Modelling the impact of submarine melting on tidewater glaciers

Glaciers and ice sheets will be the largest contributors to 21st Century sea level rise, but estimates of ice mass loss remain highly uncertain. One of the greatest challenges lies in predicting the retreat of tidewater glaciers (i.e. those glaciers that drain directly into the sea). These glaciers can retreat very rapidly in response to climate warming, discharging large quantities of ice into the ocean. Improving our ability to predict tidewater glacier retreat is therefore vital if more accurate estimates of future ice loss, and hence sea level rise, are to be developed. A likely cause of the widespread retreat of tidewater glaciers is an increase in submarine melting (i.e. melting of the submerged part of the glacier terminus) in response to warming ocean waters. Despite widespread interest in this process however (e.g. Truffer & Motyka, 2016), there remains considerable uncertainty as to how sensitive tidewater glaciers are to submarine melting.

This uncertainty reflects challenges in understanding the complex and interwoven processes of submarine melting and iceberg calving, and representing these in the numerical ice flow models that are used to simulate the response of glaciers to warming of the atmosphere and ocean. Submarine melting acts to undercut the terminus of tidewater glaciers, altering the distribution of stresses within the glacier and driving further mass loss through calving (e.g. Slater et al., 2021). These processes can be studied with increasing realism in complex 3D glacier models, which permit undercutting of the glacier terminus and the resulting effects on stresses and crevasse formation to be simulated (Benn et al., 2017). However, due to their complexity and computational requirements, such models are limited in their application to a handful of glaciers and are not suitable for simulations on the spatial and temporal scales necessary to examine the response of ice sheets to climate change. In contrast, 2D (depth integrated) ice flow models are capable of simulating ice sheet scale processes, but cannot directly predict the impact of submarine melting on the near-terminus stresses that drive calving. A method is therefore needed for the parameterisation of these processes in 2D ice flow models. This project seeks to develop this parameterisation and use it to examine the sensitivity of tidewater glaciers to submarine melting.

Research Objectives:

1. Develop a novel parameterisation of the impacts of melt-undercutting in a 2D (depth integrated) ice flow model
2. Test the new melt-undercutting parameterisation against observations and 3D model simulations at selected glaciers in Greenland and Svalbard
3. Use the new model assess the sensitivity of glaciers to increased submarine melting in response to climate change

Through these objectives, the project will deliver (a) a novel methodology addressing a key shortcoming in our ability to predict the response of glaciers and ice sheets to climate change and (b) a valuable assessment of the likely impact of submarine melting on glaciers over the coming decades.

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Image Captions

Kronebreen, a tidewater glacier in Svalbard (Image: Doug Benn)


The project will use the finite element ice flow model Úa (http://ghilmarg.github.io/ÚaSource/). The model has been widely applied across a range of glacial environments from ice sheets to mountain glaciers and has several advantages with respect to this project. The model is written in the user-friendly programming environment Matlab, making it a comparatively accessible introduction to ice flow modelling and model development. Furthermore, the large community of users in the UK (centred on the University of Northumbria) provide an excellent opportunity for training, networking and dissemination of project outputs. Úa has been previously coupled with ocean circulation models, providing a ready application for the improved melt and calving parameterisation. Calving in Úa is applied as an additional terminus melt rate term, providing a ready mechanism through which undercut-driven calving can be applied in the model.

Objective 1: Develop a novel parameterisation of the impacts of melt-undercutting in a 2D (depth integrated) ice flow model

Recent work has demonstrated that the crucial bending stresses associated with melt undercutting can be parameterised based on the depth-mean stress and bending moment at the calving front, which is itself a function of melt undercut length and shape, basal friction and the level of buttressing support provided by ice mélange (a mix of icebergs and sea ice that forms around glacier termini) (Slater et al, in prep). This provides a mechanism for incorporating the impacts of melt undercutting in 2D (depth-integrated) ice flow models. The student will work with the supervisory team to develop this theory into a melt undercutting parameterisation with the Úa framework, creating a cutting-edge tool for studying the impacts of submarine melting on tidewater glaciers.

Objective 2: Test the new melt-undercutting parameterisation against observations and 3D model simulations at selected glaciers in Greenland and Svalbard

The newly developed parameterisation must be tested and validated before it can be used more widely. To do this, the student will compare simulations using Úa against existing 3D model simulations and observations for two study glaciers, chosen based on the availability of data and as examples of contrasting calving behaviour. The first of these is Store Glacier (Sermeq Kujalleq) in west Greenland, a large tidewater glacier where observations and detailed modelling studies have shown the terminus position to be predominantly determined by the bedrock geometry and the seasonal presence of ice melange (Todd et al., 2019; Cook et al., 2020). The second is Kronebreen, a comparatively small glacier in Svalbard at where observations have demonstrated a strong seasonal advance/retreat cycle driven by variability in submarine melting (Luckman et al., 2015). The model will be spun up to match the observed position of the glacier terminus, with subsequent variability in position in response to variation in applied submarine melting tested against the published behaviour of these glaciers.

