This thesis aims to better understand the relationships between basal water pressure, friction, and sliding mechanisms at ice sheet scales. In particular, it develops a new subglacial hydrology model (Hydro) to explicitly predict water pressures in response to basal water production and water injection from the surface. Recent research suggests that the Greenland ice sheet (gis) is losing a substantial volume of ice through dynamic thinning. This process must be modelled to accurately assess the contribution of the gis to sea-level rise in future warming scenarios. A key control on dynamic thinning is the presence of water at the ice-bed interface; Zwally et al. (2002) highlight the importance of supraglacial lakes' impact on basal ice dynamics, a process now con rmed by Das et al. (2008) and Shepherd et al. (2009). Many studies focus on the effects of surface meltwater reaching the bed of the gis but the underlying processes are often ignored. Geothermal, strain, and frictional melting, which evolves with basal hydrology, provide the background basal pressure profile that surface meltwater perturbates. Without understanding how these heat terms affect the background profile it is difficult to define basal boundary conditions in models and therefore difficult to model the dynamic response of the gis to surface melting. Hydro tracks subglacial water pressures and the evolution of efficient drainage networks. Coupled with the existing 3D thermomechanical ice sheet model Glimmer, model outputs include effective pressure N and the efficient hydraulic area. Defining frictional heat flux and basal traction as functions of N allow the modelling of seasonal dynamic response to randomly draining supraglacial lakes. Key results are that frictional heat flux, as a function of N, caps potential runaway feedback mechanisms and that water converges in topographic troughs under Greenland's outlet glaciers. This leads to a background profile with low N under outlet glaciers. Therefore, outlet glaciers show a muted dynamic speedup to the seasonal surface signal reaching the bed. Land-terminating ice does not tend to have subglacial troughs and so has higher background N and consequently a larger seasonal response. This, coupled with effects of ice rheology, can explain the hitherto puzzling lack of observed seasonal velocity change on Jakobshavn Isbræ and other outlet glaciers.

The last glacial cycle (c. 115-12 kyr BP) was the most recent in a series of recurring glaciations of the subpolar continents. Massive ice sheets evolved in Eurasia and North America, which, at their maximum, were of continental scale and together lowered the global sea-level by approximately 100 m. The paleo-modelling community has focused on the last glacial maximum (LGM, ~ 20 kyr BP), leaving the longer period when the ice sheets evolved to their LGM configurations largely unexplored. In this thesis we study the mutual interaction between the time-mean atmospheric circulation and the evolution of the Northern Hemisphere ice sheets over the build-up phase of the last glacial cycle. Experiments are conducted with coupled atmosphere-ice-sheet models and a circulation model forced by geologically consistent reconstructions of the ice-sheet topography at key stages of the glacial cycle. The main findings from these studies are that the ice evolution in North America may have been controlled by circulation anomalies induced by the background topography in conjunction with the ice sheets themselves. A geologically consistent pre-LGM ice sheet could only be obtained when including the North American Cordillera. However, the ice sheets' influence on the local climate conditions is also found to be paramount for this configuration. We further suggest that the incipient ice sheets may have had a limited influence on the large-scale winter circulation as a result of their location relative the westerly mean flow. The LGM Laurentide Ice Sheet (LIS) was, however, different because of its continent-wide extent, and it may therefore have had a large influence on the planetary-scale circulation, especially in the Atlantic sector. We find that the planetary waves forced by the LIS were considerably larger than at earlier times, and, as a result of a more frequent planetary wave reflection over the Atlantic Ocean basin, an altered stationary wave field and a zonalised winter jet. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Manuscript. Paper 4: Manuscript.</p>

