SI APPENDIX Giant Boulders and Last Interglacial Storm

SI APPENDIX

Giant boulders and Last Interglacial storm intensity

in the North Atlantic

Authors: A. Rovere, E. Casella, D. L. Harris, T. Lorscheid, N.A.K. Nandasena, B. Dyer, M.R.

Sandstrom, P. Stocchi, W.J. D’Andrea, M.E. Raymo

Please address correspondence to:

Contents Glossary and Synopsis of results ...... 4 Description of the study area ...... 6 Bathymetry and Topography ...... 9 Boulder size, density and volume ...... 11 Hydrodynamic models ...... 16 Perfect Storm (1991) ...... 20 Hurricane Andrew (1992) ...... 24 Hurricane Sandy (2012) ...... 30 XBeach (1D model) ...... 33 XBeach model set up ...... 34 Cow and Bull ...... 35 Modern analog ...... 37 Threshold flows for boulder transport ...... 37 LIG Relative sea level ...... 42 Additional discussions ...... 49 References ...... 53

Index of Tables

Table S1. Names of relevant topographic features, meteorological events or other definitions used both in the main text and in the Supplementary Text.

Table S2. Summary of results obtained in this study.

Table S3. Workflow, parameters and commands used in Agisoft Photoscan to calculate 3D scenes from drone and pole photographs.

Table S4. Results of boulder density calculations.

Table S5. Calculations of paleo RSL from the elevation of RSL indicators measured in the field and from GIA models. For more details of the formulas used to calculate RSL and δRSL from the elevation of a RSL indicator, see Rovere et al. (2016). All measures are in meters. Details on the GIA models can be found in Lorscheid et al (2017).

Index of Figures

Fig.S1 Study area.

Fig.S2 Results of topographic surveys.

Fig.S3 SfM workflow.

Fig.S4 Results of the SfM workflow.

Fig.S5 Orthorectified photographs of the Cow and Bull boulders

Fig.S6 2D model grids.

Fig.S7 Input to the 2D wave model for the 1991 Perfect Storm.

Fig.S8 2D wave model results for the 1991 Perfect Storm.

Fig.S9 Input to the 2D wave model for the 1992 Hurricane Andrew.

Fig.S10 Additional model results for Hurricane Andrew.

Fig.S11 2D wave model results for the 1992 Hurricane Andrew.

Fig.S12 Input to the 2D wave model for the 2012 Hurricane Sandy.

Fig.S13 2D wave model results for the 1992 Hurricane Sandy.

Fig.S14 Examples of water levels and maximum wave-generated flow velocity against the Cow and

Bull cliffs in different RSL scenarios (0-3-6-9-12-15m) and for each modeled event.

Fig.S15 Flow velocities produced by each swell on the face of the Cow and Bull cliff in all RSL scenarios

Fig.S16 Flow velocities calculated at the modern analog.

Fig.S17 Modern analog flow velocities used for the calculation of the coefficient of lift.

Fig.S18 Probability density function derived from the solution of Eq.3 and Eq.4 for the two modern analog boulders.

Fig.S19 Probability (cumulative density) of boulder transport vs flow velocity.

Fig.S20 RSL indicators in forereef environment.

Fig.S21 Sedimentary RSL indicators.

Fig.S22 Ensamble of GIA model predictions for Eleuthera throughout MIS 5e.

Glossary and Synopsis of results In Table S1 we summarize the terminology used throughout the paper and this SI

Appendix file.

Table S1. Names of relevant topographic features, meteorological events or other definitions used both in the main text and in the Supplementary Text.

Name Description Glass Window This is the topographic name of the isthmus connecting the central and the northern parts Bridge of the island of Eleuthera. In its narrowest part, the strip of land connecting the two sides of the island is only few meters wide.

The ‘Cow and The ‘Cow and Bull’ are the local names of two among seven mega-boulders identified Bull’ boulders along the Glass Window Bridge cliffs and interpreted as deposited during ‘paleo- superstorms’ (1). These boulders are located on the top of the Glass Window Bridge cliffs, and correspond to Boulder n.1 (the Bull) and Boulder n.2 (the Cow) reported by Hearty (1997) (1) (see their Table 2 and their Fig.7).

Modern analog The modern analog boulders reported in this study were measured north of the ‘Cow and boulders Bull’ mega-boulders, in proximity of the Glass Window bridge that gives the name to the entire area. These boulders are smaller than the ‘Cow and Bull’, and historical accounts report that they have been ripped from the cliffs by the waves of Hurricane Andrew, August 1992.

Superstorm The ‘paleo-superstorm’ term has been introduced in the last interglacial climate debate by Hansen et al. (2015) (2) to indicate strong late-Eemian (MIS 5e) storminess. This definition derives from the findings of Hearty (1997) (1), who suggested that chevron ridges, runup deposits and giant boulders in the Bahamas and Bermuda were deposited by ‘massive storms […] much larger than those occurring during the Holocene’ (1). This concept was also stressed in a follow-up paper by Hearty et al. (1998) (3), where the authors affirm that chevron ridges, runup deposits and boulders were created by ‘larger and more frequent cyclonic storms in the North Atlantic than those seen today’ (3). In all these papers, “superstorms” are related to modern winter cyclonic storms generating near-hurricane wind forces (e.g. the 1991 ‘Perfect Storm’). The hypothesis that “superstorms” might intensify in future warmer climates is related to increased water vapor due to the warming of low- latitude oceans, eventually combined with a ‘cooler North Atlantic Ocean from AMOC slowdown and an increase in mid- latitude eddy energy causing more severe baroclinic storms. Increased high pressure due to cooler high-latitude ocean […] can make blocking situations more extreme, with a steeper pressure gradient between the storm’s low- pressure center and the blocking high, thus driving stronger North Atlantic storms’ (2). In another recent paper, Hearty and Tormey (2017) (4) reinforce the notion that the field evidence from the Bahamas and Bermuda has been emplaced by “superstorms”.

Structure-from- Structure from motion (SfM) is a range of imaging techniques used to estimate three- Motion dimensional structures from sequences of two-dimensional images (5)

Boulder Equations deriving minimum wave flow velocity necessary to transport boulders either by transport lifting or rolling from balances of forces and moments, cliff type and pre-transport settings equations of boulders (6)

Wave flow The flow velocity as calculated by SWAN or XBeach. The parameter extracted from the velocity model to represent flow velocity is the u vector of the Eulerian velocity in cell center.

In Table S2 we present an overview of the results of this study, which are explained in detail in the subsections below. The results of our 1D and 2D models are available in Pangea at the following link: https://doi.pangaea.de/10.1594/PANGAEA.880687.

Table S2. Summary of results obtained in this study.

