## Introduction

The Arctic is warming twice as fast as the global average1, which causes destabilization of high-latitude soils and other permafrost deposits. These systems contain terrestrial organic carbon (terrOC) stocks equivalent to twice the carbon pool in the atmosphere. Arctic permafrost soils hold about 1000 Pg OC in the top 3 m2. Another 200 Pg OC are stored in old Pleistocene-age permafrost such as coastal Ice Complex Deposits (ICD)3 that occur primarily in northeast Siberia and Alaska, and are particularly prone to collapse4,5. Furthermore, peatlands in boreal soils outside the permafrost zone are estimated to contain an additional 230 Pg OC6. Climate warming may cause release of terrOC from these pools by, e.g., deepening of the seasonally thawed active layer of permafrost soils, thermokarst, thermal collapse and erosion of ice-rich ICD, or degradation of peatlands. This may expose large amounts of terrOC to fluvial transport and to microbial degradation, with subsequent emissions of greenhouse gases (foremost CO2 and CH4), climate-carbon feedback6,7,8 and Arctic ocean acidification9. However, large uncertainties exist regarding the dynamics and processes of large-scale terrOC release in the Arctic.

Robust projections of the future Arctic carbon-climate feedback require a quantitative understanding of large-scale terrOC release. Yet, the overarching picture of terrOC release across the circum-Arctic rests on a scattered collection of location-specific observations. State-of-the-art permafrost models retain large uncertainties of (i) permafrost area, (ii) depth of the active layer, (iii) frequency and spatial extent of thermokarst; (iv) net carbon exchange between terrOC systems and the atmosphere, as well as (v) lateral leakage of carbon to aquatic conduits. Overall, non-linear terrOC release pathways are particularly challenging to predict, such as the collapse of ICD, thermokarst formation, tundra and forest fires, as well as fluvial release of OC; processes that may all affect the net ecosystem carbon balance6,7,10,11.

Lateral leakage of terrOC through aquatic conduits is a key component of the carbon cycle in the often water-logged circum-Arctic. The large rivers and coastal shelf seas act as nature’s own integrator and permit studies of terrOC release from different source compartments as well as geographically distinct drainage basins and coastal regions12,13,14,15. Arctic rivers may shed light on terrOC release on a drainage basin scale and resolve the seasonal variation of different source compartments16,17. By contrast, the seven Arctic shelf seas have the advantage to serve as natural integrators of terrOC release from the river drainage basins through the sequestration of riverine OC from dissolved and particular forms in their sediments upon aggregation and settling with increasing salinity18. Moreover, shelf seas are recipient of OC from erosion of coastal permafrost deposits (ICD), which is suggested to be the dominating vector of terrOC release to the extensive Laptev and East Siberian Seas4,5,19.

The present study leverages off the recently established Circum-Arctic Sediment Carbon DatabasE (CASCADE)20,21 and uses an inverse receptor-based approach to deduce terrOC release from different source compartments in the circum-Arctic regions (Fig. 1). The CASCADE provides OC concentrations for over 4000 locations across the Arctic Ocean shelf seas. Dual-isotope data (δ13C; Δ14C; n = 260 locations) allows to calculate the relative contribution of different sources to the terrOC sequestered in the sediments. Further, fluxes of terrOC release from different terrestrial compartments are quantified using 210Pb-based mass accumulation rates (n = 164) in the circum-Arctic shelf seas. Finally, the relative vulnerability of the different terrOC compartments to be released was investigated by comparing shelf terrOC accumulation fluxes with the corresponding catchment-specific terrOC stocks; i.e., OC in permafrost22 and non-permafrost surface soils (SurfSoil)23, ICD3, and peat6. To this end, an Integrated Carbon Release Index is introduced (I-CRI) to contrast geographical and source-specific differences of terrOC release across the circum-Arctic.

