No description available.

No description available.

Graduation date: 1994

Ice sheets and mountain glaciers are critically important components of Earth'sclimate system due to societal and ecological risks associated with sea-level change, ocean freshening, ice-albedo feedback, glacial outburst floods, and freshwater availability. As Earth warms, increasing volumes of surface meltwater will access subglacial environments, potentially lubricating the base of the ice sheets and causing enhanced ice discharge into the ocean. Since subglacial water is effectively hidden beneath the ice, the primary ways to study subglacial hydrological systems are through mathematical modelling and interpreting indirect observations. Glaciers often host subglacial or ice-dammed lakes that respond to changes in subglacial water flow, thereby providing indirect information about the evolution of subglacial hydrological systems. While monitoring subaerial ice-dammed lakes is straightforward, the evolution of subglacial lakes must be inferred from the displacement of the overlying ice surface, posing additional challenges in modelling and interpretation. This dissertation addresses these challenges by developing and analyzing a series of mathematical models that focus on relating subglacial hydrology with observable quantities such as lake level or ice-surface elevation. The dissertation is divided into five chapters. Chapter 1 demonstrates how ageneralization of Nye's (1976) canonical model for subglacial water flow admits a wide class of solitary-wave solutions---localized regions of excess fluid that travel downstream with constant speed and permanent form---when melting at the ice-water interface is negligible. Solitary wave solutions are proven to exist for a wide range of material parameter values that are shown to influence the wave speed and wave profile. Melting at the ice-water interface is shown to cause growth and acceleration of the waves. To relate dynamics like these to observable quantities, Chapter 2 focuses on modelling water-volume oscillations in ice-dammed lakes during outburst flood cycles while accounting for the potential influence of neighboring lakes. Hydraulic connection between neighboring lakes is shown to produce a wide variety of new lake-level oscillations that depend primarily on the relative sizes and proximity of the lakes. In particular, the model produces lake-level time series that mirror ice-elevation changes above a well-known system of Antarctic subglacial lakes beneath the Whillans and Mercer ice streams even though the modelled ice-dammed lakes are not buried beneath the ice. The stability of lake systems with respect to variations in meltwater input is characterized by a transition from oscillatory to steady drainage at high water supply. To create a framework for extending these models of ice-dammed lakes to thesubglacial setting, variational methods for simulating the dynamics of subglacial lakes and subglacial shorelines are derived in Chapter 3. By realizing a direct analogy with the classical Signorini problem from elasticity theory, this chapter also furnishes a new, rigorous computational method for simulating the migration of oceanic subglacial shorelines, which are strongly tied to ice-sheet stability in response to climatic forcings. In Chapter 4, this newly developed model is used to highlight the challenge of accurately interpreting ice-surface elevation changes above subglacial lakes without relying on ice-flow models. The surface expression of subglacial lake activity is shown to depend strongly on the effects of viscous ice flow and basal drag, causing altimetry-derived estimates of subglacial lake size, water-volume change, and apparent highstand or lowstand timing to deviate considerably from their true values under many realistic conditions. To address this challenge, Chapter 5 introduces inverse methods for inferring time-varying subglacial lake activity or basal drag perturbations from altimetry data while accounting for the effects of viscous ice flow. Incorporating horizontal surface velocity data as additional constraints in the inversion is shown to facilitate reconstruction of multiple parameter fields or refinement of altimetry-based estimates. In sum, this dissertation constitutes several novel approaches to understanding ice-water interaction beneath glaciers while laying the foundation for future work seeking to elucidate the role of subglacial processes in the changing climate.

