TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-12-3813-2018Seasonal to decadal variability in ice discharge from the Greenland
Ice SheetSeasonal variability of Greenland glaciersKingMichalea D.michaleaking@gmail.comHowatIan M.JeongSeongsuhttps://orcid.org/0000-0002-6844-5925NohMyoung J.WoutersBertNoëlBricevan den BroekeMichiel R.https://orcid.org/0000-0003-4662-7565Byrd Polar and Climate Research Center, Columbus, USASchool of Earth Sciences, Ohio State University, Columbus, USADepartment of Earth System Science, University of California, IrvineInstitute for Marine and Atmospheric research Utrecht, Utrecht University, Utrecht, the NetherlandsFaculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, the NetherlandsMichalea D. King (michaleaking@gmail.com)3December201812123813382527August201810September201814November201818November2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://tc.copernicus.org/articles/12/3813/2018/tc-12-3813-2018.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/12/3813/2018/tc-12-3813-2018.pdf
Rapid changes in thickness and velocity have been
observed at many marine-terminating glaciers in Greenland, impacting the
volume of ice they export, or discharge, from the ice sheet. While annual
estimates of ice-sheet-wide discharge have been previously derived,
higher-resolution records are required to fully constrain the temporal
response of these glaciers to various climatic and mechanical drivers that
vary in sub-annual scales. Here we sample outlet glaciers wider than 1 km
(N=230) to derive the first continuous, ice-sheet-wide record of total ice
sheet discharge for the 2000–2016 period, resolving a seasonal variability
of 6 %. The amplitude of seasonality varies spatially across the ice
sheet from 5 % in the southeastern region to 9 % in the northwest
region. We analyze seasonal to annual variability in the discharge time
series with respect to both modeled meltwater runoff, obtained from
RACMO2.3p2, and glacier front position changes over the same period. We find
that year-to-year changes in total ice sheet discharge are related to annual
front changes (r2=0.59, p=10-4) and that the annual
magnitude of discharge is closely related to cumulative front position
changes (r2=0.79), which show a net retreat of >400 km,
or an average retreat of >2 km, at each surveyed glacier. Neither
maximum seasonal runoff or annual runoff totals are correlated to annual
discharge, which suggests that larger annual quantities of runoff do not
relate to increased annual discharge. Discharge and runoff, however, follow
similar patterns of seasonal variability with near-coincident periods of
acceleration and seasonal maxima. These results suggest that changes in
glacier front position drive secular trends in discharge, whereas the impact
of runoff is likely limited to the summer months when observed seasonal
variations are substantially controlled by the timing of meltwater input.
Introduction
Mass loss from the Greenland Ice Sheet (GrIS) is now the single largest
cause of sea level rise (Vaughan et al., 2013; Box and Sharp, 2017), contributing
approximately 1 mm a-1 of global water equivalent over the 2010–2015
period (van den Broeke et al., 2016). Since the mid 1990s, the GrIS has been
losing ice at an increasing rate (Rignot et al., 2011; Sasgen et al., 2012;
Hanna et al., 2013; Enderlin et al., 2014) due in part to increased discharge
from marine-terminating outlet glaciers (Rignot and Kanagaratnam, 2006;
Rignot et al., 2008; Enderlin et al., 2014; Andersen et al.,
2015). Substantial
increases in ice discharge are observed at large outlet glaciers over
periods of months or less (e.g. Joughin et al., 2004; Howat et al., 2005),
demonstrating short-term sensitivity to external drivers, such as ocean
circulation (Straneo and Heimbach, 2013; Walsh et al., 2012), melt runoff
(Joughin et al., 2008; Andersen et al., 2011), and sea ice–mélange conditions near the
calving front (Howat et al., 2010; Carr et al., 2013; Moon et al., 2015;
Bendtsen et al., 2017). Thus, understanding the dynamics of these glaciers
requires measurements with a high temporal resolution.
Seasonal variability in the flow speed of marine-terminating glaciers in
Greenland has been observed for small samples of glaciers
(Howat et al., 2010, 2011; Hill et al., 2018) and for larger glacier
inventories over short time periods (Howat et al., 2008; Moon et al., 2014,
2015). Previous ice-sheet-wide estimates of discharge were
largely based on summertime velocities and, therefore, may be biased toward
higher values, demonstrating the need for decadal records of ice-sheet-wide
discharge that resolve seasonal to sub-monthly variability, potentially
associated with surface meltwater runoff and calving. Here we present the
first continuous record of daily estimates of net ice sheet discharge,
derived over the 2000–2016 period. This record is used to resolve both
distinct ice-sheet-wide and regional patterns of seasonal variability and
evaluate how seasonality has changed through time. We then compare these
records to modeled meltwater runoff data and records of glacier front
positions to assess how these terms impact discharge on seasonal to annual
timescales.
Data and methods
Following Howat et al. (2011), we derive time series of the rate of solid
ice discharge (D) for 230 glaciers (Fig. S4 in the Supplement) with widths greater than 1 km
by integrating the product of glacier thickness, ice velocity, and ice
density across the glacier width at the grounded terminus. Observations are
sampled along a static profile, i.e., fluxgate, oriented perpendicular to the
direction of flow and located upstream of the grounding line, immediately
inland of the most retreated grounding line during the 2000–2016 study
period. We use the same flux gates as Howat et al. (2011) and Enderlin et al. (2014)
except in cases in which the grounding line had retreated inland of
the gate location. Further, while Enderlin et al. (2014) used empirical
relationships to estimate cross-sectional area and discharge at glaciers for
which only along-flow profiles or no bed topography were available, we use
the BedMachine version 3 gridded bed topography dataset (Morlighem et al., 2017),
which uses ice thickness, flow speed observations, and surface mass
balance (SMB, i.e., the sum of the mass gained from accumulation and lost due
to meltwater runoff, sublimation, and snow drift erosion) to constrain a mass
conservation model. As in prior studies, we assume that changes in the
elevation of the glacier bed, due to erosion, deposition, and/or lithosphere
displacement, are small, as are variations in ice flow velocity with depth
in fast-flowing (>1 km a-1) glaciers. Bed topographic
errors across our sampled flux gates average 70±52 m. Thus,
discharge is estimated from the bed topography and repeat measurements of
surface elevation, the difference of which provides the time-variable ice
thickness, and ice flow velocity. Additional information regarding the
placement of flux gates and descriptions of the datasets is provided in the
Supplement.
