1. Introduction
Among the ramifications of climate change due to the ongoing global warming, sea level rise is a social, political, and economic issue because of its considerable impact on lowland and coastal environments (IPCC 2019, 2021). Antarctica holds massive ice on the bedrock, being an enormous reservoir of Earth-surface freshwater and a potentially dominant contributor to future sea level rise (IPCC 2013; Noble et al. 2020). Although the thermal expansion of seawater has been the main cause of the sea level rise in the twentieth century; it is speculated that the negative imbalance in the Antarctic ice sheet mass will be the dominant component in the coming centuries (IPCC 2021).
Ice shelves are the floating parts of the ice sheets. Antarctic ice shelves fringe about 74% of the Antarctic coastline (Bindschadler et al. 2011). Although ice shelves occupy only 11% of the total area of the Antarctic ice sheet (Fox et al. 1994), regional changes in their shape and their local ablation processes crucially affect the dynamics and mass balance of the whole Antarctic ice sheet. Recent satellite observations of the Antarctic ice sheet and ocean hydrographic surveys have revealed that ice-shelf basal melting affects ice sheet dynamics (Depoorter et al. 2013; Rignot et al. 2013; Liu et al. 2015) and also affects deep water properties over the Southern Ocean (Sallée 2018; Schmidtko et al. 2014; Jacobs and Giulivi 2010). A better understanding of the ocean–ice shelf interaction along the Antarctic coastal margins is required to assess present-day and future changes in the Antarctic ice sheet, Southern Ocean climate, and global sea level rise (Convey et al. 2009; Turner et al. 2009; Noble et al. 2020). It has been suggested that there exist climate tipping points for the Antarctic ice sheet and the Southern Ocean (ice sheet collapse and cessation of bottom water formation) that have a significant impact on global climate (Lenton et al. 2008; Lenton 2011). Understanding how the level of global warming affects changes in the Antarctic and Southern Ocean climate is important for projecting the future global environment.
To assess future environmental changes in a warming climate, numerical climate models, which represent Earth’s processes (e.g., atmosphere, ocean, sea ice, and land surface components), have been developed in many research institutes (Kawamiya et al. 2020). The results of climate projections are widely used in scientific research and for making policies on mitigation and adaptation to global warming (IPCC 2021; Eyring et al. 2016). However, CMIP5/6 climate models do not have an ice-shelf component that could sufficiently reproduce ice–ocean interaction in Antarctic coastal regions in a realistic way. This is because ocean models that include an ice-shelf component have been developed just over the two decades (Dinniman et al. 2016; Asay-Davis et al. 2017), which had been premature for global climate models, and because the spatial scale of some Antarctic ice shelves is too small to be adequately represented in an approximately 1° ocean model, which is a standard configuration in climate models for long-term integration. To overcome these limitations, several studies have performed numerical experiments using ocean–sea ice–ice shelf models, which were forced with prescribed future atmospheric conditions derived from future climate simulations without ice shelf–ocean interaction for obtaining future projections in Antarctic ice-shelf melting (Hellmer et al. 2012; Timmermann and Hellmer 2013; Naughten et al. 2018, 2021). These models demonstrated that changes in warm water delivery, such as Circumpolar Deep Water (CDW), onto the continental shelf regions are vital for ice-shelf basal melting in a warming climate. A limited number of numerical modeling studies have focused on the future projection of Antarctic ice-shelf basal melting (Hellmer et al. 2012; Naughten et al. 2018; Timmermann and Hellmer 2013). The impact of a warming climate on Antarctic ice-shelf basal melting is not straightforward and is likely region- and scenario-dependent. Therefore, more research on how ice-shelf basal melting responds to changes in atmospheric forcing is required.
With almost the same methodology in previous studies (Hellmer et al. 2012; Timmermann and Hellmer 2013; Naughten et al. 2018), we conducted numerical experiments using an ocean–sea ice–ice shelf model driven by the future atmospheric surface conditions derived from a climate model and analyzed the results to examine the future changes in Antarctic ice-shelf basal melting and the driving mechanisms. This study focuses on the variability in the Antarctic coastal water masses flowing into ice-shelf cavities and the physical linkage with the coastal water masses and sea ice, with special attention to their seasonal changes in future projections. The numerical experiments reveal that a large decrease in Antarctic sea ice coverage, particularly the complete disappearing of regional sea ice in summer and a pronounced reduction in the coastal sea ice production in winter, and the associated freshwater redistribution play a crucial role in future projections of Antarctic coastal water masses and subsequent ice-shelf basal melting.
2. Numerical model and experiments
a. An ocean–sea ice–ice shelf model
This study used an ocean–sea ice model (COCO; Hasumi 2006) with an ice-shelf component (Kusahara and Hasumi 2013). The model configuration is the same as that in our previous study (Kusahara 2021), which focused on the interannual variability of Antarctic ice-shelf basal melting in recent decades. The model horizontal resolution is 0.2° × 0.2° cosφ on the longitude–latitude grid system. The grid size ranges from 2.5 km at the southernmost grid cells at 83.5°S to 21 km at the northernmost grid cells at 20°S. The vertical grids consist of three levels of 5 m, one level of 15 m, 59 levels of 30 m, and 32 levels of 100 m from the surface to the bottom. The ocean bottom topography and ice-shelf draft were derived from the RTopo-2 dataset (Schaffer et al. 2016). The atmospheric surface boundary conditions to drive the ocean–sea ice model are wind stresses, wind speed, surface air temperature, specific humidity, downwelling longwave and shortwave radiation, and freshwater flux. We used observation-based ocean properties (PHC3.0; Steele et al. 2001) for the initial condition and the restoring conditions near the artificial northern wall boundary (north of 22°S). Ocean properties from the surface to the ocean floor near the wall boundary were restored to the present-day monthly climatology with a 10-day damping time scale. The same restoring with the present-day ocean conditions was done even in a series of future scenarios’ experiments. Thus, it should be kept in mind that with this configuration we can assess only the regional impact of the atmospheric changes over the Southern Ocean on the Antarctic coastal conditions, but not the remote impacts of the ocean changes north of the artificial boundary, such as long-term changes in the global thermohaline circulation. The ice-shelf shape in this model was assumed to be steady (constant in time). The ice-shelf basal melt rate was diagnosed with the thermodynamic ocean–ice shelf interaction based on the three-equation formulation (Hellmer and Olbers 1989; Holland and Jenkins 1999). The steady-shape ice-shelf base exchanges freshwater and heat with the uppermost ocean grid cell based on the diagnosed basal melt rate. In this model, we assumed that all the heat exchange on the ice–ocean interface is used for ice-shelf basal melting/freezing (e.g., no conductive heat flux into the ice-shelf interior).
