Materials and
Methods
GRACE data
We make use of the COST-G RL01 Level-3 GRACE and GRACE-FO V0002 time
series obtained from
http://gravis.gfz-potsdam.de/antarctica(44, 45 ) at 50 km
gridded resolution (noting that GRACE estimates of mass change are
correlated over 200-300 km). At the time of download the series spanned
Mar 2002 to Mar 2021 inclusive. As described by ref (45 ),
post-processing steps include replacement of coefficients C20, C30 (only
for the months starting from November 2016), C21 and S21 and its formal
standard deviations by values estimated from a combination of
GRACE/GRACE-FO and Satellite Laser Ranging (SLR); insertion of geocentre
coefficients (C10, C11, S11); and estimation and removal of a periodic
161 day-period signal due to mismodeled and aliased signal of the S2
tide. These series come corrected for glacial isostatic adjustment using
the ICE6G_D(46 ) model but we restored this model and removed
that of Caron et al.(47 ) with values for both given in Table S1.
The choice of GIA model will affect the linear trend in estimated mass
change but not variations. Qualitative comparison of time series from an
alternative GRACE solution (GFZ RL06) showed modest differences at
inter-annual timescales, and generally within uncertainties, but with
COST-G time series temporally smoother.
We also considered the supplied time series for 25 individual basins
according to the definitions of ref (48 ), taking EAIS to be the
combination of basins 302 to 317, WAIS 318 to 323 and 301, and APIS 324
to 325, all inclusive. These basin series benefit from a GRACE data
inversion which includes forward modelling of sub-basin-scale mass
distribution(44 ). Further details on the GRACE time series are
provided at
ftp://isdcftp.gfz-potsdam.de/grace/GravIS/COST-G/Level-3/ICE/GravIS_ICE_Technical_Note.pdf
SMB model outputs
We use modelled SMB from the RACMO2.3p2 27km model(30 ) covering
Jan 2002 to Feb 2021 in units of kg/m2/month. We
computed cell-by-cell SMB anomalies relative to the cell-mean SMB over
the full data period. These were then cumulatively summed and converted
to units of giga-tonnes (Gt). For differencing with GRACE series, we
interpolated the SMB grids to the GRACE grid spacing and then
interpolated them to the GRACE time steps.
Climate indices
For SAM, we adopt the station-based index of Marshall et al.(18 )
obtained from http://www.nerc-bas.ac.uk/icd/gjma/sam.html . For
ENSO, we use the Niño3.4 index obtained from
https://psl.noaa.gov/gcos_wgsp/Timeseries/ based on the HadlSST
record over 5°N-5°S, 170°W-120°W. For each index, we truncated the
portion prior to the GRACE period, then normalized, cumulatively summed,
and renormalized the series to produce the SAMΣ and
Niño3.4Σ series shown in Fig. 1 and Fig. S1. In the
presence of long-period index changes, the cumulative sum might depend
on the chosen reference period which is used to calculate climatological
mean and derive anomalies from it. For both SAM and Niño3.4 indices we
adopted a uniform reference period of 1971-1999 inclusive which provides
the advantage of being a well observed period outside the GRACE data
window. The Niño3.4Σ series is largely insensitive to
the choice of reference period as the historical Niño3.4 index has
little long-term tendency. In contrast, using 1971-1999 as the reference
period very likely underestimates the trend in SAMΣ, as
the SAM index has exhibited pronounced upward trend since the mid-1970s,
largely due to anthropogenic climate change(34 ). Adopting a
reference period later than 1971-1999 would result in removal of the
shift to positive SAM, which would be unrealistic.
The well document shift toward the positive SAM phase since the 1940s
requires that SAMΣ has a long-term positive trend. We
discuss below that working with SAM or SAMΣ is
mathematically identical in the absence of GRACE data noise but working
with SAMΣ has distinct advantages when working with real
GRACE data.
To explore the sensitivity to the choice of SAM or ENSO indices, we
tested with alternative indices in the multivariate regression that is
described below. Instead of the station-based Marshall SAM index we
tested an index computed using zonal mean sea level pressure difference
between 40°S and 65°S from the JRA55 reanalysis model (referred to as
“SAM JRA55” in Fig. S1). The zonal means at 40°S and 65°S were each
calculated. Each monthly value was then normalized over 1981-2010 and
then the 65°S values were subtracted from the 40°S values and the series
renormalized over 1971-2000. Instead of the Niño3.4Σ we
tested the Southern Oscillation Index (referred to as SOI in Fig. S1)
obtained from https://www.ncdc.noaa.gov/teleconnections/enso/soi,
computed as the normalized difference in standardized sea level pressure
between Tahiti and Darwin, renormalized over 1971-2000. For consistency
with Niño3.4 we use -SOI. The indices are shown in Fig. S1 along with
their cumulative sum and detrended cumulative sum. The SAM JRA55 index
differs to the station-based SAM index of Marshall et al. (18 )
over inter-annual timescales, but its cumulative sum is in close
agreement. -SOI has a small negative mean anomaly over the GRACE period
resulting in a small negative trend in -SOIΣ along with
some inter-annual differences from Niño3.4Σ. There is no
evidence of a long-term trend in ENSO and this is likely a result of a
small positive bias in SOI during the reference period. Other reanalysis
products are either not available up to the end of the GRACE period or
are only available after 1979 and hence do not span our full reference
period commencing in 1971.
