Introduction
Among the causes of sea level change, land-ice melting is gaining an increasing importance (see Church et al. Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer and Unnikrishnan2013 and references therein). Ice mass accumulation and loss have opposite effects on sea level: an increase in accumulation causes a mean sea level fall, while an increase in surface ablation and outflow causes mean sea level to rise (Church et al. Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer and Unnikrishnan2013). The melting of a land-based ice mass has several consequences. First, meltwater represents a spatially variable mass input for the oceans and causes a change in the global surface load, varying the ocean bathymetry with mantle material being forced under land masses (Fleming et al. Reference Fleming, Tregoning, Kuhn, Purcell and McQueen2012). Furthermore, it causes variations of the Earth’s gravity fields associated with solid Earth deformations. In turn, deformational and gravitational effects cause sea level to fall near the melting sources and to rise at larger distances (Mitrovica et al. Reference Mitrovica, Tamisiea, Davis and Milne2001). In addition, the slow isostatic disequilibrium of the Earth forced by the melting of the continental ice sheets causes rotational effects on large-scale sea level variations (Milne & Mitrovica Reference Milne and Mitrovica1998, Spada Reference Spada2016).
The Antarctic ice sheet (AIS) is currently the largest ice reservoir on Earth. It is estimated that its complete melting would cause a global sea level rise of ~58 m (see table 4.1 in Vaughan et al. Reference Vaughan, Comiso, Allison, Carrasco, Kaser, Kwok, Mote, Murray, Paul, Ren, Rignot, Solomina, Steffen and Zhang2013). According to the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC), the AIS has contributed to an average sea level rise of (0.40±0.20)mmyr-1 (probability≥66%) during 2002–11, with a notable increase with respect to 1992–2001 (0.27±0.11 mmyr-1, see §4.4.3 in Vaughan et al. Reference Vaughan, Comiso, Allison, Carrasco, Kaser, Kwok, Mote, Murray, Paul, Ren, Rignot, Solomina, Steffen and Zhang2013). Based on the previous IPCC AR4, the contribution of the AIS to sea level change was more uncertain, with (0.14±0.41)mmyr-1 during 1961–2003 and (0.21±0.35)mmyr-1 during 1993–2003, with a 90% confidence (see table 5.3 in Bindoff et al. Reference Bindoff, Willebrand, Artale, Cazenave, Gregory, Gulev, Hanawa, Le Qu’er’e, Levitus, Nojiri, Shum and Talley2007). Both reports support an acceleration in the rate of melting of the AIS and an increased confidence on its positive contribution to global sea level rise.
Despite various efforts during the last decade (see e.g. Shepherd et al. Reference Shepherd, Ivins and Geruo2012 and reference therein), several uncertainties persist on the amount and even the sign (loss or gain) of ice mass fluxes from different sectors of the AIS. On one hand, for a warming not exceeding ∼5 °C, the East Antarctic Ice Sheet (EAIS) is expected to grow by an increase in the accumulation rate (Huybrechts & de Wolde Reference Huybrechts and de Wolde1999). Nevertheless, according to the recent work of Golledge et al. (Reference Golledge, Kowalewski, Naish, Levy, Fogwill and Gasson2015) a warming exceeding 1.5–2 °C above present would be sufficient to produce the collapse of large Antarctic ice shelves, with a consequent long-term ‘unstoppable’ contribution to sea level rise. On the other hand, in the West Antarctic Ice Sheet (WAIS) a probably irreversible mass loss is predicted for the next centuries, as a result of the relatively modest snowfall and the slow ice motion in the interior (see e.g. Golledge et al. Reference Golledge, Kowalewski, Naish, Levy, Fogwill and Gasson2015). An acceleration in mass loss from the AIS over the c. 2002–present period has been confirmed by the Gravity Recovery and Climate Experiment (GRACE) mission (see e.g. Velicogna Reference Velicogna2009). Recently, much attention has been devoted to the Antarctic Peninsula (AP), where there is strong evidence that regional warming and increased meltwater ponding has led to the collapse of several ice shelves and the consequent acceleration of their associated outlet glaciers (see e.g. Scambos et al. Reference Scambos, Hulbe and Fahnestock2003).
