Projected increase of Arctic coastal erosion and its sensitivity to warming in the 21st Century

1 Arctic coastal erosion damages infrastructure, threatens coastal communities, and releases organic 2 carbon from permafrost. However, the magnitude, timing and sensitivity of coastal erosion in- 3 crease to global warming remain unknown. Here, we project the Arctic-mean erosion rate to 4 roughly double by 2100 and very likely exceed its historical range of variability by mid-21 st cen- 5 tury. The sensitivity of erosion to warming also doubles, reaching 0.4-0.5 m year − 1 ◦ C − 1 and 6 2.3-2.8 TgC year − 1 ◦ C − 1 by the end of the century under moderate and high-emission scenarios. 7 Our ﬁrst 21 st -century pan-Arctic coastal erosion rate projections should inform policy makers on 8 coastal conservation and socioeconomic planning. Our organic carbon ﬂux projections also lay out 9 the path for future work to investigate the impact of Arctic coastal erosion on the changing Arctic 10 Ocean, on its role as a global carbon sink, and on the permafrost-carbon feedback. 11

are also projected in the Arctic Ocean and along the coast [17][18][19]. Consequently, Arctic coastal 23 erosion rates are expected to increase in the coming decades. However, the extent of this increase 24 is still unknown, as no projections of Arctic coastal erosion rates are available. To fill this gap, we 25 present the first 21 st -century projections of coastal erosion at the pan-Arctic scale. 26 The thawing of permafrost globally releases organic carbon (OC) and increases atmospheric 27 and oceanic greenhouse gas concentrations, feeding back to further warming [20][21][22][23]. Arctic 28 coastal erosion alone releases about as much OC as all the Arctic rivers combined [23,24], fu-29 eling about one-fifth of Arctic marine primary production [25]. Despite consistent improvements 30 in the representation of permafrost dynamics [26,27], the current generation of Earth system mod-31 els (ESMs) does not account for abrupt permafrost thaw, which may cause projections of OC losses 32 to be largely underestimated [28,29]. Arctic coastal erosion is one form of abrupt permafrost thaw 33 [22] and a relevant component of the Arctic carbon cycle [23,30]. Nonetheless, it has not been 34 considered in climate projections so far. The scale mismatch between Arctic coastal erosion and 35 modern ESMs requires the development of holistic models, that account for the key large-scale 36 processes to bridge this gap [30][31][32]. 37 In this study, we present a novel approach to represent Arctic coastal erosion at the scales of 38 modern ESMs. We develop a semi-empirical Arctic coastal erosion model combining observations 39 from the Arctic Coastal Dynamics (ACD) database [33], climate reanalyses, ESM and ocean sur- wave heights, and constant ground-ice content from observations. Our approach allows us to make 43 21 st -century projections of coastal erosion at the pan-Arctic scale. We quantify the magnitude, 44 timing and sensitivity of Arctic coastal erosion and its associated OC loss in the context of climate 45 change. 46 Emergence of Arctic coastal erosion 47 We project the Arctic-mean coastal erosion rate to increase from 0.9±0.4 m/year during the his-48 torical period  to between 2.0±0.7 and 2.6±0.8 m/year by the end of the 21 st Century 49 (2081-2100), in the context of anthropogenic climate change, according to the socio-economic 50 pathway (SSP) scenarios SSP2-4.5 and SSP5-8.5, respectively (Fig. 1a). This translates to an 51 increase of the Arctic-mean coastal erosion rate by a factor of about between 2.2 and 2.9 by the 52 end of the century with respect to the historical period. The SSP2-4.5 and SSP5-8.5 scenarios 53 describe medium and high radiative forcings due to greenhouse gas emissions [34], respectively, 54 and include the pathway of the current cumulative CO 2 emissions [35]. In both scenarios, our 55 projections show that the Arctic-mean erosion exceeds its historical range of variability before the 56 end of the century (Fig. 1b). Historical SSP2-4.5 SSP5-8.5

Coastal Erosion
Combined thermal and mechanical drivers

Thermal driver
Yearly accumulated daily positive degrees

Mechanical driver
Yearly accumulated daily significant wave heights  . In both scenarios, it is very likely (>90% probability) that the Arctic-mean erosion emerges from its historical range by mid 21 st century, although the exact time of emergence is sensitive to our erosion model uncertainties. The thermal (c) and mechanical (d) drivers of erosion, expressed as yearly-accumulated daily positive degrees and significant wave heights, respectively. The erosion time series depict long-term means and therefore show little interannual variability in comparison to its drivers.

