Letter | Published:

Melting at the base of the Greenland ice sheet explained by Iceland hotspot history

Nature Geoscience volume 9, pages 366369 (2016) | Download Citation

Abstract

Ice-penetrating radar1,2,3 and ice core drilling4 have shown that large parts of the north-central Greenland ice sheet are melting from below. It has been argued that basal ice melt is due to the anomalously high geothermal flux1,4 that has also influenced the development of the longest ice stream in Greenland1. Here we estimate the geothermal flux beneath the Greenland ice sheet and identify a 1,200-km-long and 400-km-wide geothermal anomaly beneath the thick ice cover. We suggest that this anomaly explains the observed melting of the ice sheet’s base, which drives the vigorous subglacial hydrology3 and controls the position of the head of the enigmatic 750-km-long northeastern Greenland ice stream5. Our combined analysis of independent seismic, gravity and tectonic data6,7,8,9 implies that the geothermal anomaly, which crosses Greenland from west to east, was formed by Greenland’s passage over the Iceland mantle plume between roughly 80 and 35 million years ago. We conclude that the complexity of the present-day subglacial hydrology and dynamic features of the north-central Greenland ice sheet originated in tectonic events that pre-date the onset of glaciation in Greenland by many tens of millions of years.

Main

Recent observations indicate that strong regional variations in the geothermal flux (GF) dominate the thermal regime and melting of the ice base beneath the continental parts of the Greenland and Antarctic ice sheets1,10. Ice flows rapidly and subglacial hydrological systems develop where the GF is high and meltwater is present under ice cover11,12. Despite being small compared with the observed volumes of water discharged by surface melt13, GF-induced basal melting is important because it occurs over large areas in the accumulation zone where there are no other basal water sources, and it disproportionately affects the overall dynamic behaviour of large ice sheet sectors1,14.

Deep ice core measurements and data from airborne ice-penetrating radar support very high rates of basal melting for parts of the Greenland ice sheet (GIS)1,4, as found at the head of the longest ice stream in Greenland, which drains northeast from the summit dome1. It has been argued that an anomalously high GF, exceeding 100 mW m−2, is required to produce the estimated rates of basal melt in the north-central GIS (refs 1,4). These values significantly exceed those expected for the ancient continental crust that forms the centre of the Greenland craton15, that is, 37–50 mW m−2. Here we present a new reconstruction of the GF across north-central Greenland to explain the origin of the observed melting beneath the ice cover (Fig. 1). This reconstruction reconciles a large array of independent data sets through an iterative calibration of a coupled three-dimensional (3D) climate-forced model of the GIS and the underlying lithosphere16 with: (i) Curie depths (the 580 °C isotherm) from satellite magnetic data17; (ii) estimates of lithosphere thickness from seismic data18; (iii) bedrock borehole temperature measurements taken in eastern Greenland and at the continental shelf; (iv) ice temperature measurements from five deep ice cores19; (v) areas of basal ice melt inferred from ice-penetrating radar studies1,2,3; (vi) areas of increased ice surface velocity from satellite observations5; and (vii) measured ice thickness20 (see Methods).

Figure 1: Predicted GF at 5 km below the bedrock surface.
Figure 1

The GF was corrected for crustal heat production using a parameterization of radiogenic heat sources (see Methods). The modelled thermal state of the GIS and lithosphere was calibrated by in situ data shown by white/black triangles, crosses1,4, diamonds2 and stars3 (basal melting data are from radar and ice core measurements). Deep ice core locations are from ref. 19 (CC, NEEM, NGRIP, GRIP, GISP2 and Dye3). The measured basal ice temperatures and GF from bedrock boreholes (1–7) are presented in Supplementary Tables 4 and 5. The white curves outline the ice sheet and coastal margins.