Boulder size, density and volume Axes [m] a b c The Cow 9.4 5.2 3.8 186 2.06 383 The Bull 12.5 6.9 5.2 449 2.06 925 Modern 2.6 2 1.2 6.2 2.06 13 analog 1 Modern 6.7 1.7 1.4 15.9 2.06 33 analog 2 Hydrodynamic models Relative sea Significant wave height (Hs) [m] Smoothed peak period (Tp) [s] level [m] RSL 1991 1992 2012 1991 1992 2012 0 4.7 7.4 9.2 17.0 11.0 12.1 3 4.7 7.7 9.4 17.0 11.5 12.1 6 4.7 8.0 9.5 16.9 11.7 12.1 9 4.7 8.2 9.7 16.9 11.8 12.1 12 4.7 8.6 9.8 16.9 11.9 12.1 15 4.8 10.2 10.1 16.8 12.1 12.1 Relationship between RSL and Hs / Tp (Used in XBeach) Event This field is derived from the third-order polynomial interpolation of the data shown in the section above (see also Fig.S8, S11 and S13) Hs = 0.00007(RSL)3 - 0.0012(RSL)2 + 0.0048(RSL) + 4.7335 1991 Perfect Storm Tp = -0.00005(RSL)3 + 0.0006(RSL)2 - 0.0064(RSL) + 16.974 Hs = 0.0024(RSL)3 - 0.0394(RSL)2 + 0.2364(RSL) + 7.3967 1992 Hurricane Andrew Tp = 0.001(RSL)3 - 0.0255(RSL)2 + 0.2376(RSL) + 11.004 Hs = 0.0005(RSL)3 - 0.009(RSL)2 + 0.0942(RSL) + 9.1668 2012 Hurricane Sandy Tp = -0.00006(RSL)3 + 0.0015(RSL)2 - 0.0115(RSL) + 12.101 Threshold flows for boulder transport Flow velocity range at modern analog transect [m/s] 3.4 to 5.7 Coefficient of lift 2.006 to 2.775 Lifting 10.8 Rolling 11.2 Lifting 9.1 Rolling 9.3 MIS 5e Relative Sea Level Range from field data [m] 12.3±2.1 / 6.8±0.6 / 7.3±1.1 Range from GIA models [m] 5.2 to 9.1 / 9.5 to 13.7

Description of the study area The area of Glass Window Bridge is a narrow strip of land connecting the central and the northern parts of the island of Eleuthera. The general morphology of this area is that of a steep cliff facing the Atlantic Ocean (Fig.S1A). The top of the cliff has an elevation of ~15 meters above sea level, and the average depth of the cliff toe is 5-

10 meters below sea level. The seafloor in the proximity of the cliff on the Atlantic side is relatively flat and almost entirely rocky from the cliff toe down to at least -

15m/-25m (Fig.S1I,J). The seafloor is characterized by large boulders (Fig.S1I,J) and erosion channels excavated in the rocky bottom, likely due to abrasion from submerged boulder movement caused by high-energy wave currents.

From the top part of the cliff, the rocky surface slopes gently towards the Bahamas bank side of Eleuthera (Fig.S1A). The upper part of the cliff is characterized by some large cliff-edge boulders that are detached from the main cliff but are still hanging on the vertical walls (Fig.S1D). Other boulders have been ripped from the cliff face and are now located on top of the cliff. In particular, we surveyed two of these boulders, which we refer to as modern analogs. One is located ~13 meters from the cliff edge towards the Bahamas bank side (modern analog 1, Fig.S1B), the other is located directly on the edge of the cliff (modern analog 2, Fig.S1C). The modern analog 1 was transported to its modern position from the cliff face: on a slightly sloping rock surface, where the trajectory of movement is still clearly visible as the boulder passage broke the highly karstified rock surface. The modern analog 2 is instead upside down (the original karstified rock surface lies on the bottom of the boulder) and it appears to have been quarried directly from the cliff face, where it is still possible to identify a gap in the continuity of the cliff of approximately the same size as the boulder. The two modern analog boulders are incised by sculptures and paintings that were made after the boulders were transported in their current position

6 by the waves generated by Hurricane Andrew, in August 1992 (Bahamian office of

Tourism in Eleuthera, email communication to A. Rovere).

Along the Glass Window Bridge cliff, seven boulders are significantly bigger than the modern analogs and than the ones commonly moved by winter storms or hurricanes, that are located more to the North (1). These mega-boulders are scattered between the edge of the cliff on the Atlantic Ocean side and the shallow waters of the

Bahamas Bank side (1). Two of them are known by the local name of ‘the Cow and the Bull’ and are located near the edge of the cliff facing the Atlantic Ocean (Fig.S1

E-H). These boulders are the main focus of the paper.

Fig.S1 Study area. (A) The area of Glass Window Bridge, picture taken from the cliff on the Atlantic Ocean towards the Bahamas Bank. The boulder lying on the platform is the modern analog 1. (B) Close-up photo of the modern analog 1. (C) close-up view of the modern analog 2. (D) Boulder at the cliff edge along the Glass Window Bridge cliffs (note the bridge on the left of the photo, same boulder as in Fig.1D). (E) The Cow and Bull boulders, picture taken from the Atlantic side of Glass Window Bridge. (F) Close-up of the Cow boulder. (G) Close-up of the Bull boulder. (H) The Cow and Bull boulders and their position near the cliff (Atlantic side). (I) The rocky sea bottom at -6m depth in front of the Cow and Bull site. (J) The rocky sea bottom at -7m depth in front of the ‘Cow and Bull’ site. Note a boulder lying on top of the rocky bottom. Photos by A. Rovere and E. Casella.

Bathymetry and Topography As input to our wave and hydrodynamic models, we used a set of topographic and bathymetric datasets. The coarsest dataset we used was the GEBCO 2008 1-minute bathymetry (7) covering the wider Northern Bahamas Region (Fig.S2A). In the area of North Eleuthera, we instead interpolated a seamless topo-bathymetric raster from data digitized using nautical and topographic charts (8, 9), SRTM Digital Elevation

Models (10), and field data (Fig.S2A-D). To interpolate these topographic and bathymetric data into a seamless raster, we used the Empirical Bayesian Kriging

Interpolation tool of the ESRI ArcMap® software suite (11). The results of this interpolation are shown in Fig.S2D. The field data used in the interpolations include depth measured with a MX Biosonics Aquatic Habitat Echosounder (Depth accuracy

1.7cm±0.2% of depth; DGPS positional accuracy: <3m, 95%) and GPS points measured with a Trimble Pro XRT GPS receiving real-time Omnistar HP corrections

(2-sigma 95% accuracy of 10cm). All our field data were referred to the Mean Sea

Level defined by the EGM 2008 geoid. The datasets were used to extract topographic cross-profiles of the cliffs both in front of the Cow and Bull (Fig.S2E) and in correspondence of the modern analog boulders (Fig.S2F).

Fig.S2 Results of topographic surveys. (A) Bathymetric surveys in front of Glass Window Bridge cliffs, and additional datasets used as topographic and bathymetric inputs to wave models. (B) Field photo taken during echosounder surveys. (C) Field photo taken during GPS surveys. (D) Original GPS and echosounder data plotted against the interpolated topo-bathymetry. The pink circle indicates the site where the waves were extracted from the SWAN nested model: the wave characteristics at this site were then used as input for the 1D XBeach model. (E) Topography of the Cow and Bull transect and location of the Cow and Bull boulders. (F) Topography of the modern analog transect, where the modern analog boulders are located.

Boulder size, density and volume Structure-from-Motion. We collected photographs of the modern analog and Cow and Bull boulders with a drone (12) and a telescopic pole (13). We processed the photos with Structure-From-Motion (SfM) algorithms (14) and derived a 3D model of the boulders, from which we calculated their volume.

We used two cameras: a CANON S100 (12.1 megapixels) and a Sony RX100 M3

(20.1 megapixels). The pole we used is a simple, 3-meters long carbon fiber stick, while the aerial imagery acquisition system used in this study is composed of a small drone, a remote control, and a ground station (to check the drone route and performance during flight). Permits for drone flights were granted from the Bahamian

Civil Aviation Authorities, and flights were performed manually (i.e. without the aid of pre-programmed flight paths) to ensure full coverage around each boulder.

