yes / Batch reactive distillation is aimed at achieving a high purity product, therefore, there is a great deal to find an optimal operating condition and effective control strategy to obtain maximum of the high purity product. An off-line dynamic optimization is first performed with an objective function to provide optimal product composition for the batch reactive distillation: maximum productivity. An inferential state estimator (an extended Kalman filter, EKF) based on simplified mathematical models and on-line temperature measurements, is incorporated to estimate the compositions in the reflux drum and the reboiler. Model Predictive Control (MPC) has been implemented to provide tracking of the desired product compositions subject to simplified model equations. Simulation results demonstrate that the inferential state estimation can provide good estimates of compositions. Therefore, the control performance of the MPC with the inferential state is better than that of PID. In addition, in the presence of unknown/uncertain parameters (forward reaction rate constant), the estimator is still able to provide accurate concentrations. As a result, the MPC with the inferential state is still robust and applicable in real plants.

Thesis (MComm)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: The analysis of multidimensional (multivariate) data sets is a very important area of research in applied statistics. Over the decades many techniques have been developed to deal with such datasets. The multivariate techniques that have been developed include inferential analysis, regression analysis, discriminant analysis, cluster analysis and many more exploratory methods. Most of these methods deal with cases where the data contain numerical variables. However, there are powerful methods in the literature that also deal with multidimensional binary and count data. The primary purpose of this thesis is to discuss the exploratory and inferential techniques that can be used for binary and count data. In Chapter 2 of this thesis we give the detail of correspondence analysis and canonical correspondence analysis. These methods are used to analyze the data in contingency tables. Chapter 3 is devoted to cluster analysis. In this chapter we explain four well-known clustering methods and we also discuss the distance (dissimilarity) measures available in the literature for binary and count data. Chapter 4 contains an explanation of metric and non-metric multidimensional scaling. These methods can be used to represent binary or count data in a lower dimensional Euclidean space. In Chapter 5 we give a method for inferential analysis called the analysis of distance. This method use a similar reasoning as the analysis of variance, but the inference is based on a pseudo F-statistic with the p-value obtained using permutations of the data. Chapter 6 contains real-world applications of these above methods on two special data sets called the Biolog data and Barents Fish data. The secondary purpose of the thesis is to demonstrate how the above techniques can be performed in the software package R. Several R packages and functions are discussed throughout this thesis. The usage of these functions is also demonstrated with appropriate examples. Attention is also given to the interpretation of the output and graphics. The thesis ends with some general conclusions and ideas for further research. / AFRIKAANSE OPSOMMING: Die analise van meerdimensionele (meerveranderlike) datastelle is ’n belangrike area van navorsing in toegepaste statistiek. Oor die afgelope dekades is daar verskeie tegnieke ontwikkel om sulke data te ontleed. Die meerveranderlike tegnieke wat ontwikkel is sluit in inferensie analise, regressie analise, diskriminant analise, tros analise en vele meer verkennende data analise tegnieke. Die meerderheid van hierdie metodes hanteer gevalle waar die data numeriese veranderlikes bevat. Daar bestaan ook kragtige metodes in die literatuur vir die analise van meerdimensionele binêre en telling data. Die primêre doel van hierdie tesis is om tegnieke vir verkennende en inferensiële analise van binêre en telling data te bespreek. In Hoofstuk 2 van hierdie tesis bespreek ons ooreenkoms analise en kanoniese ooreenkoms analise. Hierdie metodes word gebruik om data in gebeurlikheidstabelle te analiseer. Hoofstuk 3 bevat tegnieke vir tros analise. In hierdie hoofstuk verduidelik ons vier gewilde tros analise metodes. Ons bespreek ook die afstand maatstawwe wat beskikbaar is in die literatuur vir binêre en telling data. Hoofstuk 4 bevat ’n verduideliking van metriese en nie-metriese meerdimensionele skalering. Hierdie metodes kan gebruik word om binêre of telling data in ‘n lae dimensionele Euclidiese ruimte voor te stel. In Hoofstuk 5 beskryf ons ’n inferensie metode wat bekend staan as die analise van afstande. Hierdie metode gebruik ’n soortgelyke redenasie as die analise van variansie. Die inferensie hier is gebaseer op ’n pseudo F-toetsstatistiek en die p-waardes word verkry deur gebruik te maak van permutasies van die data. Hoofstuk 6 bevat toepassings van bogenoemde tegnieke op werklike datastelle wat bekend staan as die Biolog data en die Barents Fish data. Die sekondêre doel van die tesis is om te demonstreer hoe hierdie tegnieke uitgevoer word in the R sagteware. Verskeie R pakette en funksies word deurgaans bespreek in die tesis. Die gebruik van die funksies word gedemonstreer met toepaslike voorbeelde. Aandag word ook gegee aan die interpretasie van die afvoer en die grafieke. Die tesis sluit af met algemene gevolgtrekkings en voorstelle vir verdere navorsing.

