Kronebreen, Svalbard – Effects of Undercutting and Sliding on Calving: a Global Approach

Australia: The Land Where Time Began

In this paper Vallot et al. present the results of their study of the effects of basal friction, subaqueous undercutting and glacier geometry on the process of calving by combining 6 different models in an offline-coupled workflow:

1) A continuum-mechanical ice flow model (Elmer/Ice),

2) A climate mass balance model,

3) a simple subglacial hydrology model,

4) A plume model,

5) an undercutting model, and

6) a discrete particle model,

to investigate fracture dynamics (Helsinki Discrete Element Model, HiDEM). They demonstrated the feasibility of reproducing the calving that had been observed at the front of Kronebreen¸ a tidewater glacier in Svalbard, during a melt season by using the output from the first 5 models as input to the HiDEM. The use of Elmer/Ice addressed the basal sliding and glacier motion, while HiDEM modelled calving. A hydrology model calculated subglacial drainage paths and it indicated 2 main outlets with different discharges. Depending on the discharge, the frontal melts rates, which are interatively projected to the actual front of the glacier at locations of subglacial discharge. Undercutting at different sizes is produced by this, as melt is concentrated close to the surface for high discharge and for low discharge is more diffuse. Vallot et al. have shown by testing different configurations that a key role is played by undercutting in the retreat of glaciers in the vicinity of the discharge locations during the melting season. Basal friction often influenced calving rates, by its effects on strain-rates and ice velocity near the terminus.

A major contributor to the rising sea level is the accelerated rate of discharge of ice into the oceans from the land, and it constitutes the largest source of uncertainty in predictions of sea level rise for the 21^st century and beyond (Church et al., 2013). This uncertainty reflects, to a large degree, the limited understanding of processes that impact calving from tidewater glaciers and ice shelves, as well as associated feedbacks with glacier dynamics. Calving occurs, in particular, by the propagation of fractures, which are not represented explicitly in the continuum models that are used to simulate the flow of ice and the evolution of glaciers.

It has been suggested recently that the warming ocean could play an important part in determining the calving rate and acceleration of a glacier by impacting the rates of submarine melting (Holland et al., 2008; Luckman et al., 2015). There are 2 mechanisms that have been proposed to be responsible for the increase in submarine melt rates at the ice-ocean interface in Greenland: A warmer, thicker layer of Atlantic water in the fjords and subglacial discharge has increased mainly during summer and autumn. Warm ocean water is entrained by buoyant plumes of meltwater (Jenkins, 2011) and is believed to enhance melt undercutting (Slater et al., 2015) as the ice cliff which triggers the collapse of iced above. Controls on seasonal variations in calving rates were investigated (Luckman et al., 2015) which showed that calving variations at Kronebreen, the glacier this study was focused on, correlated strongly with changes in temperature of the subsurface ocean linked to melt undercutting of the calving front. Direct measurements of oceanic properties, ice dynamics, frontal geometries and mean volumetric frontal rates of ablation, however, are still too scarce to quantify the relationship between ocean processes, subglacial discharge and ice dynamics and modelling must be relied on. According to Vallot et al. complex coupled process models can help in leading to a better understanding of the physics that are taking place at tidewater glacier fronts.

The dynamics of ice masses have been simulated in previous modelling work, the dynamics of ice masses (Van der Veen, 2002; Benn et al., 2007; Amundsen & Truffer, 2010; Nick et al., 2010; Cook et al., 2012; Krug et al., 2014, 2015) by the use of continuum models, in which the continuum space is discretised and include mass and energy balance processes. According to Vallot et al. continuum models cannot model explicitly fracture but must use simple parametrisations such as variables of damage or the criteria of phenomenological calving.

Discrete particle models, which represent ice as assemblages of particles that are linked by breakable elastic bonds, can be used to circumvent these problems. Each particle obeys Newton’s equations of motion as ice is considered to be a granular material. The bond is broken above a certain stress threshold, which allows the ice to fracture. It has been shown, (Åström et al., 2013,2014) that complex crevasse patterns and processes of calving that are observed in nature can be modelled using a particle model, the Helsinki Discrete Element Model (HiDEM).
A similar particle model has been used (Bassis & Jacobs, 2013) and suggested that the first order control on calving regime is provided by the geometry of glaciers. A drawback of these models is, however, that due to their high demand of computer resources, they tend to be applied to only a few minutes of physical time.