It has been suggested that, in principle, sea level signals recorded by tide gauges (TGs) can be used to assess recent changes in the mass balance of ice sheets or glaciers (Mitrovica et al. Reference Mitrovica, Tamisiea, Davis and Milne2001, Douglas Reference Douglas2008). On a short timescale (years to decades) the Earth responds elastically to the removal of surface loads, which causes a variation of relative sea level at the coasts. Hence it is expected that observations from TGs located in the vicinity of major ice sheets could be useful to constrain the recent time-history of their mass unbalance (Bindoff et al. Reference Bindoff, Willebrand, Artale, Cazenave, Gregory, Gulev, Hanawa, Le Qu’er’e, Levitus, Nojiri, Shum and Talley2007). However, the effective observation of changes in the mass balance of ice sheets by means of TGs is limited by various problems. In particular, at the end of the 1990s the state of polar TGs was generally unsatisfactory. The subject was first reviewed by Plag (Reference Plag2000), who pointed out the degradation of the observation system and emphasized the importance of Arctic data for the understanding of the ongoing climate variations. The problem of the Arctic sea level observations has been recently reassessed by Henry et al. (Reference Henry, Prandi, Llovel, Cazenave, Jevrejeva, Stammer, Meyssignac and Koldunov2012).
Despite the importance of instrumental measurements in the vicinity of the ice margins, the interest in Antarctic TGs has apparently declined over the years. The most recent review on the topic, which dates back to the work of Lutjeharms et al. (Reference Lutjeharms, Stavropoulos and Koltermann1985), has evidenced a poor coverage of continuous observations. Recent work on geodetic and tidal measurements in Antarctica (Capra & Dietrich Reference Capra and Dietrich2008) has not addressed the general state of the long-term instrumental observations in the region. Some authors (e.g. King & Padman Reference King and Padman2005) have focused attention on short time series (a few weeks to months) in order to calibrate ocean tide models, but these are not useful to study long-term sea level trends. In recent years, the Scientific Committee on Antarctic Research has activated projects involving TG observations but no substantial changes have occurred. Currently, most of Antarctic TGs have discontinuous records or are no longer operative (see http://www.psmsl.org and King & Padman Reference King and Padman2005).
Here, we use the most reliable TG observations from Antarctica, held by the Permanent Service for Mean Sea Level (PSMSL). The PSMSL database contains relative sea level information for 17 stations, mostly located across the AP (8 out of 17, see Fig. 1). For six of them, Revised Local Reference (RLR) monthly and yearly observations are available, spanning from year 1957.79 (Almirante Brown) to 2013.95 (Argentine Islands). For the remaining 11 stations, only ‘Metric’ monthly data can be obtained for the time window 1957–2013. According to the PSMSL recommendations (http://www.psmsl.org/data/obtaining/rlr.php), these should not be used for time series analysis. Henceforth, we assume that reliable averages of the RLR records can be obtained to characterize the sea level trend across the AP, despite different observation methods employed at different locations or changes in the instrumentation (see Table I).
Fig. 1 Location of the Permanent Service for Mean Sea Level (PSMSL) tide gauge (TG) stations available for Antarctica (middle). Red and blue dots show the Metric and Revised Local Reference (RLR) stations, respectively, with the corresponding time series shown in the left and right frames. These have been shifted by 500 mm along the y-axis for the purpose of visualization. The Metric records for id. 1048 and 1729 (namely, McMurdo Sound and Artigas) are not shown because they are highly anomalous.
Table I Basic data on the Antarctic tide gauges (TGs), extracted from the Permanent Service for Mean Sea Level (PSMSL) Metric and Revised Local Reference (RLR) databases on November 2015. The locations of the TGs are also shown. N a is the number of annual records. Where available, information of the type of instrumentation employed is also shown, obtained from the PSMSL and Scientific Committee on Antarctic Research (http://www.scar.org/).
AP=Antarctic Peninsula, EAIS=East Antarctic Ice Sheet, WAIS=West Antarctic Ice Sheet.
Figure 1 shows the PSMSL monthly time series for stations located in Antarctica for both the RLR and Metric datasets. The record length of the available time series do not generally exceed two decades; remarkable exceptions include the RLR station of Argentine Island, located in the AP (time span: 1958–2013, record length: 54 years, completeness: 98%), and the Metric station of Syowa in East Antarctica (1975–2012, 37 years, 92%). Basic information on the Antarctica stations is listed in Table I.
The aim of this work is threefold. First, we review the existing information relating to the Antarctic TGs during the longest possible time window (1958–2014). Second, we analyse available relative sea level observations to assess their spatial and temporal variability, by studying their cyclical components and their long-term trends. Finally, we interpret the estimated levelling off of the sea level curves in terms of accelerated ice loss.