The reconstructed GF values range from 37 to 106 mW m−2 and show a continuous area of elevated GF (75–106 mW m−2) running from Scoresby Sund in the southeast towards Melville Bugt in the northwest (Fig. 1). The GF in the zone of anomalously high values, although elevated relative to the values expected for the Precambrian Greenland crust, is lower than previous estimates1,4, which were in the range 98–970 mW m−2. These earlier GF estimates were derived from inferred basal melt rates, which may locally be modulated by factors that are independent of the solid Earth-sourced heat flux. Sources of significant local perturbations to basal melt rates include heat advection through subglacial hydrology or hydrothermal circulation, basal ice sliding and meltwater refreezing. Because melting rates are controlled by a combination of GF and non-GF influences, we build our calibration strategy on estimating the GF required to reproduce the observed thawed basal ice conditions, discounting basal ice melt rates as a proxy for GF. This means that GF estimates will probably be biased downwards where basal melt is rapid; nevertheless, our strategy is sufficiently effective to separate out the signal of a strong and spatially extensive geothermal anomaly beneath the GIS and provides a hard lower bound for the GF values at the observed basal melt locations.

The anomalous GF zone lies in the area with the highest density of direct measurements. These include two deep ice cores (NGRIP and NEEM) and radar soundings at the heart of the anomaly (Fig. 1). Three other ice cores (CC, GRIP and GISP2) bound the anomaly to the west and south. The lateral dimensions of the reconstructed geothermal anomaly are roughly 1,200 by 400 km, covering about a quarter of the Greenland land area. The GF values in the anomalous area are up to 2.5 times greater than the background GF values derived across the northern and western parts of Greenland.

One potential cause of elevated GF is illustrated by seismic data that link our west–east GF anomaly with a zone of low seismic velocity in the mantle—a ‘negative anomaly’—beneath Iceland6,7 and Greenland (Fig.2a, b). Negative anomalies in seismic velocity are commonly associated with anomalously high temperatures and compositional heterogeneity of mantle rocks21. Iceland has been classified as a geologic hotspot resulting from increased magma production attributed to a mantle plume6,22, which is a narrow zone of hotter than average mantle rock that rises several thousand kilometres from deep within the Earth23.

Figure 2: Geophysical data indicating lithosphere anomalies beneath Greenland.
Figure 2

a, S-wave velocity model for a portion of the North Atlantic region at 120 km depth5, colour-mapped for percentage velocity anomaly. Areas of hotspot-related magmatism are hatched and labelled by age30. Reconstructions of the path of the Iceland hotspot 8,9 are shown as continuous lines for 0–60 Ma and dashed lines before 60 Ma (see Supplementary Fig. 8 caption). b, P-wave velocity model of the circum-Arctic region7 shown for north-central Greenland at 150 km depth, colour-mapped for percentage velocity anomaly. Black and orange triangles mark the ice core and bedrock borehole locations in Fig. 1.

Palaeoreconstructions of the relative plate motion8,9 and evidence from igneous rocks in eastern and western Greenland22 suggest that Greenland transited over the Iceland mantle plume between 80 and 35 million years ago (Ma) (Fig. 2a). When continental lithosphere moves over mantle plumes, compositional and thermal changes, magmatism and lithosphere thinning may affect areas that are hundreds of kilometres wide24 (see Supplementary Information). These changes may be independently inferred using anomalies in the observed gravity field (Supplementary Fig. 6), seismic velocity (Fig. 2a, b) observations and reconstructed variations in the 1,300 °C isotherm depth (Supplementary Fig. 5) beneath Greenland, as well as the GF variability near its surface (Fig. 1). In addition, the reconstructed zone of anomalous GF is spatially correlated with highs in the dynamic topography25 and isostatically compensated bedrock surface (Supplementary Fig. 7), both of which are probably induced by thermal anomalies in the mantle (see Supplementary Information). Our interpretation of the origin of the geothermal anomaly is further supported by evidence of former magmatism found under the present-day ice cover and along the western and eastern margins of Greenland. Mafic dyke fragments recovered from the bedrock beneath the GISP2 ice core26 are similar to basalts from eastern Greenland and there is evidence of large volcanic crater or caldera-like formations under the north-central GIS (ref. 1). Together with abundant magmatic rocks from the Greenland margins (Fig. 2a), these provide evidence for former volcanic activity in the area of anomalous GF, which may be directly or indirectly plume-related. Taken together, the accumulated evidence indicates that the prominent geothermal anomaly beneath the ice has its origin in the residual thermal imprint and lithosphere thinning imposed by the plume’s residence beneath Greenland tens of millions of years ago. This synopsis of independent evidence supports our earlier hypothesis16 that the lithosphere thinning beneath the summit region of the GIS could have resulted from thermal erosion by the Iceland plume.

