GEOLOGY | Volume 46 | Number 7 | www.gsapubs.org 1

A sea-level fingerprint of the Late Ordovician ice-sheet collapseA. Pohl1 and J. Austermann2

1Centre Européen de Recherche et d’Enseignement des Géosciences de l’Environnement (CEREGE), Aix Marseille University, CNRS, IRD, Collège de France, 13545 Aix-en-Provence, France

2Lamont Doherty Earth Observatory, Columbia University, Palisades, New York 10964, USA

ABSTRACTThe Hirnantian glacial acme (445–444 Ma) represents the gla-

cial maximum of the long-lived Ordovician glaciation. The ensuing deglaciation and associated transgression deeply affected depositional environments and critically impacted marine living communities, con-tributing to the Late Ordovician Mass Extinction. In the absence of a better model, this transgressive event is usually considered to be a uniform (i.e., eustatic) rise in sea level, at least at low to intermediate paleolatitudes. This assumption may lead to erroneous interpretations of the geological record. Here we use a land-ice model and a gravita-tionally self-consistent treatment of sea-level change to propose the first numerical simulation of spatially varying late Hirnantian sea-level rise. We demonstrate significant departures from eustasy and compare our modeling results to key sedimentary sections. We show that previously enigmatic opposite sea-level trends (i.e., transgressive versus regressive) documented in the geological record are predicted by the model. Such sections may thus reflect patterns of sea-level change more complex than the eustatic approximation considered so far, rather than erroneous correlations. Our simulations also predict the locations where values of relative sea-level change are closest to the values predicted by a globally uniform rise and hence most rep-resentative of the volume of the ice sheet that collapsed. We identify these regions as preferential loci for future fieldwork investigating the ice volume during the Hirnantian glacial peak.

INTRODUCTIONThe latest Ordovician (Hirnantian; 445–444 Ma) records the apogee

of the protracted early Paleozoic ice age (ca. 470–425 Ma; Ghienne et al., 2009; Page et al., 2007; Rasmussen et al., 2016). A continental-scale ice sheet, with a volume as much as twice the Last Glacial Maximum (LGM) land-ice volume (Finnegan et al., 2011), extended from the South Pole to the mid- to tropical latitudes (Ghienne et al., 2009; Pohl et al., 2016). The decay of the ice sheet during the late Hirnantian induced a significant rise in sea level (e.g., Davies et al., 2016). An accurate appraisal of the glacio-eustatic sea-level rise is crucial to constrain the co-evolution of climate and the biosphere at that time (Munnecke et al., 2010). Changes in sea level as inferred from the architecture of sedimentary successions are directly used to infer the size of the ice sheet (Le Heron and Dowdeswell, 2009), and intercontinental correlations based on sequence stratigraphy help to reconstruct the phases of waxing and waning of the ice sheet and thus the temporal dynamics of glaciation (Ghienne et al., 2014). The post-glacial transgression documented in the late Hirnantian (Normalograptus persculptus graptolite zone; Davies et al., 2016) is also regarded as a key factor in the spread of anoxic conditions onto the continental shelves, which strongly impacted marine living communities and contributed to the Late Ordovician Mass Extinction (Hammarlund et al., 2012; Harper et al., 2013).

In spite of the comprehensive analysis of the sedimentary (e.g., John-son et al., 1998) and faunal (Johnson and McKerrow, 1991) records, an accurate reconstruction of the late Hirnantian sea-level change remains elusive. The “global” curve appears to be relatively robust at a stage level

(Davies et al., 2016), however regional data featuring a higher temporal resolution commonly show conflicting patterns, sometimes in opposite directions (Zhang et al., 2006; Munnecke et al., 2010). This raises the question of whether such disagreements reflect the limitations in available biostratigraphic data resulting in erroneous correlations (Munnecke et al., 2010) or capture spatial patterns of sea-level change more complex than the eustatic approximation invoked to date (Zhang et al., 2006). Local sea-level change deviates from the ice-equivalent global mean sea-level change (i.e., eustatic sea-level change) due to direct gravitational effects from the changing ice and ocean load as well as the response of Earth’s solid surface, its gravity field, and its rotation axis to this load (e.g., Hay et al., 2014). However, the impact of such effects on late Hirnantian sea level has not been quantified to date, thus limiting the interpretation of the geological record of sea-level change.

In order to overcome this limitation, we produce here numerical simu-lations of the spatially varying late Hirnantian transgression that was caused by ice-sheet collapse. We simulate the Hirnantian land-ice distri-bution using an ice-sheet model forced with climatic fields (Pohl et al., 2016) and subsequently compute patterns of relative sea-level rise using a gravitationally self-consistent method that accounts for the deformational, gravitational, and rotational perturbations to sea level on a viscoelastic Earth (Kendall et al., 2005; Creveling and Mitrovica, 2014). We discuss key field data in the light of our model results and identify regions where sea-level changes are most representative of the eustatic sea-level rise and hence of the rapid decrease in ice-sheet volume over the South Pole during the late Hirnantian.