Data and methods
Sea level time series
The limited number, short record length and the poor geographical coverage of the Antarctic TGs severely hinder a coherent visualization of the sea level variability in this region. To characterize the sea level signals available and to increase the signal-to-noise ratio, the time series are ‘stacked’ following the approach outlined by Olivieri & Spada (Reference Olivieri and Spada2013). In particular, for each month t i the sea level is:
$$SL{\rm (}t_{i} {\rm ){\,\equals\,} }{{\rm 1} \over {N{\rm (}t_{i} {\rm ) }}}\mathop{\sum}\nolimits_{j{\rm {\,\equals\,}1}}^{N{\rm (}t_{i} {\rm )}} {\left( {sl_{j} {\rm (}t_{i} {\rm )}{\,\minus\,}\overline{{sl_{j} }} } \right)} ,$$
where N(t
i
) is the number of records for which a value of mean sea level is available, sl
j
(ti) is the sea level observed at the j-th TG at time t
i
and
$$\overline{{sl}}_{j} $$
is the time-averaged sea level. Since we are considering RLR data, for which monthly (and annual) means are reduced to a common datum, in our ensuing computations the term
$$\overline{{sl}}_{j}$$
has not been subtracted. Before evaluating Eq. (1), low-pass filters were not applied to individual time series to remove multi-decadal fluctuations because the length of the stacked curve (≈54 years) exceeds the absolute minimum length (50 years according to Spada & Galassi Reference Spada and Galassi2012) required to minimize the contamination from low-frequency decadal fluctuations.
Four out of the six RLR TGs available in the WAIS are located in the AP (see Fig. 1). This allows us to obtain from Eq. (1) two curves: SWA, drawn using the whole set of six RLR TGs and representative of the WAIS, and SAP, obtained from the four AP records. The two curves, shown in Fig. 2, share similar features to denote that records from the two WAIS stations outside the AP (namely, Cape Roberts Antarctica id. 1763 and Scott Base id. 2029) are substantially coherent with the AP observations. In the EAIS, there are no RLR stations that would allow us to obtain from Eq. (1) an average curve representative for this part of Antarctica. However, six Metric TGs time series are located in the EAIS (Fig. 1). Three of them (namely, Casey id. 1886, Davis id. 1847 and Mawson id. 1814) are fairly complete, but they are affected by several recording problems. The TG record from the site of Syowa (id. 1396) is characterized by a remarkable length (1975–2012) but shows very irregular behaviour, as can be seen in Fig. 1. More information about these stations is available from the documentation page on the PSMSL website.
Fig. 2 Sea-level curves SWA and SAP obtained by averaging the observations from the six West Antarctic Ice Sheet Revised Local Reference (RLR) records and the four Antarctic Peninsula RLR records (see Table I), respectively. Blue lines show N(t i ), which represents the number of data used, at a given epoch t i , to compute the average in Eq. (1).
The SAP and the SWA time series, as well as the individual records, have been analysed using simple regression in order to estimate their linear trend. The uncertainty (corresponding to the 95% confidence interval) is evaluated by the expressions given by Spada & Galassi (Reference Spada and Galassi2012) i.e.:
$$\sigma _{k} {\,\equals\,}{{SEE_{k} } \over {\sqrt {\mathop{\sum}\nolimits_j {\left( {t_{j} {\minus}\overline{t} } \right)} ^{2} } }}\,t_{{0.975,v_k}} ,$$
where
$$\overline{t} $$
is the average of t
j
and t
0.975,νk
is the 0.975th quartile of Student’s t distribution with ν
k
=N
k
v
-2 df (with N
k
v
being the number of valid monthly data in the k-th time series), and SEE
k
is the standard error of the estimate. Since the temporal correlation of errors was not considered, the σ
k
values are probably underestimated (for a complete discussion of the topic, see Bos et al. Reference Bos, Fernandes, Williams and Bastos2013). Here, due to the limited dataset available, trends of relatively short time span will be considered. However, we are aware that in order to avoid the contamination of decadal oscillations in the computed sea level trend, it is necessary to employ series with a minimum length of some decades (see e.g. Sturges & Hong Reference Sturges and Hong2001). The stacking of relatively short time series can, at least partly, alleviate this problem.