Enderlin et al. (2014) derived annual discharge estimates from velocity data
that were mostly collected between April and September. Increased data
collection by synthetic aperture radar (SAR) sensors
(TerraSAR-X and TanDEM-X), low-light level functionality
of Landsat 8 (Jeong and Howat, 2015; Fahnestock et al., 2016), and increased
sampling density using image pairs between multiple sensors and/or acquired
from crossing orbital tracks (Rosenau et al., 2015; Jeong et al., 2017)
enable substantially better temporal resolution than available for Enderlin
et al. (2014). Thus, we combine this increased velocity sampling with a
Kalman filter approach to estimate D and its uncertainty as a continuous
series. For each glacier, we first derive a standard seasonality curve by
detrending the time series of monthly mean speeds and grouping mean speeds
by the month of year, so that a 17-year time series would provide up to 17
estimates of mean speed for a given month. The standard seasonality is then
obtained from the median value and covariance of the observations for each
month and represents a “typical” pattern of change at each respective
glacier. Months with fewer available observations will therefore tend to
have a higher range of uncertainty. If no optical or radar data exist for a
particular month throughout the time series, a standard monthly value is
estimated by fitting a periodic function to the available monthly median
values. The periodicity described here does not indicate that a symmetric,
sinusoidal seasonality is assumed, but rather that by detrending the time
series and isolating a mean seasonal pattern of change, we expect the
endpoints of the curve to be the same (i.e., the 12-month curve would
repeat). The seasonality curve is then normalized to yield an estimate of
fractional change in speed between months, which informs a simple linear
model. Within the Kalman filter framework, this linear model assimilates the
observations to optimize estimates for missing months of the time series,
with the errors equal to the combination of the observation and prediction
errors. Uncertainty in the seasonality curves tends to exceed observational
errors, resulting in formal errors that increase with distance from the
observations. A more detailed description of this approach is provided in
the Supplement. Velocity measurements for the four northernmost
glaciers (Steensby, C.H. Ostenfeld, Academy, and Hagen Brae) and several
small glaciers near the central eastern margin were too sparse to derive a
continuous time series and we instead estimate an annual D for these
glaciers. This data sparsity occurs when months of missing data exceed the
number of months containing reliable observations after filtering, preventing
a resolvable seasonality.
We use the same repeat ice surface elevation dataset as Enderlin et al. (2014),
extended through 2016, and with the addition of stereoscopic digital
elevation models produced from sub-meter-resolution DigitalGlobe Inc.
WorldView imagery for the ArcticDEM project
(https://www.pgc.umn.edu/data/arcticdem/, last access:
June 2018). The DEMs
are produced to 2 m resolution and coregistered over stationary (exposed
rock) surfaces using the algorithm of Noh and Howat (2014). Following
coregistration to remove biases, these data have an accuracy of better than
±0.5 m (Noh and Howat, 2015). Elevation profiles are filtered for
noise and smoothed as described in the Supplement before
subtracting the BedMachine v3 bed profiles from each surface elevation
profile to give ice thicknesses. The series of ice thickness estimates were
then linearly interpolated to the times of the series of velocity
observations to obtain ice discharge rate, D. Errors in discharge at velocity
observation times are calculated from propagation of measurement errors and
uncertainties of interpolated values are determined from a Monte Carlo
ensemble, as described in the Supplement. We derive total ice
sheet mass balance over the 2000–2016 period by combining our estimates of
D with SMB data obtained in a 5.5 km simulation of the Regional Atmospheric
Climate Model, RACMO2.3 version 2 (RACMO2.3p2) statistically downscaled to 1 km, and we compare these totals to monthly satellite gravimetry observations of
ice sheet mass balance from the Gravity Recovery and Climate Experiment (GRACE).
While RACMO2.3p2 applies the same model physics as described in Noël et al. (2018),
a 2 times finer horizontal resolution (5.5 km instead of 11 km)
better resolves SMB gradients over narrow glaciers at the ice sheet margins.
Based on comparison with observations, the uncertainty in modeled
basin-integrated runoff and snow accumulation (total precipitation minus
sublimation) is, respectively, 20 % and 10 %, which are combined to
obtain an uncertainty in SMB by assuming the two are independent of each
other (Noël et al., 2018; Van As et al., 2018).
We examine how D varies in response to meltwater runoff and changes in glacier
front position. Daily meltwater runoff estimates are also obtained from the
RACMO2.3p2 product. Daily runoff values at each model grid point are summed
over the ice sheet and within regional basins for comparison to D. We measure
relative changes in glacier front position manually for the period
2000–2016 using all available imagery from ASTER and LANDSAT 4–8. This
resulted in a measurement frequency of up to every few days during the
summer, declining in frequency during the polar night, especially prior to
2012 (Landsat 8 launch). Due to the very large quantity of measurements, we
used the efficient centerline methodology described in Walsh et al. (2012),
who found a negligible difference in the temporal variation in front
position between this and methods that involve digitization of the entire
front. To enable comparison with discharge and runoff time series, we
convert the irregular front position observations to daily rates of change
and then resample the rates at 7-day intervals. The new resampled subset is
then linearly interpolated to daily rates of front position change over the
study period. Individual glacier records of frontal change are combined into
regional and GrIS-wide records by first applying a discharge-dependent
weighting function, so that retreat and advance events at larger glaciers
are weighted more heavily due to the proportionally larger impact of these
glaciers on the discharge time series. We do not include front position
measurements for Zachariæ Isstrøm and the 79 North Glacier because the
perennial mélange of tabular icebergs at their fronts make delineation
of the front position arbitrary (e.g. Moon and Joughin,
2008).