Thesis (MDevF (Business Management))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: In the realm of consumer behaviour research, discussions regarding materialism – commonly defined as the desire to consume – indebtedness and low-income consumerism have become almost unavoidable. This is to be expected in a society where spending patterns are constantly evolving, levels of indebtedness are steadily increasing and interest in the so-called ‘bottom of the pyramid’ consumers has been heightened. In South Africa, studies have found changes in consumption and credit usage to not only be significant, but also particularly relevant amongst low-income consumers. While this changing culture of consumption has been widely acknowledged, there has been little empirical research on consumer behaviour in South Africa and even less on low-income consumerism. For this reason a study was developed, which sought to explore the relationship between materialism and indebtedness among a sample of low-income, instalment paying consumers of South Africa’s leading catalogue retailer. Through use of a mailed self-completion survey questionnaire, consumers of the targeted retailer were asked to indicate their level of materialism, as measured using a materialism scale, and to report their level of indebtedness, measured as the number of retail store accounts held. In addition, key demographic data, consisting of the respondents’ age, gender and monthly income, was drawn from the retailer’s database. Using this data the study assessed whether (i) the sampled consumers displayed strong characteristics of materialism and (ii) whether materialism is a significant variable in predicting the sampled consumers’ propensity for incurring debt. Data analysis techniques applied in this study included tests to measure the reliability of the materialism scale as well as a variety of descriptive and inferential statistical tools, designed to identify relationships in the collected data. Using these techniques, this study found that sampled low-income consumers are indeed highly materialistic, with levels of materialism observed in this study being significantly higher than in a previous materialism study where a low-income earning consumer sample was used. Regarding levels of indebtedness, regression and correlation analysis performed suggested the presence of statistically significant relationships between consumers’ levels of indebtedness and each of the demographic variables of age and gender. However, materialism and monthly income was not found to be significant variables in determining a consumer’s level of indebtedness. While the decision to delineate this study based on the consumers of one particular retailer limits the extent to which findings can be generalised to the larger South African population, the results do provide a number of important insights, which contributes to the scant body of literature on low-income consumer behaviour in this country. / AFRIKAANSE OPSOMMING: Op die navorsingsveld oor verbruikersgedrag het die gesprek rondom die voorkoms van materialisme (wat gewoonlik gedefinieer word as die behoefte om te verbruik), verbruikersdruk en die skuldlas onder lae inkomstegroepe byna onvermydelik geword. Dit is te verwagte in ’n samelewing waar bestedingspatrone voortdurend ontwikkel, skuldlasvlakke aan die groei is en die belangstelling in verbruikers op die onderste vlak van die sogenaamde piramide verskerp het. Studies in Suid-Afrika dui aan dat, onder lae inkomste verbruikers, die verskille in verbruikersgedrag en kredietgebruik nie net opvallend nie maar ook besonder ter saaklik is. Hoewel die verandering in verbruikerskultuur rondom besteding reeds wyd beskryf is, is daar nog nie veel empiriese navorsing oor verbruikersgedrag gedoen nie – en nog minder onder lae inkomstegroepe. Dit is om hierdie rede dat ’n studie ontwerp is om die verhouding tussen materialisme en skuldlas te ondersoek onder ’n steekproef van lae inkomste huurkoopverbruikers van Suid-Afrika se grootste kataloguskleinhandelaar. Daar is gebruik gemaak van ’n vraelys vir die opname, wat aan die verbruikers gepos is en deur hulle