Palaeoreconstructions of the history of the Iceland plume in the literature have been hampered by a high degree of uncertainty in the location and timing of its residence beneath Greenland. This has resulted in the proposed hotspot tracks being spread over a north–south band that is 1,000 km wide (Fig. 2a and Supplementary Fig. 8). The interpretation of the geothermal anomaly reconstructed here from independent geophysical data (Fig. 1) and seismic tomography data (Fig. 2a, b) provides new evidence that the Greenland lithosphere passed over the mantle plume several hundred kilometres from the tracks suggested by most existing palaeoreconstructions. Of previously proposed plume tracks, the most northerly9 (Fig. 2a and Supplementary Fig. 3) best explains the location of the reconstructed geothermal anomaly. A cursory comparison might suggest that this plume track disagrees with evidence from hotspot-related magmatic rocks at the western margin of Greenland (Fig. 2a), where the track reconstruction is less reliable (see Supplementary Information). The degree of disagreement is, however, hard to judge, as more extensive magmatic sequences supporting this northerly track may be hidden beneath the thick ice cover shielding most of the northwestern margin of Greenland (Fig. 1). In addition, previous studies have demonstrated that magmatic expression of the plume head at the surface may not necessarily coincide with the position of a plume-feeding conduit27.

The majority of the basal ice melt identified by ice-penetrating radar and ice core measurements1,2,3,4 lies within what we argue to be the area affected by the long-lived thermal and physical imprint of the Iceland plume (Fig. 1). The reconstruction of subglacial thermal conditions suggests that about half of the north-central GIS is now resting on a thawed bed, with extensive melting areas interconnecting fragmentary evidence of basal melt along the flight routes of radar-survey aircraft and at the location of the NGRIP ice core (Fig. 3a). We have also identified numerous regions where the basal ice is nearly at the pressure melting point and may contain some meltwater, for example, in proximity to the NEEM ice core.

Figure 3: Predicted basal thermal state of the present-day GIS.
Figure 3

a, Modelled basal ice temperature below the pressure-melting point (colour scale), with potential active hydrological routes superimposed in red, adopted from a subglacial topographic study3 (see Methods). Areas coloured white are where our model predicted melting at the base of the ice sheet. Triangles mark the ice core locations. b, The reconstructed geothermal anomaly (contours) superimposed on the observed surface ice velocity5 (colour scale) of the northeastern GIS shows that the head of the NEGIS is located in the area of the highest GF values (above 90 mW m−2).

The high basal melt rates estimated from internal ice layering account for several millimetres to centimetres of ice loss annually due to melting1. As substantial subglacial lakes are uncommon in Greenland28, the generated basal meltwater must be channelled towards the ice sheet margins without ponding along the way. A recent subglacial topographic study3 has suggested potential pathways for the drainage of subglacial meltwater, where this meltwater exists, from beneath the GIS. We have compared this potential drainage system with our reconstructed areas of basal melt and selected for the most likely paths along which the subglacial meltwater must be evacuated (Fig. 3a). The overwhelming majority of the potential hydrological routes3 cluster within our predicted basal melt areas, and may be active at present. Furthermore, most of these routes have their headwaters in the zone of the geothermal anomaly. We argue that the combination of enhanced melting, elevated GF, the concentration of hydrological pathways and deeply incised subglacial topography20 can be explained by the long-lasting imprint of the passage of Greenland over the Iceland mantle plume.

The tectonothermal history is also implicated in the locations where rapid ice flow has developed in central Greenland. Existing studies attribute the starting point of the 750-km-long North-Eastern Greenland Ice Stream (NEGIS, Fig. 3b) to the influence of the high GF and rapid basal melt located at its head1. Our study demonstrates that the areas of high GF and basal ice melt inferred from ice-penetrating radar studies1 and the start point of the NEGIS (ref. 5) (Fig. 3b) are all located within the reconstructed geothermal anomaly. However, the elevated GF is unlikely to be the only factor controlling the observed speed and shape of the NEGIS, which may also be modulated by ice geometrical settings, subglacial hydrology and the mechanical properties of the ice–bedrock interface29.