To enlighten the possible existence of cyclic components in the observed sea level signals, we apply the empirical mode decomposition (EMD) method of Huang et al. (Reference Huang, Shen, Long, Wu, Shih, Zheng, Yen, Tung and Liu1998). Here, an improved version of the method was used (the ‘ensemble EMD’, hereafter EEMD, see Wu & Huang Reference Wu and Huang2009), and in particular the Complete Ensemble EMD with Adaptive Noise described and implemented in MATLAB by Torres et al. (Reference Torres, Colominas, Schlotthauer and Flandrin2011). This same approach has been adopted by different authors to study multidecadal variations in sea level signals (e.g. see Galassi & Spada Reference Galassi and Spada2015 and references therein). The EEMD technique allows us to decompose non-linear and non-stationary time series sl(t) according to:
$$sl(t){\,\equals\,}\mathop{\sum}\nolimits_{k{\equals}1}^K {IMF_{k} (t)} {\,\plus\,}R(t),$$
where the IMFs are a sequence of K empirically orthogonal ‘intrinsic mode functions’ describing cyclic (i.e. recurrent) variations. These are not necessarily characterized by constant amplitudes and phases, as is the case for the traditional Fourier approach to signal decomposition. Applying the EEMD, it is possible to isolate the non-cyclic residual R(t) that reveals the long-term ‘natural trend’ of the time series. To avoid ‘end effects’ that may affect the determination of the EEMD residual a mirroring technique has been employed following Galassi & Spada (Reference Galassi and Spada2015).
Glacial isostatic adjustment and glacial melting modelling
Since the TGs are anchored to the solid Earth, they are sensitive to vertical movements of different origins. In Antarctica, vertical movements associated with glacial isostatic adjustment (GIA) are of considerable importance (Bevis et al. Reference Bevis, Kendrick, Smalley, Dalziel, Caccamise, Sasgen, Helsen, Taylor, Zhou, Brown, Raleigh, Willis, Wilson and Konfal2009). With GIA, here we refer only to the still ongoing millennial timescale response to the melting of the late-Pleistocene ice sheets (see e.g. Spada Reference Spada2016 and reference therein), not including the recent changes in ice–ocean load. The latter, referred to as glacial melting (GM), will be considered separately. The GIA contribution to sea level change is usually evaluated solving the so-called ‘sea level equation’ (SLE) (Milne & Mitrovica Reference Milne and Mitrovica1998, Spada Reference Spada2016). In terms of present-day rates of change, it reads:
$$\dot{S}(\theta ,\lambda ,t){\,\equals\,}\dot{N}{\minus}\dot{U},$$
where Ṡ is the rate of relative sea level change at co-latitude θ, longitude λ and at time t, U̇ is the rate of vertical displacement of the solid surface of the Earth and Ṅ the rate of sea surface variation (i.e. absolute sea level change).
The values of Ṡ computed at the TG locations according to different global GIA models are presented in Table II. The models include ICE-5G(VM2 L90) of Peltier (Reference Peltier2004) (hereafter, I5G), ICE-6G(VM5a) recently introduced by Peltier et al. (Reference Peltier, Argus and Drummond2015) (I6G) and the Antarctic deglaciation model W12 (Whitehouse et al. Reference Whitehouse, Bentley, Milne, King and Thomas2012). In W12, the chronology of ice sheets follows I5G outside Antarctica. According to the recent work of Purcell et al. (Reference Purcell, Tregoning and Dehecq2016), the present-day radial uplift rates obtained with I6G could be overestimated along the eastern side of the AP.
Table II Relative sea level trends Ṡ for Antarctic tide gauge (TG) records and for their stacks SWA and SAP obtained by linear regression (the data periods are presented in Table I). The errors in the observed trend correspond to the standard deviation of the mean. Columns marked by glacial isostatic adjustment (GIA) show the GIA contribution to Ṡ at the locations of TGs, obtained according to the I5G, I6G and W12 models, respectively (the rates have been rounded to one decimal place). For SWA and SAP, the GIA value represents an average of the GIA values computed for the three models for the West Antarctica and the AP TGs, respectively. The observed rates corrected for GIA are given in the last three columns.
To model the effects of GM, two different approaches have been followed. First, we adopted the SELEN program (Spada & Stocchi Reference Spada and Stocchi2007), which simulates the response of the solid Earth to the melting of continental ice sheets solving the SLE. Since we are dealing with timescales of a few decades, the SLE (Eq. (4)) has been solved in the elastic approximation ignoring delayed viscoelastic effects. Furthermore, as is appropriate for large surface loads, such as the WAIS, the SLE has been solved taking the self-gravitation of the oceans into account and including the effects of Earth rotational variations (e.g. Spada Reference Spada2016). Second, in order to model the effects of the localized ice loss in the AP (Nield et al. Reference Nield, Barletta, Bordoni, King, Whitehouse, Clarke, Domack, Scambos and Berthier2014), we used REAR (Regional ElAstic Rebound calculator), a Fortran program for computing the response of a solid, non-rotating, elastic, isotropic Earth model to surface loading (Melini et al. Reference Melini, Gegout, King, Marzeion and Spada2015). Due to the limited spatial extent of the surface load across the AP, self-gravitation of the oceans and rotational effects are not accounted for in REAR.