Changes in global climate conditions significantly impact ice sheet and glacier mass change leading to global mean sea level (GMSL) change. One of the largest present-day contributors to GMSL is the Greenland ice sheet (GrIS) and it will likely continue to be so in the future. To accurately predict future ice mass changes, it is crucial to understand the response of GrIS to a changing climate and to correctly represent this behavior in climate models. The GrIS’ contribution to GMSL can in large part be attributed to the loss of ice and snow mass from the ice sheet surface. The surface mass loss has accelerated in the past decades due to increased surface melting and runoff in response to atmospheric warming. Surface melting is strongly controlled by ice albedo, a complex and dynamic property of ice that regulates the amount of solar radiation that is absorbed or reflected by the surface. Absorbed solar radiation leads to heating and melting of the ice surface. However, we lack a comprehensive understanding of the physical processes controlling ice mass loss, including ice albedo. These processes are, therefore, often simplified or crudely parameterized in climate models and subsequently add to large uncertainties in sea level rise predictions. This uncertainty prevents effective mitigation of and adaptation to the effects of climate change and sea level rise. It is, therefore, essential to advance our understanding of these processes and their representation in climate models. In this dissertation, I describe improvements to our understanding of the behavior of the GrIS and pose improvements to climate modeling capabilities that can lead to a reduced uncertainty of sea level rise projections. In the first chapter, I put constraints on the past response of the GrIS to a changing climate. Understanding the response of the GrIS to times in the past when temperatures were as warm or warmer than today offers insights into its current and future response to climate change. The southwestern GrIS retreated inland beyond its current margin during the (at least regionally) warmer-than-present mid-Holocene, before it readvanced. To investigate the timing and magnitude of southwest GrIS retreat and readvance in response to Holocene warmth, we model the response of the solid Earth and local relative sea level (RSL) to past ice sheet change. I compare model predictions to observations of paleo and present-day RSL and present-day vertical land motion around Nuuk, Greenland. I find that the southwest GrIS minimum extent likely occurred between 5 and 3 ka and that the historical maximum extent was likely approached between 2 and 1 ka. Comparing this timing to local and regional records of temperature and ice-sheet change suggest that the evolution of the southwestern GrIS presented here was in-phase with the likely evolution of southwestern GrIS mass balance through the Holocene. In the second chapter, I assess the performance of a regional climate model in simulating the spatiotemporal variability of GrIS ice extent and ice albedo in the period 2000-2021. A large portion of runoff from the GrIS originates from exposure of the darker ice in the ablation zone when the overlying snow melts, where surface albedo plays a critical role in modulating the energy available for melting. Ice albedo is spatially and temporally variable and contingent on non-linear feedbacks and the presence of light-absorbing constituents. An assessment of models aiming at simulating albedo variability and associated impacts on meltwater production is crucial for improving our understanding of the processes governing these feedbacks and, in turn, surface mass loss from Greenland. Our findings suggest that the regional climate model Modèle Atmosphérique Régional (MAR) overestimates ice albedo on average by 22.8 % compared to the ice albedo observations derived from the Moderate Resolution Imaging Spectroradiometer (MODIS). We also find that this ice albedo bias can lead to an underestimation of total meltwater production from the GrIS ice zone of 42.8 %. In the third chapter, I build upon the second chapter and present PIXAL, a physics-informed explainable machine learning architecture for Greenland ice albedo modeling. PIXAL is an Extreme Gradient Boosting (XGBoost) model and is trained on a suite of modeled topographic, atmospheric, radiative, and glaciologic variables from MAR to capture the complex and non-linear relationships with ice albedo observations from MODIS in the period 2000-2021. PIXAL outperforms MAR in modeling ice albedo on the southwestern GrIS. The performance metrics show that PIXAL achieves an R2 of 0.563, an SSIM of 0.620, an MSE of 0.005, and a MAPE of 14.699%, compared to MAR’s R2 of 0.062, SSIM of 0.112, MSE of 0.032, and MAPE of 46.202%. Explainable artificial intelligence (XAI) analysis reveals that topographic features, specifically ice sheet surface height and slope, are primary drivers of ice albedo. Near-surface air temperature and runoff further impact ice albedo. These findings highlight that understanding the complex physical processes underlying ice albedo variability is essential for accurate climate modeling and sea level rise predictions. PIXAL represents a crucial advancement in ice albedo modeling and paves the way for improved climate models that can more accurately estimate GrIS ice surface melting and its contribution to sea level rise. Overall, my results have implications for future ice sheet modeling studies targeting Greenland and provide a deeper understanding of the interactions between the climate and the cryosphere and thus of future ice sheet change.