## Introduction

Summer warming in the Arctic has significantly outpaced global average warming over the past several decades1,2 and Arctic glaciers are consequently retreating rapidly, especially in the Eastern Canadian Arctic3, where summer air temperature explains >90% of the year-to-year variability in glacier surface mass balance4. The large influence of summer temperature on glacier mass balance also suggests that past changes in glacier dimensions can be used to place contemporary warming in a multi-millennial perspective5,6. Here we exploit the high potential for thin, cold-based, non-erosive ice caps to preserve the landscapes over which they advance, including delicate tundra plants and un-eroded rocks. Under these conditions, radiocarbon dates of plants newly exposed by recent melting (hereafter plant 14C) constrain the time of plant death due to snowline lowering and glacier expansion7,8,9. Recently reported plant 14C dates > 40 ka from four ice caps on Baffin Island, Arctic Canada, further suggest that ice cover at those locations may have persisted through the warmest part of the Holocene7. However, given the small number of sites, it is possible that local conditions may have favored anomalous preservation of plants following melt out and exposure, allowing for subsequent reburial. Here we expand the number of ice caps with plant 14C ages > 40 ka from 4 to 30, greatly reducing the likelihood that the earlier dates reflected anomalous conditions. We also provide in situ cosmogenic 14C inventories from rock surfaces (14C produced within minerals via cosmic ray bombardment; hereafter in situ 14C) adjacent to plant collections with radiocarbon ages > 40 ka to test the assertion that such sites were continuously covered by ice throughout the Holocene. The combination of 30 retreating ice caps revealing plants with pre-Holocene radiocarbon ages and measured in situ 14C inventories provides strong evidence for continuous ice coverage of these locations for >40 ka. When viewed in context of temperature records from Greenland ice cores, these results suggest that the past century of warming is likely greater than any preceding century in the past ~115,000 years.

## Results

### Newly exposed plants killed by snowline lowering >40 ka

Forty-eight in situ tundra plants collected within 1 m of the ice margin at the time of collection from 30 different ice caps on eastern Baffin Island (Fig. 1) were dated through accelerator mass spectrometry (AMS) 14C analysis; with radiocarbon ages of 40 to >50 ka, close to or beyond the range of 14C dating (Table 1). Most of the sampled ice caps are small (1–2 km2), and all lie within a region of 170 × 70 km (Fig. 1). Replicate plant collections were 14C dated at nine ice caps, including separate strands from the same plant and different plants collected within 100 m along the same ice margin. Some early collections that did not undergo rigorous pretreatment because they were expected to be < 10 ka returned apparent finite ages < 40 ka (14C age), but subsequent analyses of the same samples following rigorous pretreatment yielded 14C ages > 40 ka (sites 11 and 12; Table 1).

Plant 14C ages define the time when summer temperature decline resulted in snowline lowering, leading directly to permanent plant burial by snow or by ice margin expansion across the site shortly thereafter. Prior field observations suggest that once plants are exposed by ice recession, they are efficiently removed from the landscape by meltwater in summer and wind-blown snow in winter7. In addition, colonization by new plants, and in some instances regrowth of recently exposed dead moss, begins within 1–3 years10. The combination of rapid removal and high rate of contemporary ice retreat (0.5–1.0 m yr−1 vertical lowering of glacier surfaces3, corresponding to ~10 m yr–1 rate of horizontal retreat in most settings), suggests that plants collected within 1 m of the ice margin were likely first exposed the year they were collected. In rare cases, preservation of dead plants exposed by ice retreat has been noted up to 200 m beyond current ice margins, indicating that they have survived on the landscape for several decades following exposure11,12. Given the possibility that some plants may have been exposed and then re-entombed, we independently evaluate the exposure history of the sites using in situ 14C in associated rock samples.