Results
The results of the linear trend analysis on the TG series and on the SWA and SAP curves are shown in Table II. The spread of the computed trends can be attributed to different factors as the varying time ranges and record lengths, the different completeness of the time series and local processes can affect the measurements at different degrees. The rates of relative sea level change vary from negative (-3.4 mm yr-1 for Rothera id. 1931) to sharply positive values (+7.9 mm yr-1 for Scott Base id. 2029). The uncertainties are often of the order of 1 mmyr-1. The longest and complete time series (Argentine Island id. 913), shows a trend of +1.4 mmyr-1 for the period 1958–2013; in this case the uncertainty is relatively small (0.2 mm yr-1). During this time span, the linear trends are (2.0±0.1) mm yr-1 for the SWA curve and (1.8±0.2) mm yr-1 for the SAP.
The fields (or ‘GIA fingerprints’) corresponding to the I6G model are shown in Fig. 3. Note that in the bulk of the WAIS the rate of vertical uplift is U̇ ≈-Ṡ, characteristic of regions subject to strong post-glacial rebound. Values of Ṡ associated with GIA at the locations of the TGs considered in this study (see Table II) are all negative (with the exception of the I5G value at the Scott Base TG) and are within the range of -4.2 – -0.6 mm yr-1. A comparison with the observed rates in the first column confirms the significant contribution of GIA at all the Antarctic TGs. The GIA values representative of the sea level variations occurring in West Antarctica and the AP have been obtained by averaging the I6G modelled values of Ṡ at the TG locations, based on the fingerprints shown in Fig. 3. By subtracting the average I6G GIA contribution (-2.0 mm yr-1 for SWA and -2.2 mm yr-1 for SAP) from the observed sea level trends of the two curves, a value of 4.0 mm yr-1 is obtained for Ṡ for both.
Fig. 3 Rates of relative sea level (Ṡ), of vertical displacement (U̇) and sea surface variation (Ṅ) due to glacial isostatic adjustment, according to the I6G model. Units are mm yr-1.
The results of the EEMD of the SWA and the SAP time series are shown in Fig. 4 and Table III; the peak values of the power of their Fourier spectra are also shown in Table III. The first two IMFs of both curves capture the semi-annual and the annual periodicities of the sea level signals while the others reveal oscillations with longer periods. Both the SAP and the SWA show a relatively energetic component (IMF5) with a period of ∼4–5 years (Table III). By further computations, the same periodicity has been detected in a stacked sea level curve composed of some RLR records from southern Patagonia (i.e. Puerto Williams, Ushuaia II, Diego Ramirez, Punta Arenas, Ushuaia I and Caleta Percy). The residuals for SWA and SAP are obtained by removing all the cyclical IMF components from the stacked time series, (shown in the bottom frames of Fig. 4).
Fig. 4 Intrinsic mode functions (IMFs) and residuals (RES) obtained by ensemble empirical mode decomposition (EEMD) of the tide gauge data stacks for the West Antarctic Ice Sheet (SWA) and the Antarctic Peninsula (SAP). Units are mm.
Table III Dominating period of the intrinsic mode functions (IMFs) for the sea level curves SWA and SAP. Also shown is the maximum power of the Fourier spectra of the individual IMFs.
Discussion
Concerning the long-term trends and the periodicities of the sea level signals, the above results require some discussion. The GIA-corrected (I6G) linear trends obtained for the SWA and SAP curves (4.0 mmyr-1), can be interpreted as the result of GM and of thermosteric and halosteric oceanic contributions (Spada & Galassi Reference Spada and Galassi2012). In addition, these rates can be influenced by the feedback mechanism between temperature and salinity trends and sea ice production (see, for the AP, Meredith & King Reference Meredith and King2005). The 4–5 year component of the SWA and SAP time series has also been detected in some records from southern Patagonia, with a comparable period characterizing the propagation of the Antarctic Circumpolar Wave (∼4–5 years, see White & Peterson Reference White and Peterson1996). This is responsible for interannual variations in the atmospheric pressure at sea level, wind stress and sea surface temperature with a westward propagation. The connection between ice dynamics, sea level rise and the circumpolar wave in Antarctica has been recently assessed by Mémin et al. (Reference Mémin, Flament, Alizier, Watson and Rémy2015).
