Introduction
Since the early 1990s, the Greenland ice sheet (GrIS) has been losing mass
and is currently one of the largest
individual contributors to global sea level rise . During
this period, the partitioning of the mass loss between decreasing surface
mass balance (SMB) and increasing ice discharge has shifted from close to
50/50 between 2000 and 2005 to runoff dominating the GrIS mass loss over the
last decade . It is likely that this trend
will continue in a warming climate, making it of vital importance to
model the GrIS SMB correctly.
A key process in GrIS SMB is the retention of liquid water input (surface
meltwater and rainfall) that mitigates the amount of runoff by either
refreezing or storing liquid water in the GrIS firn layer. Recently, some
features have been discovered that enhance our understanding of meltwater
retention: water is stored year-round in firn aquifers
; and partly impermeable ice lenses cause
lateral transport of water while the underlying firn column remains
unsaturated . Currently, about 45 % of the liquid water
input is estimated to be retained .
With the firn densification model IMAU-FDM,
simulate the temporal evolution (1960–2014) of the GrIS firn layer. Using
density observations from firn cores to evaluate the simulation, they found
that model performance in the interior was good, but that the agreement
deteriorated with increasing melt rates. Two possibilities for this mismatch
were suggested: (1) a representation of liquid water processes
in IMAU-FDM that was too simplistic or (2) errors in the atmospheric forcing from the regional climate
model (RACMO2.3, ). The availability of an updated
atmospheric forcing (RACMO2.3p2, ) allows us to investigate
the impact of the latter. This RACMO2 update resulted in significantly more
accumulation inland and less surface melt ice-sheet wide, improving agreement
with SMB observations in both the accumulation and ablation zone
. Since accumulation and surface melt are defining climate
variables for the state of the firn, it is expected that the new atmospheric
forcing has a marked effect on the simulated GrIS firn layer. Here, we
present the new IMAU-FDM simulation and evaluate it using firn density and
temperature observations.
Methods and Data
IMAU-FDM
A detailed description of the firn densification model IMAU-FDM is available
in previous publications
and will only be
briefly summarized here. IMAU-FDM simulates the time evolution of firn
density, temperature, liquid water content, and surface elevation in a 1-D
column, forced at the surface by sub-daily (3- or 6-hourly) atmospheric
output from the regional climate model RACMO2 (see below). Firn compaction is
calculated using the densification equations of , with
region-specific additions for Antarctica and
Greenland . Liquid water from rain or surface melt
can percolate into the firn using a tipping-bucket model approach, where it
is either refrozen or stored depending on firn temperature and pore space. An
equilibrium initial firn column is obtained by looping over the 1960–1979
climate until the entire firn column is fully refreshed
. After this spin-up, the transient simulation run
starts. The IMAU-FDM simulations forced with RACMO2.3 (FDM2.3 hereafter) and
RACMO2.3p2 (FDM2.3p2 hereafter) cover 1960–2014 and 1960–2016,
respectively.
RACMO2 forcing
The atmospheric forcing of IMAU-FDM is provided by the regional climate model
RACMO2 , of which output of versions v2.3 and v2.3p2
are used here. Forcing consists of prescribing various SMB components (solid
and liquid precipitation, surface and drifting snow sublimation, drifting
snow erosion, and surface melt), surface temperature (Ts), and 10 m wind
speed on the native 11 km RACMO2 grid. RACMO2.3p2
is the updated version of RACMO2.3
and includes several changes: updated glacier outlines,
topography and ice albedo fields; tuned cloud scheme parameters that increase
precipitation towards the GrIS interior, correcting the underestimation of
inland accumulation in RACMO2.3; modified snow properties, i.e. lower soot
concentration and smaller grain size of refrozen snow that significantly
reduce melt production in the percolation zone. For the firn simulations, the
most important changes are that inland precipitation on the GrIS
(i.e. accumulation area) increases by 5–10 %, whereas surface melt along the
margins is significantly reduced, by up to 50 %, leading to a higher ice-sheet
integrated SMB at 11 km horizontal resolution. Statistical downscaling to
1 km resolution provides a better representation of runoff on low-elevation
outlet glaciers and in narrow ablation zones. As a result, the downscaled SMB
agrees better with in situ and basin-scale SMB observations
. Here, the 11 km data was used as it is computationally not
feasible to use the 1 km data.
Firn observations
Model output from IMAU-FDM is evaluated using firn density and temperature
observations from across the GrIS. Vertical profiles of firn density are
compared to 62 firn cores of varying depth (8–120 m) and with locations
distributed over the GrIS, although the drier northeast is slightly
under-represented. See Fig. 2 in for core names
and locations, which cover a wide range of melt and accumulation conditions
found on the GrIS. Furthermore, deep-firn temperatures (at 10 m depth,
T10m) in combination with firn density observations along a transect in
western Greenland are used to analyse the
differences in the percolation zone in more detail. The firn air content
(FAC) is used as an integrated measure for the amount of pore space present
in a firn column and is defined as the vertically integrated difference of the
firn density and the ice density (taken to be 917 kg m-3). In
IMAU-FDM, all simulated firn layers extend to below the depth at which the
ice density is reached, resulting in modelled FAC to represent the full firn
column.
