Numerical ice sheet modeling is a rather young discipline: it started in the 1950s. The "first generation" models developed at that time are currently being replaced by "new generations" ones, such as e.g. ARCTIC-TARAH. ARCTIC-TARAH is a Bert Bolin Center for Climate Research spin-off from the Pennsylvania State University Ice sheet model (PSUI). When the Bolin Center received PSUI for subsequent independent development and adaption of the code to Arctic settings in 2010, an initial inspection of the source code suggested that PSUI also contained a module that allows for the treatment of glacial hydraulics. A numerical ice sheet model including coupling of ice dynamics and hydraulics is an extremely important tool in testing new hypotheses of former geological events. E.g., based on the recent finding that Arctic Ocean sediments contain a very distinct signature, it has been suggested that ice dammed lakes at the south-eastern margin of the late Weichselian Eurasian ice sheet drained into the Arctic Ocean in a catastrophic event around 55.000 years ago. The aim of this thesis is to perform a reconnaissance analysis of the glacio-hydraulic algorithms in ARCTIC-TARAH, as "inherited" (but never with published record of functionality) from PSUI. The work is carried out in two steps: first the routines and algorithms describing the hydraulics are located and explored, and then these routines are tested and verified by performing experiment simulations. The investigation of the program code reveals the presence of two hydraulics related modules in ARCTIC-TARAH. The main tasks of the module Water are to initiate lakes and oceans and to adjust hydrostatic pressure in each lake. Further, with the module Move Water activated, transportation of water (e.g. in rivers) is possible. Results from idealized experiment simulations verify the functionality of the routines in the module Water. An in-depth analysis of the module Move Water suggests that there is a mismatch in time units when solving the equations describing flow of water. Experiment simulations also support this flaw detected in the flow model. Preliminary adjustments were made to the source code  of the module Move Water, which made it possible to simulate the transportation of water both under an ice sheet and in rivers on land. However, these adjustments do not solve the problem of mismatching time scales, and the numerical solutions obtained from the experiments were observed to be unstable and, therefore, possibly incorrect. To be able to perform more advanced simulations in support of the above mentioned hypothesis, the flow model in the module Move Water needs to be improved or replaced. One solution to the problem with mismatching time scales, could be to use a so called multiscale solution in time.

Ice sheet modeling is an important tool both for reconstructing past ice sheets and predicting their future evolution, but is complex and computationally costly. It involves modeling a system including the ice sheet, ice shelves and ice streams, which all have different dynamical behavior. The governing equations are non-linear, and to capture a full glacial cycle more than 100,000 years need to be simulated. To reduce the problem size, approximations of the equations are introduced. The most common approximation, the Shallow Ice Approximation (SIA), works well in the ice bulk but fails in e.g. the modeling of ice streams and the ice sheet/ice shelf coupling. In recent years more accurate models, so-called higher order models, have been constructed to address these problems. However, these models are generally constructed in an ad hoc fashion, lacking rigor. In this thesis, so-called Second Order Shallow Ice Approximation (SOSIA) equations for pressure, vertical shear stress and velocity are implemented into the ice sheet model SICOPOLIS. The SOSIA is a rigorous model derived by Baral in 1999 [3]. The numerical solution for a simple model problem is compared to an analytical solution, and benchmark experiments, comparing the model to other higher order models, are carried out. The numerical and analytical solution agree well, but the results regarding vertical shear stress and velocity differ from other models. It is concluded that there are problems with the model implemented, most likely in the treatment of the relation between stress and strain rate.