b. RCP scenarios
The model was first spun up with present-day climatological atmospheric conditions (repeated year forcing) for 50 years to obtain quasi-steady states in the Antarctic sea ice and coastal ocean conditions and ice-shelf basal melting. The daily surface boundary conditions for the spinup were calculated from a climatology dataset, the third version of the Ocean Model Intercomparison Project (OMIP)-Forcing (hereafter “OMIP3rd”; Röske 2006), using a bulk formula for surface fluxes (Kara et al. 2000). In this study, we used OMIP3rd as a representative atmospheric condition during the end of the twentieth century. We then performed a series of numerical experiments forced with future atmospheric conditions under various representative concentration pathway (RCP) scenarios (RCP2.6, RCP4.5, and RCP8.5) in the CMIP5 protocol (Taylor et al. 2012). The future atmospheric conditions of the RCP scenarios were derived from the results of a climate model, MIROC-ESM (Watanabe et al. 2011). We calculated the spatiotemporal anomaly of the surface boundary conditions for each month relative to the 1981–2000 monthly climatology and superimposed the monthly anomalies on the repeated year forcing to obtain future atmospheric surface boundary conditions. This treatment was conducted to minimize the climate model’s spatiotemporal biases. In appendix A, we show annual-mean maps of the atmospheric variables represented in OMIP3rd and MIROC-ESM (Fig. A1) and the anomalies for the periods 2001–20, 2080–99, and 2121–40 in MIROC-ESM (Fig. A2). As can be seen from the left and middle panels in Fig. A1, MIROC-ESM reasonably reproduced atmospheric conditions over the Southern Ocean during the end of the twentieth century (1981–2000). A detailed comparison of atmospheric fields between OMIP3rd and MIROC-ESM shows that MIROC-ESM has a circumpolar negative anomaly at 50°S with strong regional minimums in the western Pacific Ocean and the Amundsen–Bellingshausen Seas regions (Fig. A1l). Corresponding to this pressure anomaly pattern, there are negative and positive anomalies in the wind stress fields south and north of 50°S, respectively (Fig. A1c). Also, there is an almost circumpolar pattern of a negative anomaly in surface air temperature along the Antarctic coastal margins, except in the Ross Sea (Fig. A1i). Note that since MIROC-ESM reproduced the general patterns in the atmospheric fields over the Southern Ocean, we calculated separately the anomalies of the eastward and northward wind stresses in MIROC-ESM and superimposed them on those in the repeated-year forcing (OMIP3rd).
In this paper, we refer to the numerical experiments under the RCP scenarios as the RCP2.6, RCP4.5, and RCP8.5 cases to indicate the results from the ocean–sea ice–ice shelf model. A validation experiment with the repeated year forcing was also performed for the same period of the RCP cases to evaluate inherent drifts in the model (the CKDRF case). The model integration periods were 2000–99 for the RCP2.6 case due to the unavailability of the MIROC-ESM output and 2000–2141 for the other three cases. Note that MIROC-ESM followed the CMIP5 standard protocol (Taylor et al. 2012) for the RCP4.5 and RCP8.5 extensions after 2100.
3. Results
a. Future changes in Antarctic ice-shelf basal melting
Modeled future change in the total annual Antarctic ice-shelf basal melting varies greatly among the RCP cases (Fig. 1 and Table 1). In this paper, we used three periods 2001–20, 2080–99, and 2121–40 (hereafter referred to in figures as the first, second, and third periods, respectively) to determine changes in the model’s variables. At the beginning of the numerical experiments (i.e., 2001–20), there is little difference in the total basal melting amounts in the three cases. The three scenarios’ mean of the total annual mean ice-shelf basal melting is 1470 Gt yr−1, roughly consistent with observation-based present-day estimates of 1454 ± 174 Gt yr−1 (Depoorter et al. 2013) and 1500 ± 237 Gt yr−1 (Rignot et al. 2013). We provide detailed assessments of the modeled ice-shelf basal melting and ocean conditions along Antarctic coastal margins in appendix B. In 2121–40, the total ice-shelf basal melting in the RCP8.5 case reaches 2795 Gt yr−1, corresponding to a 90% increase with respect to that in 2001–20, whereas that in the RCP4.5 case (1758 Gt yr−1) shows just a 20% increase. The total ice-shelf basal melting in the RCP2.6 and RCP4.5 cases shows small gradual increases with sizeable interannual variability throughout the twenty-first century. The linear trends in the total ice-shelf basal melting in the three cases (Fig. 1) are statistically significant (>95%), measured with their interannual variabilities. It should be noted that the positive linear trends in the RCP4.5 and RCP8.5 cases are larger than those in the CKDRF case, confirming that their linear trends are a response to atmospheric forcing, not model drift. The trend of the total ice-shelf basal melting in the RCP2.6 case is comparable to that in the CKDRF case. This indiscernible trend in the RCP2.6 comes from regional compensation of increases and decreases in the ice-shelf basal melting. The RCP2.6 case also shows large regional variability as a response to future atmospheric changes, while the CKDRFT does not (shown later). In the RCP8.5 case, the total ice-shelf basal melting starts to increase dramatically after 2070–80, bifurcating from the other two RCP cases.
Mean and standard deviation of annual ice-shelf melting, sea ice production, and sea ice melting in the three periods (2001–20, 2080–99, and 2121–40) in the three cases (RCP8.5, RCP4.5, and RCP2.6). The sea ice production and melting are the sum over the coastal regions within 200 km from Antarctic coastline or ice-front. Absolute values are used in this table and it should be noted that the sign of sea ice production is opposite to the ice-shelf melting and sea ice melting.
Figure 2 shows a scatter diagram of Antarctic ice-shelf basal melting (lines in Fig. 1) versus surface air temperature over the Southern Ocean (Fig. A3a). It reveals a nonlinear response to atmospheric warming with two distinct regimes, namely at low- and high-temperature rising levels. The linear regression of the annual ice-shelf basal melting to air temperature rise in the RCP2.6 and RCP4.5 cases is 56 and 97 Gt yr−1 °C−1, respectively. The linear regression of the three cases at the low-temperature anomaly range (<3°C) is 99 Gt yr−1 °C−1. At the high-temperature anomaly range (>4°C in the RCP8.5 case), the regression coefficient becomes approximately 4 times larger (399 Gt yr−1 °C−1) than the three scenarios’ regression, indicating increased sensitivity of Antarctic ice-shelf melting to Southern Hemisphere atmospheric warming.