Evaluation of simulated firn density: (a) modelled vs. observed firn
air content for FDM2.3 (open circles) and FDM2.3p2 (closed circles) at 62
firn core locations on the GrIS; (b–f) vertical firn density profiles of
five
selected cores (black), FDM2.3 simulation (red), and FDM2.3p2 simulation
(blue). The colours in (a) represent the melt-accumulation ratio of the core
location, where green, blue, and red colours indicate the three categories as
specified in Sect. 3. In (b–f), the core name and date (black print) is
provided, as well as the 1990–2009 average accumulation (“Acc” in
mm w.e. yr-1), 1990–2009 average surface melt (“Me” in
mm w.e. yr-1), and the 1990–2009 melt-accumulation ratio (RMA,
unitless) as simulated by RACMO2.3 (red print) and RACMO2.3p2 (blue print).
Core names and locations can be found in Fig. a.
Results
Figure shows how FDM2.3p2 generally improves the simulated
density profiles, compared to FDM2.3. The firn core locations can be
separated into three categories based on the melt-accumulation ratio
(RMA): (1) the dry snow zone (RMA < 0.05), (2) locations that
experience moderate melt (RMA between 0.05–0.5), and (3) high melt
locations (RMA > 0.5). In the first and third category only small
differences are noted; the biggest improvements are found in the second
category.
For the dry snow zone (example in Fig. b), the higher
accumulation rates in RACMO2.3p2 result in slightly higher compaction rates
and therefore denser firn in FDM2.3p2. Overall, the agreement with observed
FAC in the dry snow zone is slightly worse for FDM2.3p2 (r2=0.98 and
RMSE = 1.08 m) than for FDM2.3 (r2=0.98 and RMSE = 0.88 m) for
all cores combined. This is no surprise, however, as
used the vertical density profiles of locations
with RMA < 0.05 to introduce a correction factor for the densification
equations. For comparison purposes, we chose to not repeat this calibration
procedure here, leading to a slight overestimation of density in the dry snow
zone.
For locations with moderate melt (Fig. c–f), both r2
(0.87 to 0.92) and RMSE (2.81 to 1.70 m) show a significant improvement
from FDM2.3 to FDM2.3p2. This is mainly caused by the surface melt reduction
in the RACMO2.3p2 forcing, resulting in less meltwater refreezing and
therefore less dense firn columns. In Fig. a, the open
circles show the underestimation of FAC in FDM2.3, which is much improved in
FDM2.3p2 (closed circles). Another reason for denser firn columns in FDM2.3
is an artefact in the temperature dependent part of the densification
equation reported previously by . In this equation, the
firn densification rate is overestimated when the vertically integrated
temperature far exceeds the average surface temperature. In Greenland, this
led to unrealistically high densification rates in the percolation zone and
subsequently too low FAC. In FDM2.3p2, this artefact was solved by replacing
the average surface temperature in the densification equation with the
temperature of the lowest model layer to account for the additional latent
heat of refrozen water.
Evaluation of simulated firn air content and 10 m firn temperature
with observations along a transect in the western Greenland (region indicated in
Fig. b) percolation zone: (a–b) 1990–2009 melt-accumulation
ratio (RMA) as simulated by RACMO2, (c–d) upper 10 m firn air content as
simulated by IMAU-FDM (shaded grid cells) and from firn core observation
(circles, ); (e–f) average 10 m firn temperature as
simulated by IMAU-FDM (shaded grid cells) and from thermistor string
measurements (circles, ). The figures in (a–b) represent
RACMO2.3 and RACMO2.3p2, while (c) and (e) and (d) and (f) represent FDM2.3 and FDM2.3p2,
respectively. Blue lines in (a–b) indicate the firn line (FL), chosen to be
equal to RMA = 0.7. Firn core observations in (c–d) are from July 2007
or May 2008 and the simulated field is an average of these two dates. Both
the simulated and observed firn temperatures in (e–f) are averages over
2007–2009.
For the
category “locations with RMA > 0.5”, both IMAU-FDM
simulations underestimate observed FAC (Fig. a). The
simulated FAC of ∼ 0.5 m is typical for the model ablation zone at the
end of winter, i.e. bare ice covered by a winter snow layer, while the
observations suggest that firn of multiple years should be present with FAC
varying between 1–4 m. This underestimation in FAC could be caused by
remaining biases in atmospheric forcing or processes that are currently not
represented in IMAU-FDM (see below). Theory confirms that a firn layer should
be present for RMA as large as ∼ 0.7 .
