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.