Giant boulders and Last Interglacial storm intensity in the North Atlantic

We propagate the waves generated by three historical storms toward the Glass Window Bridge cliffs using a set of 2D and 1D wave and hydrodynamic models (26, 27). We reproduce the waves generated by the Perfect Storm (1991) (Fig. 2 A, D, G, and J), Hurricane Andrew (1992) (Fig. 2 B, E, H, and K), and Hurricane Sandy (2012) (Fig. 2 C, F, I, and L). These swells produced some of the highest-amplitude and longest-period waves to hit Eleuthera in instrumental times, but each storm also differed substantially with respect to its track, intensity, and development (see tracks in Fig. 1A and nearshore significant wave heights in Fig. 2 A–C).

To account for the higher local relative sea level (RSL) during the LIG, we incrementally adjust RSL from today’s value (0 m) up to +15 m in our wave models. This range was selected to encompass MIS 5e RSL estimates at Whale Point, ∼2 km north of Glass Window Bridge (28). Field data and relative sea level predictions from glacial isostatic adjustment (GIA) models (29, 30) suggest that LIG RSL could have been between ∼5 and ∼15 m above present at this location (Fig. 3A) (see SI Appendix for details on RSL indicators in the area and GIA models).

From our hydrodynamic models, we calculate the wave-induced flow velocities impacting the Glass Window Bridge cliffs under different storm and RSL scenarios (see Methods and Fig. 3C and SI Appendix for detailed results). Because flow velocity is directly related to the energy a wave exerts on a solid boundary, we use this output to evaluate whether the historical storms generated flow velocities sufficient to transport the Cow and Bull boulders.

Using drone and field photographs analyzed with Structure-from-Motion, we built a 3D model of the boulders at Glass Window Bridge (Fig. 3E) and from this we estimate that the Cow and Bull have volumes of 186 and 449 m³, respectively. Using density estimates from rock samples (Methods and SI Appendix), we calculate their masses as 383 (Cow) and 925 tons (Bull). Using these dimensions and a set of equations determined by empirical evidence and principles of physics and fluid flow (31), we then calculate the minimum flow required to lift or roll the boulders from just below the edge of a cliff onto the cliff top. We calculate that the Cow boulder can be lifted or rolled when the flow velocity generated by waves against the Glass Window Bridge cliffs reaches at least 9.1 (lifting) or 9.3 (rolling) m/s. The larger Bull boulder can be lifted at a flow velocity of 10.8 m/s and can be rolled at flow velocities above 11.2 m/s (see SI Appendix for details). Overall, our results show that when the critical flow velocity of 10.8 m/s is surpassed, both boulders can be moved from the cliff edge across the cliff top.

Putting this all together, our results show that it is not necessary to invoke LIG superstorms to explain the current position of the Eleuthera Cow and Bull boulders. At the minimum assumed LIG sea level (∼5 m), or even slightly lower (3.5 m above present, Fig. 3A) waves generated by an event analogous to Hurricane Sandy (2012) could have produced flows great enough to transport the Cow and Bull boulders from the cliff edge to their modern position (Fig. 3 A and C). Waves from Hurricane Andrew (1992) could have moved both boulders at RSL = 12.5 m, which is still in the range of possible LIG sea levels in the area. The waves modeled for the Perfect Storm (1991) can hardly move even the smaller boulder (Cow) in any RSL scenario.

Our model results show that significantly greater flow velocities are reached at the cliff edge under higher sea levels, and also that the frequency of high flows hitting the cliff lip is much higher (compare black and cyan lines in Fig. 2 J–L). Furthermore, at higher RSLs, the wave flow over the top of the cliff would likely be great enough (above 10 m/s and flowing downward, orange lines in Figs. 2 G–I and 3D) to transport boulders similar in size to the Cow and Bull across the Glass Window Bridge isthmus toward the lagoon side of the island, consistent with the positions of five additional large boulders (17).

Based on controversial amino acid racemization dates, it was proposed that the Cow and Bull boulders were lifted from the base of the cliff face and transported up and over the cliff top (17) by waves. This would require a larger vertical displacement (∼15 m) than we have considered in our model, and would probably require much greater wave-flow velocities. While such a mode of vertical transport has been seldom, if ever, reported for modern and Holocene boulders, abundant examples of modern cliff-edge boulders being transported backward from the cliff lip by large storms (or tsunamis) are observed in Eleuthera, as well as at many other locations in the Caribbean and elsewhere (32–35). In close proximity to the Cow and Bull boulders, near the Glass Window Bridge cliffs, we identified at least one large boulder in cliff-edge position (Fig. 1D) and two smaller ones that were transported across the cliff top from the cliff edge by the waves of Hurricane Andrew (see SI Appendix for details).

The most likely transport scenario for the massive cliff-top boulders of Eleuthera is that, like the smaller modern boulders, they were lifted or rolled from the cliff edge to their current positions. The transport would have only required waves generated by storms of historical magnitude, in combination with higher Eemian sea level.

In light of these results, we suggest that the remaining geologic evidence for superstorms should also be reanalyzed using numerical and process-based approaches similar to those applied here. We also highlight that, given the large number of MIS 5e coastal deposits (e.g., boulder fields or beach ridges) identified worldwide (36), there is an unexplored potential to use coastal landforms to assess potential changes in the intensity of storms and swells during the LIG, beyond the often-reported records of Bermuda and the Bahamas.