## Results and discussion

### Dual-isotope source apportionment in the circum-Arctic

The dual-isotope information (δ13C/Δ14C) provided by CASCADE allows us to distinguish between different terrOC sources and OC produced by marine phytoplankton (Fig. 2). Given the heterogeneity of terrOC compartments around the circum-Arctic, this study employs different terrOC end members for each shelf sea (Supplementary Table 4), in each case based on large underlying end member collections of data on δ13C and Δ14C (Supplementary Text 2). Accordingly, OC from surface soils to a maximum depth of 100 cm was applied as end member in the entire circum-Arctic, with the exception of the Beaufort Sea where also deeper layers and peatlands were included due to overlapping isotopic compositions (δ13C/Δ14C) and limitation to three end members in the mixing model. Pleistocene age OC in ICD occurs in northeastern Siberia, Alaska and western Canada, and was hence considered as second terrOC end member in the Laptev, East Siberian, Chukchi and western Beaufort Sea shelves. Further, deep peat below 100 cm depth was considered as pre-aged terrOC end member for the Kara Sea, which has the world’s largest peatland in its catchment. Petrogenic OC released from rock weathering was used as 14C-depleted terrOC end member in the Canadian Arctic and the Barents Sea, to account for the significant release of petrogenic OC in these regions24,25 (Fig. 2). Each end member is described by the mean ± standard deviation (s.d.) of the underlying data collection, which represents the natural variability of the different source compartments and is mirrored in the uncertainty of the resulting source fractions.

TerrOC end members were also corrected for aging during cross-shelf transport. Cross-shelf aging of terrOC was previously quantified by 14C dating of terrestrial organic compounds26, which is here applied to correct for the transport distance of terrOC at each sampling location of the dataset (Methods, Cross-shelf transport correction). By contrast, the 13C end member was assumed to stay constant as previous studies indicated continued terrestrial 13C signatures despite major cross-shelf aging of terrOC26. Previous research also suggested aging of marine OC during cross-shelf transport27,28,29. However, the source location and the transport dynamics of marine OC are uncertain and the scale for marine OC aging in continental shelf seas is unknown, albeit likely much less than for terrOC due to both longer transports distances and lower recalcitrance.

### Circum-Arctic features of terrestrial carbon release

The large underlying CASCADE dataset offers a circum-Arctic perspective and reveals that terrOC release in the Eurasian Arctic sector is much larger than in the North American sector. The CASCADE-based terrOC sequestration in the respective shelf sea receptor sediments reveals that the East Siberian Sea drainage basin accounts for 28% of the total circum-Arctic terrOC flux, while the Kara Sea accounts for 24% and the Laptev Sea for 16% (Fig. 1; Supplementary Table 1). Including also the Barents (10%) and Russian Chukchi seas (6%), five times more terrOC is received in the Eurasian-Arctic sector than in the American-Arctic sector. This partitioning is broadly consistent with the hemispheric proportions of fluvial OC discharge and land-based terrOC stocks, which both are much larger for the Eurasian than the American watersheds of the Arctic Ocean. Consistent with this large-scale assessment, Eurasian rivers account for about 83% of the total fluvial OC input to the Arctic Ocean30,31. Moreover, the partitioning of terrOC release correlates with the relative distribution of the land-based terrOC stock in the circum-Arctic (R2 = 0.56; p = 0.05; Supplementary Fig. 1i)2,3,6, with 78% of the SurfSoil-OC and 83% of the total peat OC being located within the Eurasian drainage basin6,22,23. Although the dual-isotope receptor approach holds uncertainty, these results support the use of shelf sediments to deduce large-scale features of terrOC release and underscore the importance of the Eurasian-Arctic system for terrOC vulnerability in the Arctic.