### In situ 14C inventories

The in situ 14C inventory in the surface of rocks now emerging from beneath receding cold-based ice reflects the cumulative 14C production during exposure when the rocks were ice-free, and attenuated production when rocks were covered by thin ice, as well as losses due to the continuous decay of 14C (half-life 5700 ± 30 years13) and erosion of the rock surface. Unlike plant 14C, which records the timing of plant death by snow and/or ice cover, in situ 14C records the cumulative exposure and burial history of a rock surface over the lifespan of the isotope (i.e., several half-lives). Two mechanisms dominate in situ 14C production: (1) energetic spallation reactions between a high-energy nucleon and a target atom, and (2) low-energy (slow) muogenic reactions that occur when a negatively charged muon falls into the electron shell of an atom and is captured by the nucleus14. Various higher-energy (fast) muogenic reactions are less important for in situ 14C production15,16,17 but cannot be neglected. Although in situ 14C production is dominated by spallation in unshielded rock surfaces15,16,17, these reactions are negligible beneath ~10 m of ice18. Muogenic production in unshielded rock surfaces is much lower than production by spallation, but decreases more slowly with ice thickness, not reaching negligible amounts until ice thickness exceeds 40 m. Since any in situ 14C produced prior to ~40 ka will have decayed below detection, and all sites are expected to have been covered by at least 40 m of ice during the last glacial maximum (LGM), in situ 14C inventories19,20,21 at all our sites must have been negligible by the onset of deglaciation. Thus, measured in situ 14C inventories reflect primarily the local variation of ice thickness history during and after regional deglaciation.

Measured in situ 14C concentrations in rock surfaces adjacent to nine of the study sites with plant 14C ages > 40 ka (Fig. 1) are all above established detection limits (Supplementary Table 2)19 and range between 7000 and 133,400 at g1, with samples from all but two sites below 73,000 at g−1 (Table 2, Fig. 2, Supplementary Fig. 1). In contrast, a nearby unglaciated, steep-sided coastal summit (site a, Fig. 1) that was likely never glaciated, has an in situ 14C inventory of ~368,800 at g−1 (Table 2), consistent with continuous subaerial exposure for more than 20 ka. Farther north on Baffin Island, an in situ 14C concentration of ~249,000 at g−1 was reported in rock at 939 m above sea level (asl) from a location that has been ice-free since local deglaciation ~13 ka22. Several rocks on the central Baffin Island plateau repeatedly exposed and buried by local ice caps during the Holocene have in situ 14C concentrations of ~85,000 at g−1 23. The new inventories reported here are generally significantly less than reported elsewhere on Baffin Island, despite site-specific production rates at the new, higher elevation sites that are on average ~60% higher than at these other locations on Baffin Island (Supplementary Table 3). These comparisons indicate that most of the newly sampled sites likely experienced significantly more burial than the other Baffin Island sites.

### Ice cover simulations

We use a numerical simulation to estimate in situ 14C inventories for a range of plausible post-LGM ice thickness histories at each site, and compare these with measured inventories. The simulations make use of updated estimates of the dependence of 14C production on geomagnetic latitude24,25 and the attenuation lengths for in situ 14C production from fast and slow muons17. Rock erosion is assumed to be negligible given the field evidence that delicate tundra plants are preserved, and the expectation that the ice is well below the pressure melting point and therefore unable to slide. Prior to deglaciation we assume that ice thickness history is a simple linear function of the North Greenland Ice Core Project δ18O record26 of paleotemperature, scaling from zero during the Last Interglacial (LIG) to 70 m during the LGM (a realistic value based on ice rheology and ice cap dimensions7 as well as field observations). This leads to inventories that are near zero by the onset of deglaciation, a conclusion that is largely insensitive to the functional form of the assumed preceding thickness history (Supplemental Fig. 2). After 12 ka, we assume a local ice thickness history based on the observed and modeled melt and thinning history for the Agassiz Ice Cap, Ellesmere Island27; i.e., we impose relatively rapid thinning 12–8 ka from an assumed thickness maximum of 70 m, followed by slower thinning until 4.5 ka, which is a consensus initiation time for Holocene ice regrowth on Baffin Island7,28. At 4.5 ka ice thicknesses are specified to increase linearly until the peak of the Little Ice Age (LIA), 1900 CE, before thinning to zero at present. We test for possible ice-free intervals by allowing for exposure in increments of 10 years prior to 4.5 ka for all sample locations. All solutions that are consistent with measured in situ 14C inventories and their measurement uncertainties are considered for each site, and expressed in Table 2 as the median and range of possible Holocene and LIA ice thickness.

