| Summary: | The purpose of this thesis is to develop spatio-temporal statistical models for glaciology, using the Bayesian hierarchical framework. Specifically, the process level is modeled as a time series of computer simulator outputs (i.e., from a numerical partial differential equation solver or an emulator) added to an error-correcting statistical process, closely related to the concept of model discrepancy. This error-correcting process accounts for spatial variability in simulator inaccuracies, as well as the accumulation of simulator inaccuracies forward in time. For computational efficiency, linear algebra for bandwidth-limited matrices is used for evaluating the likelihood of the model, and first-order emulator inference allows for the fast approximation of numerical solvers. Additionally, a computationally efficient approximation for the likelihood is derived. Analytical solutions to the shallow ice approximation (SIA) of the full Stokes equation system for stress balance of ice are used to examine the speed and accuracy of the computational methods used, in addition to the validity of modeling assumptions. Moreover, the modeling and methodology within this thesis are tested on data sets collected by the University of Iceland Institute of Earth Science (UI-IES) glaciology team, including bi-yearly mass balance measurements at 25 fixed sites at Langjökull (a glacier) over 19 years, in addition to 100 meter resolution digital elevation maps. As a byproduct of the construction of the Bayesian hierarchical model, a novel finite difference method is derived for solving the SIA partial differential equation (PDE). Although the application domain of this work is glaciology, the model and methods developed in this thesis can be applied to other geophysical domains. The thesis is structured around three papers. The first of these papers reviews dynamical modeling of glacial flow, introduces a second-order finite difference method for solving the SIA PDE, presents a Bayesian hierarchical model involving this numerical ...
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