In Iceland, glaciers cover approximately 11% of the land surface and comprise the country's largest reservoir of freshwater. Increases in summer temperatures since the mid-1980s have led to rapid mass loss from the Icelandic ice caps of 9.5-11.4 Gt/yr, and continuously operating GPS stations nationwide have recorded rapid and accelerating surface uplift. Understanding the behavior of Icelandic ice caps-and their relationship to surface uplift, which is modulated by the rheological structure of the crust and upper mantle-has important implications for water resource management and geohazards analysis. The goals of this study are twofold. First, we aim improve the current estimates of glacial isostatic adjustment (GIA)-related uplift in Iceland and to examine if and how uplift rates have changed over the last several decades. Secondly, we explore the utility of motion recorded by continuously operating Global Positioning System stations (cGPS) as an independent measure of ice cap mass variation over both decadal and annual time scales. We take advantage of the now longstanding cGPS network in Iceland and consider position time series from 62 stations across the entire island. Observations made by cGPS stations from 1995-2014.7 show a broad region of rapid uplift in central Iceland with near zero uplift observed along the coastal regions to the north and west. The most rapid uplift and uplift accelerations occur near the center of the island, between the Vatnajökull and Hofsjökull ice caps, with rates exceeding 30 mm/yr and accelerations of 1-2 mm/yr². Statistically significant uplift and uplift accelerations are recorded at 27 of the 62 cGPS stations, and estimates for the timing of uplift initiation correlate with Arctic warming trends and observations of increasing summer temperatures since the mid-1980s. These results represent a significant improvement over previous uplift estimates and indicate a likely relationship between accelerated ice cap melting and contemporaneous changes in uplift rates. Incorporating cGPS-recorded information about modern-day uplift rates affects estimates of mantle viscosity. Ice cap thinning rates are computed by a weighted least squares estimation scheme utilizing cGPS-derived secular uplift rates and accelerations and Green's functions for an elastic layer over a Maxwell viscoelastic half-space. We test a range of viscosities from 8 x 10¹⁷ and 1 x 10²⁰ Pa·s and find that thinning rates computed with low viscosities between 2 x 10¹⁸ and 1 x 10¹⁹ Pa·s match independently derived ice cap thinning rates best, in accordance with previous upper mantle viscosity estimates. Similar estimation techniques demonstrate the utility of cGPS to provide a seasonal mass variation time series as a potential low-cost compliment to traditional field-based mass balance measurements. We use estimates of secular site velocity and acceleration to reduce the time series and focus only on the annual periodic motion. The increased temporal resolution afforded by the daily cGPS position estimates recovers the interannual variability in the timing and magnitude of accumulation and melt seasons with a small RMS reduction relative to a sinusoidal model. We also find we are able to identify of the effects of both ice cap insulation as well as reduced surface albedo following volcanic eruptions.

In northern Canada, the glacial isostatic adjustment (GIA) response of the Earth to the former Pleistocene Laurentide and Innuitian ice sheets contributes significantly to the Earth's past and ongoing sea-level change and land deformation. In this dissertation, measurements of Holocene sea-level change and observations of GPS-measured vertical crustal uplift rates are employed as constraints in numerical GIA models that examine the thickness and volume history of the former ice sheets in northern North America. The study is divided into two main sections; the first provides new measurements of Holocene sea-level change collected west of Hudson Bay, while the second presents a GIA modelling analysis for the entire study area of northern Canada. Radiocarbon dating of post-glacial deposits collected in an area just west of central Hudson Bay provides several new constraints on regional Holocene sea-level change. The field collection area is near a former load centre of the Laurentide Ice Sheet (LIS), and the sea-level measurements suggest that following deglaciation, regional sea level fell rapidly from a high-stand of nearly 170 m elevation just after 8000 cal yr BP to 60 m elevation by 5200 cal yr BP. Sea level subsequently fell at a decreased rate (approximately 30 m since 3000 cal yr BP). The fit of GIA model predictions to relative sea-level (RSL) data and present-day GPS-measured vertical land motion rates from throughout the study area constrains the peak thickness of the LIS to be 3.4-3.6 km west of Hudson Bay, and up to 4 km east of Hudson Bay. The ice model thicknesses inferred for these two regions represent, respectively, a 30% decrease and an average 20-25% increase to the load thickness relative to the ICE-5G reconstruction (Peltier 2004), generally consistent with other studies focussing on space geodetic measurements of vertical crustal motion. Around Baffin Island, the fit of GIA model predictions to RSL data indicate peak regional ice thicknesses of 1.2-1.3 km, a modest reduction compared to ICE-5G. A new reconstruction of the Innuitian Ice Sheet (IIS), which covered the Queen Elizabeth Islands at LGM, incorporates the current glacial-geological constraints on its spatial extent and timing history. The new IIS reconstruction provides RSL predictions that are more consistent with regional observations of post-glacial sea-level change than ICE-5G. The results suggest that the peak thickness of the IIS was 1600 m, approximately 400 m thicker than the minimum peak thickness indicated by glacial geology studies, but between 1000-1500 m thinner than the peak thicknesses used in previous regional ice sheet reconstructions. On Baffin Island and in the Queen Elizabeth Islands, however, the modelled elastic crustal response of the Earth to present-day ice mass changes is large. Accounting for this effect improves the agreement between GPS measurements of vertical crustal motion and the GIA model predictions. However, improvements such as the inclusion of spatially non-uniform mass loss and a sensitivity analysis that examines uncertainties of this effect should be incorporated into the modelling of present-day changes to glaciers and ice caps. / Graduate

