Mathematical models of glacier sliding and drumlin formation

One of the central difficulties in many models of glacier and ice sheet flow lies in the prescription of boundary conditions at the bed. Often, processes which occur there dominate the evolution of the ice mass as they control the speed at which the ice is able to slide over the bed. In part I of this thesis, we study two complications to classical models of glacier and ice sheet sliding. First, we focus on the effect of cavity formation on the sliding of a glacier over an undeformable, impermeable bed. Our results do not support the widely used sliding law $u_b = C\tau_b^pN^{-q}$, but indicate that $\tau_b/N$ actually decreases with $u_b/N$ at high values of the latter, as suggested previously for simple periodic beds by Fowler (1986). The second problem studied is that of an ice stream whose motion is controlled by bed obstacles with wavelengths comparable to the thickness of ice. By contrast with classical sliding theory for ice of constant viscosity,the bulk flow velocity does not depend linearly on the driving stress. Indeed, the bulk flow velocity may even be a multi-valued function of driving stress and ice thickness. In the second part of the thesis, attention is turned to the formation of drumlins. The viscous till model of Hindmarsh (1998) and Fowler (2000) is analysed in some detail. It is shown that the model does not predict the formation of three-dimensional drumlins, but only that of two-dimensional features, which may be interpreted as Rogen moraines. A non-linear model allows the simulation of the predicted bedforms at finite amplitude. Results obtained indicate that the growth of bedforms invariably leads to cavitation. A model for travelling waves in the presence of cavitation is also developed, which shows that such travelling waves can indeed exist. Their shape is, however, unlike that of real bedforms, with a steep downstream face and no internal stratification. These results indicate that Hindmarsh and Fowler's model is probably not successful at describing the processes which lead to the formation of streamlined subglacial bedforms

Oscillatory subglacial drainage in the absence of surface melt

The presence of strong diurnal cycling in basal water pressure records obtained during the melt season is well established for many glaciers. The behaviour of the drainage system outside the melt season is less well understood. Here we present borehole observations from a surge-type valley glacier in the St Elias Mountains, Yukon Territory, Canada. Our data indicate the onset of strongly correlated multi-day oscillations in water pressure in multiple boreholes straddling a main drainage axis, starting several weeks after the disappearance of a dominant diurnal mode in August 2011 and persisting until at least January 2012, when multiple data loggers suffered power failure. Jökulhlaups provide a template for understanding spontaneous water pressure oscillations not driven by external supply variability. Using a subglacial drainage model, we show that water pressure oscillations can also be driven on a much smaller scale by the interaction between conduit growth and distributed water storage in smaller water pockets, basal crevasses and moulins, and that oscillations can be triggered when water supply drops below a critical value. We suggest this in combination with a steady background supply of water from ground water or englacial drainage as a possible explanation for the observed wintertime pressure oscillations

Evaluation of the NCEP/NCAR Reanalysis in Terms of Synoptic Scale Phenomea: A Case Study from the Midwestern USA

We evaluate the ability of the National Centers for Environmental Prediction (NCEP)–National Center for Atmosphere Research (NCAR) reanalysis to represent the synoptic-scale climate of the Midwestern USA relative to radiosonde data. Independent, automated synoptic classifications, based on rotated principal component analysis (PCA) of 500 hPa geopotential heights, 850 hPa air temperatures, and 200 hPa wind speeds and a two-step clustering algorithm, result in a 15-type NCEP–NCAR synoptic classification and a 14-type radiosonde classification. The classifications are examined in terms of similarities and differences in the modes of variance manifest in the PCA solutions, the spatial patterns and variability of input variables within each weather type, and the temporal variability of the occurrence of each weather type. The classifications are then compared in terms of these characteristics and the degree of mutual class occupancy. Although the classifications identify a number of the same weather types (in terms of the input data, PCA solution, and mutual occupancy), the correspondence is imperfect. To assess whether the differences in the classifications are due to errant assignment of data to clusters or to differences in the fundamental modes present in the data sets as represented by the PC loadings and scores, a third targeted classification is undertaken that categorizes the NCEP–NCAR reanalysis data according to the radiosonde PCA solution. This classification exhibits a higher degree of similarity to that derived using the radiosonde data (in terms of both interpretability and mutual class occupancy), but the solutions still exhibit considerable differences. It is probable that the discrepancies are partly a function of the differing data structures and densities, but they may also reflect differences in the intensity of synoptic-scale phenomena as manifest in the data sets

Downscaling Temperature and Precipitation: A Comparison of Regression-Based Methods and Artificial Neural Networks

A comparison of two statistical downscaling methods for daily maximum and minimum surface air temperature, total daily precipitation and total monthly precipitation at Indianapolis, IN, USA, is presented. The analysis is conducted for two seasons, the growing season and the non-growing season, defined based on variability of surface air temperature. The predictors used in the downscaling are indices of the synoptic scale circulation derived from rotated principal components analysis (PCA) and cluster analysis of variables extracted from an 18-year record from seven rawinsonde stations in the Midwest region of the United States. PCA yielded seven significant components for the growing season and five significant components for the non-growing season. These PCs explained 86% and 83% of the original rawinsonde data for the growing and non-growing seasons, respectively. Cluster analysis of the PC scores using the average linkage method resulted in eight growing season synoptic types and twelve non-growing synoptic types. The downscaling of temperature and precipitation is conducted using PC scores and cluster frequencies in regression models and artificial neural networks (ANNs). Regression models and ANNs yielded similar results, but the data for each regression model violated at least one of the assumptions of regression analysis. As expected, the accuracy of the downscaling models for temperature was superior to that for precipitation. The accuracy of all temperature models was improved by adding an autoregressive term, which also changed the relative importance of the dominant anomaly patterns as manifest in the PC scores. Application of the transfer functions to model daily maximum and minimum temperature data from an independent time series resulted in correlation coefficients of 0.34–0.89. In accord with previous studies, the precipitation models exhibited lesser predictive capabilities. The correlation coefficient for predicted versus observed daily precipitation totals was less than 0.5 for both seasons, while that for monthly total precipitation was below 0.65. The downscaling techniques are discussed in terms of model performance, comparison of techniques and possible model improvements