ingevul is. Verbruikers is gevra om die vlak van hul materialisme aan te dui, soos gemeet volgens die gebruik van ’n skaal of maatstaf vir materialisme; en om hul skuldlas weer te gee, gemeet aan die aantal rekeninge wat hulle by kleinhandelwinkels het. Belangrike demografiese data, soos die respondente se ouderdom, geslag en maandelikse inkomste, is verkry uit die kleinhandelaar se databasis. Hierdie data is gebruik om te bepaal, (i) of die steekproefverbruikers ’n sterk neiging tot materialisme toon, en (ii) of materialisme ’n beduidende rol speel in die voorspelbaarheid van die mate waartoe die steekproefverbruikers hulle aan skuld sal blootstel. Tegnieke wat in die studie gebruik is vir data-analise sluit toetse in wat die betroubaarheid van die maatstawwe vir materialisme meet, asook ’n aantal beskrywende en afleibare statistiese metodes wat ontwerp is om verhoudings in die versamelde data te identifiseer. Deur die gebruik van hierdie tegnieke het die studie gevind dat hierdie steekproef van lae inkomste verbruikers inderdaad hoogs materialisties is, en dat die vlakke van materialisme wat waargeneem is, beduidend hoër is as wat gevind is in ’n vorige studie onder ’n steekproef van lae-inkomste verbruikers. Met betrekking tot skuldlasverpligtinge, het die regressie- en korrelasie-analise wat gedoen is die bestaan van statisties beduidende verhoudinge tussen verbruikers se skuldlasvlakke en die demografiese veranderlikes van ouderdom en geslag aangedui. Daar is egter gevind materialisme en maandelikse inkomste is nie beduidende veranderlikes in die bepaling van ’n verbruiker se skuldlas nie. Hoewel die ontwerp van hierdie studie om verbruikers van slegs ’n enkele kleinhandelaar in te sluit ’n beperking plaas op die toepasbaarheid van die bevindinge op die wyer Suid-Afrikaanse bevolking, het die resultate ’n aantal belangrike insigte verskaf wat bydra tot die klein hoeveelheid bestaande literatuur oor lae inkomste verbruikersgedrag in die land.

Notre thèse consiste à étudier la pratique actuelle de la RSE dans le contexte des compagnies libanaises à caractère industriel, et à examiner la relation entre les pratiques RSE d’une part et le management des risques d’autre part, en utilisant des techniques de statistiques inférentielles, des analyses factorielles exploratoires et des modèles de régression linéaire multiple. C’est dans ce dernier cas que la contribution principale de cette recherche a été réalisée. Ainsi, cette recherche a permis de percevoir la RSE comme étant plus qu’un simple outil de marketing et de relations publiques mais aussi un vrai outil influant le risque dans les entreprises. Notre recherche élargit la base de connaissances dans ce domaine dans le contexte libanais, en mettant l’accent sur le management et les pratiques de l’entreprise en terme de gestion du risque, afin de mieux gérer par la RSE les impacts sociaux, environnementaux, et communautaires de leurs activités. Les résultats de cette étude permettront aux chercheurs de créer une base théorique et empirique plus forte sur laquelle les recherches futures sur le sujet de la RSE et du management des risques par la RSE peuvent être développées. / The aim of our thesis is to study the current practice of CSR in the context of the Lebanese industrial companies and to examine the relationship between CSR practices and risk management, using statistical techniques as inferential tests, factor analysis and multiple linear regression models. It is in the latter that the main contribution of this research has been made. This research has made it possible to perceive CSR as more than just a marketing and public relations tool but also a real tool influencing risk in companies. Our research broadens the knowledge base in this field in the Lebanese context, focusing on the management and practices of the company in terms of risk management, in order to better manage the social, environmental, and community based activities by CSR. The results of this study will enable researchers to create a stronger theoretical and empirical basis on which future research on the subject of CSR and risk management through CSR can be developed.