Our reconstruction of the present-day thermal regime of the GIS reveals more extensive areas of GF-induced basal ice melt than previously recognized1,2,3,4 and introduces the possibility that a dense network of subglacial meltwater pathways, most of which spring from the zone affected the history of the the Iceland hotspot, is now operating beneath the ice. Despite the weight of aggregated evidence presented here, it has not previously been hypothesized that the observed melting beneath large sectors of the GIS and anomalous ice streaming in northeastern Greenland may be due to the passage over the Iceland plume. The geothermal anomaly suggests a more northerly hotspot track than previously proposed and will offer a useful test for palaeoreconstructions of absolute plate motion. This study indicates a previously undocumented strong coupling between Greenland’s present-day ice dynamics, subglacial hydrology and the remote tectonothermal history of the North Atlantic region.

Methods

Model description and forcing.

Description. Our modelling strategy uses a 3D fully coupled thermomechanical model of the GIS and the lithosphere16. The ice component is implemented using the 3D finite-difference ice sheet model (ISM) SICOPOLIS based on the shallow ice approximation and the rheology of an incompressible, heat-conducting, power-law fluid described by Glen’s flow law31. Numerical solutions of mass, momentum and energy balance equations describe the ice dynamics and the thermal evolution of the GIS. The model is polythermal and allows the formation of temperate ice at the ice sheet’s base, overlain by a thick layer of cold ice. Mass- and energy-flux conditions at the interface between cold and temperate ice are realized through the solution of the Stefan problem31. Surface melting and refreezing are calculated using a temperature index32 and meltwater retention33 methods. Basal sliding is described by a Weertman-type sliding law34. The parameters of the ISM (Supplementary Table 1) were calibrated using an iterative approach described below to attain the best possible fit with the observed ice thickness. The lithospheric model is implemented using the 3D finite-volume thermomechanical code Lapex 3D (refs 35,36), incorporating a nonlinear temperature- and stress-dependent visco-elasto-plastic rheology with parameters that are consistent with laboratory measurements (Supplementary Table 2). The lithosphere model includes the upper and lower crust and the lithospheric mantle, and adopts a pressure–temperature-dependent law for thermal diffusivity in both the lithospheric mantle and the crust37. The bedrock surface is constructed using the most recent compilation of ice-penetrating radar measurements20. The thickness of the crust across north-central Greenland is based on CRUST1.0 (ref. 38), regionally adjusted to fit the estimates from S-receiver functions39 and gravity data40. The crust is subdivided into two parts of equal thickness with different thermal properties: the felsic crust with a higher radiogenic production and the mafic crust with a lower radiogenic production41. Here we employ a uniform distribution of radioactive elements within the upper crust, and a mean crustal heat production of 0.3 μW m−3 estimated in our previous study for central Greenland16 in agreement with bedrock borehole measurements from western Greenland16,42. Our previous studies16,35,36,43 describe the 3D ice sheet and lithosphere model components in more detail.

Boundary conditions. The ice sheet and lithosphere components are coupled through boundary conditions, requiring continuity of the internal energy and normal stress at the exchange boundary16 using the methodology of ref. 31. The hydrostatic pressure at the base of the ice sheet is transmitted to the lithospheric model as a loading that produces a dynamic response in the lithosphere. The resulting surface subsidence or uplift is then passed back to the ISM as a correction to the bedrock topography.

The lower boundary of the thermal lithosphere is defined as the depth where the asthenospheric potential temperature reaches 1,300 °C (ref. 15). The Winkler boundary condition that implies zero viscous drag forces and hydrostatic normal-to-surface stress is prescribed at the lower boundary of the model box. Free slip boundary conditions (the normal-to-boundary component of velocity vector is zero) are set for the upper 50 km at the side boundaries, whereas the remaining boundaries are open for in–out flow. No conductive heat exchange is allowed at these boundaries, that is, the thermal gradient is zero.

