Results
We examine monthly time series of ice mass change from 19 years of GRACE
and GRACE Follow On data, covering March 2002 to March 2021. To focus
initially on variability, we remove the linear trend and then decompose
the spatiotemporal fields using empirical orthogonal function (EOF)
analysis, with the leading mode (EOF1) explaining 24% of the variance
of the detrended time series (Fig. 1a) and the second mode (EOF2) a
further 12% (Fig. 1d). These leading modes both exhibit dominant
decadal-scale temporal variability in their principal components (PCs)
(Fig. 1c, f). The respective spatial patterns correspond generally to
areas of reported volume or mass change(1, 23-25 ) along the ice
sheet margin, including key marine-grounded basins of West and East
Antarctica.
We compare GRACE PC1 and PC2 with SAM (station
based23) and ENSO (Niño3.4) climate indices (Fig. 1c
and f, respectively; Fig. S1) to explore the role of large-scale climate
forcing on ice-sheet change. Unlike previous comparison of GRACE and
climate indices(9-11, 26 ), we first cumulatively sum the
normalized indices, reflecting that the raw indices are related to mass
flux rather than the cumulative mass observed by GRACE, something
recognized in studies of ice shelf elevation change(27 ) and
time-integrated SMB(15 ). The resulting cumulative SAM index
(hereafter SAMΣ) shows an upward trend over the GRACE
period while cumulative Niño3.4 index (hereafter
Niño3.4Σ) shows mostly decadal variability(28 )
but negligible trend over this period (Fig. S1b). Detrending these shows
dominant decadal variability and comparing with GRACE PCs shows
strikingly close agreement between SAMΣ and GRACE PC1
(Fig. 1c; r=0.72, p<0.0001), and between
Niño3.4Σ and GRACE PC2 (Fig. 1f; r=0.78 unlagged, r=0.86
6-month lagged, both p<0.0001).
These close agreements suggest that recent inter-decadal to decadal
changes in ice mass are related to both SAM and ENSO. Considering the
EOF/PC pairs, positive peaks in SAMΣ occur following
periods where positive phases of SAM dominated negative phases and are
related to negative mass anomalies in much of coastal West Antarctica,
the southern Antarctic Peninsula, and coastal Wilkes Land in East
Antarctica, and notable positive mass anomalies in the northern
Antarctic Peninsula, and vice versa for negative peaks in
SAMΣ (Fig. 1a). We note that GRACE EOF1 (Fig. 1a) has a
strong resemblance to the spatial pattern of multidecadal trends in mass
change(2, 29 ), despite the EOFs being derived from detrended
data. There is a reduction of the correlation between GRACE PC1 and
SAMΣ during the 2014-2016 super El Niño (Fig. 1c) when
spatial covariances may have been altered. For ENSO, the comparison
suggests positive peaks in Niño3.4Σ, following an El
Niño-dominated state, is related to positive mass anomalies in most of
the western Antarctic Peninsula, the Amundsen Sea coast and coastal
Victoria Land in East Antarctica, and negative mass anomalies in coastal
Wilkes Land, with little signal elsewhere, and vice versa for negative
peaks in Niño3.4Σ (Fig. 1d). The EOF2 pattern of mass
variations is very similar to those observed during the strong 2014-2016
ENSO event(11, 27 ), further confirming that the second EOF mode
captures the ENSO-related signals.
Our continental view of decadal ice-sheet mass change based on GRACE
data cannot separate ocean or atmospheric drivers of this change, but
both may contribute to the observed signals. Regressing modelled
SMB(30 ) anomalies (see Methods) against the two GRACE PCs
produces very similar spatial patterns to the GRACE EOFs (Fig. 1b, e),
with very similar magnitudes to GRACE EOFs in East Antarctica. This
indicates that at least some of these dominant decadal signals are due
to SMB variations, and especially so in East Antarctica. Ice core data
suggest positive SAM results in reduced SMB (19 ), and hence
reduced overall mass balance, consistent with our findings in WAIS and
parts of EAIS (Fig. 1b). El Niño has been shown to increase
precipitation in WAIS but reduce precipitation in EAIS(8, 9, 11,
27 ), as reflected in our SMB analysis (Fig. 1e). Further regression of
modelled winds against the GRACE PCs indicates the decadal SMB
variability, dominated by precipitation, is largely related to changing
meridional atmospheric flows(31 ) (Fig. S2), with onshore winds
corresponding to mass gain and offshore winds to mass loss (Fig. 1, Fig.
S2).
Models suggest positive SAM periods (Fig. S2a) increase the flow of warm
circum-polar deep water onto parts of the continental shelf(20,
21, 32 ) and largely increase ice shelf melt(22 ). High-Niño3.4
periods may also modulate heat transfer from the Southern Ocean to the
continental shelf(20, 27 ). Both SAM and ENSO have been identified
as contributing to ice shelf thinning(27, 33 ) in West Antarctica
or the Antarctic Peninsula, possibly resulting in upstream ice
acceleration and hence the mass loss GRACE is sensitive to.
Interestingly, positive SAM and El Niño are reported(20 ) to have
maximum correlation with total ocean heat transport onto the continental
shelf at zero and 7-9 month lag, respectively, very similar to the zero
and 5 to 7-month lags found in our comparison of the respective indices
with GRACE data (Fig. 1, Methods) and, for ENSO, in some regional GRACE
studies(8, 11 ). Such an oceanic-melt contribution could explain
notable differences between GRACE observations and SMB simulations,
especially in WAIS where persistent positive SAM induces larger mass
loss in GRACE than in SMB (Fig. 1a,1b) and where modelled SMB mass gain
associated with El Niño is damped in GRACE (Fig. 1d,1e).