Under these conditions, only the highest inventory, measured at site 23, permits exposure during the Holocene (Table 2, Supplementary Fig. 3), as its inventory lies above an intrinsic threshold determined by the relationships between exposure, production, and decay. The same constraint prohibits prolonged exposure at the remaining sites. Two other sites with higher inventories (3, 21) have modeled thickness histories that reach a minimum of ~1 m of ice cover during the middle Holocene (Table 2, Fig. 3, Supplementary Fig. 4). While consistent with isotopic constraints, persistence of ice caps of this thickness for long periods is unlikely given natural glacier fluctuation. We note, however, that these are almost certainly minimum thickness estimates that result from our assumption of linear ice growth after 4.5 ka. Any thinning and increased production during that interval would have to be compensated by increased shielding and ice thickness earlier, in order to match measured inventories. Implied minimum ice thicknesses at the remaining sites are all glaciologically plausible. Although our in situ 14C simulations do not encompass all possible scenarios, they demonstrate that significant Holocene exposure at all but one of the sample sites is unlikely, and is not possible under any realistic scenario for most sample study locations.

### Variable plant 14C ages revealed by receding ice

Our results indicating continuous ice cover for at least the past ~40 ka at a large number of sites are not inconsistent with observations from other retreating ice margins in the same region that have revealed plants of Holocene age7,28. We propose two possible explanations for the range of implied ice cover histories. First, due to differences in the patterns of accumulation and ablation, ice caps rarely expand and recede symmetrically, so that upon retreat, landscapes are not necessarily exposed in uniform reverse chronological order. Second, some ice caps behave as threshold systems29. All but 7 of the 30 sites with plant 14C > 40 ka are from high elevations, 1380–1600 m asl, and most of these are from the margins of pedestal ice caps (Fig. 4). These ice caps evolve on small (<2 km2), flat-topped summits, surrounded by steep slopes where maximum ice thicknesses are limited by ice rheology to <70 m7,30. Once the equilibrium line altitude (ELA) drops below the pedestal surface, ice will grow quickly to a physically determined thickness, but no thicker, even for continued ELA descent. In contrast, lower elevation ice caps can form and expand on less constrained terrain. Consequently, such ice caps became thicker and covered larger altitudinal ranges than pedestal ice caps that formed much earlier, but with dimensions constrained by topography. The result is that the thickness of pedestal ice caps is insensitive to ELA changes below the pedestal base, but is highly sensitive to ELA change as it rises above that level (Fig. 4).

Warming over the past century has led to a rapid rise of the ELA across our field area to at least 500 m above its LIA minimum7, resulting in an ELA that is now above the highest ice caps. Consequently, ice caps are melting at all elevations in summer3. Melt at higher elevations may have been aggravated by an increase in downward longwave radiation due to increases in water vapor content of the normally dry atmosphere at these high-latitude, high-elevation locations30,31,32. The magnitude of the modern melt rate anomaly is illustrated in the simulations here that show average melt rates over the past 150 years have been five times higher than the average melt rate during the interval of peak summer insolation 11–9 ka. Under these conditions thicker, lower elevation ice caps that formed <5 ka are currently revealing plants with Holocene 14C ages, whereas thinner pedestal ice caps are revealing much older landscapes (Fig. 4). Furthermore, some intermediate elevation ice caps that shrank but did not disappear during the Holocene thermal maximum (HTM) are revealing both >40 ka and Holocene landscapes along different margins of the same ice cap (e.g., site #12). Hence the dramatic ELA rise in the Eastern Canadian Arctic over the past century33 is resulting in the simultaneous exposure of a range of late Holocene (<5 ka7,28) and much older (>40 ka) landscapes (Fig. 4).

Enhanced ice retreat due to warming summers has exposed entombed plants, still in growth position, that yield >40 ka plant 14C ages from the margins of 30 unique ice caps. These ages constrain the time when ice caps advanced across the sites, implying that they have remained continuously ice-covered until present. We tested this interpretation by measuring in situ cosmogenic 14C inventories in adjacent rock surfaces at nine of the sites. Numerical simulations of in situ 14C production and removal for a range of realistic ice thickness histories indicate that all but one of the sites must have been ice covered throughout the Holocene. Taken together, the two lines of evidence suggest that many Baffin Island landscapes that have become exposed by ice retreat during recent warming have been continuously ice-covered since at least ~40 ka, including the HTM, when local summer insolation was up to 9% higher than present34. Paleotemperature reconstructions from Greenland and Baffin Island show that the most recent time prior to the Holocene with temperatures similar to present was during the Last Interglaciation, suggesting that that these landscapes are now ice-free for the first time in ~115 ka and that modern temperatures represent the warmest century in 115 ka, despite relatively low local summer insolation. These trends are likely to continue and remove all ice from Baffin Island within the next few centuries, even in the absence of additional summer warming4,35.