The spatial change in future ice-shelf basal melting is considerably different from region to region. The horizontal distribution of the linear trend in the annual basal melt rate over the period 2001–2140 in the RCP8.5 case is shown in Fig. 1 to capture the regional pattern of change in the modeled basal melt rate. Note that appendix B also provides detailed regional maps of present-day ice-shelf basal melt rate to assess the model performance (Figs. B1–B8). In this study, we categorized the Antarctic ice shelves into 11 groups based on their locations. The regional changes in ice-shelf melting are examined in detail based on this grouping. To explore the regional response of ice-shelf melting under the warming scenarios, we calculated the ratio of the regional annual ice-shelf basal melting amount in the three periods with respect to the three scenarios’ mean of the annual mean basal melting in 2001–20 (Fig. 3).
In the RCP8.5 case, basal melting for ice-shelf groups c [Eastern Weddell Ice Shelf (EWIS)], e [Amery Ice Shelf (AIS)], f [West Ice Shelf and Shackleton Ice Shelf (WeIS/ShIS)], and k [Abbot Ice Shelf, Wordie Ice Shelf, and George VI Ice Shelf (AbIS/WoIS/GeVI)] in 2121–40 becomes more than double the three scenarios’ mean in 2001–20. In particular, basal melting of ice-shelf groups e (AIS) and k (AbIS/WoIS/GeVI) increases by a factor of 3–5, respectively, indicating that ice-shelf basal melting in these regions is very sensitive to changes in atmospheric conditions. Ice shelves a [Larsen Ice Shelves (LIS)], b [Filchner–Ronne Ice Shelf (FRIS)], d [Shirase Glacier Tongue (SGT)], g [Totten Ice Shelf, Mertz Glacier Tongue, and Cook Ice Shelf (ToIS/MGT/CoIS)], and j [Getz Ice Shelf, Thwaites Glacier, and Pine Island Glacier (GIS/ThG/PIG)] also show a substantial increase of 40%–70% relative to the present-day values. Ice shelf h [Ross Ice Shelf (RIS)] shows relatively constant basal melting throughout the integration in the three RCP cases, and ice shelf i [Sulzberger Ice Shelf (SuIS)] shows a decrease in ice-shelf basal melting in 2121–40.
The above analyses used the annual mean of ice-shelf melting to capture the long-term trend. We now show large changes in the seasonality of ice-shelf basal melting in the three periods in the three cases. Here, we only show the results for the total ice-shelf basal melting (Fig. 4); Figs B9 and B10 in appendix B show changes in seasonality for the regional ice-shelf melting. The seasonal cycle in Antarctic ice-shelf basal melting in the model has a maximum in warm months and a minimum in cold months, which is consistent with previous modeling studies (Dinniman et al. 2015; Kusahara 2021). The seasonality is mainly controlled by relative strength among cold and warm water masses. Cold water masses formed in winter suppress active ice-shelf basal melting caused by warm water intrusions, and the seasonal presence and absence of warm surface water also regulate the magnitude of ice-shelf basal melting (Kusahara 2021; Aoki et al. 2022). In 2001–20, the monthly basal melting amount reaches a higher rate in the warm months of January–April (1884 Gt yr−1 of the annual equivalent melt amount) and a lower rate in the cold months of July–November (1183 Gt yr−1), indicating substantial ice-shelf basal melting throughout the year. In the future warming cases, there are pronounced changes in the monthly melting amount in the warm months. In the RCP4.5 case, the percentage increases of the warm-months ice-shelf basal melting in 2080–99 and 2121–40 with respect to the 2001–20 scenarios’ mean are 23% and 32%, respectively. The percentage increases in the RCP8.5 case are more pronounced, with a 51% increase for 2080–99 and a 119% increase for 2121–40. The changes in the total ice-shelf basal melting in the cold months are very small (up to a 7% increase in the RCP4.5 case for 2121–40) compared to those in the warm months, except in the RCP 8.5 case. The percentage increase in the cold-months ice-shelf basal melting in the RCP8.5 case for 2121–40 is 53%, indicating an increase in the level of ice-shelf basal melting throughout the year. In the following sections, we examine the causes of the increased ice-shelf basal melting, with a focus on changes in Antarctic coastal water masses and sea ice processes.
b. Changes in Antarctic coastal water masses
Antarctic ice shelves have thicknesses ranging from several tens of meters to 100 m at the ice-shelf edge and several hundreds of meters to over 2000 m near the grounding line. The ocean beneath the ice shelves is isolated from the atmosphere by thick ice, and thus the only heat source for basal melting is the lateral ocean flow into the ice-shelf cavities. Although seawater temperature and salinity are spatially continuous and temporally variable in nature, the concept of water mass, grouping water parcels with similar water properties, is helpful to examine complex oceanographic processes with fewer variables. There are three key Antarctic coastal water masses for ice-shelf basal melting (Jacobs et al. 1992), namely Dense Shelf Water (DSW; cold and high salinity), Circumpolar Deep Water (CDW; warm and high salinity), and Antarctic Surface Water (AASW; warm and low salinity), and Jacobs et al. (1992) defined three ice-shelf basal melting modes associated with the three water masses (DSW for mode 1, CDW for mode 2, and AASW for mode 3). In this study, we analyze Antarctic coastal water masses flowing into ice-shelf cavities across the model’s ice-shelf fronts to understand the spatiotemporal variability of ice-shelf basal melting under the warming scenarios (Figs. 5–7). It should be noted that the water mass analysis is useful to capture the model results in different experiments but loses horizontal and vertical information of the water properties. To compensate for the disadvantage of the water mass analysis, we show horizontal distributions of ocean temperature at the subsurface layer and the seafloor and vertical profiles of the ocean temperature and density near the Antarctic coastline and ice-front line in 2001–20 and 2121–40 in the RCP8.5 case (Figs. B2–B8).
The definition of water masses used in this study are shown on a temperature–salinity (T-S) diagram in Fig. 5a. The water mass acronyms MC, LS, HS, and AS (described below) are used to describe the model results (Kusahara 2021). In this study, we further defined subclasses of shallow AS (sAS) and shallow MC (sMC) in a part of AS and MC, respectively, using a depth threshold for the inflowing water (<240 m). Since the water mass of AS includes water mixed with LS and MC in deeper layers, introducing the new subclass of sAS allows us to identify the water mass originated from the surface processes. We used monthly averages of ocean properties and velocities to calculate the water masses’ transport. Figure 5a shows seasonal variations in the coastal water masses’ transport flowing into the ice-shelf cavities averaged over 2001–20 in the RCP8.5 case. In the present-day conditions (e.g., 2001–20), MC, LS, HS, and AS roughly correspond to modified CDW (mCDW), Low Salinity Shelf Water (LSSW, a less-dense variety of DSW), High Salinity Shelf Water (HSSW, dense variety of DSW), and the sum of AASW and a mixed water mass of LSSW and mCDW in deep layers, respectively.
