1. Introduction
The marine isotope stage 11 (MIS11) interglacial was a period of protracted ice age warmth ~400 kyr (~400 000 yr) ago that is commonly cited as a natural laboratory for assessing the stability of polar ice sheets in the face of ongoing global warming (e.g., Hearty et al. 1999; Roberts et al. 2012). However, the peak globally averaged eustatic sea level (ESL) during MIS11 has been a matter of controversy (Hearty et al. 1999; McMurtry et al. 2007; Hearty and Olson 2008; McMurtry et al. 2008). MIS11 sea level indicators from Bermuda and the Bahamas have been interpreted as recording an ESL rise of ~20 m, which would indicate extensive collapse of the Greenland and West Antarctic Ice Sheets and an additional, significant contribution from melting of the East Antarctic Ice Sheet (Hearty et al. 1999; Hearty and Olson 2008; Olson and Hearty 2009; van Hengstum et al. 2009). McMurtry et al. (2007) have suggested, in contrast, that the elevated MIS11 sea level indicators in Bermuda were deposited by a megatsunami, whereas Bowen (2010) has argued that field evidence in Bermuda may suggest a contribution from long-term tectonic uplift. Bowen (2010) concluded, on the basis of a widely distributed suite of MIS11 high stands corrected for tectonic uplift, that ESL during MIS11 peaked close to the present-day level.
No account was taken in this previous work of the potential contamination of the elevation of local sea level indicators by glacial isostatic adjustment (GIA). Raymo and Mitrovica (2012) have shown that this contamination can be significant, particularly at Bermuda and the Bahamas, which lie on the peripheral bulge of the ancient Laurentide ice complex. Since such sites are characterized by postglacial subsidence, they would have experienced a greater GIA-induced sea level rise during the protracted MIS11 interglacial than in the current interglacial, and the correction for GIA would thus lower any observed high-stand elevation by ~10 m (Raymo and Mitrovica 2012). As an example, assuming that the geological markers at ~20-m elevation in Bermuda and Bahamas reflect local sea level high stands, which remains a contentious issue (Hearty and Olson 2008; McMurtry et al. 2008), Raymo and Mitrovica (2012) concluded that peak ESL during MIS11 was 6–13 m.
A further refinement of the estimate for peak MIS11 ESL would be noteworthy, given the implications of this peak for polar ice sheet stability in a warming world. To this end, Roberts et al. (2012) surveyed sea level markers of MIS11 age along the tectonically stable southern coast of South Africa. These markers, composed of sediment facies and interfaces between subtidal and intertidal deposits, were distributed over a ~20-km distance at the mouths of the Klein Brak River (KBR), the Hartenbos River, and Dana Bay. Using the KBR data, they inferred a peak high-stand elevation of 14 m (Roberts at al. 2012). They applied two corrections to this elevation. First, a GIA signal of −2 m, predicted for Cape Town by Raymo and Mitrovica (2012, their Fig. 3), located ~350 km west of KBR, was removed. Second, Roberts et al. (2012) applied a correction for local tectonic uplift (3 m) based on an average paleo-erosion rate of 6 m per million years (Myr) estimated using cosmogenic dating of elevated marine terraces in Sundays River, South Africa, by Erlander (2011). Sundays River is located ~400 km east of KBR. Applying these two corrections yielded a sea level high stand of 13 m [i.e., 14 − (−2) − 3 m], which Roberts et al. (2012) interpreted as the peak eustatic sea level during MIS11. They ascribed a random error of 2 m to this estimate.
The timing of ice sheet collapse during the MIS11 interglacial is an important issue in these analyses. Raymo and Mitrovica (2012) argued, on the basis of their study of the sea level records from Bermuda and the Bahamas, that the collapse likely occurred near the end of the interglacial. This argument is also implied in the analysis of Roberts et al. (2012), since the GIA signal they used to correct the sea level records at KBR (−2 m) was the GIA signal predicted by Raymo and Mitrovica (2012) at Cape Town at the end of MIS11 (see their Fig. 3).