Continuous estimates of discharge, D, for the GrIS for the
2000–2016 period, expressed as the rate of gigatonnes per year
(Gt a-1). Shading represents the 95 % confidence interval.
ResultsNet ice sheet discharge and mass balance
The net GrIS-wide D reveals a clear seasonality, typically characterized by
an annual minimum in December and a maximum in mid-July (Fig. 1),
superimposed upon multi-year variability. Removing the linearly interpolated
annual means from the time series gives an average seasonal amplitude of
30 Gt a-1, or approximately 6 % of the mean annual discharge. The
seasonal amplitude was largest in 2002, 2004, and 2005, reaching up to
46 Gt a-1, and, on average, higher before 2005 (35±8 Gt a-1,
with an uncertainty of 1-σ). This compares to an average seasonal
amplitude of 27±4 Gt a-1 after 2006, with an overall trend of
-0.7 Gt a-1 from 2000 to 2016. Beginning from a mean annual discharge
of 440±8 Gt a-1 in 2000, D increases to a maximum of 524±9 Gt a-1 in late June 2005, primarily due to the accelerations
of the Kangerdlugssuaq and Helheim glaciers in the east (Howat et al., 2007;
Joughin et al., 2008). In the following 2 years, the rapid decrease in D
from these two glaciers resulted in the greatest seasonal decrease in GrIS
D in 2006, declining to a minimum of 461±9 Gt a-1 by
January 2008. D then gradually increased, reaching the second-highest time series
annual maximum of 494±6 Gt a-1 in 2015, with a peak summertime
value of 511±6 Gt a-1 in July 2015. Annual D declined by
5 Gt a-1 in 2016 largely due to reductions in discharge observed at
Køge Bugt and Jakobshavn (Fig. S3). Thus, D has remained consistently
between 10 % and 12 % above the 2000 rates since 2010. Along with the annual
mean quantities, the seasonal discharge signal varies throughout the study
period. Prior to 2013, the seasonal variation in D is relatively symmetric,
with a single distinct peak and little variability on sub-annual timescales.
The final 4 years of the record are more variable, with minor peaks
following the seasonal maxima. This pattern is predominantly due to changes
observed in the NW region, addressed in detail in Sect. 3.2.
The ice sheet's 20 largest glaciers account for over 50 % of the total D
(Fig. S4). Of these 20, the four largest glaciers (Fig. S3) together account for 25
% of the total D and 56 % of the cumulative anomaly in GrIS-wide D
relative to annual D in 2000. Variations in these four glaciers therefore
dominate variability in total GrIS D. The secular trend in the combined D is
substantially different with the four largest glaciers removed (Fig. S5).
Following the decline in D between 2005 and 2008, the combined D of the
remaining glaciers, denoted here as Ds, continued to increase, reaching
a maximum in 2011 before declining to another minimum in 2012. The seasonal
decline in Ds during the winter of 2013–2014 was anomalously reduced
relative to other years, with speeds remaining elevated across the ice
sheet. Ds then increased to a record maximum in July 2015, reaching an
annual maximum of 374±5 Gt a-1 in 2016. Thus, an overall
continued increase in Ds since 2008 was largely offset in declines from
the four largest glaciers over that period. Removing the four largest
glaciers, however, does not change the relative seasonal amplitude of
approximately 6 %, indicating that GrIS-wide seasonality is not dependent
on the largest glaciers.
Comparative cumulative GrIS mass change relative to 2003
between GRACE and monthly SMB-D. Cumulative SMB
is also plotted, with cumulative differences among estimates plotted at the bottom of the panel, associated with the right y axis.
Our continuous estimates of D enable the first direct comparison to monthly
satellite gravimetry observations of ice sheet mass balance from GRACE. We
compute ice sheet mass balance by subtracting our estimates of net GrIS-wide
D from daily 1 km2 resolution SMB estimates obtained from RACMO2.3p2
(Noël et al., 2018). Following the methodology of van den Broeke et al. (2016),
we incorporate SMB fluxes from the ice-free tundra and peripheral
ice caps, which are included in the GRACE signal, into the ice sheet mass
balance calculations. Mass balance estimates of peripheral ice caps derived
from laser altimetry (Bolch et al., 2013) found that areal averaged mass
losses were similar for land-terminating and marine-terminating glaciers,
and thus we assume D from peripheral glaciers and ice caps is small relative
to the errors in other terms. We remove the SMB over ice shelves, downstream
of the discharge flux gates, from the total. We use GRACE ice sheet mass
updated from Wouters et al. (2013), corrected for glacial isostatic
adjustment using the model of Khan et al. (2016). The cumulative mass losses
estimated by SMB-D and GRACE, calculated by taking the difference between
the annual mean cumulative losses in 2016 and 2003, are 3263±259 and
3479±280 Gt, respectively, over the 2003–2016 period (Fig. 2).