The coupled model is driven from above by time-evolved temperature and precipitation forcing over the period of large-scale glaciations in Greenland, which are assumed to have initiated in the Mid-Pliocene44. Climate history is inferred using an empirical relation45 to combine surface temperature records from ice cores with precipitation. The air temperature forcing uses the combined Greenland Ice Core Project—European Project for Ice Coring in Antarctica (GRIP-EPICA)16,45,46 applied as a time-varying spatially uniform offset from the present-day air temperature distribution across Greenland, corrected for the monthly lapse rates inferred from in situ measurements47. The precipitation field across Greenland is derived at each time step by applying a scaling to the present-day precipitation rate48 depending on the temperature offset relative to the present. The global sea-level forcing is derived from the SPECMAP marine δ18O record49. Before the onset of large-scale glaciation at 3 Ma, we initialize the Greenland lithosphere model to a thermal equilibrium with a surface temperature of 0 °C (ref. 44) at the ice-free upper boundary. The components of the coupled model together with their boundary conditions are schematically illustrated in Supplementary Fig. 1.

Discretization. Simulations are performed with a horizontal resolution of 10 km. The ISM and the thermal component of the lithospheric model are run with a time step of 1  yr, whereas the mechanical component of the lithospheric model uses a time step of 100 yr. The vertical resolution is non-uniform and provides grid densification towards the ice–bedrock interface in both the lithosphere and ice sheet model components. The computational grids adopted by SICOPOLIS and Lapex 3D codes coincide at the interface surface (in the nodes where temperature is evaluated). The vertical grids in cold-ice and temperate-ice columns include 81 and 11 points, respectively50. The vertical resolution of the lithospheric model component is 1 km in the upper crust and 5 km below. The temperature distribution within the upper 5 km of the crust is calculated on a fine sub-mesh including 161 vertical grid points, densifying towards the surface of the lithosphere.

Model calibration.

Throughout the modelling procedure we apply a multi-step calibration of the ice–lithosphere model against magnetic and seismic data, observations of the present-day GIS and GF estimates from the bedrock temperature measurements. Major steps of model calibration are schematically shown in Supplementary Fig. 2.

Stage I. The 1,300 °C isotherm depth is first derived from a 1D model of ice and lithosphere16 using the Curie depths (580 °C) from satellite magnetic data17 and seismic lithosphere thickness from S-receiver functions18,51 as constraints. The resulting nonlinear evolution equation for vertical advection and diffusion is solved with finite differences, using the procedure described in ref. 16. The thickness and structure of the crust are taken to be identical to those adopted by the 3D ice–lithosphere model.

Stage II. The preliminary map of the 1,300 °C isotherm depth obtained from Stage I is then used to define a lower thermal boundary in a 3D GIS–lithosphere model. From a reference simulation of the GIS–lithosphere history spanning 3 million years we estimate the deviations from the observed present-day ice thickness20 and ice balance velocity52. As a result we also derive the states of the GIS and lithosphere for the 100 ka time slice, which are then used as initial conditions at Stage III (ref. 53).

Stage III. We run a suite of simulations starting from the initial condition (100 ka) to select general parameters for the ISM (basal sliding coefficient, ice flow enhancement factors, degree-day factors for snow and ice, daily temperature standard deviation and temperature-dependent snow–rain fractionation of precipitation) to achieve the best possible fit with the observed present-day ice sheet thickness20 and balance velocity52 and to derive our intermediate maps of GF distribution and basal ice temperatures across north-central Greenland. At this stage we calibrate the GIS model component using an adaptive random search algorithm developed for optimization of nonlinear systems with many parameters54,55. To reduce the computation time, the main stages of the process have been parallelized following a strategy applied to the parameter search using coupled simulations with increasing horizontal (10–20 km) and temporal (1–10 yr) resolution, thereby gradually narrowing the permissible regions for each parameter. Here we use the following objective function to measure the goodness of the fit of the ice thickness (H) and ice speed (v) to the observations: where H(x, y) and Hobs(x, y) are the computed and observed ice thickness, v(x, y) and vobs(x, y) are the computed and balance ice speed, respectively, and S is the sum of squared non-dimensional residuals.