Some climate models are still lacking features such as dynamical modelling of ice sheets due to their computational cost which results in poor accuracy and estimates of e.g. sea level rise. The need for low-cost high-order models initiated the development of the First-Order Stokes (or Blatter-Pattyn) model which retains much of the accuracy of the full-Stokes model but is also cost-effective. This model has proven accurate for ice sheets and glaciers with frozen bedrocks, or no-slip basal boundary conditions. However, experimental evidence seems to be lacking regarding its accuracy under sliding, or stress-free, bedrock conditions (ice-shelf conditions). Hence, it became of interest to investigate this. Numerical experiments were set up by formulating the first-order Stokes equations as a variational finite element problem, followed by implementing them using the open-source FEniCS framework. Two types of geometries were used with both no-slip and slip basal boundary conditions. Specifically, experiments B and D from the Ice Sheet Model Intercomparison Project for Higher-Order ice sheet Models (ISMIP-HOM) were used to benchmark the model. Local model errors were investigated and a convergence analysis was performed for both experiments. The results yielded an inherent model error of about 0.06% for ISMIP-HOM B and 0.006% for ISMIPHOM D, mostly relating to the different types of geometries used. Errors in stress-free regions were greater and varied on the order of 1%. This was deemed fairly accurate, and probably enough justification to replace models such as the Shallow Shelf Approximation with the First-Order Stokes model in some regions. However, more rigorous tests with real-world geometries may be warranted. Also noteworthy were inconsistent results in the vertical velocity under slippery conditions (ISMIPHOM D) which could either be due to coding errors or an inherent problem with the decoupling of the horizontal and vertical velocities of the First-Order Stokes model. This should be further investigated. / Vissa klimatmodeller saknar fortfarande funktioner så som dynamisk modellering av istäcken på grund av dess höga beräkningskostnad, vilket resulterar låg noggrannhet och uppskattningar av t.ex. havsnivåhöjning. Behovet av enkla modeller med hög noggrannhet satte igång utvecklingen av den s.k. Första Ordningens Stokes (eller Blatter-Pattyn) modellen. Denna modell behåller mycket av noggrannheten i den mer exakta full-Stokes-modellen men är också väldigt kostnadseffektiv. Denna modell har visat sig vara noggrann för istäcken och glaciärer med frusna berggrunder eller s.k. no-slip randvillkor. Experimentella bevis tycks dock saknas med avseende på dess noggrannhet under glidning, eller stressfria, berggrundsförhållanden (t.ex. vid ishyllor). Därför ville vi undersöka detta. Numeriska experiment upprättades genom att formulera Blatter-Pattyn ekvatonerna som ett variationsproblem (via finita elementmetoden), följt av att implementera dem med hjälp av den öppna källkoden FEniCS. Två typer av geometrier användes med både glidande och stressfria basala randvillkor. Specifikt användes experiment B och D från Ice Sheet Model Intercomparison Project for Higher-Order ice sheet Models (ISMIP-HOM) för att testa modellen. Lokala fel undersöktes och en konvergensanalys utfördes för båda experimenten. Resultaten gav ett modellfel på ca 0,06 % för ISMIP-HOM B och 0,006 % för ISMIP-HOM D, vilka var mest relaterade till de olika typerna av geometrier som användes. Fel i stressfria regioner var större och varierade i storleksordningen 1 %. Detta ansågs vara ganska noggrant och sannolikt tillräckligt för att ersätta modeller så som Shallow Shelf Approximationen med Blatter-Pattyn-modellen i vissa regioner. Dock krävs mer noggranna tester med mer verkliga geometrier för att dra konkreta slutsatser. Också anmärkningsvärt var motsägande resultat i den vertikala hastigheten under glidande förhållanden (ISMIP-HOM D) som antingen kan ha berott på kodningsfel eller ett modelproblem som härstammar utifrån särkopplingen mellan den horizontella- och den vertikala hastigheten i Blatter-Pattyn-modellen. Detta bör undersökas vidare.

Ice sheets, such as the Greenland Ice Sheet or Antarctic Ice Sheet, have a fundamental impact on landscape formation, the global climate system, and on sea level rise. The slow, creeping flow of ice can be represented by a non-linear version of the Stokes equations, which treat ice as a non-Newtonian, viscous fluid. Large spatial domains combined with long time spans and complexities such as a non-linear rheology, make ice sheet simulations computationally challenging. The topic of this thesis is the efficiency and error control of large simulations, both in the sense of mathematical modelling and numerical algorithms. In the first part of the thesis, approximative models based on perturbation expansions are studied. Due to a thick boundary layer near the ice surface, some classical assumptions are inaccurate and the higher order model called the Second Order Shallow Ice Approximation (SOSIA) yields large errors. In the second part of the thesis, the Ice Sheet Coupled Approximation Level (ISCAL) method is developed and implemented into the finite element ice sheet model Elmer/Ice. The ISCAL method combines the Shallow Ice Approximation (SIA) and Shelfy Stream Approximation (SSA) with the full Stokes model, such that the Stokes equations are only solved in areas where both the SIA and SSA is inaccurate. Where and when the SIA and SSA is applicable is decided automatically and dynamically based on estimates of the modeling error. The ISCAL method provides a significant speed-up compared to the Stokes model. The third contribution of this thesis is the introduction of Radial Basis Function (RBF) methods in glaciology. Advantages of RBF methods in comparison to finite element methods or finite difference methods are demonstrated. / eSSENCE

Geomorphological evidence of glaciations exist for the Last Glacial Maximum (about 20 kyr ago). At this time, both North America and Eurasia were covered by extensive ice sheets which are both absent today. However, the temporal and spatial evolution of the ice sheets from the previous interglacial up to the fully-glaciated conditions at LGM is still unresolved and remains a vexing question in climate dynamics. The evolution of ice sheets is essentially controlled by the prevailing climate conditions. On glacial time-scales, the climate is shaped the by the orbital variations of the Earth, but also by internal feedbacks within the climate system. In particular, the ice sheets themselves have the potential to change the climate within they evolve. This thesis focuses on the interactions between ice sheets and the time-mean atmospheric circulation (stationary waves). It is studied how the stationary waves, which are forced by the ice-sheet topography, influence ice-sheet evolution through changing the near-surface air temperature. In this thesis, it is shown that the degree of linearity of the atmospheric response controls to what extent the stationary waves can reorganise the structure of ice sheet. Provided that the response is linear, the stationary waves constitute a leading-order feedback, which serves to increase the volume and deform the shape of ice sheets. If the stationary-wave response to ice-sheet topography is nonlinear in character, the impact on the ice-sheet evolution tends to be weak. However, it is further shown that the amplitude of the nonlinear topographical response, and hence its effect on the ice-sheet evolution, can be significantly enhanced if thermal cooling over the ice sheets is taken into account. / At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 3: Submitted.