This 7 % difference equates to an integrated monthly bias of less than
1.5 Gt, nearly all of which is due to a greater loss estimated by GRACE in
the anomalously severe 2011 and 2012 melt seasons. Extended to the beginning
of the D time series, we estimate a total cumulative mass loss from 2000
through 2016 of 3730±277 Gt. We also delineate individual glacier
D records and SMB totals to align with the six regional basins used in
Wouters et al. (2013) and compare these quantities to basin-scale GRACE
estimates (Table 1, and Figs. S6, S7). We find that while the seasonal
variability in mass loss shown in GRACE is well resolved by SMB-D
estimates for all basins, the level of agreement in magnitude of cumulative
mass loss varies by basin. Estimates agree within their combined uncertainty
(<±10 Gt a-1) for three basins, which together account
for ∼65 % of the total mass loss. Annual mass loss rates
from SMB-D in Basins 1 and 2 (northern regions) exceed GRACE estimates
rates by more than 50 %, and mass loss rates from GRACE are approximately
double those from SMB-D in Basin 4 (southeast). These differences largely
cancel each other out, leading to the close agreement among estimates for
the GrIS as a whole.
GrIS-wide and basin-scale (delineated in Fig. S6) cumulative mass
changes in gigatonnes over the 2003–2016 period, listed as the
RACMO2.3p2 SMB component, SMB-D mass balance, and GRACE mass
balance estimates. Cumulative mass changes here represent the difference
between mean annual 2016 and mean annual 2003 estimates, with a negative
value indicating net mass loss. The GrIS* domain includes SMB fields from
tundra and detached ice caps.
Net regional D including (solid
line) and excluding (dashed line) the dominant glaciers in each region, with
shading representing the 95 % confidence interval. From top to bottom
these regions include the northwest (a), plotted with and without
Jakobshavn (JI), the southeast (b) with and without Helheim (HL),
Kangerdlugssuaq (KQ), and the main trunk of Køge Bugt (KB), the northeast
(c), with and without Zachariæ Isstrøm (ZI) and 79 North (Fjorden)
Glacier (79F), and the southwest (d) with and without Kangia glacier.
Regional discharge variability
Partitioning D into the four quadrants used by Enderlin et al. (2013), we
find significant spatial variability (Fig. 3a), with regional D quantities
summarized in Table 2. The northwestern (NW) region, which includes
Jakobshavn northward to and including Petermann Glacier, has the highest
combined discharge, averaging 207 Gt a-1, with a cumulative discharge
anomaly, defined as the cumulative difference from the year 2000 D, of
343±21 Gt. In the NW, we also find the highest seasonal amplitude in D of
18±3 Gt a-1 or 9 %, with Jakobshavn Glacier (Fig. S3a)
alone contributing 7±3 Gt a-1. Removing this glacier from the
sample reduces the fractional seasonal amplitude to the GrIS-wide average of
6 % (10±1.7 Gt a-1). On average, maximum D occurs on 12 July
(day 192) with a uniform, sinusoidal seasonal cycle transitioning to an
irregular sawtooth pattern in 2012. This shift is also visible in the
GrIS-wide time series and is primarily due to the emergence of a secondary,
middle to late autumn peak in D at Jakobshavn (Fig. S3a). We do not further
investigate the cause of this secondary peak but note that previous work
(Sundal et al., 2013; Bondzio et al., 2017) found that the majority of
acceleration events at Jakobshavn are closely linked to changes at the
calving front. On average, D at Jakobshavn reaches a seasonal maximum
∼1 week later than the NW regionally averaged maxima. We find
no significant trend in the timing of the seasonal maximum in the NW.
Summary of D values for the total GrIS and four distinct regions
(see Fig. 3), including the estimated mean annual D in 2000, the maximum D
over the 2000–2016 period, and the cumulative D anomaly (ΔD2000) relative to the 2000 estimate. All values are described in units
of gigatonnes per year. A negative value indicates a reduction in D relative to the
2000 value.
The southeastern (SE) region, extending northward to and including
Kangerdlugssuaq glacier, has had a cumulative D anomaly of 284±17 Gt
since 2000 (Fig. 3b). Approximately 60 % of the cumulative anomaly
occurred at Helheim and Kangerdlugssuaq, due to the rapid 2004–2005
terminus retreat and subsequent acceleration (Howat et al., 2007), resulting
in the SE reaching a period maximum rate of D of 238±4 Gt a-1 in
June 2005. Following this period of acceleration, regional D values steadily
declined to an annual average of 187±4 Gt a-1 in 2016, within
the error of D observed in 2000 (182±6 Gt a-1), prior to
acceleration. As discovered by Enderlin et al. (2014), an overall decreasing
trend in SE D of -1.7 Gt a-2after 2005 has partially offset the
overall increase of 2.7 Gt a-2 in the NW. Despite a large net regional
D, there is substantially less seasonal variation in the SE, with an average
seasonal amplitude of 9±5 Gt a-1 or 5 %. The seasonal
amplitude was greater during the 2000–2005 period of acceleration (14±6 Gt a-1) than during the 2006–2016 period (7±2 Gt a-1).
The three largest glaciers in this region (Køge Bugt,
Helheim, and Kangerdlugssuaq) together contribute approximately 40 % of
the net regional D. A seasonal signal is more visible after 2005 when
excluding these three glaciers, with the remaining glaciers showing a
slightly larger seasonal amplitude of approximately 6 %. On average, the
summertime seasonal maxima in D occur approximately one week earlier in the SE
than in the NW.