We show the annual-mean time series of the Antarctic coastal water masses inflowing into the ice-shelf cavity of all Antarctic ice shelves (Fig. 6a) and pie charts showing the proportions of the coastal water masses in the three periods for the three cases (Figs. 6b–i). The annual-mean values were calculated from the monthly transport of the coastal water masses to take account of the seasonal variations. Although the patterns of coastal water mass inflow into the ice-shelf cavity vary largely from one ice shelf or season to another, here we show the diagrams for all Antarctic ice shelves to determine the overall features in the three periods in the three cases. In 2001–20 (Figs. 6b,e,h), the sum of relatively dense and warm water masses (CD and MC) accounts for about 50% of the total water mass inflow in all cases. The sum of cold water masses (HS and LS), whose temperatures are near the surface freezing points, accounts for about 35% of the total water mass inflow. The water mass of sAS, a seasonally formed less-dense and warm water mass in the surface layers, accounts for only less than 4% of the total water mass inflow.
In 2080–99, the responses of the Antarctic coastal water mass inflow in the RCP8.5 case deviate from those in the other two scenarios (Figs. 6c,f,i). In the RCP8.5 case, the proportions of the dense and warm water masses (CD and MC) and the cold water masses (HS and LS) both decrease, whereas that of AS more than doubles to about 27% including the sAS contribution of 7%. An increase in the deep part of AS (green area without shading in Fig. 6) means an increase of AASW at deep levels and/or freshened mCDW. A similar tendency in the water masses’ change is identified in the RCP4.5 and RCP2.6 cases, but the magnitudes of the AS and sAS increases are smaller than those in the RCP8.5 case. A detailed examination of the proportions of the cold water masses in the RCP8.5 case reveals a large increase in the LS flow, indicating substantial freshening in the cold water masses. The difference in the inflow patterns among the cases becomes pronounced in 2121–40 (Figs. 6d,g). In the RCP8.5 case, the proportion of the MC inflow (including sMC) decreases to 31%, that of the AS inflow increases to about 44% (including 10% of sAS), and LS inflow becomes the dominant cold water mass inflow. In the RCP4.5 case, the water mass inflow pattern does not greatly change from those in 2080–99. These results show that the inflow pattern of the warm waters into the ice-shelf cavities changes profoundly from dense water masses to less-dense water only in the RCP8.5 case, indicating freshening of deep water masses. These results are also confirmed in the seasonality of the Antarctic coastal water masses’ inflow transport averaged over 2121–40 in the RCP8.5 case (Fig. 5b).
Next, we show the regional changes in the inflow patterns of the coastal water masses in the RCP8.5 case (Fig. 7). Here, we selected the four regions where the future changes in the modeled ice-shelf basal melting were considerable, namely ice-shelf groups c (EWIS), e (AIS), f (WeIS/ShIS), and k (AbIS/WoIS/GeVI). Ice-shelf group h (RIS) was selected as a representative region where the change in ice-shelf basal melting was very small. For ice shelves c (EWIS) and k (AbIS/WoIS/GeVI), the MC inflow dominates in 2001–20; however, the contribution of AS (including sAS) increases in 2080–99 and 2121–40, whereas that of MC decreases. For ice shelves e (AIS) and f (WeIS/ShIS), the cold water masses (HS and LS) account for more than 80% of the total inflow in 2001–20. In 2080–99, the AS inflow increases, reaching 28%–39%. In 2121–40, AS becomes the most dominant component, accounting for 57%–70% of the total inflow. This indicates an increase of the AASW inflow in summer and appearance of fresher mCDW in deep layers, both water masses being categorized in AS. For ice shelf e (AIS), the cold water masses dominate the inflow in 2001–20; however, in 2080–99, the more saline water mass (HS) almost disappears, meaning that the fresher water mass (LS) prevails in the cold water masses.
For ice shelf h (RIS), there are no large percentage changes in the sum of the cold water masses (Figs. 7j–l), and thus there are no pronounced changes in the ocean heat flux into the cavity and subsequent ice-shelf basal melting (Fig. 3h). However, there is a shift of water masses: the cold water mass shifts from HS to LS and the warm water mass shifts from CD/MC to MC/AS, indicating overall freshening in the inflowing water masses.
c. Linkage between ice-shelf basal melting and sea ice fields
In previous sections, we showed that differences in the Antarctic coastal water mass inflow into the ice-shelf cavities result in a remarkable difference in the future projections in Antarctic ice-shelf basal melting. Our model showed stronger sensitivity of Antarctic ice-shelf basal melting in summer/warm months (Fig. 4a). In particular, fresher varieties of the coastal water masses (AS and LS) become dominant in warm and cold water masses in the next century in the RCP8.5 case (Figs. 5–7). Sea ice meltwater formed in Antarctic coastal regions takes part in the water mass formation of low-salinity and less-dense water masses. AASW is a seasonal water mass that is heated in the sea ice-free area via direct atmosphere–ocean interaction, such as shortwave radiation. LSSW consists of a less-dense variety of DSW and relatively freshwater mass originating from sea ice melting in summer. Less-dense water masses, even in the surface layer, can be transported into the ice-shelf cavities via Ekman downwelling caused by coastal easterly winds (Ohshima et al. 1996). In this section, we examine in detail the changes in the modeled sea ice fields and the linkage between ice-shelf basal melting and sea ice fields.
Figures 8a and 8b show two sea ice extent metrics (winter maximum and summer minimum) to capture the decadal variability and trend in the Antarctic sea ice in the model, and Fig. 4b shows the seasonal cycles of the total sea ice extent in the three periods in the three cases. The model reproduces the seasonal cycle of the total Antarctic sea ice extent in 2001–20; it is consistent with the observed present-day climatology for the period 1981–2010, which was estimated from the satellite sea ice concentration with the NASA Team algorithm (Cavalieri et al. 1984; Swift and Cavalieri 1985). In the RCP8.5 case, the summer minimum sea ice extent begins to fall below 0.5 × 106 km2 after 2070–80. It is also clear in Fig. 4b that the sea ice extent in the RCP8.5 case remains below 0.5 × 106 km2 from January to March in 2080–99 and 2121–40.