In Fig. 5, the EMD residuals obtained for the SWA and for the SAP (red) are compared, with the trend obtained by a simple regression (blue), during the period (1958–2014). It is apparent that during the last few decades the EMD residual shows a reduced rate of variation (i.e. a levelling off) with respect to the long-term linear trend. Considering only 2000–14, the trend of the SAP residual is 0.6 mmyr-1, i.e. 1.2 mm yr-1 smaller than that shown by the linear model over the whole time window (1.8±0.2 mmyr-1). For the SWA, the 2000–14 trend of the residual is 1.2 mmyr-1, reduced by 0.9 mm yr-1 relative to the long-term linear trend. A similar deviation from the linear trend is also visible in the first part of the curves (1960–70), which could be explained by an accelerated ice mass loss, possibly occurring locally. Unfortunately, the limited knowledge about the melting history of Antarctica during this period makes further investigations impossible.
Fig. 5 Linear trend (blue) and ensemble empirical mode decomposition (EEMD) residuals (red) for the Argentine Island tide gauge (id. 913), SAP and SWA. The frames on the right show of the curves during last ∼15 years.
Since the GIA contribution to sea level change can be considered constant on the timescales of a few decades because of the relatively high viscosity values commonly employed in modelling (see e.g. Spada et al. Reference Spada, Olivieri and Galassi2014), the apparent levelling off observed for both curves since 2000 cannot be attributed to GIA. It is therefore possible that these anomalies in the observed trends have been caused by the recent ice melting, which can produce short-term elastic or viscoelastic deformations and, consequently, relative sea level variations. In his work, Douglas (Reference Douglas2008) already addressed the question of the detectability of sea level fingerprints of the current melting in Antarctica. However, he employed TG records from relatively distant locations in Argentina, New Zealand and Australia, which he found to be contaminated by a significant decadal variability and that did not seem to indicate the presence of a fingerprint of ice loss (i.e. visible levelling offs). The large signals from the recent deglaciation in Antarctica make the local instrumental records potentially useful for the detection of fingerprints, provided that the cyclic variations are isolated and removed as it has been done here using an EEMD approach.
To address the role played by present ice melting in the observed anomalies of the residual trends, we have modelled the GM elastic response according to different geometries of unloading. As shown in the work of Nield et al. (Reference Nield, Barletta, Bordoni, King, Whitehouse, Clarke, Domack, Scambos and Berthier2014), viscoelastic models having viscosities that are traditionally employed in global GIA studies (e.g. the VM2 viscosity profile) would not produce, on a decadal timescale, responses that differ significantly from the elastic solution. As discussed earlier, large uncertainties still exist for the mass balance of the AIS over recent decades. Different authors agree that the WAIS is losing mass faster than the EAIS, for which ice accumulation is not totally discounted (Church et al. Reference Church, Clark, Cazenave, Gregory, Jevrejeva, Levermann, Merrifield, Milne, Nerem, Nunn, Payne, Pfeffer, Stammer and Unnikrishnan2013). Inside the WAIS, the AP is particularly sensitive to recent changes in climate conditions that have led to the retreat and to the eventual collapse of several major ice shelves over the past∼50 years (Berthier et al. Reference Berthier, Scambos and Shuman2012, Nield et al. Reference Nield, Barletta, Bordoni, King, Whitehouse, Clarke, Domack, Scambos and Berthier2014). Between 1993–2010, the AIS contribution to the global mean sea level budget has been assessed in 0.27 mm yr-1 (0.16–0.38 mm yr-1 with a probability ≥66%), corresponding to rate of ∼ -97 Gt yr-1 (Vaughan et al. Reference Vaughan, Comiso, Allison, Carrasco, Kaser, Kwok, Mote, Murray, Paul, Ren, Rignot, Solomina, Steffen and Zhang2013). For the WAIS and the AP, the mass balance was assessed separately from the whole AIS by Shepherd et al. (Reference Shepherd, Ivins and Geruo2012). Accordingly, between 1992 and 2011, the mass of the WAIS (not including the AP) has changing at a rate of (-65±26)Gtyr-1, comparable to the whole AIS (-71±53 Gtyr-1). During this same period, Shepherd et al. (Reference Shepherd, Ivins and Geruo2012) have assessed a rate of mass change of (+14±23) Gt yr-1 from the EAIS.
