Outburst of a subglacial flood from the floor of the Greenland Ice Sheet

Subglacial lake evolution

We used repeat measurements of floor elevation derived from timestamped ArcticDEM DSMs and from the Ice, Cloud and land Elevation Satellite-2 (ICESat-2) laser altimeter to check the evolution of the Harder subglacial lake. Two-metre-resolution ArcticDEM DSMs³⁴ had been generated by the ArcticDEM undertaking, utilizing stereoscopic WorldView and GeoEye satellite tv for pc imagery⁵¹. We co-registered all of the ArcticDEM stripfiles within the examine space with seasonally aligned (March–May) ICESat-2 ATL06 information⁵², which was obtained from the National Snow and Ice Data Center for the interval 2019–2020. Points scattered by cloud, blown snow or aerosols, or flagged as low high quality, had been discarded earlier than evaluation. Artefacts within the ArcticDEM stripfiles, along with dynamic surfaces such because the collapse basin, had been masked earlier than performing a least-squares planar match to the residuals to mannequin the vertical offset between the ICESat-2 and ArcticDEM elevations^53,54:

Here, x and y are the horizontal coordinates, ∆z is the ArcticDEM–ICESat-2 elevation distinction and a, b and c are the coefficients decided from the least-squares match. We then eliminated the aircraft from the z element (elevation) of every DSM. A complete of 1,352 ICESat-2 factors had been used for co-registering the 14 DSMs within the examine space. To compute quantity adjustments related to the drainage of the subglacial lake, we first computed the realm of the collapse basin, by differencing the pre-collapse and post-collapse ArcticDEM DSMs from 2014 and 2015, respectively. We then outlined the extent of the collapse basin, primarily based upon these pixels the place the typical elevation change between these dates was larger than the 1σ elevation variability³⁸.

Regional local weather modelling

We used day by day 2-m temperature, precipitation, soften and run-off from the 1-km downscaled model of the Regional Atmospheric Climate Model (RACMO) model 2.3p2 (RACMO2.3p2)⁵⁵, which mixes the dynamical core of the High-Resolution Limited Area Model (HIRLAM) and the physics of the European Centre for Medium-Range Weather Forecasts-Integrated Forecast (ECMWF-IFS cycle CY33r1). RACMO2.3p2 is compelled by ERA5 reanalyses (1990–2020) and features a 40-layer snow module that simulates soften, run-off, water percolation, retention and refreezing in firn. Snow layers had been initialized utilizing vertical temperature and density profiles from the Institute for Marine and Atmospheric Research Utrecht-Firn Densification Model. Full particulars are offered in Noël et al.^55,56.

Ice velocity and pressure

We generated 5,800 maps of ice floor stream velocity between 1988 and 2020 by monitoring the displacement of options in satellite tv for pc optical^57,58 (Landsat-8 and Sentinel-2) and Synthetic Aperture Radar (SAR)⁵⁹ (Sentinel-1A/B, ENVISAT, RADARSAT-2, ALOS and ERS-1/2) imagery. To assess temporal adjustments within the Harder Glacier velocity, together with anomalies within the 2014 seasonal evolution, we first extracted the typical ice stream velocity inside a 4 × 4 pixel field ~5 km inland from the terminus of the glacier (at 81.81° N, 45.40° W) for all picture pairs after which we extracted weekly averaged time collection. Finally, we computed the change in velocity in every calendar week, each earlier than and after the 2014 drainage occasion, and likewise the pattern in ice velocity over the six calendar weeks following the drainage occasion utilizing linear regression.

To assess the pressure regime within the neighborhood of the outburst web site, we calculated longitudinal, transverse and shear pressure charges⁶⁰:

the place α is the stream angle outlined counterclockwise from x axis (optimistic within the x route) and ({dot{varepsilon }}_{x}), ({dot{varepsilon }}_{y}) and ({dot{varepsilon }}_{{xy}}) are the elements of the pressure price tensor outlined in response to Nye⁶¹:

Here u and v are the 2 horizontal elements of the noticed floor stream velocity area. To carry out this calculation in observe, we averaged floor stream velocity over the interval 2013–2019 to maximise the signal-to-noise ratio and decrease the uncertainties in ice stream route in contrast with a single image-pair calculation⁶⁰. Measuring any temporal change within the pressure regime and likewise the pressure regime on the time of the historic 1990 lake outburst was not doable, because of the precision of the characteristic monitoring strategies, the dearth of coherence required for interferometry and the restricted historic information availability.