An Evaluation of Two GCMs: Simulation of North American Teleconnection Indices and Synoptic Phenomena

We evaluate the ability of two coupled atmospheric–oceanic GCMs – the Hadley Center’s third generation coupled climate model (HadCM3) and the Canadian Center for Climate Modeling and Analysis second-generation coupled model (CGCM2) – to simulate the North Atlantic Oscillation (NAO), the Pacific North American teleconnection pattern (PNA), and map patterns in the Midwest region of the United States, relative to NCEP/NCAR reanalysis (NNR) data. The observed (NNR-derived) and GCM-derived probability distributions and temporal behavior of the daily teleconnection indices exhibit agreement over the 1990–2001 reference period, and both GCMs successfully reproduce the range of 500-hPa map patterns over the study region. During the reference period, observed and modeled map patterns are similar in terms of frequency, coherence, persistence, and progression, although the most common map pattern occurs too often in HadCM3 relative to NNR and CGCM2-derived map patterns generally exhibit closer agreement with those derived from NNR data. Despite the relatively high degree of correspondence between the observed and simulated teleconnection indices and map patterns in the study area, differences between the GCM and NNR-derived map-pattern frequencies in the reference period are greater than either (1) recent historical changes in map-pattern frequencies or (2) changes in the mappattern frequencies as derived from twenty-first century GCM simulations, indicating that changes in these phenomena over recent and approaching decades are of insufficient magnitude relative to model uncertainty to be definitively identified

The evolution of isolated cavities and hydraulic connection at the glacier bed – Part 2: A dynamic viscoelastic model

Many large-scale subglacial drainage models implicitly or explicitly assume that the distributed part of the drainage system consists of subglacial cavities. Few of these models, however, consider the possibility of hydraulic disconnection, where cavities exist but are not numerous or large enough to be pervasively connected with one another so that water can flow. Here I use a process-scale model for subglacial cavities to explore their evolution, focusing on the dynamics of connections that are made between cavities. The model uses a viscoelastic representation of ice and computes the pressure gradients that are necessary to move water around basal cavities as they grow or shrink. The latter model component sets the work here apart from previous studies of subglacial cavities and permits the model to represent the behaviour of isolated cavities as well as of uncavitated parts of the bed at low normal stress. I show that connections between cavities are made dynamically when the cavitation ratio (the fraction of the bed occupied by cavities) reaches a critical value due to decreases in effective pressure. I also show that existing simple models for cavitation ratio and for water sheet thickness (defined as mean water depth) fail to even qualitatively capture the behaviour predicted by the present model.</p

Conservation, diversification and expansion of C2H2 zinc finger proteins in the Arabidopsis thaliana genome

BACKGROUND: The classical C2H2 zinc finger domain is involved in a wide range of functions and can bind to DNA, RNA and proteins. The comparison of zinc finger proteins in several eukaryotes has shown that there is a lot of lineage specific diversification and expansion. Although the number of characterized plant proteins that carry the classical C2H2 zinc finger motifs is growing, a systematic classification and analysis of a plant genome zinc finger gene set is lacking. RESULTS: We found through in silico analysis 176 zinc finger proteins in Arabidopsis thaliana that hence constitute the most abundant family of putative transcriptional regulators in this plant. Only a minority of 33 A. thaliana zinc finger proteins are conserved in other eukaryotes. In contrast, the majority of these proteins (81%) are plant specific. They are derived from extensive duplication events and form expanded families. We assigned the proteins to different subgroups and families and focused specifically on the two largest and evolutionarily youngest families (A1 and C1) that are suggested to be primarily involved in transcriptional regulation. The newly defined family A1 (24 members) comprises proteins with tandemly arranged zinc finger domains. Family C1 (64 members), earlier described as the EPF-family in Petunia, comprises proteins with one isolated or two to five dispersed fingers and a mostly invariant QALGGH motif in the zinc finger helices. Based on the amino acid pattern in these helices we could describe five different signature sequences prevalent in C1 zinc finger domains. We also found a number of non-finger domains that are conserved in these families. CONCLUSIONS: Our analysis of the few evolutionarily conserved zinc finger proteins of A. thaliana suggests that most of them could be involved in ancient biological processes like RNA metabolism and chromatin-remodeling. In contrast, the majority of the unique A. thaliana zinc finger proteins are known or suggested to be involved in transcriptional regulation. They exhibit remarkable differences in the features of their zinc finger sequences and zinc finger arrangements compared to animal zinc finger proteins. The different zinc finger helix signatures we found in family C1 may have important implications for the sequence specific DNA recognition and allow inferences about the evolution of the members in this family

Class groups of real cyclotomic fields

We prove that every finite abelian group G occurs as a subgroup of the class group of infinitely many real cyclotomic fields.Comment: References have been updated and some typos have been corrected. To appear in Monatshefte f\"ur Mathemati