The NE and SW regions have fewer marine terminating outlet glaciers and
contribute less to the total GrIS D. Discharge from the northeast (NE) region
(Fig. 3c), contributes approximately 12 % of the total ice sheet D, with
the regional ice flux dominated by Zachariæ Isstrøm and the 79∘ North
Glacier. This region exhibits a relatively consistent seasonal variability
of 5±1 Gt a-1, or 8 %. The seasonal maximum typically occurs
at the end of June. Annual D increased by 4 Gt a-1 between 2013 and 2016,
largely due to increased D observed at Zachariæ Isstrøm
(Mouginot et al., 2015; Choi et al., 2017). D in the NE shows a steady increase,
accelerating from a rate of ∼0.2 Gt a-2 during
2000–2012 to over 1 Gt a-2 during the 2013–2016 period, entirely
due to acceleration of the Zachariæ Isstrøm and 79 North glaciers.
Lastly, only seven glaciers constitute the southwest (SW) (Fig. 3d), where
land-terminating glaciers dominate the margin. Kangia glacier alone accounts
for over approximately 60 % of the total SW regional D. A doubling of the
seasonal amplitude at Narssap Sermia Glacier, coinciding with rapid terminus
retreat (Motyka et al., 2017), is responsible for the increase in regional
variability after 2011.
Normalized, detrended D time
series for the total GrIS (top), NW (blue), SE (cyan), NE (green), and SW
(red) regions. The normalized discharge within each panel spans from
-1 to 1. Vertical black lines align with the annual maximum
D of the GrIS-wide series.
As mentioned above, variations in D may be due primarily to the largest
glaciers, which may or may not represent typical glacier behavior. To assess
seasonal glacier dynamics, we remove the impact of glacier size by first
subtracting the secular trend from the series and then normalizing each
glacier's detrended D series by its maximum seasonal amplitude. This process
effectively creates equally weighted time series of D for individual
glaciers, while isolating the seasonal signal. The averages of the
normalized seasonal discharge for each region and the total GrIS are shown
in Fig. 4 and reveal that a distinct seasonal signal is a ubiquitous
feature across the ice sheet, independent of glacier size. However, the
timing of the seasonal maxima in the normalized data occurs approximately
10 days earlier (late June, typically) than without normalization. As noted
above, there has also been a decrease in seasonal amplitude since 2013 of 20 %
relative to earlier years. We observe a similar decrease in amplitude in the
normalized series for the SE, NW, and NE. This widespread reduction in
seasonal amplitude corresponds with a period of relatively stable mean
annual D, as shown in Fig. 1. As was noted from the raw regional D, the SE
region exhibits the smallest seasonal variability. Unlike the raw time
series, which showed the greatest seasonal amplitude in the NW, the NE
region shows the largest seasonal amplitude in the normalized time series.
This is likely due to the reduced impact of Jakobshavn on NW seasonality
through the normalization. Figure 4 also shows that the seasonal maxima occur
coincidentally for the majority of glaciers over the majority of the GrIS,
with the few glaciers in the SW reaching a seasonal maximum slightly earlier
than the GrIS-wide average.
Variations in annual discharge, front position, and runoff
We expect that D will vary with both ice front position, due to changes in
resistive stress at the terminus (e.g. Thomas, 2004; Howat et al., 2008),
and with seasonal meltwater runoff, due to variations in basal water
pressure (e.g. Joughin et al., 2012). We first test for broad, linear
correlations between annual discharge, both over the entire GrIS and
regionally, and annual changes in front position and total runoff. We
calculate the GrIS-wide and regional annual runoff totals from daily
RACMO2.3p2 outputs. Ice-sheet-wide and regional front positions are the sum
of each glacier's change between 1 January each year, weighted by the
fractional contribution of the glacier's D to the GrIS or regional total. We
then divide these sums by the total number of glaciers across the GrIS or
region of interest and express the quantity as the mean weighted position
change.
(a) Colored dots are GrIS-wide cumulative average front
position change since 1 January 2000, with negative values indicating
retreat, versus annual average discharge, D, for
each year between 2000 and 2016. The black line is the linear best fit to
the data points, with the variance
(r2) and probability value
(p) of the fit labeled. (b) The average rate of
front position change, with negative values indicating retreat, for each year versus the
change in average annual discharge between years. (c) Same relationship
described in (a), but for glaciers in the NW region only. (d) Relationship
between average front position change and the change in annual
D from the current to the following year
(Di+1-Di). Date color scale and statistics
for (b), (c), and (d) are as described for (a).
For the entire GrIS, we find the strongest relationship between annual D and
the weighted cumulative change in 1 January front position (r2=0.79, p=10-6) (Fig. 5a). Note that the GrIS-wide weighted front
position totals do not include the 79 North Glacier and Zachariæ Isstrøm
for reasons described in Sect. 2, and thus the discharge contributions of
those two glaciers are excluded from the annual D term. This correlation is
slightly stronger than that obtained between annual D and the cumulative
front position change from the previous year (r2=0.68, p=10-4). A weaker but significant correlation is found between the
change in annual D, defined here as the difference between the current and
previous year's annual D, and annual front position change during both the
current year (r2=0.59, p=0.0005) (Fig. 5b) and the previous
year (r2=0.50, p=0.002). We test for these lagged relationships
between retreat and annual D to account for the temporal grouping of the
data. For example, front position may continue to retreat into the autumn,
after the typical peak in D. If autumn–wintertime discharge rates remain
elevated as a result of continued retreat through December of the previous
year, we would anticipate the following springtime acceleration to be
superimposed on a higher base discharge rate. These correlations are
strengthened by excluding Petermann Glacier, for which large retreats of its
uniquely thin and fractured ice shelf in 2010 and 2012 had no resolvable
impact on ice flow speed and thus D (Lemos et al., 2018; Münchow et al.,
2014). In contrast, no significant correlation is found between annual D and
total annual runoff. The addition of annual runoff as an independent
variable also does not improve the correlations with front position
described above.