Figures and confirm that the largest
differences between FDM2.3 and FDM2.3p2 are found in the percolation zone of
the GrIS. Along a transect in the percolation zone of the western GrIS
, it is clear that the firn line (FL, defined as
RMA = 0.7) is simulated further downslope in FDM2.3p2 (Fig. a–d).
From observed FAC, the FL is located around
48.7∘ W, which is almost matched by FDM2.3p2 (∼48.3∘ W),
while FDM2.3 simulates the area where no firn is present up to
∼47.5∘ W (30 km further inland). Due to the reduction of surface
melt in FDM2.3p2, a firn layer is formed at lower elevations. Quantitatively,
FAC as simulated by FDM2.3p2 (r2 = 0.71 and RMSE = 1.64 m)
also shows much better agreement than in FDM2.3 (r2 = 0.40 and
RMSE = 2.83 m).
Firn air content (FAC) and 10 m temperature (T10m) as simulated
by the IMAU-FDM: (a) FAC as simulated by FDM2.3; (b) FAC as simulated by
FDM2.3p2; (c) the difference in FAC (FDM2.3p2 minus FDM2.3); panels (d–f) are similar
to panels
(a–c) only for T10m instead of FAC. Locations in (a) indicate the
cores used in Fig. b–f, while the box in (b) indicates the region
used in Fig. .
The remaining discrepancy between the observations and FDM2.3p2, especially
for RMA > 0.5 (Fig. a), is likely caused by how
IMAU-FDM treats the vertical transport of liquid water. Currently, a
“tipping-bucket” method is used, assuming that water can only run off if both
cold content and pore space are unavailable. However, from observations it is
found that through heterogeneous percolation and/or
impermeable ice lenses , water can run off before all
cold content or pore space is used.
Firn temperature is another useful metric to evaluate the performance of
IMAU-FDM, especially in locations with substantial surface melt. The amount
and depth of refreezing to a large extent determines how much heat is stored
in the firn column, i.e. how much T10m deviates from Ts. FDM2.3p2
(r2 = 0.39 and RMSE = 3.55 ∘C) shows much improved agreement
over FDM2.3 (r2 = 0.01 and RMSE = 6.57 ∘C) for observed
T10m (Fig. e–f). For the eastern firn cores,
realistic firn columns are simulated by both FDM2.3 and FDM2.3p2 with similar
deep-firn temperatures as observed. Further west, FDM2.3 simulates lower
temperatures than observed, indicating the absence of a firn layer that can
store the heat released by refreezing. In FDM2.3p2, a band of higher firn
temperatures (around -4 ∘C) is simulated upslope of the FL, in good
agreement with observed temperatures.
When the differences between FDM2.3 and FDM2.3p2 across the entire GrIS are
considered (Fig. ), a clear pattern emerges. The largest
differences in both FAC and T10m are located in the percolation zone of
the GrIS and are dominated by the decrease in meltwater refreezing. This
results in a FAC increase of 5–15 m and a downslope migration of the
T10m-band of high temperatures. In the higher elevation regions of the
percolation zone, T10m dropped by 2–4 ∘C due to the decrease in
surface melt and subsequent refreezing and latent heat release, while in the
lower percolation zone the presence of a simulated firn layer in FDM2.3p2
results in much higher T10m. The largest differences are found in
southeast Greenland, where the influence of the previously mentioned
temperature artefact in the densification equation is also significant as the
firn is close to freezing in these firn-aquifer areas. Solving this issue
resulted in lower densification rates and therefore thicker firn layers
(i.e. high FAC) that are able to store the liquid water year-round as deep firn
temperatures are at the freezing point (Fig. e). The extent of
the firn aquifer is therefore greatly improved in FDM2.3p2 (not shown),
compared to the results presented in .
In the ice sheet interior, the differences between FDM2.3 and FDM2.3p2 are a
direct consequence of the atmospheric forcing: the increased accumulation
results in faster densification and 2–3 m lower FAC, while the T10m
increase is almost identical in magnitude and spatial pattern to the increase
in T2m from RACMO2.3 to RACMO2.3p2 (not shown). The lowest regions of
the GrIS show no differences in FAC, as it is an ablation area in both model
simulations. However, for T10m, FDM2.3p2 simulates 1–2 ∘C higher
temperatures in the ablation zone, caused by a shorter presence of bare ice
at the surface (i.e. increased insulating effect of a snow/firn layer). Over
1990–2009, FDM2.3p2 simulates 20 days yr-1 (25 %) less bare-ice
exposure than FDM2.3. Averaged over the entire GrIS (using only grid cells
that are present in both FDM2.3 and FDM2.3p2), the T10m difference is
+0.94 ∘C and the FAC difference is +1.13 m (8 %). The latter
corresponds to a volume difference of roughly 2000 km3 and is
equivalent to 11 years of meltwater storage at the 1960–1990 refreezing
rate.