Basal hydrology of the Greenland Ice Sheet (GIS) influences its dynamics and
mass balance through basal lubrication and ice–bed decoupling or efficient
water removal and ice–bed coupling. Variations in subglacial water pressure
through the seasonal evolution of the subglacial hydrological system help
control ice velocity. Near the ice sheet margin, large basal conduits are
melted by the viscous heat dissipation (VHD) from surface runoff routed to
the bed. These conduits may lead to efficient drainage systems that lower
subglacial water pressure, increase basal effective stress, and reduce ice
velocity. In this study we quantify the energy available for VHD
historically at present and under future climate scenarios. At present,
345 km
Numerical models and observations of the Greenland Ice Sheet (GIS) link
surface meltwater penetration to the bed to both short (hourly, daily) and
long (seasonal, decadal) temporal variations in ice velocity
Early in the melt season water is added to the subglacial system but cannot
be efficiently removed, increasing subglacial water pressures and ice
velocities. Later in the melt season, increased runoff causes efficient
drainage conduits to form, at least near the ice sheet margin. These large
drainage conduits reduce the subglacial water pressure and ice velocity
Studies examining surface melt, supraglacial routing, subglacial hydrology,
and the response of ice sheet outlet glaciers to those various inputs take
place predominantly in southwest Greenland, focusing largely on the Russell,
Leverett, Paakitsoq, or nearby glaciers (for example,
Here we perform a broader analysis that uses runoff over the entire GIS on
annual and decade timescales and discuss changes between a historical
baseline and the present and between the present and future RCP4.5 and 8.5
scenarios. We employ flow routing to distribute the surface meltwater under
the GIS following the common assumption of subglacial water pressure
distribution being determined by local ice weight, and we track the available
energy at the bed as water runs down the hydropotential, accounting for the
water and ice phase transition temperature (PTT) variations due to changes in
pressure. We frame the discussion in terms of changes in available power (Watts)
rather than focusing on water pressure in a conduit relative to
overhead ice pressure. We report both the total GIS-wide energy budgets, and
its distribution per basin and at a 5 km
We use 150 m resolution basal topography and surface topography (IceBridge
BedMachine Greenland, version 2) from
We report results for a historical period (1960–1999), the present (2010–2019),
and IPCC AR5 RCPs 4.5, and 8.5 (2090–2099)
We process the entire GIS at 5 km resolution, the area near Petermann Glacier at 150 m resolution, and part of West Greenland (near the Russell and Leverett glaciers) at 150 m resolution, where we extract the sample flow line segment.
We use a flow routing and energy balance model that incorporates common
assumptions about glacier hydrology (e.g.,
In most cases we assume all surface runoff that begins at elevations above
2000 m is unable to leave the surface or penetrate to the bed at those
elevations
Water storage may occur in firn or in crevasses. We assume these volumes are insignificant (at most a few percent) relative to the total runoff amount, that their relative importance is not likely to change much in the future, and that englacial storage does not release heat at the bed, which is the focus of this study.
Once at the bed, flow routing moves water down the gradient of the
hydropotential
The total hydropotential can be decomposed into an elevation term,
The water remains at the pressure-dependent PTT and energy is released based
on the change in hydropotential combined with the changing PTT. Because our
focus is on energy available at the glacier bed, we ignore heat released due
to changing PTT down the moulin (e.g.,
Our energy budget model tracks energy between inputs at the ice sheet bed where energy begins as either pressure or gravitational potential energy (which may be net positive if the source bed elevation is above the discharge elevation or negative if it is below) and the output where the energy is in one of three forms: (1) the latent heat of cumulative basal melt caused by VHD released along the subglacial water flow pathway, (2) gravitational potential energy of discharge from land-terminating glaciers with termini above sea level, or (3) pressure if discharged below sea level from a marine-terminating glacier.
Accumulation of subglacial water flowing through each grid cell.
Results are presented on a 5 km
Properties of Greenland runoff and viscous heat dissipation.