The fit is only evaluated where the present-day ice thickness exceeds 1.5 km (Hthresh = 1.5 km), as the focus of this study is on the inland areas where the GF is one of the major factors shaping subglacial thermal conditions. This also results in a minimal influence of the deficiencies of the shallow ice approximation on our choice of the general parameters of the ISM component56. Owing to the higher significance of the fit between the modelled and observed ice thickness for the reconstruction of basal ice temperatures in the targeted areas, unequal weights of WH = 0.78 and Wv = 0.22 have been empirically chosen for calibration.

Using this approach we calibrate model parameters that have the strongest influence on the modelled present-day ice thickness and ice flow pattern. Here we refrain from making assumptions about the spatial variability in parameters such as the basal sliding coefficients and ice flow enhancement factors as observational data are insufficient to support such assumptions at present. We therefore search for the best-fit single values of the relevant parameters within the ranges adopted from the existing literature that are commonly applied to the modelling of the large-scale characteristics of the GIS. The only exception is the daily temperature standard deviation parameter in the temperature-index method, which has recently been reported to be highly variable across Greenland57,58 and strongly dependent on the variations in surface temperature59,60. We have tested the performance of the two existing temperature-dependent parameterizations for the daily temperature standard deviation59,60 and concluded that the use of the latter parameterization60 over the Holocene period yields better results for the present-day GIS thickness. As the existing temperature-dependent parameterizations of the daily temperature standard deviation are inferred from the present-day observations and their applicability to glacial periods has not yet been demonstrated, our calibration strategy includes the search for a best-fit daily temperature standard deviation parameter in the period before the Holocene interglacial within the range of previously reported constant values. The ranges of tested parameter values (initial permissible regions) are provided in Supplementary Table 3.

Stage IV. After the calibration of the modelled ice thickness and ice velocity we evaluate the agreement between the model and available direct constraints from the ice sheet and bedrock (GF and ice core temperature measurements, basal melt locations from radar soundings and inland regions of high ice velocity, see Fig. 1 and Supplementary Tables 4 and 5) and outline the locations/areas that require corrections to the GF estimates. Again, we only use those constraints from the ice sheet that fall within the area with a present-day ice thickness greater than 1.5 km, for which the ISM parameters are calibrated at Stage III. In particular, this is done to exclude observational data falling within the zones where surface meltwater delivery to the ice sheet bed61 and ocean-induced variations in glacier dynamics and subglacial hydrology62 may have significant effects on the basal thermal regime of the present-day GIS. For the areas where the dynamic features are poorly captured after the calibration procedure at Stage III, we apply a fairly restrictive tuning method. In such areas local adjustments of the initial 1,300 °C isotherm depth are limited to a maximum correction of ±15% to the modelled Curie depth, which is within the range of anticipated errors in the estimates from the satellite magnetic data63. Owing to the diverse nature of available constraining data, the calibration process could not be fully automated. Across ice-covered areas, we have set up a correspondence between each direct constraint from the ice sheet and the modelled horizontal ice velocity within the grid cell where the constraint is located. For GF measurements from the bedrock the velocity value has been set to zero. The constraints have been sorted according to the corresponding velocity value to account for the growing influence of the horizontal advection on the thermal regime of the neighbouring areas towards the ice sheet margins. The calibration has therefore been organized starting from data points with minimal velocity values.

The GF estimates derived from Stage III are adjusted to fit the observations over each outlined area through successive perturbations to the preliminary map of the 1,300 °C isotherm depth from Stage II leading to local increases/decreases in subglacial heat flow, modelled basal ice temperature and vertical temperature gradients. The perturbations are performed across the neighbourhood of each data point representative of the resolution of the magnetic data17 used at Stage I. Following a simple under-relaxation procedure, only a fraction of the correction value necessary to fit each individual constraint is retained, depending on the ice flow velocity value within the grid cell where the correction was estimated: where α = (1 − v(x, y)/2vmax), vmax is the maximum absolute value of the horizontal ice flow velocity in the areas subject to corrections, and Dn(x, y) indicates the 1,300 °C isotherm depth, which is estimated to fit the surface constraint for the iteration n. Dn(x, y) and Dn−1(x, y) are the values of the 1,300 °C isotherm depths estimated after the application of an under-relaxation procedure for the iterations n and (n − 1). Overlapping corrections are combined using a weighted average, with the weights inversely proportional to the distances to the locations of the constraining data. The correction map is then smoothed using a low-pass filter. Stages II–IV are repeated until the process converges to the best-fit solution with all constraints using updated maps of 1,300 °C isotherm depths within individual threshold values established for each type of constraint.