EOF analysis
We perform a standard EOF analysis using GRACE data on an Antarctic
Polar Stereographic grid with 50 km resolution (Mar 2002 to Mar 2021).
Before this we removed a linear trend at each grid point (computed using
ordinary least squares and considering uneven data sampling) to focus on
variability. Periodic terms were not removed before the EOF analysis.
Unlike modes 1 and 2 shown in Fig. 1, the remaining modes are dominated
by higher-frequency signals and often exhibit less-organized or
noise-like spatial patterns, with their explained variances each less
than 6%. To reveal processes underlying the two leading modes, we
regressed cumulatively summed and linearly detrended SMB from
RACMO2.3p2_ANT27, as well as sea level pressure, and each of the two
components of 10m wind from ERA5 reanalysis, onto the PCs of the first
two modes.
Given the temporal correlations evident in the dominant modes (Fig. 1),
we also tested Extended EOF analysis(49 ) (EEOF), which considers
temporal correlations in the data. Using a lag of 12 months we computed
EEOFs after gap filling and interpolating to a constant monthly timestep
and found the resulting two leading EOFs to be almost temporally
constant and with PCs that are lag-smoothed versions of the PCs from the
conventional EOF analysis. Given this agreement, and for simplicity, we
retained the standard EOF analysis in the main text.
Multi-variate analysis
Using ordinary least squares, we solved the coefficients (a, b, c,
d, and e) of the functional model describing time-evolving mass
(M )
\(M\left(t_{i}\right)=a+b\left(t_{i}-t_{0}\right)+\sum_{k=1}^{3}{\left(c_{k}^{s}\sin{\left(2\pi f_{k}t_{i}\right)+}c_{k}^{c}\cos\left(2\pi f_{k}t_{i}\right)\right)+d\text{SAM}_{\Sigma}+e{Nino3.4}_{\Sigma}}\)(1)
Where fk = [1, 2, 365.25/161] cycles per
year, with the third frequency describing the S2 tidal aliasing period.
Separate periodic coefficients were estimated for each of GRACE and
GRACE-FO. \(\ \)While the S2 term was apparently removed in the GRACE
pre-processing(45 ), we found evidence of it in the GRACE-FO
period and re-estimated them to provide realistic uncertainties. We
adopted \(t_{0}\) as the mid point of the GRACE series.
We explored the impact of the presence of a trend in
SAMΣ upon its estimated regression coefficient. To do
this we repeated the regression after removing a linear trend from
SAMΣ. We found that the SAMΣ regression
coefficients were unchanged to one decimal place (compare Tables S1 and
S3). This indicates that the variability of the cumulative indices (Fig.
S1c) is dominating the regression and that the SAMΣcoefficient (d ) is largely independent from the linear regression
coefficient (b ).
The inclusion of SAMΣ in the regression model introduces
two types of uncertainties. First, it is very likely that using
1971-2000 as reference period underestimates the trend in
SAMΣ. And, so, the signal attributed to SAM might also
be underestimated as a result. For example, adopting a reference period
of 1961-1990 attributes a larger portion (64% of the total change) of
total AIS mass loss to the SAMΣ term in the regression.
However, using an earlier reference period would introduce another layer
of uncertainty in the quality of earlier data (for example, missing
station values, less observations to assimilate in reanalysis products)
used to define SAM. These sensitivities would remain if the regression
was working with unsummed SAM and time-differenced GRACE. Second,
SAMΣ has a quasi-quadratic shape over 2002-2016 (Fig.
S1c). This has broken down since 2016 and this allows separation of this
term from a pure acceleration such as could be due to monotonically
increasing ice discharge. Adding a quadratic term to Equation 1 gives a
mathematical correlation of 0.53 with the ENSO term and 0.63 with the
SAM term, indicating moderate correlation. As such, there might be some
aliasing of any quadratic-like mass change that are not related to SAM
and ENSO into the estimated SAM and ENSO terms. We note, however, that
recent ice stream speedup has been in rapid response to variable climate
forcing rather than being slow and monotonic, especially in West
Antarctica where most of the modest velocity change has occurred over
the GRACE period(50-52 ). In addition, we note the presence of
periodic decadal climate variability in Antarctica(53, 54 ) (see
also the SMB decadal variability in Fig. 1b, e, Fig S10-11). Our
analysis in the main and supplementary text suggests that the dominant
GRACE modes are linked to SAM and ENSO and much of the estimated SAM and
ENSO signal is associated with SMB.
To compare with the results of linear regression without the climate
indices, we also performed a univariate regression removing the last two
terms of Equation 1:
\(M\left(t_{i}\right)=a+b\left(t_{i}-t_{0}\right)+\sum_{k=1}^{3}\left(c_{k}^{s}\sin{\left(2\pi f_{k}t_{i}\right)+}c_{k}^{c}\cos\left(2\pi f_{k}t_{i}\right)\right)\)(2)
The results of evaluating Equation 2 include those shown in Fig. 2d and
Fig. S8 (orange).
To examine the potential contribution of SMB to the GRACE-derived
regression coefficients, we repeated the above regressions after
subtracting from GRACE time series the cumulative, detrended SMB output
from the RACMO2.3p2_ANT27 model. We also performed the regression just
on the cumulative, detrended SMB from the RACMO2.3p2_ANT27 model
outputs.