Historical (H)
period covers 1960–1999, present spans (P) 2010–2019, and the RCPs 4.5 and 8.5
periods span 2090–2099. Column 8.5
Between the input and discharge locations, all energy is assumed to dissipate
at the base as heat within the grid cell where the energy transfer occurs
This model is driven by surface runoff, but it includes flow routing at the bed, heat released due to either a gravitational potential energy drop or a pressure drop, and tracks the spatially varying PTT. However, this model does not directly represent conduits or track changing basal water pressures. This is because the results are presented on decade average timescales, while conduits and water pressures vary on hourly to seasonal timescales.
We compare our results to those of
As mentioned in Sect.
It is important to note that while TB may match the baseline data from
Annual average runoff volume has historically been 244 km
Flow routing of basal hydrology causes orders of magnitude difference in
water volume over small spatial distances as streams collect and discharge
the water. At present, the largest volume of discharge is
Net hydropotential gradient for each cell (
The zone around Greenland with active subglacial flow has distinct regions
where the flow is driven by changes in elevation (Fig.
Large differences in released heat (
A spatial map of basal VHD is shown in Fig.
At present a maximum up to
Heat released at the bed due to VHD. Labels are the same as in
Fig.
Change in GW (10
In some regions, heating is “negative”, which indicates basal freeze-on. These
regions are a subset of the regions where flow is uphill (blue
Basin-scale changes between the different time periods considered here
are well illustrated when viewed as change in VHD per basin (Fig.
Relative change in VHD per basin highlighting the impact of
different averaging periods. P/H is 100
The difference between the
Percent increase between historical and present become larger with latitude.
All of Greenland has experienced an increase, with many regions showing a
2- to 3-fold increase (
However, the choice of baseline matters. The historical and present periods
are 1960–1999 and 2010–2019 respectively. If the TR (1985–1994) and
TB (2007–2014) periods are used instead, our results approximate the
results from
Detail along a flow line in southwest Greenland.
Closeup of Petermann Glacier region at 150 m resolution. Gray
base map is shaded relief of hydropotential gradient. Blue dots and black
lines are locations of basal freeze-on predicted by the model and from
Viewing results along a flow line highlights that the hydropotential gradient
driving the flow becomes larger and more variable toward the margin
(Fig.
Frictional basal heating is up to 0.2 W m
When discussing subglacial hydrology, a simplification can be made that water decreases basal friction and leads to faster ice sliding but VHD leads to conduit formation, reduced subglacial water pressures, and slower ice sliding. However, because VHD is generated by water flow, some condition is needed to define which behavior is dominant in a given setting.
Near the margin, steep hydropotential gradients (Fig.
Existing observations support the above hypothesis. The marginal zone ice
response to VHD has been well studied and observed in the southwest sector,
where the summer increase in runoff is correlated with reduced glacier
velocities
As the climate warms in the future an increase in the supply of surface
runoff to the bed will lead to an increase in subglacial VHD. We predict a
5-to-7-times increase in VHD by the end of the century under RCP8.5. The
impact of this increase is uncertain. This is because other results show that
glaciers can either increase
In the southwest sector,
An increase in the interior ice velocity and a decrease in marginal velocity
suggests that surface slopes and driving stresses will change, a result
confirmed by
Compared to the southwest sector the 2000 m contour (used here as an
approximate boundary that defines where water accesses the bed) creates a
much wider zone of active basal hydrology in the northeast and a much
narrower zone in the southeast (Fig.
A threshold of a 50 % increase in runoff has been identified by
Under the RCP4.5 scenario, nearly every basin will experience a 0.05 GW
increase in VHD, with many gaining
Future runoff and VHD will be distributed over a longer part of a year
relative to the present since climate warming prolongs the melt season in
Greenland
When VHD occurs in new locations at the GIS bed it may convert a frozen bed
to temperate and increase ice sliding
Not all of the incoming energy is converted to VHD and used to melt conduits,
warm the basal ice, or warm the bed. The primary use of energy other than VHD
is change in heat content of the water itself, which needs to compensate for
the spatially changing PTT. Classic glacier theory (i.e.,
Our results show that different sectors may experience large changes in VHD
relative to each other due to changes in the PTT. In practice, losses near
35 % occur often – whenever elevation change across a grid cell is close
to 0, and flow is driven primarily by a pressure gradient (Fig.