Sea-level change in response to the growth and melt of ice sheets and glaciers is a process called glacial isostatic adjustment (GIA). This includes deformation of the surface of the Earth itself in response to the extreme mass exchanges between the oceans and continents, as well as changes to the gravitational potential that describe the sea surface in response to the redistribution of surface mass as well as mass within the Earth. This thesis describes four research projects I've conducted in the field of GIA modelling. Most GIA models represent the lithosphere, the outermost layer of the Earth, as functionally elastic. However, there is a large temperature gradient within the lithosphere that would lead to a reduction in viscosity with depth. Therefore, in Chapter 2, I developed and incorporated more realistic lithosphere structure into the GIA model, and demonstrate that this added structure results in a time-dependence to the response of the lithosphere. While the usual inputs to a GIA model are the ice load and Earth description, there are regions where other processes need to be accounted for. In the Mississippi Delta region, processes associated with the deposition of sediment carried by the Mississippi River are strong drivers of local sea-level change, and include isostatic adjustment as well as compaction of the sediment layers over time. Therefore, in Chapter 3, I incorporated a treatment of sediment isostatic adjustment into the GIA model and applied it to the Mississippi Delta region. Our results indicate that the sediment isostatic adjustment signal is important in the vicinity of the delta, but small otherwise. By comparing model projections to GPS measurements, we demonstrate that most subsidence in the region is due to non-isostatic processes (such as sediment compaction). Data used to constrain GIA models are generally sensitive to both ice and Earth structure. Therefore data parametrizations that are insensitive to one input or the other are valuable constraints. One such commonly used parametrization is the postglacial decay time. Previous research has shown that the decay times are relatively insensitive to the ice history, and therefore provide a more robust constraint on Earth structure. In Chapter 4 I tested the extent of the ice insensitivity of decay times by considering a suite of ice reconstructions. I found that decay times are sensitive to ice history, and that the sensitivity depends on the location of the data relative to the geometry of the ice sheet. In particular, my results suggest that James Bay (in Hudson Bay) is a location that should not be used in a decay time analysis. The GIA model applied in the projects described above is a 1-D, spherically symmetric model. However, it is known that the Earth's viscous structure is likely to feature significant lateral variation. This is evident in the differences in viscosities found in this thesis between what satisfies the RSL data in Hudson Bay (in Chapter 4) and the Gulf coast of the US (Chapter 3), as well as various previous studies. Therefore, in Chapter 5, I applied a 3-D model with lateral viscous structure determined by seismic shear wave velocity models, to determine whether incorporating this more realistic structure could resolve this apparent discrepancy. I demonstrated that the fit to relative sea level data on the Atlantic and Gulf coasts of the US can be significantly improved by incorporating lateral viscous structure, but also that there is significant uncertainty associated with the more complex viscous structure.

Among the various adverse effects of climate change, sea-level rise is expected to increase the severity and frequency of flooding events impacting the vulnerable, low-lying islands of French Polynesia. It has long been understood that sea-level changes are not spatially uniform, yet this aspect is not taken into account in the decision-making. Notably, no projections of future sea level have been produced specifically for this region so far, partly because the processes driving sea-level changes remain poorly constrained. To approach the issue, we present a detailed reconstruction of sea-level changes for the mid-to-late Holocene, based on the observation of coral proxies. This dataset is then used to calibrate a sea-level model in order to estimate the contribution of glacial isostatic adjustment to regional sea-level changes and to infer past variations in global ice volume. Building upon this baseline and exploiting recent outputs of climate models, we project that in a “worst-case” scenario, sea level would rise 1.05 meters by 2100 in French Polynesia, exceeding the value adopted in the French adaptation strategy by 0.45 meters. We conclude that spatial variability of sea-level rise should be considered in future risk studies for this and other regions.