The CASCADE facilitates also comparison of the propensity of different terrOC sources to be released and to investigate differences in this across the circum-Arctic. Dual-isotope (δ13C/Δ14C) source apportionment of OC reveals that most of the terrOC was released from surface soils (SurfSoil 61 ± 39%; Fig. 1). The relative contribution of SurfSoil-OC varies regionally, with about half of the terrOC in the East Siberian (47 ± 29%) and Laptev seas (47 ± 30%), and 59 ± 39% in the Kara Sea. The remaining terrOC originates from ICD (East Siberian and Laptev Seas) and deep peat deposits (Kara Sea; absolute fluxes are further discussed in Supplementary Discussion 1). About a third of the terrOC was released from ICD (30 ± 10%), which is characteristic for the coastline in Northeast Siberia, Alaska, and Western Canada. Peat deposits contributed a total of 10 ± 6% to the circum-Arctic terrOC accumulation in sediments, with a regional maximum of 41 ± 24% of the total terrOC in the Kara Sea catchment. In the Beaufort Sea, the combined release of SurfSoil and Peat-OC accounts for 61 ± 40% of the total terrOC release (Fig. 1). The circum-Arctic release pattern of the different terrOC sources broadly resembles its distribution pattern on land (Fig. 1)2,3,6, which supports the suitability of the receptor-based approach4,32,33.

The large portion of terrOC released from ICD emphasizes the particular importance of collapsing Arctic coastlines in northeastern Siberia, Alaska and the US Beaufort Sea (Fig. 1). While ICD is present in the catchments of only four out of the seven shelf seas (Supplementary Text 2)3, it contributes a third of the total terrOC release for the whole circum-Arctic (Supplementary Table 1), and accounts for 53 ± 17% of the total terrOC flux in the Laptev and East Siberian Sea systems. The highest input of ICD-OC to the northeastern Siberian seas likely relates to severe coastal erosion of up to 5 m yr−1, high coastal cliffs, and large volumes of ground ice in this area (Fig. 3)34. Release of ICD-OC also occurs inland (e.g. by riverbank erosion) and routes via rivers10,14,17. Yet, Pleistocene-aged permafrost OC accounts for less than a fifth of the dissolved and particulate OC export from, e.g., the Lena and Kolyma rivers that drain extensive ICD landscapes17, which points at a stronger coupling of ICD-OC release with erosion of the vast and exposed coastline. Based on a large-footprint dataset, the present study suggests that coastal erosion drives the large fluxes of ICD-OC release in the circum-Arctic.

In addition to terrOC from soils, permafrost, and peat, petrogenic rocks release considerable amounts of OC in the catchments of the Canadian Arctic and off Svalbard. For the Canadian Arctic Archipelago and the Barents Sea, petrogenic OC accounted for 37 ± 26% and 16 ± 11% (mean ± s.d.) of their total OC releases, respectively. For the Beaufort shelf, we find 51 ± 13% of the OC in sediments to originate from petrogenic sources, which agrees with the large range (19–88%) suggested by previous studies specifically addressing this region24,25,35,36. Further, the concentrations of petrogenic OC in Beaufort Sea sediments (0.66 ± 0.18%; mean ± s.d.) are also similar to the range of petrogenic OC concentrations in fluvial suspended material from within the Mackenzie basin (0.12–0.63%)35,36, which thus is broadly consistent with the results of the dual-isotope source apportionment and indicates that petrogenic OC in Beaufort Sea sediments is largely attributed to rock weathering and river export from the Mackenzie river and its tributaries36. Less certain, however, is whether petrogenic OC—likely to be highly recalcitrant—contributes to any notable emissions of CO2 and thus affects the active carbon cycle, which is why petrogenic OC contributions were not considered terrOC release in the forthcoming part of the present study.