Actual ice days (Stammerjohn et al. 2012), a sea ice metric, is helpful to capture the regional pattern of sea ice cover in different periods (Figs. 8c–e). The metric of actual ice days is the number of days in one year (from mid-February to the next-year mid-February) when sea ice concentration is above 15%. In the RCP8.5 case, there are large differences in the actual ice days between 2001–20 and 2121–40, particularly along the coastal margins in the eastern Weddell Sea and west Antarctic regions (Fig. 8e). The actual ice days in these regions are shortened by more than 160 days in 2121–40 compared to those in 2001–20. The reduction in actual ice days means a longer period of open water in the Antarctic coastal region, providing favorable conditions for AASW formation. Linking with the sea ice conditions, the water mass categorized into sAS becomes large, increasing ice-shelf basal melting in summer. Note that changes in sAS are not only found in the inflow transport (Figs. 6 and 7) but also confirmed in the mean water temperature in the warm months from January to April (Fig. 9 and Figs. B2–B8 for the horizontal and vertical distributions). The exceptions are the Ross Sea, off Wilkes Land, and the southwestern part of the Weddell Sea, where the magnitude of the change in the actual ice days is relatively small. These areas are prone to be sea ice stagnant by a combination of protruding topography and westward sea ice drift in Antarctic coastal regions, and the presence of sea ice maintains the sea surface temperatures at near-surface-freezing points. In these regions, the conditions for AASW formation in the future are not much different from the present-day conditions.
To further examine the roles of sea ice processes on the coastal water masses, we show maps of the annual sea ice formation and melting in three periods in the RCP8.5 case and the seasonal cycle (Fig. 10). In 2001–20, the model shows high sea ice production areas in the Antarctic coastal regions (Tamura et al. 2008; Nihashi and Ohshima 2015), including a reasonable representation of coastal polynyas (Kusahara et al. 2017) and substantial melting in the offshore areas. In 2080–99, it is discernable that this seasonal variation of active coastal sea ice formation and offshore melting has weakened (Figs. 10d,e), remarkably shortening the period of coastal sea ice formation (Fig. 10f). In 2121–40, the decreasing tendencies in coastal sea ice production and offshore sea ice melting become more prominent (Figs. 10g–i).
Our model results have shown a decrease in coastal sea ice production and an increase in ice-shelf melting in future warming. Both changes play a role in freshening the Antarctic coastal ocean. Here, we perform a quantitative comparison of the freshwater fluxes from sea ice processes and ice-shelf melting in the three periods in the three cases (Table 1). In the RCP8.5 case, the decreasing magnitude in coastal sea ice production is about 2.5 times as large as the increase in ice-shelf melting. Similarly, in the RCP4.5 case, the contribution of sea ice production is more significant than that of ice-shelf melting. These results indicate that the reduction in sea ice production along the Antarctic coastal margins is the primary source for the freshening of the Antarctic coastal ocean, but with a nonnegligible contribution from the increase in ice-shelf basal melting.
d. Enhanced warm water intrusion along the seafloor in the RCP8.5 case
A detailed examination of the changes in the seasonal cycle of ice-shelf basal melting in the RCP8.5 case (Figs. 4b and B2–B8) reveals that the basal melting is increased not only in summer (warm months) but also in winter (cold months) for some ice shelves (Figs. B9 and B10). The winter regional ice-shelf melting for ice shelves c (EWIS), e (AIS), f (WeIS/ShIS), and k (AbIS/WoIS/GeVI) increases by 50% from 2001–20 to 2121–40 (Fig. B10). In particular, the wintertime basal melting for ice shelves e (AIS) and k (AbIS/WoIS/GeVI) becomes more than double the present-day values. Here, we focus on the two ice shelves e (AIS) and k (AbIS/WoIS/GeVI) and examine in detail the increases in ice-shelf basal melting in the RCP8.5 case. We demonstrate that deep warm water intrusions onto some Antarctic continental shelves increase the regional ice-shelf basal melting (Figs. 11–14 and B2–B8).
A map of the ocean bottom temperature anomaly in the RCP8.5 case in 2121–40 shows almost circumpolar warming signals along the Antarctic continental shelf break zones, except in the Ross Sea and parts of the East Antarctic region [Fig. 11a, and panel d in Figs. B2–B8]. In contrast, in the RCP4.5 case, the significant bottom warming signals are found only in one part of the Bellingshausen Sea, with a smaller magnitude and extent. At the ice shelves where the basal melting is increased in winter in the RCP8.5 case, namely ice shelves c (EWIS), e (AIS), f (WeIS/SHIS), and k (AbIS/WoIS/GeVI), warming signals approach the ice-shelf cavities from the shelf break regions along the seafloor, even in the cold months (Figs. B3–B5 and B8). The combination of a decrease in coastal sea ice formation in winter and an increase in ice-shelf basal melting enhances ocean stratification in coastal areas (Figs. 8 and 10 and Table 1), providing favorable conditions for deep warm water intrusions onto the Antarctic continental shelf regions (Silvano et al. 2018).
An examination of the bottom temperature and vertical section of the water properties near ice shelf e (AIS) (Fig. 12) indicates that the continental shelf (Prydz Bay) is covered with the cold water mass with a near-freezing-point temperature and high salinity in 2001–20. In 2121–40, a fresher water mass dominates the coastal ocean near the ice shelf. There are two warm anomalies in the surface and bottom layers. In the RCP4.5 case, the bottom warm anomaly does not appear (Fig. 11b). A detailed inspection of the bottom temperature and the vertical profile (Figs. 11 and 12) indicates deep warm water intrusion from the shelf break regions to the ice-shelf cavities becomes more active in the RCP8.5 case, causing the pronounced increase in the regional year-round ice-shelf basal melting. These findings are also confirmed in the T-S diagram for the water properties in the ice-shelf cavity within 10 km of the ice-shelf front (Figs. 13a,b). In the T-S analysis, we separately plotted the profiles in the warm and cold months to clearly see the seasonal differences in 2001–20 and 2121–40. In 2001–20, cold water masses, in particular LS, prevail over the ice-front region throughout the year (Figs. 13a and 7d). However, the T-S diagram in 2121–40 (Fig. 13b) is quite different from that in 2001–20 (Fig. 13a), showing overall freshening, year-round warming signals in deep layers, and summertime warming signals in surface layers. Note that although the deep ocean temperatures in 2121–40 are warmer than −1.0°C, they are categorized into AS due to the overall freshening. Pronounced warming of the surface layers in the warm months (i.e., warm AASW formation) is also clearly confirmed in the figure.
Similarly, at ice shelf k (AbIS/WoIS/GeVI), deep warm water intrusions with relatively high salinity are confirmed in both the RCP8.5 and RCP4.5 cases (Figs. 11 and 14). They contribute to the gradual increase in the local ice-shelf basal melting in these cases and throughout the RCP8.5 case (Fig. 3k). The magnitude and extent of the warming signal in the RCP8.5 case are more prominent and broader than those in the RCP4.5 case (Fig. 11). Again, we can find the corresponding large differences in the T-S properties in 2001–20 and 2121–40 (Figs. 13c,d). Along with the enhanced intrusions of the warm deep water in the RCP8.5 case, the regional water temperatures in MC increased from approximately −1.0°C in 2001–20 to + 1.5°C in 2121–40. In the cold months in 2121–40, the water properties in this region are roughly on the line connecting the warm MC and the fresher LS in the T-S space. In the warm months, the surface water significantly increases the temperature, forming warm AASW (i.e., sAS in our analysis).