Retreat was widespread over the study period in the NW, with glaciers there
retreating, on average, 2.8 km from 2000 to 2016. The cumulative weighted
regional front position change shows a near-linear annual retreat with small
interannual variation. A similarly strong linear trend is present in annual
D, resulting in a nearly perfect correlation with annual cumulative front
position change (r2=0.92, p=10-9) (Fig. 5c). This
relationship is slightly strengthened at a 1-year lag, with a correlation
of r2=0.94 (p=10-9) between annual D and cumulative front
position up through the previous year. Only a weakly significant
(r2=0.25, p=0.048) relationship exists between the change in NW annual
D and the annual, rather than cumulative, front change during the previous
year. Retreat also dominated in the SE region over the study period,
averaging 1.7 km. Unlike in the NW, however, D in the SE correlated to the
annual weighted change in front position, rather than cumulative change.
Annual D is significantly correlated to the previous year's annual front
position change (r2=0.28, p=0.033). Even stronger is the
correlation between the change in annual D and the annual front position
change of the previous year, (r2=0.60, p=10-4) (Figs. 5d
and S8). As with the complete GrIS, no significant correlations are
found between D or interannual change in D and annual runoff in either the SE
or NW regions.
Cumulative GrIS D (black, left
y axis) plotted with raw daily runoff totals (gray bars, right y axis). The
timing of the seasonal maximum runoff is emphasized by vertical dotted
lines. Regional runoff totals, smoothed by a 31-day running mean, are shown
for the NW and SE regions.
Seasonal variations in discharge, front position, and runoff
Runoff on the ice sheet typically begins in May and continues through
September, reaching a maximum daily rate in July. Smoothing daily runoff
values with a monthly (31-day) running mean results in a seasonal
distribution with one or several distinct peak(s). Comparing GrIS-wide D to
the smoothed runoff series (Fig. 6), we find that seasonal acceleration of
D is greatest at the onset of runoff and reaches a seasonal maximum, on
average, 13±9 days after the greatest increase in runoff and 12±7 days before the seasonal maximum in runoff. The only exception to
this progression was in 2013, when the peak in D occurred after the seasonal
maximum in runoff. The maximum D occurs, on average, 40±8 days after
the onset of significant runoff. Since the distribution of daily runoff
includes a long tail of small values, we define the significant runoff onset
as the day when runoff exceeds the 50th percentile of daily runoff
values between 1 April and 1 November. We use this threshold to delineate
the onset of significant runoff by separating days with negligible runoff
contributions from those with non-negligible runoff contributions. We find a
significant correlation between the date of runoff onset and the date of
maximum D (r2=0.33, p=0.015), indicating that a later-occurring
peak D may be related to later onset of runoff. However, despite the near
synchronous timing between seasonal peaks in runoff and D, we find no other
significant relationships between the timing of runoff and discharge, nor
between the magnitude of runoff and the magnitude of the seasonal maximum
D, or total annual D.
There is regional variability in the timing and amplitude of runoff. The NW
region reaches an average maximum of 2.6±0.5 Gt day-1 on day
199 (±8), totaling 82±21 Gt annually. Significant runoff
onset occurs in early June (day 160±7), 1 week later than runoff
in the SE (day 15±8) and preceding the timing of the regional
maximum D by approximately 1 month (32±10 days). There is a
significant relationship in the NW region between the timing of runoff onset
and the timing of the seasonal maximum in D (r2=0.46p=0.003). In the SE, there is a similar magnitude of total annual runoff (75±16 Gt), but a substantially lower maximum daily rate of 1.7±0.5 Gt day-1 that occurs, on average, on day 208 (±10). There
is also a greater interannual variability in the temporal separation between
onset of runoff and maximum D (33±22 days) in the SE region and, as a
result, there is no significant correlation in their timing. As with the
GrIS as a whole, we find no significant relationships between the magnitudes
of runoff and D, or total annual D, in either region.
Front position also varies seasonally. Integrated over the GrIS, net
weighted retreat begins in early April (day 92±33) and continues
through the end of September (day 265±17). Daily rates of retreat
increase most rapidly in early June (day 153±41), reaching, on
average, a maximum retreat rate on day 180 (±35). We test for linear
relationships between the timing of initial retreat and the greatest increase in
retreat, and between timing and magnitude of maximum daily rate of retreat with the
same seasonal D metrics described above (e.g. magnitude and timing of maximum
D and timing of greatest increase in D). We find no significant relationships
between the timing or magnitude of seasonal frontal change quantities with
seasonal D. The seasonal progression of retreat and advance occurs earlier in
the NW relative to the GrIS-wide average. In this region, total weighted
front change rates show the greatest increase in retreat in mid-May, on
average (day 135±46), and reach a peak retreat rate in mid-June
(day 167±38). In the SE region, by contrast, retreat accelerates the
most in mid-June (day 169±46) and reaches a maximum rate on day 200
(±23). As with the GrIS-wide results, we find no significant
correlations between the seasonality of retreat and D at the regional scale.
Discussion
Our GrIS-wide estimate of D in 2000 (440±8 Gt a-1) is
approximately 5 % and 20 % lower than annual estimates derived for
2000 in Enderlin et al. (2014) and Rignot et al. (2011), respectively. Our
2003–2010 mean D of 484±9 Gt a-1 agrees within margins of
uncertainty to estimates by Kjeldsen et al. (2015) over the same time period
(465±65.5 Gt a-1) with a bias of less than 20 Gt a-1. Annual
D estimates for 2007 and 2011 are approximately 5 % and 7 % lower than
those estimated in Andersen et al. (2015), but also within margins of
uncertainty. Approximately half of the difference from Enderlin et al. (2014)
can be explained by the bias resulting from the study's use of,
mostly, summertime median velocities and therefore higher discharge values.