The final series of simulations is run to introduce final adjustments at the locations where the smoothing procedure, or interference between perturbations over neighbouring areas, affected the fit with observations.

Stage V. At the last stage we infer the potential subglacial hydrology beneath the north-central GIS from the hydrology network calculated by ref. 3 using the hydraulic potential equation of ref. 64 and the approach of ref. 65 for routing subglacial meltwater over the hydraulic potential surface. We have superimposed these potential hydrological routes on the reconstructed basal ice temperature of the present-day GIS. Among them, the routes that fall within the areas of predicted basal ice melting have been selected as the most probable routes of now-active subglacial hydrology (shown by solid red curves in Fig. 3a). We have also retained the potential hydrological routes that fall within the areas with the ice base close to the pressure melting point (dashed red curves in Fig. 3a) where the presence of meltwater is probable but may not be retrieved by our model due to insufficient horizontal resolution that acts as a filter of high-frequency signals present in the original bedrock topography data set20.

Description of model constraints.

At Stage I we use estimates of Curie depths17 from satellite magnetic data and lithosphere thickness from seismic data18,51 to derive our initial 1,300 °C isotherm depths. The Curie depth map was inferred with a horizontal resolution of a few hundred kilometres and an uncertainty of about ±15% (ref. 63). The estimates of seismic lithosphere thickness are provided as average values over eight areas of variable size18 and along S–N profiles in central Greenland51. Most of the average values are derived across the areas with the dimensions of about 500 km (S–N direction) by 200 km (W–E direction).

At Stage III the model is calibrated versus ice thickness from radar soundings20 and balance ice velocity52. Ice thickness is provided with a horizontal resolution of 1 km (Supplementary Fig. 3), although this resolution may not locally be reached due to uneven distribution of radar measurements across Greenland20. The uncertainty in the observed ice thickness mostly exceeds 100 m, with the highest uncertainty of more than 150 m occurring in East Greenland and along the GIS margin20. Following the approach described in (ref. 52), we determine balance velocity by minimizing the difference between balance and observed surface speed, using accumulation and its associated uncertainty as a control variable. Its distribution is given on an unstructured grid densifying towards the areas of rapid flow, with an average horizontal resolution of 2 km. Balance, rather than observed velocity is used for its continuity around the ice divide and lack of noise in regions of low speed. To enable a one-to-one comparison between the modelled and observed fields, we have smoothed the observational fields by assigning an average value to each model grid cell.

At Stage IV we calibrate our model versus in situ measurements of basal ice temperature and GF and basal ice melt from radar soundings. The uncertainties in ice core measurements are low (for example, 0.0045 °C for GISP2; ref. 66), whereas GF estimates are probably less reliable, as most of the GF values have been derived from relatively shallow boreholes (<1 km depth) and have not been corrected for palaeoclimate signal42,67,68. To constrain the areas of melting beneath the GIS we use three data sets derived from ice-penetrating radar measurements1,2,3 (schematically shown in Fig. 1). The first data set1 comprises estimates of melt rates beneath the north-central GIS from an interpretation of the internal ice layering. To date, this is the only data set that includes quantitative analysis of basal melt rates across a large sector in Greenland. The estimated rates may be corrupted by the assumption of equilibrated climate conditions and simplified treatment of the horizontal flow1 but the inference of basal melt locations is relatively robust. The second data set2 hypothesizes the presence of subglacial water based on an empirical relation between relative reflection intensity and thawed/frozen interfaces69. Comparison of the first and second data sets across the area included in both studies reveals comparable large-scale patterns of basal melt, with local discrepancies in the predicted melt locations. This may be partly explained by high sensitivity of the method used in the second study to the uncertainties in the bed roughness2,69. In addition, the empirical relation uses a somewhat arbitrary threshold to distinguish between melting and frozen areas. Indeed, the authors admit that their inferred subglacial meltwater is not always consistent with ice core measurements (for example, subglacial meltwater is found in the vicinity of the Camp Century (CC) ice core where basal temperature of −13 °C has been measured, see Supplementary Table 4). The third data set3 is based on an analysis of the reflections in the radar soundings used to detect basal units of refrozen meltwater, which can be indirectly linked to subglacial melting in the vicinity of these areas. Although the exact locations of subglacial melt cannot be directly inferred from this data set, here we assume that the identified basal units are situated in a close proximity to the hypothesized subglacial melt (in the same grid cell). Over the overlapping areas we assign higher weights to the constraints from the first data set.