In this study, we refine our understanding of peak ESL during MIS11 by revisiting several aspects of the important Roberts et al. (2012) analysis. First, we estimate the uncertainty in the GIA correction for coastal South Africa using a large suite of numerical models of the GIA process in which the duration of the MIS11 interglacial and the viscoelastic structure of Earth are varied within plausible ranges. We also consider, using these numerical results, the additional uncertainty related to the appropriate timing of the GIA correction (i.e., the timing of ice sheet collapse: early, middle, or late in the MIS11 interglacial). Second, we test the accuracy with which the local (GIA corrected) sea level high stand in this region is a proxy for peak ESL. Rapid melting of ice sheets produces a strong geographic variability in sea level, and thus equating a GIA-corrected sea level measurement at any specific site to eustatic sea level may introduce a significant systematic bias into the estimate of ESL (Mitrovica et al. 2001; Hay et al. 2014).
2. Methods
We adopt a gravitationally self-consistent ice age sea level theory that accounts for (Maxwell) viscoelastic deformation of a spherically symmetric, self-gravitating Earth model, time-varying shoreline geometry, and the impact of perturbations in Earth rotation on sea level (Kendall et al. 2005). The calculations require models for both the space-time geometry of ice cover and viscoelastic Earth structure.
Our model of ice geometry over the past 500 kyr is composed of two parts. The first, taken from Raymo and Mitrovica (2012, see their Figs. 3 and S1), is a reconstruction covering the last 500 kyr in which it is assumed that ice volume and geometry during all interglacials (including MIS11) is fixed in time and equal to the present global ice cover (see dashed green line in each of the insets to Fig. 1). During the last glacial cycle, the model is based on the ICE-5G history (Peltier 2004). We use a version of this ice history (ICE-5G version 1.2) that includes ice load increments from 122 ka BP to the present (Peltier and Fairbanks 2006). For previous cycles, the ice volume is scaled to match the stacked δ18O time series of Lisiecki and Raymo (2005). During this pre-MIS5e period, whenever the ice volume matches the volume in one of the time slices of the ICE-5G deglaciation history, we set the geometry of ice cover equal to that time slice of ICE-5G. Using this ice history for the last 500 kyr yields a measure of relative sea level during interglacials that is associated with GIA alone, with no contribution from differences in ice volume between a previous interglacial and the present. In a sensitivity analysis described below, we vary the duration of the model MIS11 hiatus in ice volume changes from 7 to 11 kyr (Raymo and Mitrovica 2012). Sea level predictions based on the 500-kyr ice history will be termed the “GIA signal.”
Histograms of predictions for the GIA correction at Klein Brak River determined from a suite of ~426 simulations distinguished on the basis of the adopted Earth model and duration of the model interglacial. The latter ranged from 7 to 11 kyr. Moreover, the thickness of the elastic lithosphere (LT), upper mantle viscosity (νum), and lower mantle viscosity (νlm) were varied within the following bounds: 25 km < LT < 100 km, 2 × 1020 Pa s < νum < 5 × 1020 Pa s, and 3 × 1021 Pa s < νlm < 5 × 1022 Pa s. The calculations are based on a gravitationally self-consistent postglacial sea level theory (see text). In the insets, the blue line shows the prediction of relative sea level due to GIA assuming a model MIS11 deglaciation of duration 9 kyr and the test Earth model, where LT = 100 km, νum = 4 × 1020 Pa s, and νlm = 5 × 1021 Pa s. The dashed green line shows the ESL variation associated with the ice model for the case of a deglaciation of duration of 9 kyr. The blue and green lines are reproduced in each inset. The three frames are distinguished on the basis of the assumed timing of the GIA correction: (top)–(bottom) start, midpoint, and end of the model deglaciation (as indicated by the red dot in each inset).
Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00282.1
The second component of the ice history (the “ice collapse signal”) is a model for polar ice sheet collapse during the MIS11 interglacial. We will consider a suite of simulations in which the volume of each ice sheet [West Antarctic Ice Sheet (WAIS), East Antarctic Ice Sheet (EAIS), and Greenland Ice Sheet (GIS)] is reduced linearly in time from its present-day value to zero over a time interval ΔT. This interval is a free parameter of the modeling. Our modeling will consider melt durations in the range 0 kyr ≤ ΔT ≤ 3 kyr. In the case of the EAIS, we assume that melt is limited to grounded, marine-based sectors of the ice sheet.
We will normalize the sea level change computed in each ice collapse scenario using the ESL change associated with the melt event. (In this context, we define the term “ESL change” as the uniform change in global sea level arising from a change in ice volume under the assumption that the Earth is rigid and nonrotating, no load self-gravitation is included, and any exposed marine-based sectors have been filled with water. We assume, for the purpose of normalization, present-day topography.) Thus, the normalized sea level predictions have units of meters per meter of ESL. The sea level change for a specific melt scenario on a given polar ice sheet is nearly linearly related to the ESL change, as we have defined it, and thus it can be computed by scaling the normalized sea level prediction for this ice sheet by the equivalent ESL rise associated with that scenario. The quasi linearity also allows us to compute the total sea level change by simply adding the individual (dimensional) signals associated with melting from the WAIS, EAIS, and GIS. It is important to emphasize that the sea level changes associated with each load component described above, the GIA signal, and the ice collapse signal are computed separately, not as part of the same numerical simulation.
The second input into the sea level predictions is a model of the radial profile of Earth’s (Maxwell) viscoelastic structure. We adopt the elastic and density structure given by the seismic Preliminary Reference Earth Model (PREM; Dziewonski and Anderson 1981). The viscosity structure is prescribed by the thickness of a high viscosity (essentially elastic) lithosphere (LT) and constant viscosities within the upper (νum) and lower (νlm) mantle. The boundary between the latter two regions is taken to be at 670-km depth. In investigating the GIA signal, we will perform a sensitivity analysis in which these free parameters are varied within the ranges 25 km < LT < 100 km, 2 × 1020 Pa s < νum < 5 × 1020 Pa s, and 3 × 1021 Pa s < νlm < 5 × 1022 Pa s. These ranges cover essentially all estimates of mantle viscosity within the GIA literature spanning the past few decades.
Since the model ice collapse occurs over a relatively short time scale (i.e., less than 3 kyr), the sea level change predicted in response to this collapse will, in contrast to the GIA signal, be only weakly sensitive to the viscosity structure of the Earth model. Accordingly, our calculations of the sea level change in response to polar ice sheet collapse will be based on a single viscosity model (called the test model): LT = 100 km, νum = 4 × 1020 Pa s, and νlm = 5 × 1021 Pa s.
3. Results and discussion
Figure 1 (insets) shows a prediction of the GIA-induced relative sea level change across the MIS11 time window at Klein Brak River. The prediction is based on an MIS11 duration of 9 kyr and the test Earth model. KBR is in the far field of the Late Pleistocene ice centers and, as a consequence, the GIA signal at this site is characterized by a monotonic fall in sea level during the model interglacial (Raymo and Mitrovica 2012; Dutton and Lambeck 2012; Lambeck et al. 2011). The physics of this sea level change involves two processes. The first, continental levering, is a tilting of coastal regions (upward toward the continent and downward toward offshore) driven by ocean meltwater loading (Nakada and Lambeck 1989; Mitrovica and Milne 2002). KBR is in the zone of uplift, and hence the levering process contributes a sea level fall at this site. The second process, ocean syphoning, involves the migration of water away from the far field to fill accommodation space created by both the subsiding bulges at the periphery of ice covered regions and offshore regions of levering-induced subsidence (Mitrovica and Milne 2002). Ocean syphoning also contributes a sea level fall at KBR. The net effect of both processes is a net drop in sea level of ~2.5 m across the ice melting hiatus and a relative sea level that falls from a value of 0.6 m at the beginning of the interglacial to −2.1 m at the end of this phase.