METHODSIn order to simulate the Hirnantian ice sheet, we force the ice-sheet

model GRISLI (Grenoble Ice Shelf and Land Ice model; Ritz et al., 2001 [updated]) with the Ordovician climatic fields obtained by Pohl et al. (2016) at 2240 ppm CO2 (see the GSA Data Repository1 for details). At steady state, the modeled ice sheet reaches the mid-latitudes (Fig. 1; e.g., Ghienne et al., 2009) and its volume is equivalent to 214 m of eustatic sea-level rise, which is well within the range of current estimates of the volume of ice stored over the continents during the Hirnantian (Loi et al., 2010; Finnegan et al., 2011). In a second step, we simulate the sea-level change associated with the melt of the ice sheet using a simple ice-collapse scenario (see the Data Repository). We employ a gravitationally self-consistent sea-level model following the algorithm by Kendall et al. (2005). The model accounts for the gravitational and viscoelastic effects caused by ice and ocean changes, the migration of shorelines associated with sea-level rise and fall, and the influence of load-induced perturba-tions in the Earth’s rotation axis (Milne and Mitrovica, 1998). We use a radially symmetric Earth model with a 96-km-thick elastic lithosphere, upper and lower mantle viscosities of 5 × 1020 Pa∙s and 5 × 1021 Pa∙s,

1 GSA Data Repository item 2018206, supplemental information and model runs (Sections DR1–DR4, Figures DR1–DR12, Table DR1, and Videos DR1–DR3), is available online at http://www.geosociety.org/datarepository/2018/ or on request from editing@geosociety.org.

GEOLOGY, July 2018; v. 46; no. 7; p. 1–4 | GSA Data Repository item 2018206 | https://doi.org/10.1130/G40189.1 | Published online XX Month 2018© 2018 Geological Society of America. For permission to copy, contact editing@geosociety.org.

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respectively, and elastic parameters and density structure of the seismic model PREM (Preliminary Reference Earth Model; Dziewonski and Anderson, 1981).

In our baseline run, we consider a linear decrease of Ordovician land-ice height to zero over a time span ∆T of 5 k.y., a duration close to the one associated with the collapse of the Laurentide ice sheet during the post-LGM deglaciation (Peltier et al., 2015) though somewhat longer than the 2–3 k.y. used in modeling studies of the Snowball Earth deglaciation (Creveling and Mitrovica, 2014) and of ice-sheet collapse events during Quaternary interglacial periods (Hay et al., 2014). We explore the sensitiv-ity of our results to different ice geometries and deglaciation scenarios as well as changes in the Earth’s viscoelastic structure in the Data Repository.

RESULTSThe collapse of an ice sheet produces characteristic spatial patterns

of sea-level change commonly referred to as the sea-level fingerprint (cf. Hay et al., 2014), which is computed here as the total sea-level change across the interval ∆T (i.e., 5 k.y. in our baseline runs; Fig. 1A). The main

pattern in Figure 1A is a near-field to far-field gradient, with relative sea level falling in areas that were formerly covered by ice, and rising in the far field, with an increasing amplitude in sea-level rise with increasing distance from the former land-ice front. This modulation of the trans-gression results from the combination of two effects: (1) the viscoelastic adjustment to the redistribution of water and ice including the rebound of the formerly glaciated regions and subsidence of the peripheral foreb-ulge; and (2) the loss in gravitational attraction associated with decreasing land-ice volumes, forcing water masses previously piling up around the ice sheet to flow from the near field to the far field. Imposed on this is a quadrantal signal resulting from the change of Earth’s rotation axis, which, in order to minimize rotational energy, migrates toward the melting ice sheet. The asynchronous adjustment of the gravity field and solid Earth to the changing centrifugal force leads to a quadrantal sea-level signal with a sea-level change that is smaller than the eustatic change in Gondwana and in the opposite quadrant north of Siberia, and larger than the eustatic change over Baltica and in the Northern Hemisphere Panthalassic Ocean (Fig. 1A; see the Data Repository). Sensitivity tests to land-ice volume and extent and to Earth’s viscosity structure, as well as additional model runs featuring partial and asynchronous deglaciations, confirm that the first-order patterns of simulated sea-level change are relatively insensitive to these identified uncertainties in the boundary conditions and model parameters. The quadrantal signal, however, gets weaker when the dura-tion of the deglaciation is increased because a longer duration allows the viscoelastic response to keep up with the change in ice and ocean load (see the Data Repository).