Code and data availability.

All data and the components of the coupled 3D ice sheet–lithosphere model are available in a digital form on request from (irogozhina@marum.de).

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Acknowledgements

This study is part of the multinational research initiative IceGeoHeat. We thank C. F. Maule for sharing the map of Curie depths with us and W. Chu and R. Bell for providing us with their modelled subglacial hydrology network. We also greatly appreciate the suggestions of A. Newton, T. Gerya and J. X. Mitrovica on how to improve the manuscript. This work was partly supported by Netherlands Research Centre for Integrated Solid Earth Sciences (grants ISES-NorMar-2.6 and ISES-UU-PC-cluster), the German Research Foundation (grant PE 2167/1-1) and the Federal Ministry of Education and Research, PalMod project.

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Affiliations

  1. Helmholtz Centre Potsdam GFZ German Research Centre For Geosciences, Potsdam 14473, Germany

    • Irina Rogozhina
    • , Alexey G. Petrunin
    • , Bernhard Steinberger
    • , Mikhail K. Kaban
    •  & Maik Thomas
  2. Center for Marine Environmental Sciences, University of Bremen, Bremen 28334, Germany

    • Irina Rogozhina
  3. Faculty of Earth Sciences, Goethe University, Frankfurt am Main 60438, Germany

    • Alexey G. Petrunin
  4. Schmidt Institute of Physics of the Earth, Moscow 123242, Russia

    • Alexey G. Petrunin
    •  & Mikhail K. Kaban
  5. Midland Valley Exploration Ltd, Glasgow G2 1RW, UK

    • Alan P. M. Vaughan
  6. Department of Geology, Trinity College, Dublin 2, Ireland

    • Alan P. M. Vaughan
  7. Centre for Earth Evolution and Dynamics (CEED), University of Oslo, Oslo 0315, Norway

    • Bernhard Steinberger
  8. Department of Computer Science, The University of Montana, Missoula, Montana 59812, USA

    • Jesse V. Johnson
  9. Potsdam Institute for Climate Impact Research (PIK), Potsdam 14473, Germany

    • Reinhard Calov
  10. Department of Earth Sciences, Utrecht University, 3508 TC Utrecht, The Netherlands

    • Florian Rickers
  11. Berlin Free University, Institute of Meteorology, Faculty of Geosciences, Berlin 12165, Germany

    • Maik Thomas
  12. Institute of Petroleum Geology and Geophysics, Novosibirsk 630090, Russia

    • Ivan Koulakov
  13. Geological Department, Novosibirsk State University, Novosibirsk 630090, Russia

    • Ivan Koulakov

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Contributions

I.R. developed the concept. I.R. and A.G.P. designed and performed all numerical experiments. I.R. and A.P.M.V. wrote the manuscript, with the assistance of A.G.P., B.S. and J.V.J. A.G.P. analysed the seismic tomography models provided by F.R. and I.K., prepared the map of crustal thickness, assembled the measured GF values from the continental shelf of Greenland and prepared and described the materials related to the model set-up and thermal state of the Greenland lithosphere. B.S. prepared and described the materials related to existing plume track reconstructions and contributed to the design of the Supplementary Information. J.V.J. tested the GF map using his high-resolution Greenland ice sheet model VarGlaS. M.K.K. performed the analysis of the observed gravity data. All authors contributed to discussions and interpretations of the results.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Irina Rogozhina.

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DOI

https://doi.org/10.1038/ngeo2689

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