Ice viscosity governs hydraulic fracture that causes rapid drainage of supraglacial lakes

TL;DR

The study develops a two-scale computational framework to model rapid hydrofracture-driven drainage of supraglacial lakes in an idealised glacier. It couples elastic and viscoelastic ice responses with a cohesive zone fracture model and a thermo-hydro-mechanical flow formulation that accounts for turbulent meltwater transport and local melting/freezing. Across simulations and a 2008 North Lake drainage case, viscoelastic creep dominates fracture propagation and uplift on short timescales, while thermal effects play a secondary role; a near-surface ice temperature threshold around $-8^ ext{o}C$ can halt propagation under certain conditions. The results imply rapid lake drainages may occur without refreezing in warmer regions, have meaningful implications for subglacial hydrology and basal friction, and motivate integrating two-scale fracture models into large-scale ice-sheet simulations to better predict sea-level rise.

Abstract

Full thickness crevasses can transport water from the glacier surface to the bedrock where high water pressures can open kilometre-long cracks along the basal interface, which can accelerate glacier flow. We present a first computational modelling study that describes time-dependent fracture propagation in an idealised glacier causing rapid supraglacial lake drainage. A novel two-scale numerical method is developed to capture the elastic and viscoelastic deformations of ice along with crevasse propagation. The fluid-conserving thermo-hydro-mechanical model incorporates turbulent fluid flow and accounts for melting/refreezing in fractures. Applying this model to observational data from a 2008 rapid lake drainage event indicates that viscous deformation exerts a much stronger control on hydrofracture propagation compared to thermal effects. This finding contradicts the conventional assumption that elastic deformation is adequate to describe fracture propagation in glaciers over short timescales (minutes to several hours) and instead demonstrates that viscous deformation must be considered to reproduce observations of lake drainage rate and local ice surface elevation change. As supraglacial lakes continue expanding inland and as Greenland Ice Sheet temperatures become warmer than -8 degree C, our results suggest rapid lake drainages are likely to occur without refreezing, which has implications for the rate of sea level rise.

Figures (16)

• Figure 1: Schematic diagrams describing the physical phenomena associated with lake drainage driven by hydraulic fracture. (a) In the 3D real case scenario, the vertical crevasse below the lake propagates and eventually reaches the bedrock, upon which fluid flow is sustained by horizontal fracture propagation and basal uplift. (b) Assuming uniformity in the out of plane direction, the problem can be idealised assuming 2D plane strain conditions to reduce the computational burden.
• Figure 2: Schematic sketch showing the macro-scale domain description, boundary conditions, and the in-plane $x-y$ coordinates assuming 2D plane strain conditions. The ice and rock domain is denoted by $\Omega$ and the fracture interface is denoted by $\Gamma_d$. The inset image shows the micro-scale domain and the corresponding $\xi-\eta$ coordinates used for describing turbulent fluid flow and thermal conduction.
• Figure 3: Range of Maxwell time-scales following from Eq. \ref{['eq:timescale']} and the material parameters from Table \ref{['tab:properties']}, assuming an effective deviatoric stress ranging from near zero to the tensile strength of the ice. Shaded area indicates the range of the timescale due to variations of temperature (and thus creep coefficient) with depth. Logarithmic scale used for vertical axis, ranging from $6\;\text{minutes}$ to $100\;\text{hours}$.
• Figure 4: Range of Maxwell time-scales following from Eq. \ref{['eq:timescale']} and the material parameters from Table \ref{['tab:properties']}, evaluated after $2\;\text{hours}$ of hydraulic fracture propagation. Deformations are magnified by $\times1000$, and a logarithmic colour scale is used.
• Figure 5: Depth dependence of the ice sheet temperature, and resulting creep coefficient and tensile strength.