To build georeferenced 3D models of the boulders we used the software AgiSoft

Photoscan (15). The workflow and parameters used are summarized in Table S3 and some phases of the data collection and analysis process are shown in Fig.S3A-E. The procedure to calculate a digital elevation model and an orthophoto from SfM algorithms is described in detail in several studies (12, 16, 17). To calculate the volume of each boulder we used the ‘Measure Area and Volume’ tool of AgiSoft Photoscan.

The Axes of the boulders (a,b,c) have been directly measured on the 3D models, keeping the axis size proportional to the volume extracted from the 3D model (푎 × 푏 ×

푐). The photogrammetric approach requires a set of points of known coordinates

(ground control points, GCPs) or scale bars (SBs) of known length to compute pixel- to-earth transformations and georeference the data point cloud. In total, we used 12

GCPs and 4 SBs. As GCP targets, we used markers with different colors and numbers fixed on the ground (Fig.S3D), which could be easily identified in the aerial pictures

11 and metered rods have been used as SBs. GCPs were collected using the GPS system described above.

Table S3. Workflow, parameters and commands used in Agisoft Photoscan to calculate 3D scenes from drone and pole photographs.

Align photo Accuracy High Pair Preselection Disabled Build mesh (preliminary step to insert GCPs) Surface type Arbitrary Source data Sparse cloud Interpolation Enabled Point classes All Locate and place GCPs in the scene and import GCPs coordinates Measurement accuracy (for GCPs) Camera accuracy (m) 10 Marker accuracy (m) 0.05 Scale bar accuracy 0.001 (m) Projection accuracy 0.1 (pix) Tie point accuracy 4 (pix) Build dense cloud Quality High Depth filtering Aggressive Number of resulting 110,282,714 Points Build mesh Surface type Arbitrary Face count Medium (7,352,180) Source data Dense cloud Interpolation Enabled Point classes All Generate Orthophoto Generate 3D Model

Fig.S3 SfM workflow. (A) Sequence of overlapping aerial photographs; (B) Sequence of land/pole photographs; (C) Operation of small drone (the flying drone is visible inside the yellow inset); (D) Target used as Ground Control Point; (E) Locations of images (center of camera, red dots) as calculated by Agisoft Photoscan and Ground Control Points measured with differential GPS. The image represents the orthophoto calculated merging all the photographs.

Size and volume of boulders. We analyzed the photographs taken in the field in three distinct SfM projects with the following characteristics:

 Modern analog 1. 55 photos; DEM resolution: 1.08 cm/pix; 3 GCPs;

estimated X error: 50.3 cm; estimated Y error: 34.2 cm; estimated Z error: 6

cm.

 Modern analog 2. 142 photos; DEM resolution: 3.29 cm/pix; 4 GCPs;

estimated X error: 19.5 cm; estimated Y error: 12.3 cm; estimated Z error: 5.3

cm.

 Cow and Bull. 738 photos; DEM resolution: 0.89 cm/pix; 12 GCPSs;

estimated X error: 19 cm; estimated Y error: 11 cm; estimated Z error: 44 cm.

The size of the three main axes for each boulder, together with a 3D representation derived from each SfM project, is shown in Fig.S4A-C. The orthorectified photographs calculated from each SfM project are shown in Fig.S5A-C.

Fig.S4 Results of the SfM workflow. 3D representation and size of the three main axes (a,b,c, from the biggest to the smallest) for the Cow and Bull boulders, the modern analog 2 and the modern analog 1. Units are in meters.

Fig.S5 Orthorectified photographs of the Cow and Bull boulders (A), the modern analog 1 (B) and the modern analog 2 (C).

Boulder density. We measured the wet (waterlogged) and dry (minimum water content) densities of the boulders using a liquid displacement method. Four hand samples from the Cow and Bull boulders were measured along with four other hand samples from nearby boulders and rock units of similar composition. Each hand sample was first weighted dry on an electronic balance, with 2σ error (= ±0.023g) calculated by multiple repeated measurements on two of the samples. Samples were then carefully wrapped in stretched parafilm to best preserve their original volume, and placed into a large graduated cylinder containing 500mL of water at a temperature of ~23.5°C. The water displacement was recorded in mL and assumed

15 to represent “dry” sample volume in cm3. The experiment was then repeated with the same samples, but the parafilm was removed and the samples were submerged and sonicated in the cylinder for 5 minutes to remove as much air as possible from the internal pores in the rock. Water displacement was recorded, this volume recording the “wet” weight of the samples, which would be the maximum weight of the rock if completely waterlogged. Error estimates for water displacement were calculated using a number of known and measured non-porous weights. The density calculated for each of the eight hand samples collected in the field is presented in Table S4.

Using the average of the wet and dry densities (=2.06 g/cm3) and the volume of each boulder derived from SfM we calculate the volume and weight estimates shown in

Fig.S5.

Table S4. Results of boulder density calculations.

Density Density Dry Water Water Max Min Porosity Sample ID weight displaced Displaced (wet, (dry, % (g) (mL) WET (mL) DRY g/cm3) g/cm3) BEL-BC-2K 69.26 35 40 1.98 1.73 12.5% BEL-BC-2A 26.75 11 12 2.43 2.23 8.3% BEL-BC-2C 57.75 27 30 2.14 1.93 10.0% BEL-C1A 121.61 60 77 2.03 1.58 22.1% BEL-BC-1B 51.58 20 21 2.58 2.46 4.8% BEL-C1D 66.40 29 35 2.29 1.90 17.1% BEL-C1C 107.80 50 65 2.16 1.66 23.1% BEL-BC-1A 119.00 59 67 2.02 1.78 11.9%

Hydrodynamic models In order to calculate wave flow velocities in our study area, we set up a modeling chain aimed at propagating waves generated offshore towards the Glass Window

Bridge cliffs. We first propagated offshore waves towards Eleuthera using a 2D nested SWAN model (implemented through Delft3D-Wave ver.4.95) (18). We then extracted significant wave height and peak period nearshore and used them as input for XBeach, a non-hydrostatic nearshore wave model (19). We model waves

16 produced by the Perfect Storm (1991), Hurricane Andrew (1992) and Hurricane

Sandy (2012) events. The main characteristics and boundary conditions of each run are described in the following sections.

In order to propagate offshore waves towards the Glass Window Bridge cliffs area, we ran the 2D wave model on a series of nested grids. We interpolated the topo- bathymetric data in three modeling grids: one coarse, one intermediate and one high-resolution. The spatial resolution of the coarser grid (regional grid in Fig.S6B,C) is 500m. As topography associated to this grid, we used the GEBCO (2014) terrain model (topography and bathymetry). The spatial resolution of the intermediate grid

(North Eleuthera grid in Fig.S6B,D) is 300m and that of the high-resolution grid is

40m (Glass Window Bridge grid in Fig.S6D,E). The latter two grids were run on more detailed topographies extracted from nautical charts and surveyed in the field (see sections above and Fig.S2).

Fig.S6 2D model grids. (A) Location of the study area and of the main NDBC stations used as either wind input or validation of the CAWCR wave hindcast. (B) location of the Regional and North Eleuthera grids. (C) comparison between the size of the three nested grids used in this study. (D) Regional grid. (E) North Eleuthera and Glass Window Bridge grids (F) Glass Window Bridge grid.

