uncertainty analysis and control the phenomenon of equifinality. The results showed that the SMC-CUA method was able to provide better uncertainty analysis results with high computational efficiency compared to the SUFI-2 and GLUE methods and control parameter uncertainty and the equifinality effect without sacrificing simulation performance. Fourth, an innovative response based statistical evaluation method (RESEM) was proposed for estimating the uncertainty propagated effects and providing long-term prediction for hydrological responses under changing climatic conditions. By using RESEM, the uncertainty propagated from statistical downscaling to hydrological modeling can be evaluated. Fifth, an integrated simulation-based evaluation system for uncertainty propagation analysis (ISES-UPA) was proposed for investigating the effects and contributions of different uncertainty components to the total propagated uncertainty from statistical downscaling. Using ISES-UPA, the uncertainty from statistical downscaling, uncertainty from hydrological modeling, and the total uncertainty from two uncertainty sources can be compared and quantified. The feasibility of all the methods has been tested using hypothetical and real-world case studies. The proposed methods can also be integrated as a hydrological modeling system to better support hydrological studies under changing climatic conditions. The results from the proposed integrated hydrological modeling system can be used as scientific references for decision makers to reduce the potential risk of damages caused by extreme events for long-term water resource management and planning.

Regional flood frequency analysis for Newfoundland and Labrador using the L-Moments index-flood method

The L-moments based index-flood procedure had been successfully applied for Regional Flood Frequency Analysis (RFFA) for the Island of Newfoundland in 2002 using data up to 1998. This thesis, however, considered both Labrador and the Island of Newfoundland using the L-Moments index-flood method with flood data up to 2013. For Labrador, the homogeneity test showed that Labrador can be treated as a single homogeneous region and the generalized extreme value (GEV) was found to be more robust than any other frequency distributions. The drainage area (DA) is the only significant variable for estimating the index-flood at ungauged sites in Labrador. In previous studies, the Island of Newfoundland has been considered as four homogeneous regions (A,B,C and D) as well as two Water Survey of Canada's Y and Z sub-regions. Homogeneous regions based on Y and Z was found to provide more accurate quantile estimates than those based on four homogeneous regions. Goodness-of-fit test results showed that the generalized extreme value (GEV) distribution is most suitable for the sub-regions; however, the three-parameter lognormal (LN3) gave a better performance in terms of robustness. The best fitting regional frequency distribution from 2002 has now been updated with the latest flood data, but quantile estimates with the new data were not very different from the previous study. Overall, in terms of quantile estimation, in both Labrador and the Island of Newfoundland, the index-flood procedure based on L-moments is highly recommended as it provided consistent and more accurate result than other techniques such as the regression on quantile technique that is currently used by the government.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Solitons in Exciton-Polariton System: Reduced Modelling, Analysis, and Numerical Studies

In this dissertation, we study the behavior of exciton-polariton quasiparticles in semiconductor microcavities, under the sourceless and lossless conditions.

First, we simplify the original model by removing the photon dispersion term, thus effectively turn the PDEs system to an ODEs system,

and investigate the behavior of the resulting system, including the equilibrium points and the wave functions of the excitons and the photons.

Second, we add the dispersion term for the excitons to the original model and prove that the band of the discontinuous solitons now become dark solitons.

Third, we employ the Strang-splitting method to our sytem of PDEs and prove the first-order and second-order error bounds in the $H^1$ norm and the $L_2$ norm, respectively.

Using this numerical result, we analyze the stability of the steady state bright soliton solution. This solution revolves around the $x$-axis as time progresses

and the perturbed soliton also rotates around the $x$-axis and tracks closely in terms of amplitude but lags behind the exact one. Our numerical result shows orbital

stability but no $L_2$ stability.