Other differences are likely due to a combination of observational error,
uncertainties associated with empirical assumptions made in the absence of
ice thickness data, methodological differences in the processing and
filtering of surface elevation data, and uncertainties associated with ice
thickness derivations using hydrostatic equilibrium assumptions (Rignot et al., 2011).
The higher temporal resolution of D presented here also avoids
nonuniform temporal sampling biases, and, once combined with SMB data from
RACMO2.3p2, is in close agreement with independent estimates of ice sheet
mass balance from GRACE. Significant discrepancies, however, between the SMB-D and GRACE estimates still exist at the regional scale (Fig. S6), with
SMB-D predicting nearly twice the loss north of the ice sheet, but
approximately half the loss of GRACE in the southeast. The difference in the
SE may be due to an underestimation o runoff, partly from the high
slope of the ablation zone, overestimated accumulation rates, or ice
thickness for glaciers lacking radio echo sounding measurements near the
terminus. The differences in the north may be due to unrealistically low net
SMB predicted there by RACMO2.3p2, with some years showing zero or negative
SMB, and cumulative SMB loss in region 1 (Fig. S7).
The seasonal variation in D of 6 % is significantly less than the
∼10 % typically assumed for the GrIS (e.g. Rignot and
Kanagaratnam, 2006; Andersen et al., 2015). While individual regions have
larger relative seasonal variations, differences in the timing of their
peaks cause them to offset each other in total. For instance, the GrIS-wide
seasonal amplitude would be 60 Gt a-1, or nearly 13 %, if the
seasonal signals expressed at individual glaciers were exactly in phase.
This effect of offsetting variability was especially strong in 2013, when
early increases in D in the SE region dampened the winter minimum. The
seasonal amplitude of GrIS has also declined since 2013 due to the
widespread 20 % reduction in the discharge seasonality of SE glaciers.
Changes in glacier discharge are due to changes in both ice flow speed and
thickness, with less known about short-term (seasonal to interannual)
variations in the latter. Consistent with numerous studies (e.g. Helm et al., 2014;
Csatho et al., 2014; Kjeldsen et al., 2015), 89 % of the glaciers,
including the 25 largest, thinned over the study period. Holding ice
thickness constant, so that the change in discharge is due entirely to
changes in flow speed, results in an increase in D of 110 Gt a-1 by 2016,
or 60 Gt a-1 greater than estimated when including ice thickness change
(Fig. S9). Thus, ice thinning has offset the increase in D due to ice flow
acceleration by over 50 % since 2000, and this fraction is steadily
increasing with time since the initial rapid acceleration in the SE in 2004
and 2005 (Fig. S10b). Ice thickness changes on sub-annual timescales also
reduce the seasonal amplitude of D. Holding thickness constant, as above,
results in a seasonal variation that is, on average, 10 % larger than if
thickness changes are included. Thus, inclusion of ice thickness change on
sub-annual to decadal timescales is essential for accurate estimates of D.
Changes in ice thickness also modulate the relationship between changes in
D and ice front position. As described in Sect. 3.3, cumulative annual front
change and annual D are uncorrelated in the SE region. However, holding ice
thickness constant, as above, results in a strong correlation (r2=0.79, p=10-6), which is similar to that in the NW. Holding ice
thickness constant (Fig. S10b) also increases the strength of the
correlation between annual changes in front position and the change in
annual D the following year (r2=0.75, p=10-5). These increased
correlations reflect the expected dependence of ice velocity on changes in
ice front position (e.g. Howat et al., 2008; Nick et al., 2009; Vieli and
Nick, 2011). The SE underwent a sudden large increase in velocity and
retreat in ice front position between 2002 and 2005, with another smaller
acceleration and retreat in 2010 but has since remained largely stable
through 2016. Recent work by Bunce et al. (2018) describes increased
interannual variability in the SE front position, due to asynchronous retreat
observed at glaciers in that region. This asynchrony may also contribute to
the more recent muted seasonality in the SE region, as previously described.
While velocity has remained stable, ice thinning has resulted in a declining
D that is uncorrelated with cumulative ice front retreat. In contrast, both
retreat and D have been increasing steadily in the NW throughout the record,
indicating steadily increasing ice speeds, resulting in a high correlation
between annual D and cumulative front position change (i.e., retreat).
Lastly, we expect glaciers to respond to changes in basal water pressure due
to the seasonal input of runoff. Previous work focused on land-terminating
glaciated regions of the GrIS (Sundal et al., 2011; Tedstone et al., 2015) and
work using modeled channelization processes (Schoof, 2010) demonstrated that
meltwater impacts on glacier velocities operate on narrow temporal windows
and may even result in a net deceleration on seasonal to annual timescales.
While both D and meltwater runoff show a similar pattern of seasonal
variability, with a possible relationship between the timing of the onset of
runoff and the seasonal peak in D, neither the seasonal maximum in runoff
nor the seasonally integrated runoff is significantly correlated to annual
D. These indicate a more complex interaction among runoff, ice flow
velocity, and D, for which the rate and distribution of runoff into the subglacial
system are more relevant to glacier flow than total runoff (Stearns and van
der Veen, 2018). For example, the sensitivity of D to runoff may vary
throughout the melt season, with increased sensitivity early in the melt
season when drainage channels are inefficient and unable to support the
influx of runoff into the system (Chandler et al., 2013), thus increasing
water pressure at the bed and enhancing basal flow (Palmer et al., 2011;
Bartholomew et al., 2010). This is consistent with a 13±9-day average
lag in timing between the fastest increase in runoff and the maximum
GrIS-wide D, which is close to the 18-day average residence time between
the production of melt runoff on the ice sheet and its transport to the
margin estimated by van Angelen et al. (2014). Thus, taking this residence
time into account, the seasonal maximum flow speed, and therefore D, occurs
near the time we would expect maximum pressurization of the subglacial
drainage system. Future work will build on these concepts by closely
examining discharge rates of acceleration and deceleration in response to
the distribution of runoff throughout the melt season, giving consideration
to runoff residence times.