Our results also show that the maximum flow velocity against the top of the Eleuthera cliffs, generated by waves from each of the three storms, is greater as sea level is increased in the model. Comparing the maximum flow calculated at each RSL to the maximum flow modeled at present RSL for each storm (Fig. 4), we calculate that ∼90% of the maximum wave flows at higher RSLs are greater than the maximum modeled at present sea level. As an example, under median sea-level projections for the year 2200 (see black lines in Fig. 4), the flow velocity against the Glass Window Bridge cliffs by a Category 5 Hurricane (such as Andrew) might increase by ∼15% with respect to present. Our results (Fig. 2 J–L) also suggest that these high flows are more frequent during a single storm event when sea level is higher than at present.

These results point to an important conclusion concerning the future: Even without an increase in the intensity of coastal storms, rising sea levels have the potential to cause significant increases in both the frequency of strong waves delivered during a given storm event as well as the magnitude of flow velocities (and hence wave-related energy) experienced by coastlines, coastal communities, and infrastructure. Even cliffs and hard coastal barriers such as the one studied here, barriers which are often considered the more resistant elements of our coastlines, will be subject to higher erosional energy with sea level only a few meters higher than today. Future research on coastal processes at higher sea level (37) will therefore be critical to efforts aimed at adapting to and mitigating global warming and its impact on the people that currently live within the coastal zone.

We use two independent workflows to calculate, respectively, the flow velocity generated by waves hitting the Glass Window Bridge cliffs under different sea-level scenarios and the flow velocity required to initiate the boulder transport from the cliff edge. The description of each method employed in this study is summarized in Fig. 5. In SI Appendix we report the full details on our methods as well as detailed results for each step in the workflows.

We mapped the topography and bathymetry of the Glass Window Bridge area using a differential GPS and a single-beam echosounder, respectively. We interpolated these data with large-scale datasets from SRTM (38) and GEBCO (39). We used photogrammetry and representative rock samples to calculate exact measurements of the external dimensions, volumes, and masses of the Cow and Bull boulders.

The bathymetric and topographic data were used as input to a modeling chain consisting of a 1D nonhydrostatic wave model (26) coupled with a 2D phase-averaged model (27). The 2D model was used to propagate offshore waves from the global model WaveWatch III (40, 41) toward the area of Glass Window Bridge, while the 1D model was used to propagate the waves toward the cliff and calculate the cliff-top flow velocities generated by each swell modeled in this study. We modeled three storm-swell scenarios driven by historical observations: the Perfect Storm (1991), Hurricane Andrew (1992), and Hurricane Sandy (2012). RSL was changed from 0 to 15 m above present sea level at intervals of 3 and 0.5 m for, respectively, 2D and 1D simulations.

To evaluate the threshold flow velocities needed to transport the boulders, we use the cliff-edge boulder transport equations of Nandasena et al. (31). These equations are sensitive to a number of variables, such as boulder shape, suspension load in the fluid, particle–particle interaction, bottom roughness, and a set of coefficients. In particular, they are most sensitive to the coefficient of lift that determines the lift force/moment needed to transport a boulder from the cliff edge. We used two smaller boulders (13 and 33 tons, respectively) that were deposited on the upper part of the Glass Window Bridge cliff by the waves of Hurricane Andrew to calculate the coefficient of lift for the carbonate rocks of the Eleuthera cliff. This value was determined to be between 2.006 and 2.775 (see SI Appendix for details). In SI Appendix we further discuss potential uncertainties related to our modeling approach, including 1D, 2D, and boulder transport model uncertainties and the possible influence of different paleo topography of Glass Window Bridge during the LIG.

To calculate the percentage of maximum flow increase at higher RSLs (Fig. 4), we used the following formula:

where $F_i^{\%}$ is the percentage increase in flow velocity, $F_{\text{RSL}}^{\max }$ is the maximum flow for the specific swell at one RSL (from 1 to 15 m), and $F_0^{\max }$ is the maximum flow at RSL = 0 for the same swell. As also shown in Fig. 3C, $F_0^{\max }$ is 6.0 m/s for the Perfect Storm (1991), 7.5 m/s for Hurricane Andrew (1992), and 10.2 m/s for Hurricane Sandy (2012).

We acknowledge P. J. Hearty and J. Hansen for discussions on LIG “superstorms.” We acknowledge useful discussions during the workshops of Project 1603P (Modelling Paleo Processes, International Union for Quaternary Sciences, INQUA) and of the Paleo Constraints on Sea Level Rise (PALSEA) working group (Past Global Changes, PAGES/INQUA). Sarah Dendy and Alexander Janßen are acknowledged for help in the data analysis process. This research has been done under the permits issued by the Bahamas Environment, Science & Technology Commission [G-258] and the Bahamas Civil Aviation Authority (BCAA). We thank the staff at the Gerace Research Centre (San Salvador Island, The Bahamas) for logistical support for this research, the BCAA staff for assistance with aerial permits applications, and the staff at the Eleuthera Tourist Office for information on modern analog boulders. Boundary conditions and topography used in this study were extracted from datasets by the National Oceanic and Atmospheric Administration (NOAA), the US Geological Survey (USGS), the National Aeronautics and Space Administration (NASA), the Australian Bureau of Meteorology, the Commonwealth Scientific and Industrial Research Organisation (CSIRO), and the British Oceanographic Data Centre (BODC). The map in Fig. 1A was created using Esri ArcGIS basemaps and software (ArcMap). This research was financially supported by the Institutional Strategy of the University of Bremen, funded by the German Excellence Initiative (ABPZuK-03/2014); the Leibniz Centre for Tropical Marine Research (ZMT); National Science Foundation (NSF) Grant OCE-1202632 “PLIOMAX” and NSF GRFP Grant DGE-11-44155; and the World Surf League PURE through a grant from the Center for Climate and Life at the Lamont-Doherty Earth Observatory of Columbia University.