A compromise should be found by the coupling of a continuum model, such as Elmer/Ice, to a discrete model, such as HiDEM, to successfully describe the ice as a fluid and as a brittle solid. The discrete particle model uses sliding velocities and ice geometry that are calculated with a dynamic model to compute a new position for the calving front. The effect of mixing subglacial drainage with the ocean during the melt season is taken into account by the use of a plume model that estimates melt rates at the ice front according to pro-glacial ocean temperatures that are observed, subglacial discharge that is derived from surface runoff and the height of the ice front, taking into account.

In this paper Vallot et al. use the capabilities of the continuum model Elmer/Ice and the discrete element model HiDEM. They used the ability of HiDEM to model fracture and calving events, while retaining the long-term ice flow solutions of a continuum approach. The aim was to investigate the influence the velocity of basal sliding, geometry, and undercutting at the calving front has on the calving rate and location. The undercutting was determined with a high-resolution plume model that calculated melt rates from the rates of subglacial discharge. The simple hydrological model that calculates subglacial discharge is based on surface runoff that is assumed to be transferred directly to the bed and routed along the surface of hydrological potential. Vallot et al. illustrate the approach by using data from Kronebreen, which is a fast-flowing glacier in western Spitsbergen, Svalbard (topography, meteorological and oceanographic data, as well as horizontal surface velocity and front positions from 2013) to assess the feasibility of modelling retreat of the calving front (rate and position).

Conclusions

In this study the abilities of different models were used which represent different processes in glaciers at Kronebreen, Svalbard, with the focus on calving during the melt season of 2013. Data were provided for inputs to the models and validation, which included surface velocity, position of the front, topography, bathymetry and ocean properties.

The continuum ice flow model Elmer/Ice, which computes basal velocities by inverting surface velocities that are observed and evolves the geometry, which includes the position of the front, is the best model for representing the long-term fluid-like behaviour of ice. A subglacial hydrology system is formed during the melt season which allows the water to be evacuated at the front of the glacier. Vallot et al. used a simple hydrology model that was based on surface runoff to transmit directly to the bed and routed the basal water along the deepest gradient of the hydraulic potential. There are 2 subglacial discharge locations that have been identified by this approach:

· the northern one evacuates water of high rate (⁓10-100 m³/sec) and

· a southern one that has a low rate of ⁓1-3 m³/sec.

Subsequently this fresh water is mixed with ocean water. Warm fjord water is entrained by rising plumes of meltwater [fresh water is lighter, less dense, than sea water, so rises to the surface of the ocean] which melts the subaqueous ice that forms undercuttings at the location of the glacial discharge. The plume was modelled with a simplified 2-D geometry by the use of a high-resolution plume model that was based on the fluid dynamics code Fluidity adapted to the height of the front and the ocean properties of Kronebreen. Melt rates are dependent on the rates of discharge and the shape of the plume greatly differs with its magnitude. There is a tendency for the plume to rise to the surface close to where the melt rates are at their highest, while low discharges concentrate the melt at lower elevations. While taking into account the shape of the subaqueous ice front of the former time step the melt rates are then projected to the actual frontal geometry. According to Vallot et al. it is interesting to note that the undercutting that is modelled for high subglacial discharges are spatially close to the calving front that is observed, whereas such a correspondence is not evident for small discharges. A discrete particle model, HiDEM, was used to model the elastic-brittle behaviour of the ice, such as the formation of crevasses and calving processes. In this study 2 factors were investigated which impact the calving of glaciers using the HiDEM model:

i) melt undercutting that is associated with buoyant plumes, and

ii) basal friction, which influences strain rates and velocity near the terminus.

The performance of the calving model was quantitatively evaluated by comparison of modelled mean volumetric and observed calving rate and quantitatively by comparing calved regions. It was shown by results that during the melt season in the absence of melt calving, modelled calving rates are lower than observed values, and that there is a closer match with observations if undercutting is included. Also there is good agreement before (t₀) and after (t₁₁) the melt season between modelled and observed calving, when there is no undercutting. After the melt season the modelled and observed calving rates are much greater than before, which Vallot et al. attribute to lower basal friction and higher strain rates in the region near the terminus at t₁₁. Model experiments that transposed early- and late-season values of friction, had a large effect on modelled calving, corroborating the influence of basal friction on calving rates. These results are consistent with the conclusions reached by Luckman et al (2015), that the primary control on calving at Kronebreen at the seasonal scale, is melt undercutting, whereas at times of higher velocity (i.e. low basal friction) dynamic factors are important.

According to Vallot et al., they have shown in this paper that offline coupling the ice-flow, surface melt, basal drainage, plume-melting, and ice-fracture models can provide a good match to observations and yield improved understanding of the controls on calving processes. Full model coupling, which includes forward modelling of ice flow by the use of physical sliding law, would allow a further extension of this work to include prediction of the response of glaciers to atmospheric forcing and ocean forcing.

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