Once the ice sheet has fully collapsed, sea level continues to change as a result of ongoing viscoelastic deformation of the solid Earth. Figure 1B displays the changes in sea level simulated over the 10 k.y. follow-ing the end of deglaciation. Sea level keeps falling in the area that was formerly ice covered due to isostatic rebound, while the strip along the coast of Gondwana shown in red in Figure 1B shows the ongoing subsid-ence, or equivalently sea-level rise, associated with the collapse of the peripheral forebulge. The rotational signal is now reversed because the response of the solid Earth to the migrating rotation axis is catching up with the instantaneous response of the Earth’s gravity field. This results in sea-level rise in Gondwana and Siberia, and sea-level fall over Baltica (see the Data Repository).

In Figure 1B, we identify key sedimentary sections that we compare to model predictions. In areas located under the retreating ice sheet (light-gray point in Fig. 1B), sea level falls during the deglaciation as a result of the combined effects of isostatic rebound and loss in gravitational attraction (Fig. 2). Dark-gray and red sites are on the peripheral bulge of the ice sheet (Fig. 1B). During the deglaciation, these sites experience a combination of sea-level rise due to the eustatic rise (i.e., ice melt) and forebulge subsidence, and sea-level fall due to the loss of gravitational attraction of the ice sheet. Overall, these locations experience less than the eustatic rise during the deglaciation (Figs. 1A and 2). After the deglacia-tion, these sites experience a continued sea-level rise due to the ongoing collapse of the peripheral bulge on which they are located (Figs. 1B and 2). It is noteworthy that the sea-level history simulated at ice-proximal sites is highly dependent on the geometry of the retreating ice front. In particular, the red and light-gray sites could experience a local sea-level fall followed by a rise if the ice sheet retreated in this region first (dashed lines in Fig. 2; see the Data Repository), which is a scenario that agrees with studies that identified phases of sea-level fall during the early stages of the late Hirnantian deglaciation and concomitant retreat of the ice front in North Africa (e.g., Ghienne et al., 2009). All other sites are in the far field and experience significant sea-level rise during the deglaciation mainly due to the eustatic rise. During and after the deglaciation, these sites also see a combination of gravitational and rotational effects, continental levering, and ocean syphoning (cf. Mitrovica and Milne [2002] for a description of these mechanisms during the Holocene Epoch). The magnitude of each

Rela!ve sea-level change (m)

Rela!ve sea-level change (m)

Lauren!a

Gondwana

Bal!ca

Siberia

12

3 45 6

7

8

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46

7

8

910

11

A

B

Figure 1. Sea-level change simulated in our baseline run over the degla-ciation phase (time span of 5 k.y.) (A) and over the 10 k.y. following end of deglaciation (B). Colored circles in A represent geological estimates of glacio-eustatic sea-level rise, using same color scale as simulated results. Individual references and values are provided in Table DR1 (see footnote 1). Thick yellow line shows extent of ice sheet prior to collapse. In B, colored circles represent some of the sites shown in A, relative sea-level histories of which are shown in Figure 2 (colors are arbitrary). Same references as in A, except for yellow point (Cornwallis Island, Canadian Arctic), which was added to permit comparison with sea-level changes reconstructed by Zhang et al. (2006) but for which no paleodepth estimate is available, and light-gray point, which was added under melting ice sheet for descriptive purposes. Note that color scale used in B differs from that in A. Subaerial landmasses at 5 k.y. (A) and 15 k.y. (B) into model run are drawn in white and outlined with thick black line.

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of these effects varies from one place to another, giving rise to a variety of sea-level signals.

DISCUSSIONZhang et al. (2006) reconstructed variations in late Hirnantian sea level

from the distribution of conodont communities in two localities on Lau-rentia, namely Anticosti Island (Quebec, Canada; light-blue point in Fig. 1B) and Cornwallis Island (Canadian Arctic; yellow point), and demon-strated that the two sections exhibit opposite (regressive and transgressive, respectively) trends. Building on their knowledge of the Pleistocene, they attributed such patterns to variable glacial isostatic adjustment. However, Zhang et al.’s (2006) hypothesis was subsequently challenged by Trotter et al. (2016), based on the weak correlation between their oxygen isoto-pic data and the curves from Zhang et al. (2006). Munnecke et al. (2010) further identified erroneous temporal correlations as a potential cause of mirrored sea-level changes during the late Hirnantian. Our simulations confirm that sea level may have varied in opposite ways at these sites: while the modeled sea level keeps rising on Cornwallis after the end of deglaciation, it drops on Anticosti (Figs. 1B and 2). This trend results mainly from the motion of Earth’s rotation axis, and might therefore be even stronger when considering the faster-spinning Ordovician Earth (Berger et al., 1989) but weaker when considering a more prolonged deglaciation (see the Data Repository). The unexpected fall in modeled relative sea level simulated on Anticosti shows that glacial isostatic adjust-ment is a key factor in interpreting sedimentological data. The sea-level fall simulated during postglacial times may otherwise be interpreted as the sedimentological expression of glacial re-advance, thus biasing recon-structions of the temporal dynamics of the glaciation.