Conclusions
GrIS-wide D has remained near 490 Gt a-1 following a period of rapid
acceleration before 2006, representing an 11 % increase from 2000. This
apparent stabilization, however, is due to steady or declining flow speeds
and ice thinning at the four largest glaciers, which dominate the ice-sheet-wide total. Excluding these, the combined D of the remaining glaciers
increased steadily over the time period, reaching a maximum in 2016,
indicating that the largest glaciers are not representative of typical
outlet glacier change. Trends in D vary regionally, increasing in the NW and
NE and remaining steady in the SE, where sustained higher flow speeds are
completely offset by ice thinning and D has returned to its year-2000 values.
In total over the GrIS, ice thinning has offset the impact of increased ice
flow speeds on D by over 50 % since 2000, substantially modulating the
contribution of glacier dynamics on mass loss.
We find that annual changes in GrIS D can be mostly attributed to the
cumulative weighted change in glacier front position. This relationship is
the strongest in the NW region, where continuous retreat has accompanied a
near-linear increase in annual D and, therefore, changes in D are driven by
changes in flow speed. In the SE, however, where speeds have remained
relatively stable since 2005 while the glaciers have thinned, it is instead
the annual changes in front position that correlate to changes in annual D
the following year. In contrast, we find no correlations between annual D, or
year-to-year changes in D, and modeled meltwater runoff. These results
indicate that multi-year changes in D are dominated by changes in ice front
position, through its impact to glacier dynamics, and that the magnitude of
meltwater runoff has no consistent discernible effect on total annual
outlet glacier discharge.
We resolve a persistent, ubiquitous seasonal increase in D averaging 6 %.
Regionally, this signal varies from 5 % in the SE to 9 % in the NW,
with ±1-month differences in timing resulting in an offsetting effect
that decreases the combined total. There was also a marked decline in
seasonality after the period of rapid ice flow accelerations in the SE,
resulting in a ∼23 % decrease in seasonality after 2006
and a near-complete disappearance of a seasonal signal in the SE after 2013.
While not correlated on an annual basis, seasonal variations in D do
correspond to those of runoff. We observe that maximum D occurs
∼2 weeks after maximum increases in runoff, which is similar
to the expected time for runoff to reach the margin, and ∼2 weeks
before the seasonal maximum runoff. We also observe significant
correlation between the onset of runoff and the timing of peaks in D, with
earlier-occurring runoff onset corresponding to earlier peaks in D. This is
consistent with the expected impact of increasing meltwater input to an
inefficient subglacial drainage system at the start of the melt season,
increasing the subglacial water pressure and glacier sliding velocity. This
is followed by a decline in D before the peak in runoff is reached,
attributed to the transition to efficient subglacial drainage. Such a
transition also may explain the lack of correlation between the magnitudes
of seasonal runoff and maximum D. Thus, while changes in front position, and
their resulting persistent changes to the balance of forces at the glacier
terminus, appear to dominate multi-year variability in regional and total
GrIS D, seasonal variations are substantially controlled by the timing of
meltwater input.
We have assessed the bulk behavior of ice sheet discharge and its broad
relationships to possible external forcing, enabled by this first complete
estimate of continuous D over nearly 2 decades for all of Greenland's large
marine-terminating glaciers. It is well established, however, that the
behavior of glaciers in close proximity and under similar environmental
forcing can vary substantially (e.g., McFadden et al., 2011; Moon et al., 2012;
Carr et al., 2017). This is likely due to the sensitivity of outlet glacier
dynamics to their particularly geometry (e.g., Enderlin et al., 2013; Porter
et al., 2014; Carr et al., 2015; Bartholomaus et al., 2016; Catania et al., 2018)
and we do not attempt to account for these differences here. However,
detailed analysis of the relationships between particular glacier
characteristics and their dynamics at a range of timescales using these
data will be the subject of future work.
All ice velocity and topographic products are publically available online.
The velocity data maps and GIMP DEM are distributed through the NASA
Distributed Active Archive Center at the NSIDC (http://nsidc.org/data/measures/gimp, last
access: April 2018). Bed topography can also be accessed
through the NSIDC portal at https://nsidc.org/data/idbmg4 (last access:
July 2017). Information on the RACMO2.3p2 SMB data can be found at
http://www.projects.science.uu.nl/iceclimate/models/greenland.php (last access:
April 2018).
The supplement related to this article is available online at: https://doi.org/10.5194/tc-12-3813-2018-supplement.
MDK and IMH conceived this study and synthesized the required datasets. MDK performed the analyses and led writing the paper. SJ
developed the orthorectified velocity maps and MJN developed algorithms for
surface elevation, both used to derive the ice discharge estimations. BW
processed and provided mass balance estimates derived from GRACE
observations, and BN and MRB developed the surface mass balance model,
RACMO2.3p2, which was combined with discharge estimates to derive an ice-sheet-wide record of mass balance. All authors contributed thoughtful
discussions and insights to the study, and all authors contributed to
editing the paper.
The authors declare that they have no conflict of interest.
Acknowledgements
This work was supported by grants 80NSSC18K1027 and NNX13AI21A from the
US National Aeronautics and Space Administration and a fellowship from the
Ohio State University. Contributions of BW were funded by NOW VIDI grant
016.Vidi.171.065. The authors thank the two anonymous referees and the
editor, A. Vieli, for their helpful comments.
Edited by: Andreas Vieli
Reviewed by: two anonymous referees
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