Inference of regulatory relations in dynamical systems is a promising active research area. Recently, most of the investigations in this field have been stimulated by the researches in functional genomics. In this thesis, the inferential modeling problem for switching hybrid systems is studied. The hybrid systems refers to dynamical systems in which discrete and continuous variables regulate each other, in other words the jumps and flows are interrelated. In this study, piecewise linear approximations are used for modeling purposes and it is shown that piecewise linear models are capable of displaying the evolutionary characteristics of switching hybrid systems approxi- mately. For the mentioned systems, detection of switching instances and inference of locally linear parameters from empirical data provides a solid understanding about the system dynamics. Thus, the inference methodology is based on these issues. The primary difference of the inference algorithm is the idea of transforming the switch- ing detection problem into a jump detection problem by derivative estimation from discrete data. The jump detection problem has been studied extensively in signal processing literature. So, related techniques in the literature has been analyzed care- fully and suitable ones adopted in this thesis. The primary advantage of proposed method would be its robustness in switching detection and derivative estimation. The theoretical background of this robustness claim and the importance of robustness for real world applications are explained in detail.

My goal for this paper can be presented as follows: I will attempt to show that objections to intuitionism, although they are serious, do not undermine entirely its fertility for knowledge and moral reasoning. This is probably the perception of contemporary philosophers like David Enoch, Robert Audi, Russ Shafer-Landau or John McDowell. In order to fulfill the objective mentioned above, I will do the following. First, I will outline broadly two of the paradigmatic features of moral intuitionism in order to identify it as a particular metaethics doctrine. Secondly, I will summarize some of the main objections that have been raised in order to discredit the value of moral intuitionism as a source both of moral knowledge and of valid support for moral reasoning. In third place, I will try, also briefly, to explain some of the possible (not all of course) answers to the objections previously mentioned in the paper. Fourth, I will recapitulate the more fruitful aspects of intuitionism, especially in regard to moral reasoning. / Mi objetivo para este trabajo puede presentarse de la siguiente forma: se intentará mostrar que las objeciones al intuicionismo, si bien son serias, no minan en forma absoluta su fertilidad para el conocimiento y el razonamiento moral. Probablemente esta sea la percepción de filósofos contemporáneos como David Enoch, Robert Audi, Russ Shafer-Landau o John McDowell. Para poder cumplir con el antes dicho objetivo, en este trabajo haré lo siguiente. En primer lugar, esbozaré, a grandes rasgos, dos de las características paradigmáticas del intuicionismo moral a fin de que podamos identificarlo como una corriente metaética particular. En segundo lugar, sintetizaré algunas de las principales objeciones que, por diversos conductos, han buscado desacreditar el valor del intuicionismo moral como fuente de conocimiento moral y también de apoyo válido para el razonamiento moral.En tercer lugar, intentaré, también de manera sumaria, explicitar algunas de las posibles (no todas, desde luego) respuestas a las antes mencionadas objeciones. En cuarto lugar, recapitularé los aspectos rescatables del intuicionismo, especialmente en lo que atañe al razonamiento moral.

Naturally occurring dialogue is by far the most frequent manifestation of human speech and therefore has a legitimate claim to being regarded as a prime object of study in the sciences of language. Looking at the factors which determine the structure of natural dialogue, one cannot escape the conclusion that not only what is being said but also what is being inferred from what is said contributes towards determining the sequence and content of moves as well as the choice of grammatical features which are crucial for dialogue cohesion and for the interpretation of utterances in dialogue: `Constellations of surface features of message form are the means by which speakers signal and listeners interpret what the activity is, how semantic content is to be understood and how each sentence relates to what precedes follows.`

Learner’s processing styles may play a vital role in their approach to learning, more specifically; the ability to make inferences plays an important role in all areas of language and learning and may contribute to difficulties learners are experiencing at school. It is therefore that the research was directed at investigating a possible relationship between the left hemispheric analytical and right hemispheric holistic processing styles and the types of errors inferential versus literal, made in reading comprehension tasks. The hemispheric processing styles were operationalised as the approach taken to the Rey- Osterreith Complex Figure (ROCF) and the types of errors made on the Stanford Diagnostic Reading Test (SDRT) across two levels of educational development. The sample consisted of grade 4 and grade 10 model C learners from the same schooling district. The data obtained from both assessments were subjected to correlation analyses, chi squared tests, analyses of variances (ANOVAs) and logistic regressions. Finally the results and associative conclusions indicated that there were only modest positive relationships between the predominant hemispheric processing styles and the error types on reading comprehension tasks and the demographics of the learners were the main contributors and accounted for the results discovered in the study as opposed to general hemispheric processing. Thus there is a need to understand the unique dynamics within the country and to explore alternatives to teaching practices to account for the variations evident in the classrooms.