Thermal modelling

To assess the thermal circumstances on the ice mattress, we remedy an vitality equation for ice temperature, T(y, z), within the 2D glacier part between the collapse basin edge (y = 0 km) and the fracture zone (y ≈ 1 km), the place y is the horizontal distance from the basin edge and z is peak throughout the ice column:

Our mannequin assumes regular state (∂T / ∂t = 0) as it’s designed to simulate the long-term circumstances earlier than outburst and accounts for advective and conductive warmth transport, along with viscous dissipation. In this mannequin, η is the ice viscosity, (tau) is the efficient stress and v and w approximate the rate area. The parameters κ, ρ_i and c_p signify identified ice properties, and we impose the floor temperature in 2014 as a boundary situation. The materials constants used are the thermal diffusivity κ (36.1 m² yr⁻¹), density ρ_i (916 kg m⁻³) and particular warmth capability c_p (2 × 10³J kg⁻¹ Okay⁻¹) of ice. Given that ice velocity will increase from ~ 0 m yr⁻¹ on the basin edge to about 20 m yr⁻¹ a number of kilometres downstream, each downward advection of chilly ice and viscous dissipation are doable, and so our mannequin accounts for each processes. Specifically, the stream configuration resembles flank stream off an ice divide, and so we specify the rate area v ≈ v(y) = (y{dot{varepsilon }}_{{yy}}) and w ≈ w(z) = (mbox{-}z{dot{varepsilon }}_{{yy}}) (which satisfies the continuity equation below aircraft stream) to seize the thermal advection to main order. For the horizontal pressure price, we assume ({dot{varepsilon }}_{{yy}}=0.0035) yr⁻¹, which equates to the imply floor worth over the primary 1.5 km, as decided from our velocity observations. In the dissipation time period of the mannequin, the ice viscosity (eta={[2,A({T}),{{tau}^{n-1}}]}^{-1}) is evaluated utilizing Glen’s legislation exponent n = 3 and printed⁶² values of the temperature-dependent issue A. The efficient stress (tau) is calculated by Newton–Raphson iteration by way of ({tau}^{2}={{tau}_{yy}}^{2}+{{tau_{yz}}^2}) = (({dot{varepsilon }}_{{yy}}/A{tau }^{n-1}))² + (ρ_i g(H – z)sin α_s)², the place sin α_s = 0.02 is the ice floor slope and g = 9.81 m s⁻² is gravitational acceleration.

Regarding the mannequin boundary circumstances, we specify T to be the floor temperature at z = H, ∂T / ∂y = 0 at y = 2 km and the geothermal warmth flux situation −ok_i∂T/∂z = G at z = 0, the place ok_i = 2.1 W m⁻¹ Okay⁻¹ is the ice thermal conductivity and G is geothermal warmth flux. The latter situation presumes a chilly base with no sliding, which is per our simulations that present T_b to be under the melting level. At the upstream boundary, y = 0, no details about the temperature within the ice column is obtainable. In this regard, you will need to observe that y = 0 locates the collapse basin edge and never essentially the doubtless dynamic margin of the subglacial lake; with lake water in all probability positioned at y < 0 whereas the lake was rising. As a conservative measure, we due to this fact account for the potential presence of comparatively heat ice on the interface with the subglacial lake (which might function an extra supply of warmth to the downstream ice), by prescribing a parabolic temperature profile T(0, z) that decreases from the melting level on the mattress to T_s on the floor. This boundary situation represents a stringent take a look at for the existence of a chilly mattress additional downstream as a result of it prescribes the ice to be close to the melting temperature for a substantial part of deep ice on the boundary (that’s, it favours overestimation of T_b). Internal mannequin consistency can be established for various (much less stringent) simulations the place we changed this boundary situation with ∂T / ∂y = 0 at y = 0 (primarily based on the symmetry of an ice divide), which resulted in predicted T_b values that had been uniformly extra detrimental than these reported right here.