Given the GRACE time series spans only two decades, the presence of
large inter-decadal to decadal variations means that the estimation of
underlying trends, which reflect larger-scale ice dynamic or SMB trends,
will be sensitive to if and how the inter-annual and inter-decadal
variations are handled in time series analyses. This applies in
particular to the SAM which exhibits not only considerable variations
but also a long-term shift to its positive phase due to anthropogenic
climate change(34 ). While variability over these timescales can
be treated as a stochastic process(5, 6 ), our approach is to take
advantage of the indicated and expected link with physical processes
expressed in climate index variability. Specifically, the above EOF
analysis, which is a purely data-driven and objective approach to
identifying dominant modes of variability, inspires us to construct a
regression model including both SAMΣ and
Niño3.4Σ to further quantify their contributions to
ice-mass change.
We regress GRACE drainage basin time series and on a regular 50 km grid
with respect to time, SAMΣ, 6-month lagged
Niño3.4Σ and various periodic terms (annual,
semi-annual, 161-day), as described in Eq. 1 in Methods and Materials.
This approach is equivalent to regressing the derivative of GRACE
against the unsummed indices but avoids the need to interpolate the data
and the smoothing of amplified high-frequency noise (see Methods). The
regression coefficients for SAMΣ (Fig. 2a) and
Niño3.4Σ (Fig. 2b) are significant (95% confidence
interval, considering temporal correlations) over large parts of the ice
sheet, especially in the coastal margin where they show
spatially-coherent patterns. For
SAMΣ, these are
concentrated in regions of West Antarctica not protected by large ice
shelves, the Antarctic Peninsula and, in East Antarctica: Droning Maud
Land, Wilkes Land, and Victoria Land. Significant
Niño3.4Σ coefficients are found across the same regions
but have a bimodal distribution with opposite sign in much of East
Antarctica compared with the rest of the ice sheet.
We compute the partial variance explained (R2;
Methods) by the Niño3.4Σ and SAMΣ terms,
accounting for the conflating effects of the other regression terms,
including the linear component of SAMΣ. The
Niño3.4Σ and SAMΣ regression terms
together explain a median of 22% of the partial variances of the
gridded time series (Fig. 2c), and R2 often exceeds
50%, and reaches 70%, in coastal regions of the ice sheet, with
smaller values mainly in the ice sheet interior.
In WAIS, the effect of SAMΣ dominates that of
Niño3.4Σ (Fig. 3, Fig. S6), contributing heavily to the
59% of WAIS variance explained by the two terms. In APIS,
Niño3.4Σ contributes most to the 61% variance explained
by the two terms. The apparently negligible role of SAMΣin APIS (Fig. 3) overall disguises substantial relationships in the
southern and northern Peninsula, but which have opposite phase and
similar magnitude (Fig. 2a, Fig. S5). Niño3.4Σ again
dominates in EAIS, where it explains 46% of the variance. Examination
of smaller regions down to drainage basin scale (basin outlines shown in
Fig. 2f) shows that the high level of partial variance explained by the
two regression coefficients continues to hold (Fig. S4-5) and summing
these estimates to ice-sheet scale produces near identical estimates to
those derived from the ice sheet time series (Table S1). Excluding three
basins with little signal, basin R2, using only these
two terms, is 20-77% with a median of 50% variance explained.
While not dominant in WAIS, the Niño3.4Σ term is about
the same magnitude and phase as for the APIS, and together they sum to
the same magnitude as EAIS but with opposite sign such that the full AIS
has negligible Niño3.4Σ signal (Fig. 3). Partly due to
this, R2 for the AIS is smaller at 26% but the
regression still captures important variability (Fig. 3) that is robust,
as indicated by the effects of SAM and ENSO variability on AIS
regression parameters being nearly identical to the sum of WAIS, APIS,
and EAIS regression parameters, with their higher variances (Table S1).
Our regression allows partitioning of the GRACE time series trends into
short-term and long-term components. We interpret the purely linear
trend as being a response to forcing before and/or through the data
period that is apparently not simply related to SAM and ENSO, plus
errors in models of glacial isostatic adjustment(35 ). Our
estimate of this purely linear term is ‑90±32 Gt/yr (95% confidence
level) for the AIS over 2002-2021 (Fig. 4). The positive phase of SAM
over the data period necessarily requires a trend in
SAMΣ (Fig. S1). Time-varying trends are dominated by the
SAMΣ term at the whole ice-sheet scale, and they add
further overall mass loss over the data period. Repeating the
regression, but without the SAMΣ and
Niño3.4Σ terms, gives a purely linear trend of
‑158±14 Gt/yr (Fig. 4); that is, the SAMΣ and
Niño3.4Σ terms together contribute ‑68 Gt/yr, or 43%,
of the total rate of mass change, and hence total mass change, over this
period (Table S1). This contribution is dominated by the effect of SAM
in WAIS where the estimated time-varying SAM trend adds 68±2 Gt/yr (48%
of the total 139±9 Gt/yr) mass loss to the underlying linear trend over
the GRACE period. Repeating the WAIS solution but using time-difference
GRACE data yields equivalent results (Fig. S12, Methods). In EAIS the
underlying linear trend becomes modestly more positive when the effect
of ENSO is considered, increasing by 3 Gt/yr to 20±21 Gt/yr. Over these
regions, time-varying rates of mass loss become more stable when SAM and
Niño3.4 are considered, with residual signal dominated by inter-annual
variability with periods ~3-6 yr (Fig. S7) (26 ).
Over regions down to basin scale and smaller, estimating the
SAMΣ and/or Niño3.4Σ terms also has a
substantial impact on the estimated long-term linear trend (Text S1,
Fig. S8-9, Figure 1f) suggesting that climate variability is
contributing to trends over the GRACE period at all spatial scales.