No description available.

In an era of rapidly growing data sets, information reduction techniques such as extracting and highlighting characteristic features, are becoming increasingly important for efficient data analysis. Particularly relevant features of scalar fields are their critical points since they mark locations in the domain where a field's level set undergoes fundamental topological changes. There are well-established methods for locating and relating such points in a deterministic setting. However, many real-world phenomena studied in the computational sciences today are the result of a chaotic system that cannot be fully described by a single scalar field. Instead, the variability of such systems is typically captured with ensemble simulations, which generate a variety of possible outcomes of the simulated process. The topological analysis of such ensemble data sets, and uncertain data in general, is less well studied. In particular, there is no established definition for critical points of uncertain scalar fields. This thesis therefore aims to generalize the concept of critical points to uncertain scalar fields. While a deterministic field has a single set of critical points, each outcome of an uncertain scalar field has its own set of critical points. A first step towards finding an appropriate analog for critical points in uncertain data is to look at the distribution of all these critical points. In this work, different methods for analyzing this distribution are presented, which identify and track the likely locations of critical points over time, estimate their local occurrence probabilities, and eventually characterize their spatial uncertainty. A driving factor of winter weather in western Europe is the North Atlantic Oscillation (NAO), which is manifested by fluctuations in the sea level pressure difference between the Icelandic Low and the Azores High. Several methods have been developed to describe the strength of this oscillation. Some of them are based on certain assumptions, such as fixed positions of these two pressure systems. It is possible, however, that climate change will affect the locations of the main pressure variations and thus the validity of these descriptive methods. An alternative approach is based on the leading empirical orthogonal function (EOF) computed from the sea level pressure fields over the North Atlantic. The critical points of these fields indicate the actual locations of maximum pressure variations and can thus be used to assess how climate change affects these locations and to evaluate the validity of methods that use fixed locations to characterize the strength of the NAO. Because the climate is described by a chaotic system, such an analysis should incorporate the uncertain nature of climate predictions to produce statistically robust results. Extracting and tracking the positions of the maximum pressure variations that characterize the NAO therefore serves as a motivating practical application for the study of critical points in uncertain data in this work. Because uncertain data tend to be noisy, filtering is often required to separate relevant signals of variation from irrelevant fluctuations. A well-established method for extracting dominant signals from a time series of fields is to compute its empirical orthogonal functions (EOFs). In the first part of this thesis, this concept is extended to the analysis of spatiotemporal ensemble data sets to decompose their variation into modes describing the variation in the ensemble direction and modes describing the variation in the time direction. An application to different climate data sets revealed that, depending on the way an ensemble has been generated, temporal and ensemble-wise variations are not necessarily independent, making it difficult to separate these signals. Next, a computational pipeline for tracking likely locations of critical points in ensembles of scalar fields is presented. It computes leading EOFs on sliding time windows for all ensemble members, extracts regions