Our simulations require data of the ice thickness H and geothermal warmth flux G on the examine web site, each of that are unsure. Notably, H within the area of curiosity (inside 1–2 km downstream of the collapse basin) has not been surveyed by in situ or geophysical strategies. Although the proximity of a nunatak and bedrock to the northwest might counsel comparatively skinny ice, direct observational proof is missing. The ice thickness from BedMachine lies within the approximate vary 30–50 m, with a nominal uncertainty of ~ ± 20 m. However, this uncertainty is itself unsure, given the thickness is derived from mattress topography interpolated by kriging from the close by ice margin and the mattress beneath the southern department of Harder Glacier. G can be poorly constrained. A current map of basal soften charges⁶³ signifies G < 0.05 W m⁻² for the catchments close to Victoria Fjord, however our area lies simply past the sting of its gridded information. Given these uncertainties, we carry out a number of simulations throughout the parameter house 25 ≤ H ≤ 500 m and 0.01 ≤ G ≤ 0.1 W m⁻² (taking into account that low H and low G in these ranges are most possible), to make sure the robustness of our conclusion of a frozen mattress interface. For all simulations, we remedy the vitality equation by including a leisure time by-product to its left-hand facet and evolving the temperature area to regular state, with T_s mounted at −13.2 °C (the imply floor temperature of the current decade) and ignoring sub-annual temperature variations. This method ensures conservative outcomes, as a result of accounting for (1) the discount in warmth retained within the ice column as a result of latent warmth loss related to any floor meltwater manufacturing throughout summer season and (2) traditionally colder circumstances (–14.6 °C within the Sixties) alongside modern glacier thinning (~13 m since 1990) inside a time-dependent mannequin would lead to a colder ice column and, consequently, decreased T_b. Finally, we take a look at whether or not initially warm-based circumstances beneath the floor outburst web site might be self-sustainable below excessive geothermal flux supplemented by the warmth launched from basal sliding, by utilizing a one-dimensional steady-state warmth conduction mannequin:

the place H_min is the minimal thickness for sustaining a heat base. The ultimate time period within the equation describes the warmth dissipation from sliding. Because of its inclusion, this mannequin directs the warmth sources maximally to the basal interface; the mannequin additionally ignores downward advective cooling and latent warmth loss to basal melting, so it severely underestimates H_min to offer a conservative take a look at. Setting T_s = –13.2 °C (the upper of the decadal imply floor temperatures comparable to the 1990 and 2014 drainage years), G = 0.1 W m⁻² and v_s = 10 m yr⁻¹ yields H_min = 243 m, which guidelines out a heat base between the lake and the 2014 outburst web site until the ice is way thicker than anticipated.

Hydraulic potential

To examine whether or not the circumstances required to power water from the subglacial lake to the floor on the fracture zone had been met, we assessed whether or not the lake hydraulic potential exceeded the hydraulic potential on the fracture web site. If z_L and z_R denote the ice floor elevation above the lake (pre-outburst) and on the fracture zone, respectively, and H_L is the ice thickness above the lake, then this entails that ρ_i gH_L + ρ_wg(z_L – H_L) > ρ_wgz_R, the place ρ_w = 1,000 kg m⁻³ is the density of water. Hence:

the place z_L ≈ 690 m and z_R ≈ 655 m primarily based upon the ArcticDEM floor elevation mannequin. Equation (8) due to this fact constrains H_L to be lower than 420 m. As the ice above the lake might be thinner than this worth, it’s possible that this situation is met, wherein case water from the lake might be compelled to the floor on the fracture zone.

Meltwater flux estimation and subglacial water routing

We modelled the floor and basal meltwater fluxes over each the subglacial lake’s and the Harder Glacier’s floor and basal upstream catchments, utilizing estimates of (1) floor soften from the 1-km downscaled model of the RACMO2.3p2 (ref. ⁵⁵) and (2) basal soften as a result of geothermal warmth flux, frictional heating and the warmth launched by floor meltwater reaching the mattress⁶³. This evaluation was designed to evaluate (1) the sources of water feeding the lake (by way of an evaluation of the meltwater generated throughout the lake’s upstream catchment) and (2) the extent to which the drainage overloaded the Harder Glacier’s subglacial system (by way of an evaluation of the soften generated over your entire Harder Glacier catchment itself). The derived run-off estimates signify an higher certain on the water out there as a result of they assume that (1) all floor water was routed to the mattress (that’s, no water is saved on high or throughout the ice) and (2) no refreezing occurred on the ice base. Where floor storage or basal refreezing does happen, this can cut back the background quantity of water flowing by the subglacial system and therefore the relative dimension of the perturbation attributable to the lake drainage would have been even greater.

