Bayesian methods in glaciology

Thesis (Ph.D) University of Alaska Fairbanks, 2017The problem of inferring the value of unobservable model parameters given a set of observations is ubiquitous in glaciology, as are large measurement errors. Bayes' theorem provides a unified framework for addressing such problems in a rigorous and robust way through Monte Carlo sampling of posterior distributions, which provides not only the optimal solution for a given inverse problem, but also the uncertainty. We apply these methods to three glaciological problems. First, we use Markov Chain Monte Carlo sampling to infer the importance of different glacier hydrological processes from observations of terminus water flux and surface speed. We find that the opening of sub-glacial cavities due to sliding over asperities at the glacier bed is of a similar magnitude to the opening of channels due to turbulent melt during periods of large input flux, but also that the processes of turbulent melting is the greatest source of uncertainty in hydrological modelling. Storage of water in both englacial void spaces and exchange of water between the englacial and subglacial systems are both necessary to explain observations. We next use Markov Chain Monte Carlo sampling to determine distributed glacier thickness from dense observations of surface velocity and mass balance coupled with sparse direct observations of thickness. These three variables are related through the principle of mass conservation. We develop a new framework for modelling observational uncertainty, then apply the method to three test cases. We find a strong relationship between measurement uncertainty, measurement spacing, and the resulting uncertainty in thickness estimates. We also find that in order to minimize uncertainty, measurement spacing should be 1-2 times the characteristic length scale of variations in subglacial topography. Finally, we apply the method of particle filtering to compute robust estimates of ice surface velocity and uncertainty from oblique time-lapse photos for the rapidly retreating Columbia Glacier. The resulting velocity fields, when averaged over suitable time scales, agree well with velocity measurements derived from satellites. At higher temporal resolution, our results suggest that seasonal evolution of the subglacial drainage system is responsible for observed changes in ice velocity at seasonal scales, and that this changing configuration produces varying degrees of glacier flow sensitivity to changes in external water input

NASA Sea Ice Validation Program for the Defense Meteorological Satellite Program Special Sensor Microwave Imager

The history of the program is described along with the SSM/I sensor, including its calibration and geolocation correction procedures used by NASA, SSM/I data flow, and the NASA program to distribute polar gridded SSM/I radiances and sea ice concentrations (SIC) on CD-ROMs. Following a discussion of the NASA algorithm used to convert SSM/I radiances to SICs, results of 95 SSM/I-MSS Landsat IC comparisons for regions in both the Arctic and the Antarctic are presented. The Landsat comparisons show that the overall algorithm accuracy under winter conditions is 7 pct. on average with 4 pct. negative bias. Next, high resolution active and passive microwave image mosaics from coordinated NASA and Navy aircraft underflights over regions of the Beaufort and Chukchi seas in March 1988 were used to show that the algorithm multiyear IC accuracy is 11 pct. on average with a positive bias of 12 pct. Ice edge crossings of the Bering Sea by the NASA DC-8 aircraft were used to show that the SSM/I 15 pct. ice concentration contour corresponds best to the location of the initial bands at the ice edge. Finally, a summary of results and recommendations for improving the SIC retrievals from spaceborne radiometers are provided

Image Understanding by Hierarchical Symbolic Representation and Inexact Matching of Attributed Graphs