In terms of absolute values, model-data agreement is limited (Fig. 1A). Some interesting trends stand out—for instance, the value +80 m proposed by Haq and Al-Qahtani (2005; point 10 in Fig. 1A) based on sedimentary data from Arabia is lower than the estimate of >120 m reported by Tesakov et al. (1998; point 7) for Siberia, which is in agreement with the near-field to far-field gradient predicted by the model. However, most field data do not match modeled values. Values derived from field observations are lower and do not follow similar spatial patterns. While some disagreement,

particularly regarding the absolute values, can stem from our simplified model setup, we point out that the qualitative trends shown in Figure 1 are a robust model output. The spread of field estimates combined with the absence of a consistent spatial pattern suggest that limitations in our mod-eling may not be responsible for the entire model-data mismatch. Possible additional sources for this mismatch include additional processes such as local tectonics and uncertainty in the observations. The most striking example of the model-data mismatch is probably the low sea-level rise (+70 m) documented in the far field by Johnson and McKerrow (1991) for Baltica (point 6 in Fig. 1A) where the model predicts a local maximum rise in sea level. The value reported by Johnson and McKerrow is smaller than the value of +80 m documented by Haq and Al-Qahtani (2005) during the Hirnantian in Arabia (point 10) and, more critically, even smaller than the sea-level variations of 150 m documented by Rasmussen et al. (2016) on Baltica during the presumably warmer Middle Ordovician Darriwilian. Because margins of error in estimating the glacio-eustatic sea-level rise based on sedimentological and paleontological indicators are on the same order of magnitude as the emerging signal (see discussion in the Data Repository), we doubt that currently available absolute values of sea-level variations can be used to infer changes in the volume of the Hirnantian ice sheet. Exhaustive compilation and scrutiny of published estimates in combination with further analysis of the glacial isostatic and tectonic deformation are required to overcome such limitations (e.g., Rygel et al. [2008] for the late Paleozoic ice age).

Our simulations can be used to predict the regions where values of relative sea-level change are closest to the eustatic mean at the end of the deglaciation phase and thus most representative of the volume of the ice sheet that collapsed (Fig. 3). We identify these locations—equatorial Gondwana, the northern coast of Baltica, and the shallow shelves around Laurentia except for the northern one—as preferential loci for forthcoming fieldwork investigating the volume of the Hirnantian ice sheet. Should the moderate rise in sea level at these locations be confirmed by future com-pilations, the emerging visions of an only partial retreat of the Hirnantian ice sheet (Finnegan et al., 2011; Hayton et al., 2017) may bring model-ing values and geological estimates into closer agreement (see the Data Repository). Our simulations confirm that deglaciation induces different sea-level trends depending on the proximity to the ice sheet, and provide the first quantitative estimate of the relative sea-level change in response to the late Hirnantian deglaciation in space and time.

ACKNOWLEDGMENTSPohl thanks the CEA/CCRT (French Alternative Energies and Atomic Energy Com-mission / Research and Technology Computing Center) for providing access to

Time a!er the end of deglacia"on (k.y.)

Rela"v

e se

a-le

vel c

hang

e (m

)

Normalized sea-level change (% of eusta!c change)97.5 98.75 100 101.25 102.5

Figure 3. Normalized sea-level fingerprint simulated over deglaciation phase (time span of 5 k.y.) using eustatic sea-level change of 214 m for normalization. Only regions that experience sea-level change close to eustatic change (within 2.5%) at end of deglaciation are represented. Subaerial landmasses are in gray.

Figure 2. Sea-level histories for each site identified in Figure 1B (thin lines). Each line represents relative sea-level change simulated at site of same color in Figure 1B. Thick gray line represents purely eustatic sea-level change, which is here calculated as sea-level change aver-aged over initial ocean area (i.e., prior to ice-sheet collapse). Vertical black dashed line (x = 0) represents end of model deglaciation. Red and gray dashed lines represent sea-level histories resulting from asynchronous deglaciation, with land-ice front first retreating over North Africa (see Data Repository [see footnote 1]).

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the HPC (High Performance Computing) resources of TGCC (Très Grand Centre de Calcul du CEA) under the allocation 2014-012212 made by GENCI (Grand Équipement National de Calcul Intensif). Austermann acknowledges funding from the Royal Society (London). We thank E. Chan for helpful discussions on the rotational signal, J.-F. Ghienne (University of Strasbourg) for fruitful discussions, J. Totman Parrish for editorial handling, and M.C. Pope, M. Calner, and D.A.T. Harper for helpful and constructive reviews.

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Manuscript received 21 February 2018 Revised manuscript received 4 May 2018 Manuscript accepted 6 May 2018

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