For comparison, the T-S diagram for the water properties near ice shelf h (RIS), where the future change in ice-shelf basal melting is small (Fig. 3h), is shown in Figs. 13e and 3f. As explained in the two ice shelves, the overall freshening is also confirmed in this region. However, the ocean temperature changes in the water masses within the ice-shelf cavity are small in both the warm and cold months, thus leading to the small change in the ice-shelf basal melting. Finally, it should be noted again that while the water mass analysis used in this study (Figs. 5–7) is very useful for capturing the characteristics of the modeled ocean conditions in different periods and locations, the other fundamental analyses, such as the T-S diagram (Fig. 13) and the horizontal–vertical distribution (Figs. B2–B8), are required to compensate for the disadvantages of the water mass analysis, which come from the discretization of continuous properties with the specified thresholds, for an integrated understanding changes of the modeled fields in different climates.
4. Summary and discussion
We have examined future changes in Antarctic ice-shelf basal melting and the linkages with Antarctic sea ice processes and coastal water masses, using results from an ocean–sea ice–ice shelf model forced by future atmospheric conditions. In this study, the atmospheric surface boundary conditions were derived from a CMIP5 experiment with a single climate model, MIROC-ESM (Watanabe et al. 2011). Until about 2070, there is not much difference in the total amount of Antarctic ice-shelf basal melting under the three warming scenarios (RCP2.6/4.5/8.5) considered, with only a gradual increase of a few percent with respect to the present-day value (Figs. 1 and 3 and Table 1). After 2070, the difference in ice-shelf basal melting among the scenarios becomes prominent. The relatively modest warming cases (RCP2.6 and RCP4.5) show gradual increases throughout the experiment periods (e.g., an approximately +20% increase in the period 2121–40 in the RCP4.5 case), and the extreme-warming case (RCP8.5) shows a rapid increase after 2070, with an approximately 90% increase by 2140. The total Antarctic ice-shelf melting scaled with the degree of air temperature rise over the Southern Ocean (Fig. A3a) reveals a nonlinear response of ice-shelf basal melting to future atmospheric changes, indicating the presence of a warming-level threshold between RCP4.5 and RCP8.5 scenarios (Fig. 2).
We found that differences in the sea ice fields and coastal water masses significantly impact the future changes in Antarctic ice-shelf basal melting (Figs. 6–10) and that there are substantial increases in contributions of the summertime warm surface water and the warm deep water to ice-shelf basal melting in the extreme-warming case. Coastal sea ice conditions in summer (Fig. 4b) play a key role in AASW formation and volume (Figs. 5, 9, and 13). The presence of sea ice along the Antarctic coastal margins keeps the temperature of coastal surface water at surface-freezing points, where the heat input into the ocean surface is exclusively used for melting the sea ice. In the absence of coastal sea ice, as in the second half of the RCP8.5 case, the anomalous heat input to the ocean surface directly leads to increases in upper ocean temperatures (Fig. 9). Part of the warmed surface water is transported into ice-shelf cavities, causing intense ice-shelf basal melting at relatively shallow depths (Figs. B2–B8). Inflow of Antarctic surface water has been observed only in limited areas, and thus it is not a dominant mode in the present-day ice-shelf melting (Malyarenko et al. 2019; Thompson et al. 2018; Hattermann et al. 2012; Stewart et al. 2019; Aoki et al. 2022). However, in the extreme-warming scenario (RCP8.5), the AASW contribution to ice-shelf basal melting would substantially increase in a warming climate when the seasonal Antarctic sea ice cover is largely shrunk, accompanied by a longer sea ice free period along Antarctic coastal margins (Fig. 10). It should be noted that the increased AASW contribution was also observed in the previous future projection (Naughten et al. 2018), but has not been examined in detail.
Along with the increased AASW contribution to ice-shelf basal melting, the model shows an increased contribution of deep warm water inflow along the seafloor in several places in the RCP8.5 case (Figs. 11–14). In our results, the most prominent signals are found in Prydz Bay and the Bellingshausen Sea. The findings of enhanced intrusion of deep warm water into ice-shelf cavities in a warming climate causing substantial increases in the regional ice-shelf basal melting are consistent with previous modeling studies (Hellmer et al. 2012; Timmermann and Hellmer 2013; Naughten et al. 2018), albeit with different locations and magnitudes. Hellmer et al. (2012) and Timmermann and Hellmer (2013), using two different ocean–sea ice–ice shelf models [the Bremerhaven Regional Ice Ocean Simulations (BRIOS) and a finite-element sea ice–ocean model (FESOM)] forced with future atmospheric conditions from climate models (A1B and E1 scenarios), demonstrated that a redirection of warm CDW in the southern Weddell Sea could be a trigger for boosting ice-shelf basal melting at Filchner-Ronne Ice Shelf. Our model also reproduces enhanced CDW across the shelf break in the southern Weddell Sea (Fig. B2), but the signals are too weak to increase ice-shelf basal melting at Filchner-Ronne Ice Shelf. Naughten et al. (2018) also performed numerical experiments using FESOM forced with CMIP5 outputs to estimate future projections in Antarctic ice-shelf melting and showed that enhanced CDW intrusion over the Amundsen Sea could cause a pronounced increase in ice-shelf basal melting. Figure B8 clearly demonstrates that our model represents the enhanced CDW intrusion in the eastern part of the Amundsen Sea, but the areal extent is smaller than the previous study.
At this stage, it is difficult for us to identify the root causes of differences of the locations and magnitudes in the enhanced CDW intrusions between this study and previous studies, such as whether the differences in numerical models and atmospheric surface boundary conditions cause the different responses of Antarctic ice-shelf basal melting. Numerical modeling of Antarctic ice-shelf basal melting requires relatively high resolution, compared to the CMIP models, to resolve ice shelves themselves and the causal Antarctic coastal processes, requiring an enormous computational cost. Therefore, it is difficult to conduct multimodel, multiscenario, and extensive ensemble experiments for future changes in the Antarctic ice-shelf melting. Under such circumstances, in addition to the previous studies, we consider that this study contributes to presenting additional potential regions where CDW could be enhanced for triggering drastic increase in the future ice-shelf basal melting. A major limitation of this study also corresponds to the difficulty in conducting many numerical experiments; we have performed the numerical experiments with one ocean–sea ice–ice shelf model under one ensemble member of atmospheric conditions per warming scenario from a single climate model, just showing rational physical interpretation for the model results. In our RCP8.5 case, we observed intriguing ocean responses, such as increased total inflow to the ice-shelf cavity and changes in the CDW inflow pattern (Figs. 6, 7, and 11). Since, in our numerical experiments, we simultaneously changed both dynamical (wind stresses) and thermodynamic surface boundary conditions, it is not possible to identify the driving forces behind these changes. It will be important to conduct additional numerical experiments in the future to scrutinize the dynamical drivers for these changes.