### Comparison of terrestrial carbon release with circum-Arctic carbon stocks

Terrestrial OC accumulation in the recipient shelf seas can be compared with the vast terrOC stocks of the circum-Arctic source compartments to provide a metric and perspective on regional differences in large-scale terrOC releases. To this end, the Integrated Carbon Release Index (I-CRI) represents the percentage of the total terrOC, SurfSoil-OC, ICD-OC, and Peat-OC stock in each drainage basin (Supplementary Table 2)3,6,22,23 that accumulates in sediments over the course of 100 years (Supplementary Table 3), where the estimate of the total uncertainty (s.d.) includes the spatial variability of OC accumulation fluxes, as well as the uncertainties of the source apportionment and that of the land-based terrOC stock estimates. For total terrOC, the results exhibit large differences between the geographical regions, from the lowest relative release in the Beaufort Sea basin (I-CRIterr 0.2 ± 0.1, % terrOC translocated 100 yr−1) to five times higher relative release in the basins of the Canadian Arctic Archipelago (1.0 ± 0.7) and the East Siberian Sea (1.0 ± 0.4; Fig. 3; Supplementary Table 3). The dynamic range is yet larger for the source-compartment-specific I-CRISurfSoil, ranging from 0.2 ± 0.1 in the Beaufort Sea to 1.4 ± 0.9 in the East Siberian Sea, suggesting that relative OC release from surface soils varies by a factor of seven in the circum-Arctic. By contrast, the I-CRIICD reveals a smaller range from 0.4 ± 0.2 in the Chukchi Sea to about two times higher values in the US Beaufort Sea (1.1 ± 0.3), and in the East Siberian Sea (0.8 ± 0.3). The I-CRI clearly shows differences in terrOC release propensities across the seven Arctic shelf sea catchments and between the terrOC source compartments.

Comparing the I-CRI with environmental properties of the circum-Arctic drainage basins offers an approach to explore possible drivers behind regional differences in terrOC release. First, the variability in I-CRIterr and I-CRISurfSoil resembles the spatial pattern of catchment-specific summer warming trends for the period 1960-2015 (Fig. 4a; Supplementary Fig. 1c, d)37,38. At the same time, terrOC release from surface soils is consistently higher in small shelf catchments with coverage of mostly high-latitude areas (I-CRISurfSoil > 1; Chukchi, East Siberian, Barents Seas and the Canadian Arctic Archipelago) than in larger drainage basins that extend further to the south (Beaufort, Laptev and Kara Seas; I-CRISurfSoil < 0.4; Fig. 4b; Fig. Supplementary Fig. 1a). In addition, the I-CRIICD correlates with the regional pattern of average coastal erosion in the ICD-hosting shelf sea catchments (Supplementary Fig. 1b), with average erosion rates of 1.1 and 0.9 m yr−1 in the East Siberian and Beaufort Seas when compared with 0.7 and 0.4 m yr−1 for the Laptev and Chukchi Seas34 (R2 = 0.92; p = 0.04). We hypothesize that the large differences in relative terrOC release to the Arctic Ocean receptors reflect a combination of processes, including regional differences of Arctic climate change, degradation during transport via hydrological conduits, and the thermal state of the ground. Key hypothesized mechanisms are further addressed below.

### Potential effects of recent climate warming on carbon release

The amplified rise in Arctic temperatures may be an important driver of terrOC release from circum-Arctic permafrost soils. For the period 1960–2015, circum-Arctic average summer temperatures (May-October) increased by 1.4 °C in the Beaufort Sea catchment and up to 2.2 °C in the Canadian Arctic Archipelago37,38. This caused notable warming of permafrost soils, particularly those situated in the continuous permafrost zone39. One of the effects of Arctic change is the deepening of the seasonal permafrost active layer, which is suggested by an increasing number of yet-scattered records8,40,41. Furthermore, first signs of accelerated coastal erosion in the circum-Arctic have been reported42,43.