where critical points can be expected from the resulting ensembles of EOFs for every time window, and finally tracks the barycenters of these regions over time. An application of this pipeline to sea level pressure fields over the North Atlantic revealed systematic shifts in the locations of the maximum pressure variations that characterize the NAO. These found shift were more pronounced for more extreme climate change scenarios. Existing methods for the identification of critical points in ensembles of scalar fields do not distinguish between uncertainties that are inherent in the analyzed system itself and those that are additionally introduced by using a finite sample of fields to capture these variations. In the next part of this thesis, two approaches for estimating the occurrence probabilities of critical points are presented that explicitly take into account and communicate to the viewer the additional uncertainties caused by estimating these probabilities from finite-sized ensembles. A comparison with existing works on synthetic data demonstrates the added value of the new approaches. The last part of this thesis is devoted to the question of how to characterize the spatial uncertainty of critical points. It provides a sound mathematical formulation of the problem of finding critical points with spatial uncertainty and computing their spatial distribution. This ultimately leads to the notion of uncertain critical points as a generalization of critical points to uncertain scalar fields. An analysis of the theoretical properties of these structures gave conditions under which well-interpretable results can be obtained and revealed interpretational difficulties when these conditions are not met. / In Zeiten immer größerer Datensätze gewinnen Techniken zur Informationsreduktion, etwa die Extraktion und Hervorhebung charakteristischer Merkmale, zunehmend an Bedeutung für eine effiziente Datenanalyse. Besonders relevante Merkmale von Skalarfeldern sind ihre kritischen Punkte, da sie Orte in der Domäne kennzeichnen, an denen sich die Topologie der Niveaumenge eines Feldes grundlegend verändert. Es existieren etablierte Methoden, um diese Punkte in deterministischen Feldern zu lokalisieren und sie miteinander in Beziehung zu setzen. Viele Alltagsphänomene, die heute untersucht werden, sind jedoch das Ergebnis chaotischer Systeme, die sich nicht vollständig durch ein einzelnes Skalarfeld beschreiben lassen. Stattdessen wird die Variabilität solcher Systeme mit Ensemblesimulationen erfasst, die eine Vielzahl möglicher Ergebnisse des simulierten Prozesses erzeugen. Die topologische Analyse solcher Ensemble-Datensätze und unsicherer Daten im Allgemeinen ist bisher weniger gut erforscht. Insbesondere gibt es noch keine etablierte Definition für die kritischen Punkte von unsicheren Skalarfeldern. In dieser Dissertation wird daher eine Verallgemeinerung des Konzepts kritischer Punkte auf unsichere Skalarfelder angestrebt. Während ein deterministisches Feld einen einzigen Satz kritischer Punkte hat, hat jede Realisierung eines unsicheren Skalarfeldes ihre eigenen kritischen Punkte. Ein erster Schritt, um ein geeignetes Analogon für kritische Punkte in unsicheren Daten zu finden, besteht darin, die Verteilung all dieser kritischen Punkte zu untersuchen. Zu diesem Zweck werden in dieser Arbeit verschiedene Methoden vorgestellt, die es ermöglichen, die wahrscheinlichen Orte kritischer Punkte zu identifizieren und über die Zeit zu verfolgen, die lokalen Wahrscheinlichkeiten für das Auftreten kritischer Punkte zu schätzen und schließlich die räumliche Unsicherheit von kritischen Punkten zu charakterisieren. Ein bestimmender Faktor für das Winterwetter in Westeuropa ist die Nordatlantische Oszillation (NAO), die sich in Schwankungen des Druckunterschieds auf Meereshöhe zwischen dem Islandtief und dem Azorenhoch äußert. Es existieren unterschiedliche Methoden, um die Stärke dieser Oszillation zu beschreiben, von denen einige auf bestimmten Annahmen beruhen, wie etwa der fixen Position der beiden Drucksysteme. Es