In summary, we observed pronounced differences in Antarctic ice-shelf basal melting between the extreme and modest warming scenarios and found that the enhanced ice-shelf basal melting in the extreme-warming scenario is explained by increased contributions from the two warm water masses of AASW and modified CDW. Both changes in the AASW formation process and the transport of modified CDW toward the ice-shelf cavities are mainly controlled by sea ice changes: A reduction in sea ice covered period results in active warmer AASW formation, and a decrease in coastal sea ice production leads to coastal freshening and stratification, providing favorable conditions for warm deep water intrusions onto some continental shelf regions.
A sophisticated ice sheet model is necessary to better project and evaluate future sea level changes in a warming climate. A fully coupled ice sheet–ocean–atmosphere model that can directly represent the interaction of the Antarctic ice sheet with the global ocean and atmosphere would be desired (Holland and Holland 2015). Climate models incorporating ice-sheet and ice-shelf components are emerging (Smith et al. 2021; Pelletier et al. 2022; Comeau et al. 2022), and it is a very active research area in Antarctic science and climate modeling communities. However, at present, there are no such fully coupled global climate models that can simulate the processes contributing to long-time scale sea level rise due to several difficulties in direct coupling between ice-sheet/shelf and ocean–atmosphere models, such as large gaps in the time steps or the technical difficulty of the representing moving boundaries of the ice shelf–ocean interface and the grounding line. Regarding stand-alone ice sheet models, the representation of ice-shelf basal melting is one of the major uncertainties for ice-sheet modeling (Seroussi et al. 2020; Noble et al. 2020; Nowicki and Seroussi 2018). Current-generation ice-sheet models use some parameterizations for ice-shelf basal melting (Pelle et al. 2019; Reese et al. 2018a; Jourdain et al. 2020; Lazeroms et al. 2018). The parameterizations are tuned to reproduce the present-day conditions, where warm deep waters mainly drive the ice-shelf basal melting in warm ice shelves (mode 2 melting) and cold shelf waters regulate it in cold ice shelves (mode 1 melting). This study suggests the possibility of increasing the contribution of warm surface water for ice-shelf basal melting (mode 3 melting). The effect of the increased basal melting with warm surface water must be taken into account in ice-shelf basal melting parameterization under extreme warming conditions (Jourdain et al. 2020). It should be noted that the AASW contribution to the increased ice-shelf basal melting is confined to relatively shallow ice-front regions (Figs. B2–B8). It does not affect the ice sheet interior instantaneously (Reese et al. 2018b), but can change the buttressing through changes in shape and thickness, eventually affecting changes in the inner ice sheets.
Acknowledgments.
This work was supported by the Integrated Research Program for Advancing Climate Models (TOUGOU) Grants JPMXD0717935715 and JPMXD0717935457 from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. KK was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI (Grants JP19K12301, JP17H06323, JP21H04918, JP21H04931, and JP21H03587). All numerical experiments with the ocean–sea ice–ice shelf model were performed on HPE Apollo6000XL230k Gen10 (DA system) in JAMSTEC. We are grateful to two anonymous reviewers for their thorough review and constructive comments on the manuscript.
Data availability statement.
All model results are available on request from the first author (K. Kusahara; kazuya.kusahara@gmail.com, kazuya.kusahara@jamstec.go.jp).
APPENDIX A
Representation and Key Metrics of the Southern Hemisphere Atmospheric Conditions
This study used the results from a single climate model, MIROC-ESM (Watanabe et al. 2011), to calculate the future atmospheric surface boundary conditions under the RCP scenarios in the CMIP5 protocol (Taylor et al. 2012). Generally speaking, climate models have inherent model biases due to insufficient resolutions, unresolved processes, and uncertainties in parameterization. As mentioned in the main text, in order to reduce the model biases in the future atmospheric conditions, we used only the spatiotemporal anomalies calculated from MIROC-ESM and added the anomalies to the present-day atmospheric surface boundary conditions (OMIP3rd). In appendix A, we perform a comparison of the Southern Hemisphere atmospheric conditions during the end of the twentieth century between OMIP3rd and MIROC-ESM (Fig. A1) and show the spatiotemporal anomalies of the future conditions in MIROC-ESM (Fig. A2). After that, to quantitatively see the time evolution of the Southern Hemisphere atmospheric conditions in the climate model, we show temporal variability of surface air temperature over the Southern Ocean (Fig. A3a) and the Southern Annular Mode (SAM) index (Fig. A3b) during the period from the end of the twentieth century to the beginning of the twenty-second century. Furthermore, we briefly show the position of MIROC-ESM among CMIP5 models based on model intercomparison studies and conclude that the results from MIROC-ESM are reasonable for the present-day condition and plausible for the future conditions.
Figure A1 shows maps of eastward wind stress, northward wind stress, surface air temperature (SAT), and sea level pressure (SLP) in OMIP3rd (which was used as the present-day condition for the end of the twentieth century) and MIROC-ESM in 1981–2000. The most striking difference is found in the eastward wind stress, with almost circumpolar negative and positive anomalies south and north of 50°S, respectively (Fig. A1c). There is a negative SLP anomaly band in the latitudes from 35° and 60°S (Fig. A1l), explaining the anomalies in the eastward wind stress. There are a few minimums in the SLP anomaly band, and they accompany the northward and southward wind stress anomalies in the western and eastern parts, respectively (Fig. A1f). Figure A1i clearly shows that MIROC-ESM has cold biases in SAT along Antarctic coastal regions south of 60°S, except the Ross Sea.
Figure A2 shows the spatiotemporal anomalies of the future atmospheric conditions in the three periods (2001–20, 2080–99, and 2121–40) as deviations from those in 1981–2000. There are stronger eastward wind stresses linking with a circumpolar negative SLP anomaly in the southern high latitudes and a positive SLP anomaly in the midlatitudes. Atmospheric warming signals are found all over the Southern Ocean, particularly south of 60°S.