The Coast Mountains in British Columbia contain over 10,000 km2 of glacial ice. While these glaciers have lost significant mass since the Little Ice Age (LIA; around 300 years before present), the melting rate has significantly increased over the past decade, likely due to the effects of climate change. The purpose of this study was to develop an approach to quantifying the isostatic response to LIA glacier change and investigate how it can further our understanding of the Earth’s rheology through GIA modelling. The Coast Mountains in southwestern British Columbia were chosen due to their significant ice mass loss since the LIA, their location in a tectonically active region, which includes a volcanic arc, and the presence of information of vertical land motion. The GIA models in this study use a wide range of Earth rheological parameters that are then constrained through comparison to observations of vertical land motion in the region. The study used available Global Navigation Satellite System (GNSS) vertical velocity data as the observable from seven GNSS sites in southwestern BC, using a combination of Western Canada Deformation Array (WCDA) and British Columbia Active Control System (BCACS) GNSS stations. Raw data were analyzed using the GIPSY 6.4 software following the Precise Point Positioning processing strategy. Two ice load histories were developed based on gridded estimates of present-day ice thicknesses in the region in order to simulate the change in the surface loading as the glacial ice mass fluctuates over time. Ice Load A used a simple uniform thickness change profile over 3 time-steps based on extrapolated modern melt rates. Ice Load B is more complex and utilized a published profile of glacier change through time basing the magnitude of volume changes on the volume-area scaling relationship with a range of coefficient values. This allowed for a range of ice change magnitudes to be tested. The Earth models used were spherically symmetric Preliminary Reference Earth Models (PREM). Their viscosity structure is based on VM5a for the transition zone and lower mantle, but with variable lithospheric thickness and asthenospheric viscosity. The goodness of fit for the modeled velocities were compared to the observed velocities using a normalized RMS (NRMS) statistic. Ice Load A models had a best fitting lithospheric thickness of 50 km and an asthenospheric viscosity of 2×1019 Pa s. For all variations of Ice Load B, the best fitting model parameters had lithospheric thicknesses ranging from 45 km to 55 km and asthenospheric viscosities between 6×1018 Pa s and 3×1019 Pa s. Corrected GNSS vertical velocity observations were tested to check the effects of interseismic vertical signal and assumed residual GIA from the Cordilleran Ice Sheet. However, the corrections did not improve the NRMS fit. Overall, the asthenospheric viscosity results from this study overlap with all the ranges found in the previous studies while lithospheric thicknesses agree with some past studies. The results of this study generally align with previous work and the current understanding of the Coast Mountains region and can inform a future round of sea-level projections for the region as ice mass loss continues in the Coast Mountains. This study serves to further refine constraints on Earth rheology and can be used to guide future work on GIA in the region. / Graduate

This thesis focuses on the physics of static sea-level changes following variations in the distribution of grounded ice and the influence of these changes on the stability and dynamics of marine ice sheets. Gravitational, deformational and rotational effects associated with changes in grounded ice mass lead to markedly non-uniform spatial patterns of sea-level change. I outline a revised theory for computing post-glacial sea-level predictions and discuss the dominant physical effects that contribute to the patterns of sea-level change associated with surface loading on different timescales. I show, in particular, that a large sea-level fall (rise) occurs in the vicinity of a retreating (advancing) ice sheet on both short and long timescales. I also present an application of the sea-level theory in which I predict the sea-level changes associated with a new model of North American ice sheet evolution and consider the implications of the results for efforts to establish the sources of Meltwater Pulse 1A. These results demonstrate that viscous deformational effects can influence the amplitude of sea-level changes observed at far-field sea-level sites, even when the time window being considered is relatively short (≤ 500 years). / Earth and Planetary Sciences