The routing of subglacial water was modelled utilizing the Shreve hydraulic equation⁶⁴:

the place (varnothing) is the hydropotential, ({rho }_mathrm{w}) and ({rho }_mathrm{i}) are the densities of water and ice, respectively (1,000 and 916 kg m⁻³), ({z}_mathrm{b}) and H are the mattress elevation and ice thickness⁴⁶ and ok is a ‘flotation factor’. We don’t estimate routing on the time of the 1990 lake drainage as a result of the spatially resolved ice thickness downstream of the lake web site stays unsure at the moment. The flotation issue is the ratio between the subglacial water strain and the ice overburden strain, the place ok > 1.0 suggests the subglacial water strain exceeds overburden and (ok < 1.0) means that subglacial water strain is lower than overburden. Because subglacial water strain is unknown, we compute downstream routing pathways for the subglacial flood utilizing a spread of believable ok values (0.8, 0.9, 1.0 and 1.1) to account for this uncertainty⁶⁵. Specifically, we calculate the hydropotential utilizing equation (9), take away sinks, decide the variety of upstream cells contributing to every cell (to establish stream paths) and retain all cells that are related to greater than 100 cells upstream (to take away small tributaries). For all 4 values of ok, our evaluation signifies that subglacial water stream from the subglacial lake basin is routed to the northern lobe of the Harder Glacier. To delineate the upstream catchments used to compute the floor and basal meltwater fluxes, the ArcticDEM 100-m mosaic³⁴ was used to outline the floor catchments, and the subglacial catchments had been estimated by calculating the hydropotential (equation (9)) utilizing the floor and mattress topography from BedMachine v3⁴⁶, assuming that the subglacial water was at overburden strain, after which delineating the ensuing drainage basin by following the steepest gradients within the hydropotential.

Ice thickness change

Ice thickness change between the 1990 and 2014 drainage occasions was computed within the neighborhood of the lake web site, primarily based upon ICESat (2003–2009) and CryoSat-2 (2010–2020) observations, along with RACMO2.3p2 (ref. ⁵⁵) simulations (1990–2020). CryoSat-2 Baseline-D Level-2I Synthetic Aperture Radar Interferometric (SARIn) altimeter observations had been used to compute peak evolution time collection at 60-day epochs between October 2010 and October 2020, utilizing a mannequin match technique^66,67, which was utilized on a 5 × 5 km grid. This processing included a backscatter correction⁶⁸ and filtering utilizing the next statistical thresholds: a minimal of 70 information factors, a minimal time collection size of two years, a most root imply sq. distinction of 12 m, a most elevation price magnitude of 10 m yr⁻¹ and a most floor slope of 5°. We then computed time collection of peak evolution by averaging the gridded elevation anomalies inside 60-day intervals for the northern sector of the ice sheet the place the subglacial lake is positioned (particularly, between elevations of 500 and 800 m above sea degree, in response to ArcticDEM⁶⁹). ICESat laser altimeter measurements had been used to compute elevation adjustments between 2003 and 2009. We used launch 34 of the GLAS/ICESat Level-2 GLAH12 product⁷⁰ processed with a plane-fitting technique⁷¹ to acquire estimates of the temporal evolution of the ice floor. These information had been pre-processed to take away the intercampaign bias⁷² and the saturation biases offered in GLAH12. RACMO2.3p2 simulations had been used to compute 1990–2020 peak change on account of floor mass stability processes.

Nunatak supraglacial lake quantity

To estimate the quantity of water saved within the supraglacial lake adjoining to the subglacial lake instantly earlier than the 2014 subglacial lake drainage, we manually delineated the lake boundary to find out its extent, utilizing a Landsat-8 scene acquired on 22 July 2014. We then estimated lake depth utilizing a radiative switch method⁷³, utilized to the inexperienced band, which is anticipated to offer an higher certain on the lake quantity⁷⁴:

Here z is the lake depth, A_d is the underlying lake mattress reflectance, R_∞ is the reflectance from optically deep water, R_w is the reflectance measured by the satellite tv for pc and g is the coefficient for spectral radiance loss within the water column. To estimate A_d, we used the imply reflectance values from the lake mattress, utilizing a picture acquired on 1 August 2014 instantly after the lake had drained. R_∞ was assumed to be 0, which represents a conservative decrease certain, and g was estimated as 2kd, the place kd is the diffuse attenuation coefficient for downwelling gentle^75,76. Finally, to compute lake quantity, depth estimates had been built-in spatially over the lake space.

Calving entrance change

Terminus positions of the Harder Glacier had been manually digitized from all Landsat and Sentinel-2 optical imagery acquired between 1988 and 2020, utilizing the Google Earth Digitization Tool⁷⁷. Images obscured by cloud, or the place ice mélange made it tough to establish the calving entrance, had been excluded. Changes within the calving entrance location had been estimated utilizing the centreline technique within the Margin change Quantification Tool⁷⁷.