Probability of Emergence
We find it likely (≥66% probability) that the Arctic-mean erosion exceeds its historical range 58 by around 2023, and very likely (≥90% probability) by 2049 (Fig. 1b) vice-versa), because the Arctic-mean wave exposure increases more than the thawing temperature 90 exposure along the coast, with respect to their historical values (Fig. S1a).

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Spatial variability of erosion 92 The thermal and mechanical drivers of erosion explain about 36-47% of its observed spatial to thaw and hence erosion. Our results are in accordance with previous work, which reported weak 108 spatial correlations between ground-ice content and erosion rates [33]. Strong temporal correla-  distribution to make projections of erosion rates at the coastal segment resolution ( Fig. 2d-f). 113 The geographical distribution of low and high-erosion segments does not change substantially 114 from observations over time in our projections, which is partially a consequence of our model 115 design, as explained by the three following reasons. First, we assume that the spatial model coef-116 ficients, empirically determined, remain unchanged throughout our simulations. Second, ground-117 ice content, an explanatory variable in our regression model, is also assumed constant over time.

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Third, our regression model accounts for only a fraction of the spatial variability in erosion, and 119 may thus underestimate larger spatial changes to occur over time. Moreover, and independent from 120 model design, local anomalies of the dynamical variables (i.e. local wave and thawing tempera-121 ture exposure) are smaller in magnitude than their Arctic-mean increase. Therefore, our modelled 122 changes in the spatial variability of erosion are small in comparison to its Arctic-mean increase.

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Temporally resolved erosion rate observations are rare, often sparse in time, and only available at 127 a relatively small number of locations [10]. Only with such observations, temporally resolved and 128 at the pan-Arctic scale, would empirical models be able to better constrain the temporal evolution 129 of spatial variability of coastal erosion.

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Spatial variability of organic carbon losses 131 The pan-Arctic OC loss from coastal erosion increases from 6.9 (1.5-12.3) TgC year −1 during the 132 historical period to between 13.1 (6.4-19.7) TgC year −1 and 17.2 (9.0-25.4) TgC year −1 by the end 133 of the century in the SSP2.4-5 and SSP5-8.5 scenarios, respectively (Fig. 3). For the present-day 134 climate (i.e. the period for which erosion observations are available), we estimate a pan-Arctic 135 OC loss from coastal erosion of 8.5 (3.3-13.7) TgC year −1 . Both our simulated present-climate 136 mean and uncertainty range are comparable with previous estimates from observations [24,33].

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Our projections suggest a pan-Arctic OC flux increase by a factor of between 1.5 and 2.0 with 138 respect to the present-day climate, or by a factor of between 1.9 and 2.5 by 2100 with respect to 139 the historical period. [23] is 43-57% larger than other observations-based estimates [24] and about 69% larger than our 155 present-climate modelled value. These differences are likely due to extensive and high-resolution 156 sampling, allowing for more accurate upscaling [23]. However, the uncertainties associated with 157 the contribution between coastal and subsea erosion comprehend our modelled range (their Table   158 S6 [23]). Therefore, an underestimation from our side is not conclusive. From the LESS coast, Arctic and the regional totals. global SAT, i.e. the AA factor is consistently larger than 1 (Fig. 4c). Therefore, the sensitivity   Arctic coastal observations. 293 We use the Arctic Coastal Dynamics (ACD) database [33] as our observational reference. The

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ACD compiles several sources of data and provides a list of variables for a total of 1314 coastal 295 segments along the Arctic coast, including: long-term erosion mean rates, organic carbon concen-296 tration, soil bulk density, ground-ice fraction, mean elevation and length. From the 1314 segments, 297 we take those classified as erosive and non-lithified, which excludes segments from the rocky 298 coasts in Greenland and in the Canadian Archipelago and other segments that present stable or 299 aggrading dynamics. We also select segments containing excess ice, which excludes all the non-300 erosive segments from Svalbard, for example. We this work with a subset of 306 coastal segments 301 in our analysis.