We impose waves at NE, NW, SE and SW boundaries of the regional grid (Fig.S6B) using the CAWCR wave hindcast (20). This is an ocean wave hindcast (1979-2010), that uses the WaveWatch III v4.08 wave model forced with NCEP CFSR hourly winds. In order to evaluate how the Wavewatch III model predicted each storm we modeled, we compared the WaveWatch III data with measured wave data in the

Central Atlantic (NOAA NBDC network Buoy 41010 (21)). In each model run, we imposed time-varying, but spatially uniform winds (see detailed description of boundary conditions for each event below).

Using the SWAN nested model, we propagated wave characteristics from offshore towards the Island of Eleuthera and the Glass Window Bridge area. Our initial run was done in modern sea level conditions (RSL=0). Five successive model runs were performed updating the topography to reflect changes in sea level of 3, 6, 9, 12 and

15 meters above present. The topography of each of these runs was calculated adding to each node of the model grid a value equivalent to the magnitude of relative sea level change (3 to 15 meters above present). It is worth pointing out that these model runs do not account for storm surge as they were not coupled with a hydrodynamic flow simulation. Storm surge was instead accounted for (when necessary) in the XBeach 1D model runs (see below).

Perfect Storm (1991) General description of the event. This event took place between the end of

October and the first days of November 1991. On October 27th, Hurricane Grace generated large swells offshore of North Carolina and the Florida coastline. On

October 28th, an extratropical cyclone developed east of the coast of Nova Scotia.

On October 29th these two systems merged. The entire meteorological event was later called ‘the 1991 Perfect Storm’ or the ‘Halloween Gale’ (22, 23). The 1991

‘Perfect Storm’ was one of the most severe storms hitting North America (24).

The effect of waves generated by the 1991 Perfect Storm at Glass Window Bridge were widely reported by local press and technical accounts (25), as the bridge was severely damaged during this event. Anglin and Macintosh, 2005 (25) report that, during this event, the bridge deck was ‘lifted and shifted by repeated wave impacts, with the deck sliding approximately 2.5m towards the Bight (west) along the North abutment’. The same authors report that further damage was caused to the bridge by Hurricanes Andrew (1992), Floyd (1999), Michelle (2001), Isabelle (2003) and

Frances (2004).

Validation of SWAN inputs. The data from WaveWatch III hindcast by CAWCR

Australia compare well with the significant wave height and peak period recorded during this event by the NOAA NDBC buoy 41010 and by the wind speed and direction recorded by the NOAA NDBC station SPGF1 (Fig.S7A). No data on wave direction are available from the NDBC buoy 41010.

Input to SWAN model. As wave inputs at the boundaries of our SWAN model we used waves extracted at the NE-NW-SE-SW boundaries of our domain from the

WaveWatch III hindcast by CAWCR Australia. As wind input we imposed a time- varying timeseries extracted in the center of our regional computational grid extracted from WaveWatch III hindcast data (Fig.S7B).

Results. The modeled significant wave height at the peak of the 1991 Perfect Storm at present sea level (RSL=0) is shown in Fig.S8. Both significant wave height and period do not change significantly as RSL is increased in the simulations (Fig.S8).

The offshore wave height modeled in this study is comparable with the ‘one per cent exceedance condition of Hs/Tp ~ 4 m/10 s’ reported by Anglin and Macintosh, 2005

(25) offshore Eleuthera. With a Hs of ~4.7m and a Tp of ~17s the 1991 Perfect

Storm can be regarded as one of the most powerful swells not caused by the direct impact of an hurricane on Eleuthera.

Fig.S7 Input to the 2D wave model for the 1991 Perfect Storm. (A) Input data from WaveWatch III CAWCR compared with the closest NOAA NDBC stations (SPGF1 and 41010). (B) Boundary wind and wave conditions used in our 2D wave model runs.

Fig.S8 2D wave model results for the 1991 Perfect Storm. Upper panels: modeled significant wave height at the swell peak (left: North Eleuthera computational grid; right: Glass Window Bridge computational grid). Lower panels: Change in significant wave height (Hs) and peak period (Tp) with different RSL scenarios. The point where these values have been extracted off Glass Window Bridge is shown in Fig.S3.

Hurricane Andrew (1992) General description of the event. Hurricane Andrew formed from a tropical wave in the East Atlantic Ocean on August 14th, 1992. It reached hurricane strength on

August 22nd (26). Andrew was a category 4 hurricane when its eye passed over northern Eleuthera on August 23rd. The anemometer at Harbour Island (North

Eleuthera) measured a wind speed of 62 m/s shortly after 2100 UTC on the 23rd

(27). The storm surge flooding caused by this hurricane in low-lying parts of

Eleuthera made this hurricane one of the most severe ever recorded in the Bahamas

(28), with damages estimated in a quarter of a billion USD (60). In 2004, a reanalysis of the intensity of the hurricane indicated that Andrew made landfall on Eleuthera at its minimum value pressure and maximum wind speed of 82 m/s (29).

Validation of SWAN inputs. The data from WaveWatch III hindcast by CAWCR

Australia underestimate the significant wave height recorded during this event by the

NOAA NDBC buoy 41010 (Fig.S9A), while they are consistent with the peak period recorded by the same buoy (Fig.S9A). No data on wave direction are available from the NOAA NDBC buoy 41010. The wind speed recorded by the NOAA NDBC station

SPGF1 is in agreement with WaveWatch III winds, but they do not represent the hurricane-force wind field that developed in the Northern Bahamas during the passage of Hurricane Andrew (29).

Input to SWAN model. As wave inputs at the boundaries of our SWAN model we used waves extracted at the NE-NW-SE-SW boundaries of our domain from the

WaveWatch III hindcast by CAWCR Australia. As wind input we imposed a time- varying time series extracted in the center of our regional computational grid

(Fig.S9B). The wind data were extracted from an hydrodynamic model that simulated the wind field via the Delft Dashboard ‘Tropical Cyclone’ toolset (Fig.S10A) (30). This model used Hurricane Andrew track properties from HURDAT2 (31, 32). We used

24 default settings except for the whitecapping formulation (for which we used the formulation of van der Westhuysen et al., 2007 (33), that is more suitable in the modeling of waves generated by hurricanes (34)) and a wind drag formulation characterized by three breakpoints (analog to that used in Vatvani et al., 2012 (35), their Fig.1). As Hurricane Andrew hit directly the Eleuthera and caused a significant storm surge, we extracted from the NOAA SLOSH surge model (36) for Hurricane

Andrew (32) the storm surge at the peak of the hurricane. The storm surge was not used in the 2D SWAN simulations, but it was instead accounted for in the 1D

XBeach ones.