Objective 3: Use the new model assess the sensitivity of glaciers to increased submarine melting in response to climate change

The final aim of the project is to use the validated model to assess the sensitivity of the study glaciers to the increase in submarine melting projected under anthropogenic climate change. This will be achieved by increasing the applied submarine melt rate in keeping with the plausible range that may occur in response to rising ocean and atmospheric temperatures over the 21st Century (Slater et al., 2020). To gauge the importance of submarine melting in these systems, the results will be compared to alternative simulations in which only projected changes in surface mass balance (affecting the glacier mass flux to the terminus) are included. If time permits, this analysis may be extended to a wider range of glaciers (or idealised glaciers) to examine the controls on the sensitivity or insensitivity of individual glaciers to submarine melting.

Project Timeline

Year 1

Literature review, model development (objective 1)

Year 2

Complete model development (objective 1) and undertake validation exercises (objective 2)

Year 3

Complete validation exercises (objective 2) and undertake sensitivity tests (objective 3)

Year 3.5

Completion of experiments, complete thesis write up

& Skills

The student will develop the skills necessary to undertake the modelling and data analysis outlined in the project description. This will be delivered primarily through in-house expertise in numerical modelling and calving parameterisations, with additional Úa support through an external training course (if available) or through a short placement at the University of Northumbria. No existing experience in numerical modelling is required. The student will also be encouraged to attend a glaciology summer school such as the Advanced Climate Dynamics Course (hosted in Greenland) or the Karthaus Summer School on Ice Sheets and Glaciers in the Climate System. The project will run alongside larger NERC funded projects on related themes, and the student will benefit from the experience of working as part of a larger team spanning several institutions. Although no fieldwork is included as part of the PhD project, there may be the opportunity to join other groups undertaking fieldwork at this time.

Further training in transferable skills, including project management, oral and written presentation and media and outreach engagement is available through the Centre for Educational Enhancement and Development (CEED) at the University of St Andrews. The student will be expected to present their work at appropriate national and international conferences throughout their PhD research.

References & further reading

Benn, D. I., Åström, J., Zwinger, T., Todd, J., Nick, F. M., Cook, S., Hulton, N. R., & Luckman, A. (2017). Melt-under-cutting and buoyancy-driven calving from tidewater glaciers: new insights from discrete element and continuum model simulations. Journal of Glaciology, 63(240), 691-702. https://doi.org/10.1017/jog.2017.41

Cook, S. J., Christoffersen, P., Todd, J., Slater, D., & Chauché, N. (2020). Coupled modelling of subglacial hydrology and calving-front melting at Store Glacier, West Greenland. The Cryosphere, 14(3), 905-924. https://doi.org/10.5194/tc-14-905-2020

Luckman, A., Benn, D. I., Cottier, F., Bevan, S., Nilsen, F., & Inall, M. (2015). Calving rates at tidewater glaciers vary strongly with ocean temperature. Nature Communications, 6, Article 8566. https://doi.org/10.1038/ncomms9566

Slater, D. A., Benn, D. I., Cowton, T. R., Bassis, J. N., & Todd, J. A. (2021). Calving Multiplier Effect Controlled by Melt Undercut Geometry. Journal of Geophysical Research: Earth Surface, 126(7), e2021JF006191. https://doi.org/https://doi.org/10.1029/2021JF006191

Slater, D. A., Felikson, D., Straneo, F., Goelzer, H., Little, C. M., Morlighem, M., Fettweis, X., & Nowicki, S. (2020). Twenty-first century ocean forcing of the Greenland ice sheet for modelling of sea level contribution. The Cryosphere, 14(3), 985-1008.

Todd, J., Christoffersen, P., Zwinger, T., Råback, P., & Benn, D. I. (2019). Sensitivity of calving glaciers to ice-ocean interactions under climate change: New insights from a 3D full-Stokes model. The Cryosphere, 2019, 1-21. https://doi.org/10.5194/tc-2019-20

Truffer, M., & Motyka, R. J. (2016). Where glaciers meet water: Subaqueous melt and its relevance to glaciers in various settings. Reviews of Geophysics, 54(1), 220-239. https://doi.org/10.1002/2015RG000494

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