Grain size and heavy mineral analysis of Sander in Schleswig-Holstein, Germany

Die Sandergebiete sind von 5 Zentren her geschüttet, den Gletschertoren bei Flensburg, Frörup/Översee, Idstedt/Lürschau, Schleswig, Owschlag. Die Körnung der Schmelzwassersande nimmt mit zunehmender Entfernung von den Gletschertoren zunächst schnell, von Medianwerten über 1 mm auf Medianwerte um 0,4 mm in 10 km, dann langsam bis auf Medianwerte unter 0,2 mm in 30 km Entfernung ab. Sortierung und Symmetrie der Sande steigen entsprechend. Aus den Kornverteilungen lassen sich die Fließgeschwindigkeiten bei der Ablagerung ablesen. Sie sind geringer gewesen, als es die mächtigen und verbreiteten Akkumulationen erscheinen lassen. Bereits in 6 km Entfernung vom Eisrand flossen die Schmelzwässer als träge Bäche (0,3 m/sec) ab. In den Gletschertoren traten stoßweise extreme Fließgeschwindigkeiten auf, waren aber nur in geringem Maße am Gesamtaufbau der Sander beteiligt. Die Verbreitung der Würmsande paßt sich den Formen einer älteren Landschaft an. Sie läßt sich im behandelten Gebiet mit Hilfe der Schwermineralanalyse deutlich gegenüber den rißzeitlichen Ablagerungen abgrenzen, da die Verteilungen in den verschiedenaltrigen Sedimenten unterschiedlich sind. Vor Allem das Hornblende/Epidotverhältnis (Hornblendezahl nach STEINERT) ist ein gutes Kriterium. Da rißzeitliche Ablagerungen von den Schmelzwässern aufgearbeitet wurden, und zudem die Hornblenden im Laufe des Transportes stark abrollen, verwischen sich die Unterschiede in weiter Entfernung vom Eisrand. Schmelzwassersande der Würmvereisung sind vor Allem im Norden des Arbeitsgebietes weit nach Westen, bis an die nordfriesischen Inseln, geschüttet worden. Die Schmelzwässer benutzten als Durchlässe zu den Senken des Eemmeeres an der Westküste Täler in rißzeitlichen Hochgebieten. Die Wassermengen wurden hier gebündelt, sodaß sich auf den Eemablagerungen im Anschluß an die Durchlässe "Sekundärsander" ausbreiteten. Die Mächtigkeit der anstehenden Würm-Sandergebiete beträgt bis zu 20 m, meistens zwischen 10 und 15 m. An der Westküste sind die Schmelzwasserablagerungen von marinem Alluvium überdeckt. Teile der morphographisch als junge Sanderebenen erscheinenden Gebiete bestehen in Wirklichkeit aus rißzeitlichen, von jungen Schmelzwässern allenfalls oberflächlich umgearbeiteten Ablagerungen der älteren Vereisung. So ist der westliche und südwestliche Teil des Schleisanders schon während der Rißvereisung aufgeschüttet.

Presence and possible cause of periodicities in 20th-century extreme coastal surge: Belfast Harbour, Northern Ireland.

Identifying 20th-century periodic coastal surge variation is strategic for the 21st-century coastal surge estimates, as surge periodicities may amplify/reduce future MSL enhanced surge forecasts. Extreme coastal surge data from Belfast Harbour (UK) tide gauges are available for 1901–2010 and provide the potential for decadal-plus periodic coastal surge analysis. Annual extreme surge-elevation distributions (sampled every 10-min) are analysed using PCA and cluster analysis to decompose variation within- and between-years to assess similarity of years in terms of Surge Climate Types, and to establish significance of any transitions in Type occurrence over time using non-parametric Markov analysis. Annual extreme surge variation is shown to be periodically organised across the 20th century. Extreme surge magnitude and distribution show a number of significant cyclonic induced multi-annual (2, 3, 5 & 6 years) cycles, as well as dominant multi-decadal (15–25 years) cycles of variation superimposed on an 80 year fluctuation in atmospheric–oceanic variation across the North Atlantic (relative to NAO/AMO interaction). The top 30 extreme surge events show some relationship with NAO per se, given that 80% are associated with westerly dominant atmospheric flows (+ NAO), but there are 20% of the events associated with blocking air massess (− NAO). Although 20% of the top 30 ranked positive surges occurred within the last twenty years, there is no unequivocal evidence of recent acceleration in extreme surge magnitude related to other than the scale of natural periodic variation.

A multi vector energy analysis for interconnected power and gas systems

This paper presents the first multi vector energy analysis for the interconnected energy systems of Great Britain (GB) and Ireland. Both systems share a common high penetration of wind power, but significantly different security of supply outlooks. Ireland is heavily dependent on gas imports from GB, giving significance to the interconnected aspect of the methodology in addition to the gas and power interactions analysed. A fully realistic unit commitment and economic dispatch model coupled to an energy flow model of the gas supply network is developed. Extreme weather events driving increased domestic gas demand and low wind power output were utilised to increase gas supply network stress. Decreased wind profiles had a larger impact on system security than high domestic gas demand. However, the GB energy system was resilient during high demand periods but gas network stress limited the ramping capability of localised generating units. Additionally, gas system entry node congestion in the Irish system was shown to deliver a 40% increase in short run costs for generators. Gas storage was shown to reduce the impact of high demand driven congestion delivering a reduction in total generation costs of 14% in the period studied and reducing electricity imports from GB, significantly contributing to security of supply.

Spectral analysis of four 'hypervariable' AGN: a micro-needle in the haystack?

We analyze four extreme AGN transients to explore the possibility that they are caused by rare, high-amplitude microlensing events. These previously unknown type-I AGN are located in the redshift range 0.6-1.1 and show changes of > 1.5 magnitudes in the g-band on a timescale of ~years. Multi-epoch optical spectroscopy, from the William Herschel Telescope, shows clear differential variability in the broad line fluxes with respect to the continuum changes and also evolution in the line profiles. In two cases a simple point-source, point-lens microlensing model provides an excellent match to the long-term variability seen in these objects. For both models the parameter constraints are consistent with the microlensing being due to an intervening stellar mass object but as yet there is no confirmation of the presence of an intervening galaxy. The models predict a peak amplification of 10.3/13.5 and an Einstein timescale of 7.5/10.8 years respectively. In one case the data also allow constraints on the size of the CIII] emitting region, with some simplifying assumptions, to to be ~1.0-6.5 light-days and a lower limit on the size of the MgII emitting region to be > 9 light-days (half-light radii). This CIII] radius is perhaps surprisingly small. In the remaining two objects there is spectroscopic evidence for an intervening absorber but the extra structure seen in the lightcurves requires a more complex lensing scenario to adequately explain.