For the AP alone, two different ice distributions were considered. The first, referred to as ‘coarse’, is spatially uniform and assumes a rate of ice mass change of (-20±14) Gt yr-1 between 1992−2011, in agreement with Shepherd et al. (Reference Shepherd, Ivins and Geruo2012). For the second, the detailed geometry proposed by Nield et al. (Reference Nield, Barletta, Bordoni, King, Whitehouse, Clarke, Domack, Scambos and Berthier2014) was adopted, based on elevation changes data from digital elevation model and ICESat observations (hereafter referred to as DEM+ICESat), with a mass balance of ∼-16 Gt yr-1 from 1996–2014. The two ice models for the AP are presented in Fig. 6, where the locations of the RLR TGs are also shown. Figure 7 shows the results of the REAR simulation using the ‘coarse’ distribution (Fig. 7a–c) and those of the DEM+ICESat-based model (Fig. 7d–f). In both cases, there is an intense relative sea level fall across the whole AP (Fig. 7c & f) with values of several millimetres per year along the coastlines. These patterns are strongly anti-correlated with the map of vertical uplifts induced by unloading (Fig. 7a & d). The rates of absolute sea level change (Fig. 7b & e) have a comparatively smaller amplitude, as expected in areas that are subject to intense deglaciation. The sea level fingerprint computed by SELEN assuming a uniform rate of melting across the WAIS is shown in Fig. 8. Since in this simulation the AP is included into the WAIS, the rate of ice mass change adopted corresponds to the total amount estimated by Shepherd et al. (Reference Shepherd, Ivins and Geruo2012) for the AP and the WAIS during 1992–2011, i.e. -85Gtyr-1. Across the region, significant gradients of sea level change can be observed, with values ranging between ∼-1.0 mm yr-1 near the load margins to ∼0.2 mm yr-1 in the far field along the east coasts of Antarctica.
Fig. 6 Ice distribution and rate of ice loss (in Gt yr-1) for a. ‘coarse’ distribution and b. the DEM+ICESat-based model used in Nield et al. (Reference Nield, Barletta, Bordoni, King, Whitehouse, Clarke, Domack, Scambos and Berthier2014). The locations of the Revised Local Reference (RLR) tide gauges are also shown.
Fig. 7 Rates of vertical displacement (U̇), sea surface variation (Ṅ) and relative sea-level change (Ṡ=Ṅ − U̇), modelled by the REAR program for an ice melt rate of 20 Gt yr-1 uniformly distributed across the Antarctic Peninsula (a.–c.) and for the Nield et al. (Reference Nield, Barletta, Bordoni, King, Whitehouse, Clarke, Domack, Scambos and Berthier2014) ice mass balance and distribution (d.–f.).
Fig. 8 Rate of relative sea-level change (Ṡ, in mm yr-1) due to melting of the West Antarctic Ice Sheet (WAIS), modelled by SELEN assuming a uniformly distributed rate of ice loss of 85 Gt yr-1.
The modelled rates of relative sea level change computed at the TG locations are summarized in Table IV, according to the AP and WAIS ice sources considered in Figs 7 & 8, respectively. The rate of ice mass loss has been assumed constant for the TG data period. As expected, the spatial distribution of the ice sources and their mass balance influence the computed rates. At the Argentine Island and Almirante Brown TGs, the rates obtained using the ‘coarse’ AP source (-2.9 and -4.8 mmyr-1, respectively) exceed those obtained considering the realistic DEM+ICESat-based model (-1.7 and -3.8 mmyr-1, respectively). The importance of the choice of ice distribution is also reflected in the average values of the sea level fingerprints evaluated along the coastlines and at the TG locations. The averaged sea level rates computed at the TG locations for the two AP simulations is -2.4 mm yr-1 for the ‘coarse’ model and -1.7mmyr-1 for the DEM+ICESat-based model. Interestingly, these rates mostly reflect the different amplitudes of the two mass balances employed, and less their spatial distribution. An average of -0.5 mm yr-1 was found for the WAIS.
Table IV Modelled values for the rate of relative sea level change (Ṡ) due to melting of the West Antarctic Ice Sheet (WAIS) and the Antarctic Peninsula (AP), compared with the observed trends (from Table II). The values for WAIS have been obtained by SELEN computing the elastic response to an ice loss of 85 Gt yr-1. For the AP, the ‘coarse’ uniform ice loss of 20 Gt yr-1 and the DEM+ICESat mass balance used in Nield et al. (Reference Nield, Barletta, Bordoni, King, Whitehouse, Clarke, Domack, Scambos and Berthier2014) (∼-16 Gt yr-1) are assumed. For the SWA and the SAP curves, the modelled values have been averaged at the location of tide gauges used in each stack.