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Reanalysis 304 We take 2-meter air temperature and significant wave heights from ERA20C reanalysis [58] as   Semi-empirical Arctic coastal erosion model 329 We present a simplified model for Arctic coastal erosion, compatible with the scales of Earth

E(t) = a T D T (t) + a T A H(t) (2)
The thermal driver of erosion is represented by Arctic-mean yearly-accumulated daily-mean 358 We assume that the thermal and mechanical drivers a T D T (t) and a T A H(t) contribute in equal 359 proportions to the Arctic-mean erosion during the reference time. We do that by setting the pro-360 portionality factor q to 0.5. We test the sensitivity of our results to this assumption by making 361 scenarios with q = 0.1 and q = 0.9 (see Table S1 and Fig. S1a in the supplementary material).

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The spatial component 364 The spatial component of our erosion model calculates local erosion anomalies with respect to 365 the Arctic-mean temporal evolution, and consists of two multiple linear regression (MLR) models. 366 We split the coastal segments in two groups by classifying them between extreme and non-extreme 367 with respect to erosion, using 2.5 m/year as a threshold (∼90th percentile). We do not find a dis- Swapping the combinations and groups, that is, using θ+H day for the extreme and θ+T day for 400 the non-extreme erosion segments, yields overall poorer fits (Fig. S3a,b) and less robust estimation 401 of regression coefficients (Fig. S3c-e). We also test the sensitivity of these results to the choice 402 of the threshold to define extreme erosion. Allowing for an overlap between the extreme and non-403 extreme segments by lowering the threshold to 2.0 m/year, for example, increases the robustness of 404 the T day regression coefficient estimate for the extreme group (Fig. S3d) by increasing the number 405 of data points, and yields a similar fit to that of the higher threshold (θ+T day in Fig. S3a,b) and also 406 similar ground-ice coefficients (θ+T day in Fig. 3Sc).

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Finally, the total erosion is constrained to the open-water period, and set to zero whenever and 408 wherever sea-ice concentration (SIC) is above 15% at the coast. Combining the temporal (Eq. 2) 409 and spatial (Eq. 5) components into our total erosion model (Eq. 1), conditioned by open-water 410 and the extreme-erosion threshold, our model assumes the complete form: Bias correction 412 Before forcing the erosion model with MPI-ESM data, we adjust the historical and scenario simu- weight]. We integrate over the coastal segments: to obtain the total Arctic flux.

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Sensitivity to climate change 426 We estimate the sensitivity of the organic carbon release by Arctic coastal erosion to climate change  Probability and onset of emergence from the historical range 441 We define the yearly probability density distribution of a modelled variable ψ as the normal dis-

446
We calculate the area of distributions A hist = N hist dψ and A(t) = N (t)dψ to determine their 447 overlap A hist ∩ A(t). We define the probability of emergence from the historical range P (t), i.e.

448
the probability that N (t) be different from N hist , as the fraction of A(t) that emerges from A hist : We define the onset of emergence as the year when the ensemble mean is larger than µ + 2σ 450 from historical range N hist .

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All ranges of uncertainties, except when clearly stated otherwise, are calculated with a Bootstrap 453 method, which suits cases where the number of data is relatively small. From any vector X of 454 arbitrary length, a large number (i.e. 10 thousand) of vectors X i (i = 1, 2, · · · 10k) is generated 455 by sampling with replacement from X. The uncertainty of any statistics of X is estimated from 456 the distribution of i realizations of the statistics obtained from X i .