The GIA signal at the end of the model interglacial (−2.1 m; insets of Fig. 1) accords with the prediction from Raymo and Mitrovica (2012) adopted by Roberts et al. (2012). To estimate the uncertainty in this correction, we performed a sensitivity analysis involving a large suite of such predictions in which the viscosity profile, elastic lithospheric thickness, and duration of the ice melt hiatus were varied over the ranges cited in section 2. Figures 1a–c (main plots) are histograms of the GIA correction computed using this large set of simulations and adopting a timing (of the ice sheet collapse) at the end, middle, and start of the interglacial (see the respective insets). The mean of each distribution is −1.9 ± 0.5 m, −0.8 ± 0.4 m, and 1.0 ± 0.4 m (1σ), respectively. In the analysis below, we adopt the range from 22.4 to 11.4 m for the GIA correction at the KBR site. We note that we also performed a sensitivity analysis in which the duration of the deglaciation phase prior to MIS11, which is 20 kyr in the ice history constructed in the manner discussed above, was varied from 15 to 25 kyr. We found that these additional simulations did not significantly alter the above ranges.
Roberts et al. (2012) interpreted their (GIA- and tectonic-corrected) local sea level measurement at KBR as being equivalent to peak eustatic sea level during MIS11. However, since millennial-scale collapse of grounded ice sheets will lead to a complex spatial pattern of sea level change (Mitrovica et al. 2001), this assumption is subject to error (Hay et al. 2014). The geographical variability will be distinct for each ice sheet and the patterns are known as sea level fingerprints. As an ice sheet melts, the gravitational attraction it exerts on the ocean weakens and water migrates from the near field of the ice sheet to the far field. This migration, together with the rebound of the crust in the vicinity of the melting ice sheet, leads to a region of sea level fall that extends ~2000 km from the ice sheet. At further distance, water migration and meltwater loading drive a sea level rise that, to a first approximation, increases progressively. The peak far-field sea level rise is ~30% higher than the ESL value for the melt event.
In Fig. 2, we show normalized fingerprints over southern Africa computed for the instantaneous collapse of the WAIS, EAIS, and GIS. The number listed on each frame is the normalized sea level change at Klein Brak River [1.16, 1.10, and 1.20 meter per meter ESL, respectively]. These values indicate that rapid melting of any of the three major polar ice sheets will produce a local sea level change at this site that exceeds the ESL associated with the melt event by 10%–20%. We conclude that interpreting the peak (GIA- and tectonic-corrected) sea level change at the KBR site as being equivalent to eustatic sea level will overestimate ESL rise or, equivalently, overestimate the total volume of ice melt.
Computed sea level changes over South Africa following the collapse of the (a) West Antarctic, (b) East Antarctic, and (c) Greenland Ice Sheets. The calculations are normalized by the eustatic sea level change associated with each melting event. Thus, the plots may be interpreted as predictions of postglacial sea level change in meters per meter of eustatic sea level change. The solid dot in each frame is the location of the study site (Klein Brak River) and the associated number is the normalized sea level prediction at this specific site. The calculations are based on a gravitationally self-consistent postglacial sea level theory (see text), and they show the sea level change the instant after the collapse (i.e., the response of the Earth model is purely elastic).
Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00282.1
The calculations in Fig. 2 are based on the assumption of an effectively instantaneous melting, and in this case the predictions involve elastic deformation of the solid Earth. These calculations are therefore insensitive to the adopted mantle viscosity profile. The following question arises: How will the normalized sea level change at KBR be impacted if the ice sheet collapse took place over a millennial time scale? In Fig. 3, we plot the normalized sea level change at KBR for each ice sheet as a function of the duration of the melt event (the parameter ΔT, as defined in section 2). The ΔT = 0 kyr case is the case treated in Fig. 2. These calculations adopt the test Earth model defined above; however, the results are relatively insensitive to this choice. The normalized sea level change at KBR in the case of either WAIS or EAIS collapse stays relatively constant for melt durations up to 3 kyr. In contrast, the analogous amplitude of the GIS sea level fingerprint decreases from 1.2 to 1.1 across the full range of ΔT values.
Computed (normalized) sea level change at Klein Brak River as a function of the duration of the melt event. Results are shown for WAIS, EAIS and GIS melt scenarios (as labeled). The calculations are based on a gravitationally self-consistent sea level theory (see text), and in all cases but ΔT = 0 they incorporate viscoelastic deformation. The ΔT = 0 case, which was adopted in Fig. 2, involves elastic deformation alone.
Citation: Journal of Climate 27, 23; 10.1175/JCLI-D-14-00282.1
These results have important implications for the Roberts et al. (2012) inference of peak ESL during MIS11. They estimated a tectonically corrected high stand at Klein Brak River of 11 m, and they then applied a GIA correction of −2 m to this value to estimate peak ESL (13 m; see section 1). If we replace their single GIA correction with the range we derived above (−2.4 to +1.4 m), we estimate a (GIA- and tectonic-corrected) MIS11 high stand at Klein Brak River of 9.6–13.4 m. Let us assume, for example, that polar ice sheet collapse took place over a time scale of 1 kyr. In this case, the normalized sea level change at KBR associated with melting from either the WAIS or GIS ice sheets is ~1.16 m (Fig. 3). If these two ice sheets, which are widely considered to be the most susceptible to collapse (Church et al. 2014), were solely responsible for the GIA- and tectonic-corrected peak sea level at Klein Brak River, then the eustatic sea level rise associated with the collapse was ~8.2–11.5 m. If we increase the time scale of ice sheet collapse to 2 kyr, then this estimate is impacted by less than 0.2 m. Some of the observed sea level rise at KBR may have come from melting of mountain glaciers and ocean thermal expansion, but the sum of these is unlikely to have been greater than 1 m [see Radić and Hock (2011) and McKay et al. (2011) for the case of MIS5e], and the estimate of ESL would be insignificantly revised. Since melting from WAIS and GIS can contribute up to ~12 m of ESL rise (Masson-Delmotte et al. 2013), our revision weakens any requirement for additional, minor melting of the EAIS. We note that any mapping of our estimate of ESL rise into total ice melt volume will depend on the volume of marine-based sectors exposed by the melting.
4. Final remarks
Sea level indicators from South Africa collected by Roberts et al. (2012) provide a new constraint on ESL rise during the protracted MIS11 interglacial. They estimated, under the assumption of a late MIS11 collapse, a local (GIA- and tectonic-corrected) sea level peak at KBR of 13 m, which they interpreted as being equivalent to the eustatic sea level rise associated with the ice collapse. Assuming that the tectonic correction they applied is robust and taking into account uncertainties in the GIA correction and the geographical variability in sea level following ice sheet collapse, we revise the estimated peak ESL rise based on the KBR record to ~8–11.5 m. The downward revision of the estimate by 1.5–5 m is significant; for example, it is equivalent to 30%–100% of the total ESL associated with the present-day WAIS volume.
Roberts et al. (2012) cited an error of 2 m in their estimate, arising almost entirely from uncertainty in the tectonic correction. It is important to emphasize that our downward revision corrects for systematic errors or bias related to the timing of the appropriate GIA correction and the mapping between local sea level at KBR and eustatic sea level, and it is distinct from the uncertainty in the tectonic signal cited by Roberts et al. (2012), which may be significant.
Acknowledgments
The authors acknowledge support from Harvard University, the National Science Foundation, and the Canadian Institute for Advanced Research.
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