We analyze the mean annual cycles of total (GRACE) and cumulative SMB
(RACMO2.3) mass anomalies over the period 2003–2013 (Fig. ).
To derive them, we divide the entire period into 11 overlapping 13-month
time intervals, each of which starts in December of the previous year and
ends in December of the current year. Then, the mean mass anomaly for each
calendar month is estimated by linear regression, together with one bias
parameter per time interval, which accounts for a long-term variability. This
scheme is less sensitive to gaps in data time series than the plain averaging
of mass anomalies per calendar month. For more details about this scheme, we
refer the reader to . The uncertainties of mean mass anomalies
from GRACE are propagated from errors in each monthly GRACE estimate. The
uncertainties of cumulative SMB mean mass anomalies are computed by assuming
9 % and 15 % errors in modeled mean mass anomalies due to precipitation
and runoff, respectively, as suggested by . The
uncertainties of the total–SMB residuals are the mean root sum square of the
standard deviations of noise in GRACE and cumulative SMB estimates.
The whole-Greenland mean annual cycles of total and cumulative SMB mass
anomalies present smooth month-to-month variations (Fig. ).
Importantly, the estimates of both types refer to the mean values for the
months considered. The total mass anomaly from GRACE reaches its maximum in
March and then steadily decreases until September. The most rapid monthly
mass loss is observed in July–August (∼200 Gt). In contrast, the
cumulative SMB decreases over a much shorter period – only from May to
August.
A simple method of quantifying short-term meltwater storage
The total–SMB residuals show some periods of almost null variations (nearly
flat segments in Fig. ): February–March, May–July, and
November–December. The total–SMB residuals represent the cumulative sum of
ice discharge, meltwater storage, GRACE errors, and SMB model biases. If we
assumed that the main contributor to the total–SMB residuals is ice
discharge, these nearly flat features would indicate that ice discharge is
negligible or even negative, which is unphysical, since this implies that
discharge is contributing to Greenland mass gain. Therefore, these features
should be explained either by meltwater storage or by errors in SMB- and
GRACE-based estimates. Based on the robustness analysis of the total–SMB
estimates in Appendix C, we infer that the quasi-null total–SMB
variations during February–March and November–December are likely caused by
noise in the estimates. In the following, therefore, they will not be
discussed. The summer flat feature of May–July, however, always persists, no
matter what data processing scenario is followed. Thereby, we suggest that it
is attributed to a physical signal, i.e., short-term meltwater storage.
Monthly variations of ice discharge of Jakobshavn Glacier over the
period 2009–2013 (Gt yr-1).
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Hereafter, we propose a simple method with which to elucidate and quantify short-term
meltwater storage. According to RACMO2.3, meltwater is mostly produced
between May and September, and peaks in July (cf. Fig. ).
Averaged over the GRACE period, approximately 800 Gt of meltwater is
produced on average in Greenland during the melt season from May to
September, of which ∼250 Gt is estimated to refreeze within the
snowpack, and the rest runs off of the ice sheet. RACMO2.3 does not calculate
lateral meltwater transport, i.e., the time lag between meltwater production
and the moment when the runoff reaches the ocean. During late spring and
early summer, this lag is particularly significant due to an inefficient
subglacial channelized network and replenishing of
firn aquifers (mainly in the SE and NW) .
In order to estimate the instantaneous amount of meltwater subject to runoff,
we first fit the total–SMB residuals in two periods, before and after the
flat feature (i.e., in April–May and September–November), with a linear
function. This function can be interpreted as an empirical estimation of the
mean combined effect of ice discharge and the difference between the modeled
meltwater refreezing and the actual one. Then, we force the mass budget at
the beginning and the end of the melt season to be closed by subtracting the
obtained linear function from the total–SMB residuals (Fig. ).
In this way, we find that meltwater is retained in Greenland between May and
October, with a 100±20 Gt maximum in July. Note that the estimates of
meltwater storage are sufficiently robust with respect to the choice of the
GRACE-based mascon solution, but they may vary in a small range in timing and
amplitude (Fig. ). The uncertainties of meltwater storage are
computed as the root sum square of the standard deviations of noise in GRACE-
and SMB-based estimates. It is worth mentioning that the error in the SMB
estimates is then computed assuming 9 % and 15 % errors in modeled
mean mass anomalies due to precipitation and runoff signals, respectively,
after applying the same linear regression function (see above) to each
component.
Estimates of non-SMB mass anomalies could reflect the delayed release of
meltwater into the ocean and the variability of ice discharge. We test the
effects of ice discharge variability using a monthly resolved data set of ice
discharge for 55 glaciers in Greenland (See Fig. ). These
glaciers are largely located in the NW and SE Greenland drainage systems,
which are the largest contributors of ice mass wastage into the ocean. The
sum of the obtained estimates over all 55 glaciers is shown in
Fig. a. One can see that at the whole-ice-sheet scale
the increase in ice discharge during the melt season is minor in all years
(∼10 % or less). In the absence of complete coverage of the GrIS with
observations of glacier velocities at the seasonal timescale, we compute a
scale factor as the ratio between the ice discharge estimates from 55
glaciers considered in this study and the discharge over the entire GrIS in
terms of the long-term linear trend by , and apply this
scale factor (i.e., ∼2) to the ice discharge estimate of each glacier.
Then, similar to Fig. , we represent the ice discharge related
mean mass anomaly per calendar month in terms of the deviation from the
linear function fitting the values in April–May and September–November (cf.
Fig. c). One can see that the effect of ice discharge
amounts to only a few gigatonnes; i.e., its contribution to the total signal
is negligible. This supports our hypothesis that that delayed runoff is
likely the major contributor to the signal isolated in Fig. .
Finally, we examine individual drainage systems (cf.
Figs. and ). We refrain from an
analysis of the SW and NE regions due to a relatively high level of noise in
the obtained meltwater storage estimates. Regionally, the SE shows the
largest meltwater accumulation per unit area. This is consistent with the
fact that the rate of meltwater production is large in the sector
(Fig. ), as is the storage potential owing to high
accumulation rates . In the N and NW regions, the signal
related to meltwater storage is less pronounced, which can be explained by
the dry climate of this region, meaning that less pore space is available in
the firn layer to store liquid water.
In terms of the total mass, the largest meltwater accumulation takes place in
the NW and SE regions: the contribution of each region may reach around
40 Gt in July–August (cf. Figs. and
).
As for the increase in ice discharge during the melt season, we find that it
is relatively minor for both NW and SE drainage systems (less than 20 % and
10 %, respectively; see Fig. ). As such, the
contribution of ice discharge to the signal reported in
Figs. and is minor for both
drainage systems: not more than 2.0±1.9 and 0.3±0.5 Gt,
respectively (cf. Fig. ). Interestingly, a much larger
increase in ice discharge during the melt season is found for the single
major contributor to ice discharge, Jakobshavn Glacier: up to 60 % in
2012 (Fig. ). This finding is consistent with that of
.
Note that the meltwater storage signal at the drainage system scale is
present in all GRACE mascon solutions but shows some discrepancies in the
timing and amplitude. This means that further effort is still needed to
improve the accuracy of GRACE-based estimates.