Results. The winds modeled in this study are, at the peak of the storm in Eleuthera,

65 m/s, (Fig.S10A), consistent with the maximum values reported by the anemometer at Harbour Island, Eleuthera (62 m/s). The peak of the storm surge on the Atlantic side of Glass Window Bridge was modeled at 1.3m (Fig.S10B). The modeled significant wave height at the peak of the Hurricane at present sea level

(RSL=0) is shown in Fig.S11. Both significant wave height and wave period increase as RSL is increased in the simulations (Fig.S11). The offshore wave height modeled in this study is ~17 m. While we cannot compare this value with any direct measurement offshore Eleuthera, it is consistent with the wave height modeled off

Eleuthera for Hurricane Floyd (1999), that peaked at ~18m (25), and with observed offshore wave heights at the passage of Hurricane Andrew in the Gulf of Mexico (37,

38). Our modeled offshore waves are also comparable with the maximum wave height modeled by the CAWCR wave hindcast (20) for this region in the period 1979-

2015 (corresponding to Hurricane Floyd, Hs 13.6m, Tp 15 seconds) and is lower than the highest waves ever recorded on the center of a hurricane (Hurricane Ivan,

2004, Gulf of Mexico, 21m (39)). These data confirm that Hurricane Andrew was,

25 from the point of view of wave impact, one of the most intense hurricanes directly hitting the island of Eleuthera in historical times. The partial topographic sheltering from the main wave direction caused the nearshore wave height to be lower than those by other hurricanes (e.g. Hurricane Sandy).

Fig.S9 Input to the 2D wave model for the 1992 Hurricane Andrew. (A) Input data from WaveWatch III CAWCR compared with the closest NOAA NDBC stations (SPGF1 and 41010). (B) Boundary wind and wave conditions used in our 2D wave model runs.

Fig.S10 Additional model results for Hurricane Andrew. (A) Wind field calculated using D-FLOW and the Delft Dashboard Tropical Cyclone Toolbox and used as input to the SWAN 2D wave model. (B) Storm surge (meters) for Eleuthera extracted from the NOAA SLOSH model and used in XBeach simulations of the 1992 Hurricane Andrew.

Fig.S11 2D wave model results for the 1992 Hurricane Andrew. Upper panels: modeled significant wave height at the swell peak (left: North Eleuthera computational grid; right: Glass Window Bridge computational grid). Lower panels: Change in significant wave height (Hs) and peak period (Tp) with different RSL scenarios. The point where these values have been extracted off Glass Window Bridge is shown in Fig.S3.

Hurricane Sandy (2012) General description of the event. Hurricane Sandy developed from a tropical wave that left the west coast of Africa on October 11th, 2012. On October 22nd it became a tropical depression and subsequently turned to a tropical storm in the Caribbean

Sea. Sandy became a hurricane on October 24th, and passed between Cat Island and Eleuthera on the night between October 25th and 26th. Damage in Bahamas was generally not as severe as in previous hurricanes (40). Overall, Sandy is considered a hurricane of exceptional magnitude, with a 900-1600 years of return period for storm tides in the North Atlantic (41, 42), and is characterized by a 10% probability of realization in 100 years (43).

Validation of SWAN inputs. The data from WaveWatch III hindcast by CAWCR

Australia compare well with the significant wave height and peak period recorded during this event by the NOAA NDBC buoy 41010 and by the wind speed recorded by the NOAA NDBC station SPGF1 (Fig.S12A). No data on wave direction are available from the NOAA NDBC buoy 41010.

Input to SWAN model. As wave inputs at the boundaries of our SWAN model we used waves extracted at the NE-NW-SE-SW boundaries of our domain from the

WaveWatch III hindcast by CAWCR Australia. As wind input we imposed a time- varying timeseries extracted in the center of our regional computational grid from

WaveWatch III hindcast data (Fig.S12B).

Results. The significant wave height at the peak of the 2012 Hurricane Sandy at present sea level (RSL=0) is shown in Fig.S13. Both significant wave height and period do not change significantly as RSL is increased in the simulations (Fig.S13).

The offshore wave height modeled in this study compares well with the ‘100 year extreme condition of Hs/Tp ~ 10 m/16 s’ as reported by Anglin and Macintosh, 2005

(25) offshore Eleuthera.

Fig.S12 Input to the 2D wave model for the 2012 Hurricane Sandy. (A) Input data from WaveWatch III CAWCR compared with the closest NOAA NDBC stations (SPGF1 and 41010). (B) Boundary wind and wave conditions used in our 2D wave model runs.

Fig.S13 2D wave model results for the 1992 Hurricane Sandy. Upper panels: modeled significant wave height at the swell peak (left: North Eleuthera computational grid; right: Glass Window Bridge computational grid). Lower panels: Change in significant wave height (Hs) and peak period (Tp) with different RSL scenarios. The point where these values have been extracted off Glass Window Bridge is shown in Fig.S3.

XBeach (1D model) We used GPS and echosounder data collected in the field to calculate two cross- shore transects, one in front of the modern analog boulders and the second in front of the Cow and Bull (Fig.S2E,F). These data were used as input for a series of 1D runs of the model XBeach (19). As in the SWAN model, the first run was done in modern sea level conditions (RSL=0). We then performed all the successive runs changing the base level from zero to 15 meters above present, following increments of 0.5 m. For all the 1D simulations, we used the non-hydrostatic module of XBeach.

This means that our 1D model can resolve the wave field on the basis of individual waves, and can therefore model the non-linear evolution of the wave field more accurately than time-averaged ones (44). Each 1D XBeach model was run for a total of 10,800 seconds (3 hours), representing the peak of each swell. We run XBeach using the ‘King’s Day’ Matlab toolbox, and we maintain standard parameters (19) for all our runs.

The wave boundary conditions for our XBeach simulations were derived from the

SWAN 2D model runs described above. In particular, we varied the significant wave height (Hs) and peak period (Tp) in our 1D XBeach model runs according to changes in sea level following the relationship between RSL and these parameters shown in the lower panels of Fig.S8, S11 and S13. The likely sea states based on the offshore significant wave height (Hs) and peak period (Tp) were generated using a

JONSWAP spectrum. In the simulations for the 1992 Hurricane Andrew, we linearly added to RSL a storm surge of 1.3m (Fig.S10B) as a constant water level.

From the XBeach results, we extracted the Eulerian Velocity in Cell Center for the entire simulation time, which represents the flow velocity generated by each wave against the cliff, in meters per second. For which concerns the XBeach model, we note two main results: i) the flow velocities increase as the RSL is increased in the

33 simulation (Fig.S14, S15); ii) a similar increase is recorded also in the water level at the edge of the cliff.

On the second point, the fact that the boulders are submerged by water is a necessary condition for their transport (6). We note that, while some flow velocities in our present RSL simulations are high enough to move the Cow boulder (Fig.3C), it is unlikely that a boulder of this size could move in a present-day setting as the flow depth (i.e. the amount of water on top of the cliff edge during a swell) is too low, but increases as RSL is increased in our simulations (Fig.3D-F).

XBeach model set up Below we report an example of the matlab code we used to run XBeach.