What do people think about running barefoot/with minimalist footwear? A thematic analysis

Objectives

Barefoot running describes when individuals run without footwear. Minimalist running utilizes shoes aimed to mimic being barefoot. Although these forms of running have become increasingly popular, we still know little about how recreational runners perceive them.
Design

In-depth interviews with eight recreational runners were used to gather information about their running experiences with a focus on barefoot and minimalist running.
Methods

Interviews were analysed using a latent level thematic analysis to identify and interpret themes within the data.
Results

Although participants considered barefoot running to be ‘natural’, they also considered it to be extreme. Minimalist running did not produce such aversive reactions. ‘Support’ reassured against concerns and was seen as central in protecting vulnerable body parts and reducing impact forces, but lacked a common or clear definition. A preference for practical over academic knowledge was found. Anecdotal information was generally trusted, as were running stores with gait assessment, but not health professionals.
Conclusion

People often have inconsistent ideas about barefoot and minimalist running, which are often formed by potentially biased sources, which may lead people to make poor decisions about barefoot and minimalist running. It is important to provide high-quality information to enable better decisions to be made about barefoot and minimalist running.

Statement of contribution

What is already known on this subject?
There is no known work on the psychology behind barefoot and minimalist running. We believe our study is the first qualitative study to have investigated views of this increasingly popular form of running.
What does this study add?
The results suggest that although barefoot running is considered ‘natural’, it is also considered ‘extreme’. Minimalist running, however, did not receive such aversive reactions.
‘Support’ was a common concern among runners. Although ‘support’ reassured against concerns and was seen as central in protecting vulnerable body parts and reducing impact forces, it lacked a common or clear definition.
A preference for practical over academic knowledge was found. Anecdotal information was generally trusted, as were running stores with gait assessment, but not health professionals.

GRASP and statistical bounds for heuristic solutions to combinatorial problems

The quality of a heuristic solution to a NP-hard combinatorial problem is hard to assess. A few studies have advocated and tested statistical bounds as a method for assessment. These studies indicate that statistical bounds are superior to the more widely known and used deterministic bounds. However, the previous studies have been limited to a few metaheuristics and combinatorial problems and, hence, the general performance of statistical bounds in combinatorial optimization remains an open question. This work complements the existing literature on statistical bounds by testing them on the metaheuristic Greedy Randomized Adaptive Search Procedures (GRASP) and four combinatorial problems. Our findings confirm previous results that statistical bounds are reliable for the p-median problem, while we note that they also seem reliable for the set covering problem. For the quadratic assignment problem, the statistical bounds has previously been found reliable when obtained from the Genetic algorithm whereas in this work they found less reliable. Finally, we provide statistical bounds to four 2-path network design problem instances for which the optimum is currently unknown.

Convex Optimization Algorithms and Statistical Bounds for Learning Structured Models

Thesis (Ph.D.)--University of Washington, 2016-08

Reviews pages: Extreme weather events caused by climate change

Starting from the relationship between urban planning and mobility management, TeMA has gradually expanded the view of the covered topics, always remaining in the groove of rigorous scientific in-depth analysis. During the last two years a particular attention has been paid on the Smart Cities theme and on the different meanings that come with it. The last section of the journal is formed by the Review Pages. They have different aims: to inform on the problems, trends and evolutionary processes; to investigate on the paths by highlighting the advanced relationships among apparently distant disciplinary fields; to explore the interaction’s areas, experiences and potential applications; to underline interactions, disciplinary developments but also, if present, defeats and setbacks. Inside the journal the Review Pages have the task of stimulating as much as possible the circulation of ideas and the discovery of new points of view. For this reason the section is founded on a series of basic’s references, required for the identification of new and more advanced interactions. These references are the research, the planning acts, the actions and the applications, analysed and investigated both for their ability to give a systematic response to questions concerning the urban and territorial planning, and for their attention to aspects such as the environmental sustainability and the innovation in the practices. For this purpose the Review Pages are formed by five sections (Web Resources; Books; Laws; Urban Practices; News and Events), each of which examines a specific aspect of the broader information storage of interest for TeMA.

A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes I: A Priori Error Analysis

We consider the a priori error analysis of hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local finite element spaces employed. In particular, we prove a priori hp-error bounds for linear target functionals of the solution, on (possibly) anisotropic computational meshes with anisotropic tensor-product polynomial basis functions. The theoretical results are illustrated by a numerical experiment.

Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.