ist jedoch möglich, dass der Klimawandel die Lage der Hauptdruckschwankungen und somit die Gültigkeit dieser Beschreibungsmethoden beeinträchtigt. Ein alternativer Ansatz basiert auf der führenden empirischen Orthogonalfunktion (EOF), welche aus den Druckfeldern auf Meereshöhe über dem Nordatlantik berechnet wird. Die kritischen Punkte dieses Feldes entsprechen den tatsächlichen Orten maximaler Druckschwankungen. Sie können daher verwendet werden, um die Auswirkungen des Klimawandels auf diese Orte zu bewerten und dadurch die Gültigkeit von Methoden, die feste Positionen zur Charakterisierung der Stärke der NAO verwenden, zu beurteilen. Da das Klima durch ein chaotisches System beschrieben wird, sollte eine solche Analyse die Unsicherheit von Klimavorhersagen berücksichtigen, um statistisch zuverlässige Ergebnisse zu erhalten. Die Extraktion und Verfolgung der für die NAO charakteristischen Positionen maximaler Druckschwankungen dient daher als motivierende praktische Anwendung für die Untersuchung kritischer Punkte in unsicheren Daten in dieser Arbeit. Da unsichere Daten oft verrauscht sind, ist meist zunächst eine Filterung erforderlich, um relevante Signale von irrelevanten Fluktuationen zu trennen. Ein etabliertes Konzept zur Extraktion dominanter Signale aus Zeitreihen von Skalarfeldern ist die empirische Orthogonalfunktionsanalyse (EOF-Analyse). Im ersten Teil dieser Arbeit wird dieses Konzept auf die Analyse von zeitabhängigen Ensemble-Datensätzen erweitert, um deren Variation in Moden zu zerlegen, die die jeweiligen Schwankungen in Ensemble- und Zeitrichtung beschreiben. Eine Anwendung auf verschiedene Klimadatensätze hat gezeigt, dass je nachdem, wie ein Ensemble generiert wurde, zeitliche und ensemblebezogene Variationen nicht zwangsläufig unabhängig sind, was eine Trennung dieser Signale erschwert. Im weiteren wird eine Berechnungspipeline zur Verfolgung der wahrscheinlichen Positionen kritischer Punkte in Ensemblen von Skalarfeldern vorgestellt. Sie berechnet zunächst die führenden EOFs auf gleitenden Zeitfenstern für jedes Ensemblemitglied, extrahiert dann aus den resultierenden Ensemblen von EOFs an jedem Zeitfenster Regionen, in denen kritische Punkte zu erwarten sind, und verfolgt schließlich die Baryzentren dieser Regionen über die Zeit. Die Anwendung dieser Pipeline auf die nordatlantischen Meeresspiegeldruckfelder hat eine systematische Verschiebungen der für die NAO charakteristischen Orte der maximalen Druckvariationen offenbart. Dabei führten extremere Klimawandelszenarien zu stärkeren Verschiebungen. Vorhandene Methoden zur Identifikation von kritischen Punkten in Ensemblen von Skalarfeldern unterscheiden nicht zwischen Unsicherheiten, die dem analysierten System selbst innewohnen, und solchen, die durch die Verwendung einer endlichen Stichprobe von Feldern zur Erfassung dieser Variationen zusätzlich verursacht werden. Im nächsten Teil dieser Arbeit werden daher zwei Ansätze zur Schätzung der Auftrittswahrscheinlichkeiten kritischer Punkte vorgestellt, die explizit auch die zusätzlichen Unsicherheiten berücksichtigen, die durch die Schätzung dieser Wahrscheinlichkeiten aus endlichen Ensemblen entstehen, und diese an den Betrachter kommunizieren. Der Mehrwert der neuen Verfahren wurde in einem Vergleich mit bestehenden Arbeiten auf synthetischen Daten demonstriert. Der letzte Teil dieser Arbeit ist der Frage gewidmet, wie sich die räumliche Unsicherheit kritischer Punkte charakterisieren lässt. Es wird eine fundierte mathematische Formulierung des Problems der Suche nach kritischen Punkten mit räumlicher Unsicherheit und der Berechnung ihrer räumlichen Verteilung erbracht. Das führt schließlich zum Begriff unsicherer kritischer Punkte als Verallgemeinerung von kritischen Punkten auf unsichere Skalarfelder. Eine Analyse der theoretischen Eigenschaften dieser Strukturen hat Bedingungen ergeben, unter denen einfach zu interpretierende Ergebnisse erzielt werden können, und offenbarte Interpretationsschwierigkeiten, die entstehen, wenn diese Bedingungen nicht erfüllt sind.