% load the bathymetric data data=load(['cowbull.csv']); x=data(:,1)'; z=data(:,2)'; z=fliplr(z); y=zeros(1,length(x)); T=20; % Model different SL scenarios and save them into different nc files BaseName='OUT_'; format='.nc' SL=9; Fn=9; % At each iteration, add changes in Hs and Tp as in Table S2 % Below example for Perfect Storm (1991) Hs=0.00007*(SL^3)-0.0012*(SL^2)+0.0048*SL+4.7335 Tpeak=-0.00005*(SL^3)+0.0006*SL^2-0.0064*SL+16.974 Hm0 = repmat(Hs,T,1); Tp= repmat(Tpeak,T,1); FileName=[BaseName,num2str(Fn),format]; % Generate waves xbm_model = xb_generate_model('waves', {'type', 'jonswap', 'Hm0', Hm0, 'Tp', Tp,}); xbm_model=xb_bathy2input([xbm_model],x,y,z); % Model settings xbm_model = xs_set(xbm_model, 'outputformat', 'netcdf', 'ncfilename', FileName, 'morphology', 0, 'zs0',SL, 'random', 0,'tstop',10800, ... 'sedtrans', 0, 'swave', 0,'nonh',1,... 'break', 'roelvink1','gamma',0.50); % Write XBeach input files xb_write_input('params.txt',xbm_model) % Run XBeach (change dir) run_xb = 'call "C:\DIRECTORY WHERE XBeach EXE is contained\XBeach\2015-10- 22_XBeach_v1.22.4867_Kingsday_x64_netcdf\xbeach.exe"'; system(run_xb);

Fig.S14 Examples of water levels and maximum wave-generated flow velocity against the Cow and Bull cliffs in different RSL scenarios (0-3-6-9-12-15m) and for each modeled event. Note that elevation [m], water level [m] and flow velocity [m/s] are all shown on the same Y-Axis. Dashed lines indicate the RSL elevation for each frame.

Cow and Bull The maximum significant wave height and peak period simulated by XBeach at the

Cow and Bull transect (see Fig.S2D,E for location) in different conditions of sea level are shown in Fig.S14. The entire range of simulated flows against the same cliff is shown in Fig.S15. We assume that each flow shown in Fig.S15 could be representative of cliff-edge flow. Therefore, we compared the threshold flows to

35 transport the Cow and Bull boulders with the cumulative flow at the cliff face as shown in Fig.S15. It is worth highlighting that, besides the steep flow velocity peak generated against the cliff, all the model runs show a second flow velocity peak, that is generated as waves run downwards towards the Bahamas bank side of the transect (Fig.S14). We suggest that this increase in flow velocity might explain the position of the other mega-boulders identified by Hearty, 1997 (1).

Fig.S15 Flow velocities produced by each swell on the face of the Cow and Bull cliff in all RSL scenarios (locations where the flow were extracted from the model are shown in the top panel). We consider these flows as representative of cliff-edge flows. The last column shows all the flows combined from the previous 4 and is the basis for the Fig.3C of the main paper.

Modern analog The maximum significant wave height and peak period simulated by XBeach at the modern analog transect (see Fig.S2D,F for location) was calculated only for RSL=0

(Fig.S16).

Fig.S16 Flow velocities calculated at the modern analog. Upper panels: representation of the highest water level and flow velocity generated during Hurricane Andrew (1992). Lower panel: representation of the flow velocities generated against the modern analog cliff during Hurricane Andrew 1992 as calculated in our 3-hrs XBeach model. The lower panel represents the same data shown in Fig.S17B.

Threshold flows for boulder transport To estimate the minimum flow velocities required to transport a boulder of known size and density from the edge of the cliff to the top of it, we used the boulder transport equations developed by Nandasena et al., 2013 (6). These equations are derived from the balance of hydrodynamic forces and moments applied to the boulder (6). Under this approach, the boulder is represented as a rectangular prism to which drag, lift, gravity and friction forces are applied when subjected to water flow. The water flow hits perpendicularly the area of the boulder ‘ac’ (a, b and c being

37 respectively the long, intermediate, and short axes of the boulder). According to these equations, the minimum flow velocity (u) to initiate the lifting of a boulder is:

2{(휌 ⁄휌)−1}푐푔 푢2 ≥ 푏 [Eq.1] 퐶푙−휇푠퐶푑(푐/푏)

Instead, the minimum flow velocity (u) to initiate the rolling of a boulder is:

2 2{(휌푏⁄휌)−1}푐푔 푢 ≥ 2 [Eq.2] 퐶푙−퐶푑(푐/푏)

The parameters and their units in the equations [1-2] are as follows:

 axes of the boulders (a, b, c) [m]

3  density of the boulder (휌푏) 1.66 to 2.58 g/cm (derived from field

measurements)

 density of water (휌) 1.02 g/cm3

 acceleration of gravity (g) 9.8 m/s2

 coefficient of drag (Cd) 1.95 (see 45,46)

 coefficient of static friction (휇푠) 0.7 (see 6, 47);

 coefficient of lift (Cl) (see below for the value adopted)

The coefficient of lift is the most important parameter in these equations, as it determines the lift force/moment needed to transport a boulder from the cliff edge

(6). In literature the most common value attributed to the coefficient of lift is 0.178

(6,48 – 61). Using this conventional coefficient of lift, we calculated that it is impossible to either lift or roll the modern analog boulders, which were instead moved by the waves of Hurricane Andrew (1992). This is due to a very simple issue with the most commonly used value for the coefficient of lift, briefly summarized hereafter.

Most of the works using 0.178 as coefficient of lift in boulder transport equations cite the studies of Einstein and El-Samni, 1949 (62) and Helley, 1969 (63) as justification

38 for this choice. In fact, this value (0.178) has been calculated by Einstein and El

Samni during an experimental work conducted in 1949 (62), where they studied the dynamic forces acting on particles in the surface layer of a sediment bed using spherical balls with a diameter of 6.9 cm. Helley, 1969 (63) applied the same coefficient of lift (0.178) in a study aimed to determine bed velocities necessary to initiate motion of coarse bed material in Blue Creek (a small tributary to the Klamath

River in northern California). They stated that the justification to use this value is related to the dimension of the particles, which in their study is less than 60 cm.

The dimensions of boulders are at least two orders of magnitude bigger than the particles studied in the works of Einstein and El Samni (62), and the equations they used to calculate the coefficient of lift are different from the ones used for boulder transport. There are no studies specifically conducted to calculate the coefficient of lift for boulders. Nandasena et al. (2013) (6) suggest that the coefficient of lift must be derived from site-specific measures of wave flow and boulder displacement.

Therefore, in our study we calculated the coefficient of lift using the information available for the modern analog boulders. As the modern analog boulders were transported by the 1992 Hurricane Andrew waves, we first use the XBeach model runs on the modern analog cliffs (Fig.S16) to calculate the maximum (top 1%) wave flows that developed on the cliff face during the 1992 Hurricane Andrew (Fig.S17).

We calculate that the top 1% flow velocities against the modern analog cliffs range from 3.4 to 5.7 m/s. Then, we make explicit the coefficient of lift in Eqs. 1 and 2 as follows:

2(휌 /휌−1)푐푔 푐 Lifting 퐶푙 = 푏 + (휇 퐶 ( )) [Eq.3] (푢2) 푠 푑 푏

2(휌 /휌−1)푐푔 푐 Rolling 퐶푙 = 푏 + (퐶 ( )2) [Eq.4] (푢2) 푑 푏

We calculate the coefficient of lift by reiterating the solution of Eq.3 and Eq.4 for 105 times randomly sampling the possible values for the density of the boulders (휌푏, 1.58 to 2.58 g/cm3, Table S2) and the flow velocity at the modern analog cliff (u, 3.4 to 5.7 m/s, see Fig.S18). We calculate that the most likely value of the coefficient of lift needed to initiate the transport of the modern analogs at their original position is between 2.006 and 2.775 (Fig.S18).