We study the symbolic representation of imagery information by a powerful global representation scheme in the form of Attributed Relational Graph (ARG), and propose new techniques for the extraction of such representation from spatial-domain images, and for performing the task of image understanding through the analysis of the extracted ARG representation. To achieve practical image understanding tasks, the system needs to comprehend the imagery information in a global form. Therefore, we propose a multi-layer hierarchical scheme for the extraction of global symbolic representation from spatial-domain images. The proposed scheme produces a symbolic mapping of the input data in terms of an output alphabet, whose elements are defined over global subimages. The proposed scheme uses a combination of model-driven and data-driven concepts. The model- driven principle is represented by a graph transducer, which is used to specify the alphabet at each layer in the scheme. A symbolic mapping is driven by the input data to map the input local alphabet into the output global alphabet. Through the iterative application of the symbolic transformational mapping at different levels of hierarchy, the system extracts a global representation from the image in the form of attributed relational graphs. Further processing and interpretation of the imagery information can, then, be performed on their ARG representation. We also propose an efficient approach for calculating a distance measure and finding the best inexact matching configuration between attributed relational graphs. For two ARGs, we define sequences of weighted error-transformations which when performed on one ARG (or a subgraph of it), will produce the other ARG. A distance measure between two ARGs is defined as the weight of the sequence which possesses minimum total-weight. Moreover, this minimum-total weight sequence defines the best inexact matching configuration between the two ARGs. The global minimization over the possible sequences is performed by a dynamic programming technique, the approach shows good results for ARGs of practical sizes. The proposed system possesses the capability to inference the alphabets of the ARG representation which it uses. In the inference phase, the hierarchical scheme is usually driven by the input data only, which normally consist of images of model objects. It extracts the global alphabet of the ARG representation of the models. The extracted model representation is then used in the operation phase of the system to: perform the mapping in the multi-layer scheme. We present our experimental results for utilizing the proposed system for locating objects in complex scenes

Petrochronology and Statistical Analysis to Integrate Different Types of Data to Solve Complex Earth Systems Problems

Complex Earth systems problems, like reconstructing orogens and calibrating the geologic time scale, require investigations that link time to geologic processes. To use time as a means of organizing geologic evidence, geochronometric dates must be contextualized by integrating with different data types. This is the work of petrochronology—linking mineral ages to geochemical, textural, or other geologic information. The U-Pb isotopic system as preserved in the minerals zircon (ZrSiO4) and titanite (CaTiSiO5) can be used in a petrochronological context to date geologic events including the age of granitoid pluton emplacement, the age of rock fabric formation in deformed granitoids, and the age of volcanic ash beds. One focus of my dissertation was to use petrochronology to investigate high-temperature crustal strain partitioning and localization on the micro- to macro-scale using the western Idaho shear zone (WISZ), west-central Idaho. The WISZ is a crustal-scale structure that localized arc magmatic process and deformation related to terrane accretion and translation along the North American Cordillera. I used a WISZ orthogneiss to examine how fabric develops during high-temperature deformation on the micro-scale. By integrating the geochronometric, geochemical, and microstructural titanite record using statistical and petrologically-relevant visualizations, I document the local preservation of titanite related to magmatic and subsolidus processes. Importantly, this petrochronological workflow results in a date for the onset of deformation in the WISZ, confirming tectonic interpretations of WISZ deformation as a separate event from local terrane suturing. I expanded this work to the macro-scale with a suite of samples that transect the WISZ near McCall, Idaho to track the spatial-temporal patterns of pluton emplacement and deformation. My tandem zircon and titanite petrochronology results show that 1) the propensity of titanite to (re)crystallize in response to changes in pressure and temperature makes titanite petrochronology a useful approach for documenting subtle subsolidus fabric development, 2) strain localizes in time and space in response to local intrusions, and 3) WISZ fabric development is observed further east than previously mapped, causing the model of a west-to-east younging of pluton emplacement and deformation to be updated in favor of a model in which deformation focuses young magmatism within the center of the shear zone. In a second focus of my dissertation work, I integrated geochronology and statistical modeling to recalibrate and refine the Devonian time scale. The Devonian is a period in Earth history with significant biologic, climatic, and tectonic events. I dated Devonian ash beds using high-precision zircon geochronology and used those dates with a Bayesian age-depth model as the statistical framework to relate geochronometric and astrochronologic data to biostratigraphic data. I produced an updated Devonian time scale with new stage boundary ages with robust uncertainty estimates. This integrated stratigraphic approach is broadly applicable to time scale modeling. This work is united under a theme of using petrochronology and statistical modeling to link time to geologic processes including magmatism, deformation, and stratigraphic accumulation. Time constraints on the initiation and duration of geologic processes can deepen our understanding of the evolution of complex Earth systems