Figure A3a is time series of the SAT averaged over the Southern Ocean (<50°S), shown as an anomaly from the climatology for the reference period 1981–2000. It is clear from Fig. A3a that differences in CO2 emissions cause pronounced differences in atmospheric temperature increases over the Southern Ocean. In the early twenty-first century (2001–20), there are no significant differences in the SAT anomalies in all three cases. In the late twenty-first century (2080–99), the air temperature anomalies in the RCP2.6, RCP4.5, and RCP8.5 scenarios are +1.9°, +2.71°, and +4.02°C, respectively. In the twenty-second century, the SAT anomaly in the RCP4.5 and RCP8.5 scenarios gradually increases, reaching +3.11° and +6.16°C for the period 2121–40, respectively. Note that these time series of the SAT anomaly are used for scaling Antarctic ice-shelf basal melting (Fig. 2).
Figure A3b is the time series of the SAM index under the three scenarios and an atmospheric reanalysis (ERA5; Hersbach et al. 2020). The SAM is the dominant atmospheric mode in the Southern Hemisphere and is characterized by its almost annular structure (Thompson and Wallace 2000; Marshall 2003). The index represents fluctuations in the atmospheric mass between the southern middle and high latitudes, and it is a measure of the location and strength of the prevailing westerly winds in the Southern Hemisphere (Marshall 2003; Fogt et al. 2009). The positive phase means higher pressure in the midlatitudes and lower pressure over the Antarctic coastal regions with the local minimum in the eastern Pacific sector. The SAM index has been reported to shift to a more positive phase in recent decades (Abram et al. 2014) and in extreme-warming climate conditions (Bracegirdle et al. 2013). The more positive SAM index indicates stronger circumpolar westerlies over the Southern Ocean. In this study, we calculated the SAM index in MIROC-ESM and ERA5, using the difference in the normalized zonal mean sea level pressure at 40° and 65°S (Gong and Wang 1999). A CMIP5 intercomparison study (Zheng et al. 2013) reported that the SAM index trend in MIROC-ESM for the historical period 1958–2005 is comparable with station-based and reanalysis-based SAM index, showing that MIROC-ESM reasonably represents changes in the Southern Hemisphere atmospheric circulation in the period. Bracegirdle et al. (2013) demonstrated that the future change in the SAM index in the CMIP5 RCP8.5 scenario bifurcates from the other scenarios after the second half of the twenty-first century. The SAM index in MIROC-ESM also shows similar behavior (Fig. A3b), indicating plausible atmospheric responses to the different levels of CO2 emissions.
Sea ice becomes an effective thermal insulator between the atmosphere and ocean, and the presence or absence of sea ice significantly affects lower atmospheric conditions in a climate model. Therefore, the sea ice representation in climate models is an important metric for assessing their performance in polar regions. The sea ice representations in the present-day and future conditions in this study (Figs. 4b and 8) are similar to those in the MIROC-ESM simulation (not shown). In model intercomparison studies targeting the present-day Antarctic sea ice (Turner et al. 2013; Shu et al. 2015), seasonality in the sea ice extent in MIROC-ESM is reasonable compared with the satellite observation, providing us some confidence to use the lower atmosphere states as the future atmospheric boundary conditions for the ocean–sea ice–ice shelf model. However, it should be noted that climate models have had difficulty in reproducing Antarctic sea ice in recent decades when the total Antarctic sea ice extent gradually increased from 1979 to 2015 (Roach et al. 2020). This is partially confirmed in Fig. A3a; SAT can be used as a metric for validating lower atmospheric conditions interacting with sea ice (Hobbs et al. 2020). SAT in ERA5 is relatively stable in the period 1981–2020, while that in MIROC-ESM shows gradual increases in the same period, reflecting the common difficulty in reproducing Antarctic sea ice in recent decades in climate models.
APPENDIX B
Detailed Assessments of the Modeled Ice-Shelf Basal Melting and Ocean Conditions along Antarctic Coastal Margins
Figure B1a shows a map of the annual mean ice-shelf basal melt rate in 2001–20 in the RCP8.5 case. There are no significant differences in ice-shelf basal melting in the three RCP cases in the beginning of the experiment (Fig. 1), and thus in appendix B, we use the result from the RCP8.5 case as the representative fields in 2001–20. The model circumpolar average of the annual mean ice-shelf basal melt rate is 1.04 ± 0.06 m yr−1, being slightly higher than the observation estimates ranging from 0.81 ± 0.11 m yr−1 (Depoorter et al. 2013) to 0.85 ± 0.1 m yr−1 (Rignot et al. 2013). The model shows active ice-shelf basal melting in several regions, such as near ice-front and grounding lines (see orange- and red-colored regions). The Southern Ocean melts the Antarctic ice shelves’ base as a whole, but some places in the large ice shelves (e.g., FRIS and RIS) show freezing (dark blue regions). The overall distribution of the modeled ice-shelf basal melting/freezing pattern is consistent with the observations to some extent.
Next, we calculated regional ice-shelf basal melting amount to quantitatively assess the model basal melting with the observation-based estimates (Rignot et al. 2013; Depoorter et al. 2013) as in our previous studies (Kusahara 2020, 2021) (Fig. B1b). As mentioned in the main text, the three scenarios’ mean of total Antarctic ice-shelf basal melting in 2001–20, 1470 Gt yr−1 (Table 1), is roughly consistent with the observational range from 1454 ± 174 Gt yr−1 (Depoorter et al. 2013) to 1500 ± 237 Gt yr−1 (Rignot et al. 2013). However, it should be noted that there are regional model biases in the ice-shelf basal melting. At ice shelf groups c (EWIS), h (RIS), and i (SuIS), the modeled basal melt amounts are much larger than the observations. These overestimations are caused by biases in the warm water intrusions (Kusahara 2021). Figures B2–B8 are collections of ice-shelf basal melting and horizontal/vertical ocean temperature in 2001–20 and 2121–40 to assess the regional representations and the future changes in this model. At ice shelf j (GIS/ThG/PIG), the model underestimates the basal melting due to exaggeration of cold waters inflowing into the cavities (Fig. B8a), whereas in reality warm deep water dominates the inflow transport. The model deficiency in active basal melt rate at the Amundsen Sea ice shelves probably comes from a combination of overestimation of sea ice production and cold water mass formation and underestimation of warm CDW intrusion onto the continental shelf region (Fig. B8), as discussed in previous modeling studies (Kusahara and Hasumi 2013; Timmermann and Hellmer 2013; Nakayama et al. 2014; Naughten et al. 2018).
Figure 3a in the main text shows the seasonal cycle of the total Antarctic ice-shelf basal melting. Figure B9 is the same, but for the regional ice shelves, a–k. To highlight the seasonal amplification of the regional ice-shelf basal melting, Figure B10 shows the ratios of the seasonal ice-shelf melting with respect to the three scenarios’ mean in 2001–20.
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