Fig.S17 Modern analog flow velocities used for the calculation of the coefficient of lift. (A) Cliff at the modern analogs location. The yellow dots indicate the model nodes where the flow velocities in B and C have been extracted. (B and C) flow velocities [m/s] modeled at the locations in A for the entire XBeach simulation. The circled flows indicate the 1% top flow velocities. We assume that these circled flow velocities may have transported the modern analog boulders.

We then turn to the two large boulders, the Cow and Bull. We reiterate the solution of

Eq.1 and Eq.2 using a similar approach to the one used for the modern analogs.

Here, we reiterate the solution of Eq.1 and Eq.2 for 105 times randomly sampling the

3 possible values for the density of the boulders (휌푏, 1.58 to 2.58 g/cm , see Table S4) and the coefficient of lift between 2.006 and 2.775 (Fig.S18). We plot the results of the reiterated calculations in Fig.S19A,B.

Our results indicate the following:

 It is very likely that the Bull boulder is lifted from the cliff edge when the flow

velocity is at least 10.8 m/s, and is rolled when it is at least 11.2 m/s.

 It is very likely that the Cow boulder is lifted from the cliff edge when the flow

velocity is at least 9.1 m/s and is rolled when it is above 9.3 m/s.

These are the values shown in Fig.3.

Fig.S18 Probability density function derived from the solution of Eq.3 and Eq.4 for the two modern analog boulders. The areas in common between the pink and blue histograms represent the coefficient of lift that can move both modern analogs under the flow velocity conditions generated during the Hurricane Andrew (1992). The black line represents the sum of the two probability density functions

Fig.S19 Probability (cumulative density) of boulder transport vs flow velocity. (A) Transport of the boulder by lifting. (B) Transport of the boulder by rolling. The likelihood is defined following the IPCC guidelines (64). The dashed lines represent the flows above which the lifting or rolling of each boulder becomes ‘very likely’. Pink and green lines represent the Cow and the Bull, respectively.

LIG Relative sea level It has been inferred that global (eustatic) peak MIS 5e sea level was between 6 and

9 meters above present (65, 66). This range represents global averages and can vary locally due to various isostatic and/or tectonic effects (67 – 69). In order to assess the local paleo sea level, one needs to measure and interpret relative sea- level (RSL) indicators that were formed in direct connection with sea level (70, 71).

For example, fossil corals or beach deposits can be used as RSL indicators. After identification in the field, the elevation of the indicator has to be measured with the highest available accuracy (for example with high-precision GPS). Then, for each indicator, it is necessary to quantify the relation to paleo sea level using the

42 indicative meaning (72). To calculate the indicative meaning, the upper and lower elevations at which the indicator occurs in modern settings have to be defined (71).

To assess RSL in northern Eleuthera, we measured and re-interpreted RSL indicators from the Whale Point section that was originally reported in Hearty (1998)

(73), located roughly one kilometer north of the mega-boulders. Using the GPS system described above, we re-measured the relative sea-level indicators at this site. There are two geologic elements in this section that can be connected to MIS

5e RSL: a fossil reef unit and the top of foreshore beds.

Fossil reef. We measured the highest in situ coral at an elevation of 4.42 ± 0.3 m;

15 other in situ corals were measured with elevations ranging from 3.27 to 4.35m.

The coral belongs to the Diploria genus (Fig.S20B). The facies surrounding the coral head is represented by a fossil corallinaceous algae buildup, locally characterized by the boreholes of mollusks (Fig.S20A). The fossil reef contains also not in situ corals

(Fig.S20C), and is in contact with a cemented sandy deposit (Fig.S20E), also containing large gastropods (Fig.S20D). This environment can be interpreted as a forereef developing in shallow waters. In order to assess the paleo RSL at the time of formation of this reef, one must understand at which depth the reef was during

MIS 5e. To assess this, we followed the methodology suggested by Hibbert et al.

(2016) (74). Briefly, these authors use the modern living depth of corals to calculate paleo RSL. According to the OBIS/AGRRA database (75), all reported Diploria corals in the Bahamas are found at depths between -0.6m and -13.6 m. Using all values in this database for Diploria in the Bahamas, we calculate the upper and lower limits of the indicative meaning at 68% confidence interval (Table S5). This results in a paleo

RSL at 12.3±2.1m (1-sigma). Although this value lays at the upper end of likely MIS

5e RSL in the area, it is still likely that, with an eustatic sea level of 6-9 m, RSL is found nowadays higher due to the effects of GIA (67).

Fig.S20 RSL indicators in forereef environment. (A) Coralline algae buildup with mollusks borings. (B) In situ Diploria sp. coral. The elevation of this coral has been used in sea level calculations. (C) Not in situ small coral head; (D) Large gastropod embedded in a fine sandy matrix. (E) Contact between fossil coralline algae / coral buildup and fine sands.

Top of planar-laminated beds. Above the fossil forereef unit, we measured a sedimentary sequence composed of herringbone cross-bedding layers (interpreted as subtidal) grading into planar-laminated beds that are in contact with a boulder / rubble layer (that could represent a deposit created by storms). The entire facies is capped by aeolian sands (Fig.S21A,B). The top of the planar-laminated beds can be tracked almost continuously for several meters, and its maximum elevation is

6.71±0.1m. Following this stratigraphic information, there are two possible interpretations for these beds. In modern beach environments, planar-laminated beds can in fact occur from the upper shoreface to the limit between the lower and upper shoreface (76). Therefore, we interpret these deposits either as: i) foreshore beds forming in the intertidal (HAT to LAT); or ii) a more broad beach environment between the breaking depth of ordinary waves and the HAT. We quantified both interpretations using tidal models and breaking depth of waves derived from global significant wave height maps (TableS5). This results in a paleo RSL at either

6.8±0.6m (foreshore) or 7.2±1.2m (beach deposit, with a broader indicative meaning).

Fig.S21 Sedimentary RSL indicators. (A) Sedimentary sequence above the forereef shown in Fig.S20. Note that the photos taken in Fig.S20 have been taken at a better exposure of this forereef, that reaches slightly higher elevations (~30m to the North of the location of this photo). See description of the different units in the text. (B) Close-up of Planar-laminated beds, used as a RSL indicator.

Another possible way to infer peak RSL during MIS 5e in Eleuthera is to calculate it using GIA models and different ice history scenarios. Here we use two different approaches. First, we use the results of the simulations of the ANICE-SELEN model

(77) for Eleuthera to calculate RSL (Fig.S22) modulating the melting of Greenland and Western Antarctic ice sheets according to the four scenarios described by

Lorscheid et al (2017) (78). Varying mantle viscosity values and ice-sheet

46 configurations, these models produce 12 different predictions, which indicate that that peak MIS 5e RSL could have varied, in Eleuthera, between 5.2 and 9.1 meters above present. We also use a second set of GIA predictions, from Austermann et al.

(2017) (79) added with the 6-9m ESL scenarios of Kopp et al. (2009) (65). We calculate that, for this set of models, peak LIG RSL was 9.5 to 13.7m above present.

Fig.S22 Ensamble of GIA model predictions (ANICE-SELEN (77)) for Eleuthera throughout MIS 5e. The predictions are calculated employing the 4 different ice melting scenarios and earth viscosity structure described in Lorscheid et al (2017) (78).

Table S5. Calculations of paleo RSL from the elevation of RSL indicators measured in the field and from GIA models. For more details of the formulas used to calculate RSL and δRSL from the elevation of a RSL indicator, see Rovere et al. (2016) (80). All measures are in meters. Details on the GIA models can be found in Lorscheid et al (2017) (78) and Austermann et al., 2017 (79).

