High dimensional space-time datasets are available nowadays in various aspects of life such as economy, agriculture, health, environment, etc. Meanwhile, it is challenging to reveal possible connections between climate change and weather extreme events such as hurricanes or tornadoes. In particular, the relationship between tornado occurrence and climate change has remained elusive. Moreover, modeling multivariate spatio-temporal data is computationally expensive. There is great need to computationally feasible models that account for temporal, spatial, and inter-variables dependence. Our research focuses on those areas in two ways. First, we investigate connections between changes in tornado risk and the increase in atmospheric instability over Oklahoma. Second, we propose two multiscale spatio-temporal models, one for multivariate Gaussian data, and the other for matrix-variate Gaussian data. Those frameworks are novel additions to the existing literature on Bayesian multiscale models. In addition, we have proposed parallelizable MCMC algorithms to sample from the posterior distributions of the model parameters with enhanced computations. / Doctor of Philosophy / Over 1000 tornadoes are reported every year in the United States causing massive losses in lives and possessions according to the National Oceanic and Atmospheric Administration. Therefore, it is worthy to investigate possible connections between climate change and tornado occurrence. However, there are massive environmental datasets in three or four dimensions (2 or 3 dimensional space, and time), and the relationship between tornado occurrence and climate change has remained elusive. Moreover, it is computationally expensive to analyze those high dimensional space-time datasets. In part of our research, we have found a significant relationship between occurrence of strong tornadoes over Oklahoma and meteorological variables. Some of those meteorological variables have been affected by ozone depletion and emissions of greenhouse gases. Additionally, we propose two Bayesian frameworks to analyze multivariate space-time datasets with fast and feasible computations. Finally, our analyses indicate different patterns of temperatures at atmospheric altitudes with distinctive rates over the United States.

Die Gletscher Hochasiens beeinflussen durch ihr Schmelzwasser die Wasserverfügbarkeit eines der gefährdetsten ‚globalen Wassertürme‘. Des Weiteren stellen diese Gletscher und die Gletscherseen eine Gefahr durch Überschwemmungen, Lawinen und Erdrutsche dar. Die Sensitivität und Variabilität von Gletschermassenbilanzen in Hochasien werden in dieser Dissertation untersucht. Das Energie- und Massenbilanzmodell „COupled Snowpack and Ice surface energy and mass balance model in PYthon (COSIPY)“ ist dabei das Hauptwerkzeug. Neun verschiedene gegitterte Niederschlagsdatensätze wurden verglichen, um Aussagen über deren Anwendungsmöglichkeiten zu treffen. Es wurden Verfahren für die Vorverarbeitung von Reanalyse-Datensätzen entwickelt, um diese als klimatische Antriebsdaten für COSIPY zu verwenden. Dazu standen Daten von drei automatischen Wetterstationen an verschiedenen Gletschern zur Verfügung. Die Modellevaluation auf der Basis von Beobachtungsdaten bildete den Ausgangspunkt, um die klimatische Massenbilanz von 14 Gletschern in allen großen Gebirgszügen Hochasiens mit einem konsistenten Ansatz zu modellieren. Die räumlich aufgelösten klimatischen Massenbilanzen von 2000 bis 2018 wurden mithilfe geodätischer Massenbilanzen aus Fernerkundungsdaten kalibriert. Generell haben mehr südöstlich gelegene Gletscher höhere Massenumsätze und diese sind sensitiver gegenüber Schwankungen von Temperatur und Niederschlag. Alle Gletschermassenbilanzen sind am sensitivsten gegenüber Temperaturänderungen im Sommer und gegenüber Niederschlagsänderungen im Sommer oder Frühling. Die Resultate unterstreichen die Notwendigkeit zukünftiger Forschung zu räumlich aufgelösten Reaktionen von Gletschern auf Klimaantrieb und daraus resultierender Variabilität von Schmelzwasser unter Verwendung interdisziplinärer Methoden in Hochasien. Aufgrund der Heterogenität der Gletscher in Hochasien ist diese Forschung essentiell für die künftige Anpassung an Klimavariabilität und Klimawandel in der Region. / The meltwater from the glaciers of High Mountain Asia (HMA) impacts water availability of one of the most vulnerable ‘water towers’ of the globe. Furthermore, glaciers and glacial lakes represent a danger through floods, avalanches and landslides. The climatic sensitivity and variability of the glacier mass balances are investigated within this thesis. The COupled Snowpack and Ice surface energy and mass balance model in PYthon (COSIPY) is thereby the main tool. Nine gridded precipitation datasets have been compared to evaluate possible applications in HMA. The variability and timing of precipitation between May and September 2017 are consistent between the datasets, whereas great differences in precipitation amount were found. A preprocessing toolbox has been developed to use reanalysis datasets as climate forcing for COSIPY within the thesis. Measurements of three automatic weather stations at different glaciers were available for bias correction. Based on these model validations with observed data, climatic mass balances of 14 glaciers in all major mountain ranges in HMA were simulated using a consistent approach. The distributed climatic mass balances for the period from October 2000 to September 2018 were calibrated with remote-sensing-based geodetic mass balances. In general, glaciers with higher mass turnover are located in the southeast of HMA. They are more sensitive to perturbations of temperature and precipitation. All glaciers are most sensitive to monthly temperature perturbations in summer and to precipitation perturbations in summer, spring or spring and summer. The results emphasise the need for future research on spatially resolved responses of glaciers to climate forcing and resulting variability of meltwater using coherent interdisciplinary methods in HMA. Due to the heterogeneity of glaciers in HMA, such research is essential for adaptation to future climate variability and climate change in the region.