## Methods

### Plant 14C collection and preparation

Plant samples were collected late in August, to capitalize on the accessibility of plants exposed by ice margin retreat during the summer melt season. Plants (mostly bryophytes), still in growth position, were collected within 1 m of the modern ice margin at most sites7. For this study, one to six strands from each sampled plant (and in rare cases, a single lichen) were sonicated in deionized water and treated with an acid-base-acid36 wash before being converted to graphite by the Laboratory for AMS Radiocarbon Preparation and Research (NSRL, Univ. of Colorado). Graphite targets were measured at the W.M. Keck Carbon Cycle Accelerator Mass Spectrometry Laboratory at the University of California Irvine.

### In situ 14C collection and analysis

14C is produced in situ in quartz from rock surfaces by spallation reactions between incoming secondary nucleons (neutrons + protons) and Si and O. More than ~6 m of ice cover eliminates most in situ 14C production by spallation. However, muons are only weakly attenuated with depth, allowing low rates of in situ 14C production via muogenic reactions beneath >6 m of overlying ice. Rocks continuously beneath >6 m of ice since the LIG will have low concentrations of in situ 14C that reflect muogenic production and decay. Any exposure during the Holocene will greatly increase 14C inventories by spallation reactions.

Stable granitic rock surfaces located near nine of the plant 14C collection sites were sampled for in situ 14C to a maximum depth of 4 c using a hammer and chisel. Quartz was isolated and purified from whole rock at the University of Colorado Boulder Cosmogenic Isotope Laboratory using standard techniques37. Samples for in situ 14C concentration were prepared at the Purdue Rare Isotope Measurement Laboratory (PRIME Lab) using current methods21. The automated extraction process involves combusting ~5–10 g of quartz at 600 °C for 1 h to remove atmospheric contaminants, followed by dissolution in a previously degassed LiBO2 flux at 1100 °C for 3 h. Both steps take place in an atmosphere of ca. 50 torr of Research Purity O2. Any carbon species released during the high-temperature step are oxidized to CO2, which is then purified, measured quantitatively, diluted with 14C-free CO2, and converted to graphite for 14C measurement by AMS at PRIME Lab21. In situ 14C concentrations were calculated from measured AMS isotope ratios38, less representative sample-specific procedural blanks.

### In situ 14C concentrations

Laboratory procedural blank values reflect an approximately linear decrease between May 5, 2016 and July 29, 2016 from a stable mean value of 401,000 ± 30,000 14C atoms to 154,200 ± 30,900 14C atoms21 (Supplementary Table 2). A linear least squares fit to the upper, lower, and two intermediate values was used to estimate the blanks during the time-dependent period. In all, 30,900 14C atoms is a conservative error estimate for all process blanks. M14-B090R was analyzed on a separate extraction system with a corresponding process blank of 160,700 ± 12,100 14C atoms. The detection limit is considered to be the uncertainty associated with the process blank measurement19. Accounting for the 10 g of quartz dissolved for each sample, all reported concentrations are above established detection limits21.

### In situ 14C production simulation

For each realization of ice thickness history for each sample, we determine the production rate at the rock surface (Po; at g−1 yr−1) from site elevation, latitude (LSDn scaling framework)25,39,40,41, while accounting for attenuation of spallogenic14,42 and muogenic15,16,17,43 production due to ice thickness at each timestep. The in situ 14C concentrations are iteratively calculated at annual time steps using the following equation44,45,46,47,48,49:

$$N = \left[ {N_{\mathrm{o}} \ast {{\mathrm{e}}}^{ - \lambda {{{\mathrm{d}}t}}}} \right] + \left[ {\frac{{P_{\mathrm{o}}}}{\lambda } + \left( {1 - {{\mathrm{e}}}^{ - \lambda {{{\mathrm{d}}t}}}} \right)} \right]$$
(1)

where No is the existing in situ 14C concentration (at g−1) at the beginning of each timestep, λ is the decay constant of 14C (yr–1), and dt is the annual timestep. Differences in production arising from changes in atmospheric density at each site due to sea level rise are negligible at these elevations44. Rock erosion is assumed to be negligible given the field evidence that ice cover was cold-based.