Elevation Upper Lower Reference of SL Elevation Indicative RSL indicator limit limit Water RSL δRSL Details indicator error (Ee) Range (Ul) (Ll) Level (E) The upper limit and lower limits are derived from the 1- Whale Point in 4.42 0.3 -5.77 -10 -7.9 4.2 12.3 2.1 sigma limits of the distribution of modern Diploria corals situ coral in the Caribbean Interpreted as forming in the intertidal zone, between Whale Point top the Highest Astronomical Tide (HAT) and Lowest of planar- Astronomical Tide (LAT). HAT and LAT values were laminated beds 6.71 0.1 0.5 -0.6 -0.1 1.1 6.8 0.6 calculated with the OTPS model using tidal constituents (interpreted as from the TPXO8 inverse tidal predictions (81, 82), run foreshore) for an entire tidal cycle. Whale Point top Interpreted as forming in a broad beach environment, of planar- from the breaking depth (lower limit of upper shoreface) laminated beds to the HAT (above sea level).The breaking depth was 6.71 0.1 0.5 -1.7 -0.6 2.2 7.3 1.1 (interpreted as calculated using the formula suggested by Rovere et al. upper shoreface (2016) (80) and the average wave height extracted from to foreshore) wave hindcast models (20) Models used to estimate ESL assumed RSL range Notes RSL ANICE-SELEN RSL Varying ice histories, ESL up See Lorscheid et al. (2017) (78) for details on the model 5.2 to 9.1 estimates to 8m configuration used. GIA from Austermann et al., 6-9m from Kopp et al. (2009) See Sup. Mat. of Austermann et al. (2017) (79) for 9.5 to 13.7 2017 (79) (65) details on the GIA models. Additional discussions In the main text, our discussions address the main points related to the interpretation of the Eleuthera boulders as generated by “superstorms”. Below we address some further discussion points that might be of interest to understand the background of our study and the uncertainties that might be related to our approach.

Comparison of the flow velocities calculated in this study with other known events. The maximum flow we model in this study at present sea level is slightly higher than 10 m/s and the maximum flow velocity modeled at any RSL is ~13 m/s

(Fig.3C). By comparison, the peak flow velocities produced by Typhoon Haiyan

(Philippines, 2013) were modeled at ~8 m/s (83). These flows were high enough to shift a boulder with roughly similar dimensions and weight of the Cow by ∼40m along the shoreline (84). Wave flow velocities generated by Typhoon Tembin (2012) on an island offshore Taiwan peaked at 9-12 m/s (85). Also in this case, the movement of large boulders on the shore was documented (86). The magnitude of our calculated flow velocities, required to move Cow and Bull, is also similar to those obtained by wave-tank experiments simulating Irish cliffs (87).

Transport of the Eleuthera boulders by a tsunami. One of the alternative explanations offered for the movement of boulders at Glass Window Bridge is that they have been dislocated by a local tsunami generated by a flank collapse of the continental slopes offshore Eleuthera. While it is possible that submarine slope failures along the Bahamas Bank may have triggered tsunamis in the past (88), no significant tsunami events are known to have struck the coastlines of the Bahamas in historical times. One study modeled the flow velocities that would be generated by a tsunami caused by a flank collapse offshore Eleuthera, and calculated that it would 49 produce waves impacting the cliffs of Glass Window Bridge with a flow of 20 m/s

(89). This flow would be more than enough to transport boulders, but potential sources of tsunamis in this area need to be found and quantified for the tsunami hypothesis to be considered further. From the results of Schnyder et al. 2016 (88) a tsunami wave generated on the Bahamas Bank (in front of Cuba) would be greatly dissipated by the shallow waters and by the topography of the islands on the banks before reaching Eleuthera (see their Fig.5). Therefore, it appears also unlikely that a tsunami wave coming from the Bahamas Bank side would be strong enough to transport the mega-boulders uphill towards the ocean side off the bight (i.e., the inverse direction of the one considered in this study).

Uncertainties associated with 2D wave models. The 2D models we employ here are relatively simple and, as shown in the SI Appendix, they are forced with the best available topography and by wind and wave hindcast data that compare well with observations. As there is no wave buoy that can be considered representative of the offshore wave climate of Eleuthera, we cannot directly validate our wave models against observations during the three events modeled. Nevertheless, the wave heights we reproduce are well within the possible heights and periods that develop at the passage of extreme storms or hurricanes (37).

Uncertainties associated with the 1D wave models. As for the 2D models, the main uncertainty related to the 1D model used in this study is that we do not have the possibility to validate them using local wave data collected against the Glass Window

Bridge cliffs. This would require positioning wave gauges on the Eleuthera cliffs to record the passage of an extreme storm or a hurricane. For this reason, we maintained an XBeach configuration as close as possible to the standard one. We 50 remark that any study attempting to reproduce our results using different model configurations than the one presented here must not only simulate flow velocities at the Cow and Bull and compare them with our calculated movement thresolds, but also simulate flow velocities at the modern analogs and re-calculate the coefficient of lift following the approach explained in this SI Appendix.

Uncertainties associated with the boulder transport equations. The boulder transport equations employed in this paper are among the most used in tsunami and extreme storm studies. Although different approaches to calculate boulder transport thresholds exist (e.g., 90), the ones we used are those most often applied in real- case scenarios. One of the main sources of uncertainty in these equations is the quantification of the coefficients associated to them. In this study we focus our attention on the coefficient of lift, that is the one to which the equations are more sensitive, and the one that is less constrained from empirical studies. The rigorous quantification of other parameters might allow to refine our results, but it would also need more data that are difficult to calculate or quantify.

One significant change could be related to the erosion of the boulders through time: due to this process, the volume the boulders could have been bigger than today in the Last Interglacial. Although it is difficult to quantify how much the boulders may have been eroded since the LIG, we performed a sensitivity test increasing all axes of the Cow and Bull by 20%. Using these new axes, we calculate that it is still possible that the boulders are lifted by the waves of Hurricane Sandy (2012) in higher sea levels: the Bull is lifts when the flow is above 11.8 m/s, and rolling when flow is above 12.2 m/s; the Cow is lifting when flow is above 9.9 m/s, and the Cow is rolling when flow is above 10.1 m/s.

Paleo topography. In all our model runs, we do not attempt to account for the possibility that the LIG paleo topography was different than the modern one. As the continental shelf in front of Glass Window Bridge is very narrow, there is little possibility that, in the LIG, this site was characterized by a low-lying coastal morphology (e.g., a beach, or a shore platform) that could break the waves before they reach the coast. The paleo cliff could have been slightly higher above the paleo sea level than the modern one (91), but quantifying this increased height would be difficult without a proper estimates of local long-term limestone lowering and cliff erosion rates. We highlight, though, that even with a higher cliff, the results of this study would not change. The cliff edge is 15m above present sea level, and with

RSL=3.5m, Hurricane Sandy (2012) produces waves high enough to displace the boulders from the edge. If the cliff was 3m higher in the LIG than at present, it is reasonable to assume that the minimum RSL to displace the boulders would have to be 3m higher than 3.5m, i.e., 6.5m. This is still in the range of MIS 5e sea levels and at this RSL Hurricane Sandy still produces flows that can move the Cow and Bull

(Fig. 3C).

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