To increase our understanding of how ice sheets and glaciers interact with the climate system, numerical models have become an indispensable tool. However, the complexity of these systems and the natural limitation in computational power is reflected in the simplifications of the represented processes and the spatial and temporal resolution of the models. Whether the effect of these limitations is acceptable or not, can be assessed by theoretical considerations and by validating the output of the models against real world data. Equally important is to verify if the numerical implementation and computational method accurately represent the mathematical description of the processes intended to be simulated. This thesis concerns a set of numerical models used in the field of glaciology, how these are applied and how they relate to other study areas in the same field. The dynamical flow of glaciers, which can be described by a set of non-linear partial differential equations called the Full Stokes equations, is simulated using the finite element method. To reduce the computational cost of the method significantly, it is common to lower the order of the used elements. This results in a loss of stability of the method, but can be remedied by the use of stabilization methods. By numerically studying different stabilization methods and evaluating their suitability, this work contributes to constraining the values of stabilization parameters to be used in ice sheet simulations. Erroneous choices of parameters can lead to oscillations of surface velocities, which affects the long term behavior of the free-surface ice and as a result can have a negative impact on the accuracy of the simulated mass balance of ice sheets. The amount of basal sliding is an important component that affects the overall dynamics of the ice. A part of this thesis considers different implementations of the basal impenetrability condition that accompanies basal sliding, and shows that methods used in literature can lead to a difference in velocity of 1% to 5% between the considered methods. The subglacial hydrological system directly influences the glacier's ability to slide and therefore affects the velocity distribution of the ice. The topology and dominant mode of the hydrological system on the ice sheet scale is, however, ill constrained. A third contribution of this thesis is, using the theory of R-channels to implement a simple numerical model of subglacial water flow, to show the sensitivity of subglacial channels to transient processes and that this limits their possible extent. This insight adds to a cross-disciplinary discussion between the different sub-fields of theoretical, field and paleo-glaciology regarding the characteristics of ice sheet subglacial hydrological systems. In the study, we conclude by emphasizing areas of importance where the sub-fields have yet to unify: the spatial extent of channelized subglacial drainage, to what degree specific processes are connected to geomorphic activity and the differences in spatial and temporal scales. As a whole, the thesis emphasizes the importance of verification of numerical models but also acknowledges the natural limitations of these to represent complex systems. Focusing on keeping numerical ice sheet and glacier models as transparent as possible will benefit end users and facilitate accurate interpretations of the numerical output so it confidently can be used for scientific purposes. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.</p> / Greenland Analogue Project

Changes to ice sheet surface mass balance (SMB) are going to play a significant role in future sea level rise (SLR), particularly for the Greenland ice sheet. The Coupled Model Intercomparison Project Phase 5 (CMIP5) found that Greenland ice sheet (GIS) response to changes in SMB is expected to contribute 9 ± 4 cm to sea level by 2100 (Fettweis et al 2013), though other estimates suggest the possibility of an even larger response. Modern ice sheet geometry and surface velocities are common metrics for determining a model’s predictability of future climate. However, care must be taken to robustly quantify prediction uncertainty because errors in boundary conditions such as SMB can be compensated by (and therefore practically inseparable from) errors in other aspects of the model, complicating calculations of total uncertainty. We find that SMB calculated using the Community Earth System Model (CESM) differs from established standards due to errors in the CESM SMB boundary condition. During the long ice sheet initialization process, small SMB errors such as these have an opportunity to amplify into larger uncertainties in GIS sensitivity to climate change. These uncertainties manifest themselves in ice sheet surface geometry changes, ice mass loss, and subsequent SLR. While any bias in SMB is not desirable, it is not yet clear how sensitive SLR projections are to boundary condition forcing errors. We explore several levels of SMB forcing bias in order to analyze their influence on future SLR. We evaluate ensembles of ice sheets forced by 4 different levels of SMB forcing error, covering a range of errors similar to SMB biases between CESM and RACMO SMB. We find that GIS SMB biases on the order of 1 m/yr result in 7.8 ± 3.4 cm SLR between 1850 and 2100, corresponding to 100% uncertainty at the 2σ level. However, we find unexpected feedbacks between SMB and surface geometry in the northern GIS. We propose that the use of elevation classes may be incorrectly altering the feedback mechanisms in that part of the ice sheet. / text

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 (&le; 500 years). / Earth and Planetary Sciences

This thesis consists of two papers dealing with a stabilization method for free-surface flows. The method was initially developed to stabilize mantle-convection simulations, but is in this work extended to ice-sheet- and glacier modeling. The objective of this thesis is to assess the method when applied glaciological simulations, with regards to stability and accuracy. It is shown that the method works well and increases stable time-step sizes substantially both for ice-sheet- and glacier simulations, without loss of accuracy. The increased stability properties might be useful for performing long-term simulations and increasing sea-level-rise predictions on a centennial time scale. / Denna avhandling består av två artiklar som inom ramen för ismodellering undersöker en stabiliseringsmetod för flöden med en fri yta. Metoden framtogs först för stabilisering av simuleringar av mantelkonvektion, men har i den här avhandlingen anpassats till ismodellering. Avhandlingens mål har varit att utvärdera metoden med avseende på stabiltet och noggrannhet. Från de utförda studierna framkommer det att metoden ökar längden på stabila tidssteg avsevärt, utan att nämnvärt påverka noggrannheten hos islösaren. De ökade stabilitetsegenskaperna hos metoden kan exempelvis innebära ökad nogrannheten i fastställandet av framtida havsnivåhöjning genom möjliggörandet av långtidssimuleringar på en tidsskala av flera hundra år.