Meltwater pulse 1A (MWP-1A) is the largest land ice melt event of the last deglaciation. In a period of no more than 340 years, between 14.65 and 14.31 ka (Dechamps et al, 2012), ~10% of the total deglacial sea-level rise occurred (Hanebuth et al, 2000; Peltier and Fairbanks, 2006; Deschamps et al, 2012), resulting in the highest reported rate of global mean sea-level rise in the geological record, which may have exceeded 4 m per century (Deschamps et al, 2012). Yet, the implications of MWP-1A for constraining the rates of the underlying processes and its role in the sequence of climate events during Termination 1 remain unclear due to the lack of information on its melt source distribution. While glacial isostatic adjustment (GIA) modelling experiments (Clark et al, 2002; Bassett et al, 2005; Deschamps et al, 2012) and recent assessments of ice-sheet histories (Carlson and Clark, 2012) suggest that at least 50% of the event may have come from Antarctica, other interpretations of Antarctic ice-extent and sea-level records suggest a substantially smaller (including zero) Antarctic contribution (Ackert et al, 2007; Mackintosh et al, 2011; Whitehouse et al, 2012). In this study, we show that after reassessments of local MWP-1A amplitudes at Barbados and Sunda Shelf based on the well-constrained timing derived from the Tahiti sea-level record (Deschamps et al, 2012), the sea-level data from Barbados, Sunda Shelf, and Tahiti do not provide as tight of a constraint on the Antarctic contribution as previously thought. We find that between 1 to 10 m sea-level equivalent (sle) could have melted from the Antarctic, compared to 7 to 15 m sle from previous analyses (Clark et al, 2002; Bassett et al, 2005; Deschamps et al, 2012). To better constrain the source of MWP-1A, we also consider sea-level data from Scotland (Shennan et al, 2000), which have, until now, been excluded from MWP-1A fingerprinting experiments because they are strongly influenced by local ice unloading. To overcome this, we isolate the elastic MWP-1A amplitude (i.e. fingerprint signal) at this location using a suite of models that provide optimal fits to the Scottish data, and thereby remove near-field contamination. Preliminary results show that the inclusion of these data leads to an improved MWP-1A source distribution constraint compared to that obtained using the far- and intermediate-field data alone.

Projections of sea level rise for the east coast of North America at 2100CE were generated considering contributions from: ocean warming, land ice melting and isostatic land motion. The primary contribution of this study is the development of an improved Glacial Isostatic Adjustment (GIA) model that includes an assessment of model uncertainty using 36 ice loading histories, 363 Earth models and a new sea level proxy database comprising over 500 sea level index points. We find that, while there are differences between our projections and the Global Mean Sea Level (GMSL) projections from the recent International Panel on Climate Change (IPCC) Assessment Report, the two sets of results agree to within uncertainty largely because some of the regional processes cancel. Our results indicate that the isostatic signal is large, contributing up to 1/4 of sea level change at 2100CE, and so must be included to generate accurate projections for this region.

Meltwater pulse 1A (MWP-1A) is the largest land ice melt event of the last deglaciation. In a period of no more than 340 years, between 14.65 and 14.31 ka (Dechamps et al, 2012), ~10% of the total deglacial sea-level rise occurred (Hanebuth et al, 2000; Peltier and Fairbanks, 2006; Deschamps et al, 2012), resulting in the highest reported rate of global mean sea-level rise in the geological record, which may have exceeded 4 m per century (Deschamps et al, 2012). Yet, the implications of MWP-1A for constraining the rates of the underlying processes and its role in the sequence of climate events during Termination 1 remain unclear due to the lack of information on its melt source distribution. While glacial isostatic adjustment (GIA) modelling experiments (Clark et al, 2002; Bassett et al, 2005; Deschamps et al, 2012) and recent assessments of ice-sheet histories (Carlson and Clark, 2012) suggest that at least 50% of the event may have come from Antarctica, other interpretations of Antarctic ice-extent and sea-level records suggest a substantially smaller (including zero) Antarctic contribution (Ackert et al, 2007; Mackintosh et al, 2011; Whitehouse et al, 2012). In this study, we show that after reassessments of local MWP-1A amplitudes at Barbados and Sunda Shelf based on the well-constrained timing derived from the Tahiti sea-level record (Deschamps et al, 2012), the sea-level data from Barbados, Sunda Shelf, and Tahiti do not provide as tight of a constraint on the Antarctic contribution as previously thought. We find that between 1 to 10 m sea-level equivalent (sle) could have melted from the Antarctic, compared to 7 to 15 m sle from previous analyses (Clark et al, 2002; Bassett et al, 2005; Deschamps et al, 2012). To better constrain the source of MWP-1A, we also consider sea-level data from Scotland (Shennan et al, 2000), which have, until now, been excluded from MWP-1A fingerprinting experiments because they are strongly influenced by local ice unloading. To overcome this, we isolate the elastic MWP-1A amplitude (i.e. fingerprint signal) at this location using a suite of models that provide optimal fits to the Scottish data, and thereby remove near-field contamination. Preliminary results show that the inclusion of these data leads to an improved MWP-1A source distribution constraint compared to that obtained using the far- and intermediate-field data alone.

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