The fingerprints shown in Figs 7 & 8 for the AP and the WAIS can help to obtain insight into the trends shown by the SWA and SAP sea level curves during last decades. From both our modelled AP fingerprints, the levelling off observed in Fig. 5 points to an accelerated melting in the AP and in particular to an increase in the rate of mass loss of ∼10Gtyr-1 in its mass balance during 2000–14, relative to 1958–2014. This is likely to be a conservative lower boundary, since our computations did not consider the amplifying effects that could be associated with the presence of a low viscosity layer beneath the lithosphere (Ivins et al. Reference Ivins, Watkins, Yuan, Dietrich, Casassa and Rülke2011). Indeed, Nield et al. (Reference Nield, Barletta, Bordoni, King, Whitehouse, Clarke, Domack, Scambos and Berthier2014) demonstrated that by reducing the viscosity of the whole upper mantle to ∼1018 Pa·s, the rates of uplift in response to unloading in the AP are approximately tripled with respect to a high viscosity (or elastic) mantle. They found that a very low viscosity was needed for the upper mantle to explain the rapid change in GPS uplift.
Although direct observations are not available for the AP during the entire period encompassed by the SAP TG-based curve, our estimate above supports an acceleration in the rate of melting in the AP, which has been effectively inferred from satellite data over decadal timescales (Shepherd et al. Reference Shepherd, Ivins and Geruo2012). Indeed, according to table 1 in Shepherd et al. (Reference Shepherd, Ivins and Geruo2012), during 2000–11 the rate of mass change in the AP was estimated at (-29±12)Gtyr-1, significantly larger than during 1992–2000 (-8±17 Gt yr-1), with a corresponding increase in the rate of melting of ∼(21±21)Gtyr-1 (the uncertainty is obtained by summing the errors in quadrature). Similarly, for the WAIS, a significant fraction of the observed levelling off shown by the SWA curve since 2000 (∼0.9 mm yr-1) could manifest the recently observed accelerated rate of ice melting across the WAIS.
According to Shepherd et al. (Reference Shepherd, Ivins and Geruo2012), it has seen a variation from (-46±36)Gtyr-1 during 1992–2000 to (-114±25)Gtyr-1 during 2000–11 (note these values include the contribution of the AP). The deviation from a constant rate observed in the earlier parts of the records (shown in Fig. 5) could be indicative of an early episode of deceleration in the rate of mass loss in the AP and in the WAIS, but this is not supported by direct observations.
Conclusions
All of the available RLR PSMSL records are from the WAIS, with most of them (four out of six) located in the AP. The stack of all of the RLR TGs (SWA) reveals a sea level rise of (2.0±0.1) mm yr-1, a value that essentially matches that obtained considering the SAP curve built from the AP records alone (1.8±0.2 mmyr-1). After correcting for the effects of GIA using the I6G model, the observed rate of relative sea level change is (4.0±0.1)mmyr-1 for the SWA and (4.0±0.2) mm yr-1 for the SAP, where the uncertainty only reflects the error on the linear trend. Using other GIA models (I5G and W12), these rates would only change by 15% at most. Since 2000, the non-cyclic residual of the SAP and SWA curves obtained by an EEMD analysis, shows a levelling off of the linear trend of ∼0.9 mm yr-1 for the SWA and 1.2 mm yr-1 for the SAP. This phenomenon could represent changes in the mass balance of melting sources located in the vicinity of the TGs. With the aid of the sea level fingerprints associated with the melting of ice sources in the WAIS and AP, we have shown that the recent acceleration in the rate of melting may be partly responsible of the slowing down observed in the rate of sea level rise across the AP since 2000. This may constitute the first evidence of sea level fingerprints of glacial melting in Antarctica.
Acknowledgements
We thank Matt King for providing mass balance data and very constructive comments, and two anonymous reviewers for useful suggestions. Marco Olivieri is thanked for fruitful discussions and advice. The GIA data for models ICE-5G(VM2 L90) and ICE-6G(VM5a) have been downloaded from the home page of Richard Peltier (http://www.atmosp.physics.utoronto.ca/∼peltier/data.php). The W12 data have been kindly provided by Pippa Whitehouse. All the figures have been drawn using the Generic Mapping Tools (http://gmt.soest.hawaii.edu/). This work was funded by Programma Nazionale di Ricerche in Antartide (PNRA; CUP D32I14000230005) and by research grants from the Department of Pure and Applied Sciences (DiSPeA) of the Urbino University ‘Carlo Bo’ (CUPs H32I160000000005 and H32I15000160001). The SELEN and REAR programs can be downloaded from https://geodynamics.org/cig/software/selen/ and http://hpc.rm.ingv.it/rear, respectively.
Author contribution
Both authors contributed equally to data gathering, data analysis, figure drafting and discussion, and to the preparation of the manuscript.