There are some disagreements in the location of basal freeze-on between our
model and
It seems likely that part of the cause for the disagreement between our model
results and
GHF is expected to be more spatially uniform than VHD, at least near the
margin where conduits concentrate the flow. GHF is temporally more steady
than VHD, which primarily occurs when surface melt is active. Nonetheless, it
is worth comparing the magnitude and distribution of the two. Historically
the total VHD of 46 GW under the runoff area was similar to the total GHF of
35 GW in that same area. That is no longer the case in our calculations for
the recent time period and, although GHF flux does not change, the integrated
amount does change because the area of integration changes. By the end of
this century under RCP8.5, VHD will contribute 310 GW but GHF only increases
to 44 GW due to a slight increase in the runoff area that reaches the bed,
when surface runoff is routed to 2000 m elevation before moving to the bed.
If the 2000 m limit is removed, then under the RCP8.5 scenario the area of
runoff nearly doubles in size (Fig.
VHD and GHF comparisons and relative changes between present and future are
most likely to matter in the region
VHD dominates other basal heating terms considered in some glaciological
models (for example,
Large amounts of eroded material are also flushed out from under the GIS each
year
In addition to the various limitations to this model discussed throughout the
text, here we address the limits of the spatial resolution. The model
resolution is a 5 km
Our treatment of englacial and subglacial hydrology is simplified because it does
not represent actual conduits but is at the same time more comprehensive
than in existing global climate or ice sheet models (e.g.,
The high potential energy contained in large volumes of GIS surface meltwater
is mostly dissipated as heat at the ice sheet bed. This dissipated energy
averaged 46 GW each year between 1960 and 1999 but has recently increased to
66 GW and will likely increase to 110 or 310 GW by the end of the century
under RCP4.5 or 8.5 respectively. This VHD by
subglacial water is the dominant basal heat source near the margin, and its
impact will move inland due to increasing flux, even if conduits do not form
in the interior. Under RCP8.5, VHD will be about 7 times larger than the
44 GW contributed by geothermal heat flux to the same area. That may decrease
to 4 times larger if runoff penetrates to the bed at elevations
Up to 7 times additional future VHD at the ice sheet bed (relative to the historical amount) should result in a similar 7-fold increase in basal ice melt volume and is expected to contribute to more numerous, larger, longer-lasting, and more widespread subglacial conduits in the margin zone. Based on recent measurements by others and glaciological theory of ice sliding, increased VHD may decrease glacier velocity at the margin and accelerate it in the interior where conduits either do not form or have insufficient impact on subglacial water pressures to influence ice sliding rates. The marginal decrease may be offset by other processes and there may still be a net acceleration, especially at marine-terminating glaciers.
Data used in this work are available from first principles because all code used
in this work is provided in the Supplement (see Appendix A). Alternatively,
processed data can be accessed via
This paper is prepared with the intent to create a “fully reproducible”
scientific publication. We may not have completely succeeded, but we have made
progress in this direction. In order to be fully reproducible at the
binary level, a clone of our operating system with the full analysis software
should be provided. This could be done with a virtual machine (VM), but we
have not taken this step because VMs require
Instead, we used only free and open-source software above the operating
system level, document in detail the version(s) of all software packages
used, and provide every line of code required to reproduce the document,
beginning with the commands to download the MAR
The supplementary data are in a plain-text file that contains the paper text
and all of the code. As plain text, it can be viewed in any editor or
document viewer. However, its internal structure is that of an Emacs Org Mode
The authors declare that they have no conflict of interest.
We thank D. van As for initial discussions on this topic, M. Morlighem and X. Fettweis for providing accessible and documented data, R. Bell for sharing data, and D. Pollard, anonymous referees, and The Cryosphere Discussion reviewers for comments. Kenneth D. Mankoff was funded by NASA Headquarters under the NASA Earth and Space Science Fellowship Program (Grant NNX10AN83H) and the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, with funding provided by the Ocean and Climate Change Institute. Slawek M. Tulaczyk was funded by NASA grant NNX11AH61G. Edited by: O. Gagliardini Reviewed by: three anonymous referees