Geographical variability in the temperature increase across the circum-Arctic might contribute to the regional differences in terrOC release. This is supported by the spatial correlation of the I-CRIterr (R2 = 0.86; p = 0.003) and I-CRISurfSoil (R2 = 0.54; p = 0.059) with the average summer warming trends 1960–2015 in the circum-Arctic (Fig. 4c; Supplementary Fig. 1c, d). These observations are also broadly in line with the scattered observational dataset of active layer development, with significant deepening in, e.g., northeastern Siberia over the past decades8. Further, a biogeochemical model suggests that the largest increase of OC release during the past century was in the high-latitude Canadian Arctic Archipelago (22%), and in the drainage basins of the East Siberian (19%) and Chukchi seas (incl. Bering Strait; 42%)44, which is also supported by the increased discharges of rivers in northeastern Siberia45,46. While this may suggest a connection between terrOC release and recent warming trends across the circum-Arctic, the range in warming is only 50% while the range in I-CRI is a factor of 5–7. In addition, recent Arctic warming, terrOC release and translocation may operate over different time scales. It therefore seems unlikely that temperature increase alone can explain the large differences in terrOC release across the circum-Arctic pinpointed in this study.

### Potential effects of degradation during fluvial transport on carbon release

A portion of terrOC released from surface soils, peat or other deposits is generally remineralized during transport within the catchment area47. This may be particularly anticipated for the circum-Arctic, where large parts of the catchment area are water-logged, and freshwater runoff governs terrOC release and degradation10. The I-CRI of the different shelf seas varies by a factor of five for total terrOC (I-CRIterr), and by a factor of seven for surface soils (I-CRIsurfsoil), showing generally higher source-receptor fluxes for smaller high-latitude basins, and lower fluxes in larger, southward-extending, catchments. Hence, the I-CRI is spatially correlated with the southward extent (R2 = 0.68 and p = 0.022 for I-CRIterr; R2 = 0.67 and p = 0.025 for I-CRIsurfsoil; Supplementary Fig. 1g, h), which may reflect efficient underway degradation and significant loss of organic material of distantly sourced organic matter.

Apart from the transport distance, the presence of permafrost or peat within the basin may have decisive impact on degradation rates under the different circum-Arctic freshwater regimes48. The two northernmost basins, the Canadian Arctic Archipelago and the East Siberian Sea, are underlain mostly by continuous permafrost (79 and 100%)49 and show high I-CRISurfSoil values, while the two southernmost basins (Beaufort and Kara seas) host only 43% and 17% of continuous permafrost (Fig. 4; Supplementary Fig. 1f)49 and lower I-CRISurfSoil. These more southward-extending drainage basins are characterized by discontinuous permafrost and peatlands, which are known to provide deeper hydraulic conduits in the soil with longer reservoir times for transported terrOC14, presumably leading to more efficient degradation48. Terrestrial OC transport through permafrost-free areas may thus contribute to degradation over long distances, and may contribute to the large differences of terrOC release along the circum-Arctic.

Comparing terrOC release with riverine CO2 evasion provides yet another additional perspective on large-scale carbon cycling and terrOC remineralization in the circum-Arctic. The scale and spatial pattern of I-CRI are largely in line with previous estimates of inland CO2 evasion from Arctic river catchments50, and its relationship to the corresponding riverine export of total OC to the Arctic Ocean31,51. The atmospheric CO2 evasion is 9-10 times higher than fluvial terrOC export in the large drainage basins of the Kara and Beaufort Seas (Fig. 4; Supplementary Fig. 1e)31,50,51,52. For the Ob River basin (Kara Sea) specifically, CO2 emissions are up to nine times higher than the ocean export53,54, with the highest CO2 emissions in the more southerly, non-continuous permafrost and peat-dominated part of the catchment. By contrast, the Laptev Sea catchment—to 80% underlain by continuous permafrost—reveals CO2 evasion only twice that of the fluvial terrOC export. The basins of the Chukchi and East Siberian Seas, which are smaller and more northerly, also associate with notably less CO2 evasion relative to the terrOC export (CO2 evasion three and four times higher than export) than for the Kara and Beaufort Seas basins. This further supports the argument of stronger terrOC degradation in southerly and permafrost-free areas. In addition, this suggests the importance of efficient remineralization of released terrOC as part of the carbon cycle and constitutes a potentially significant source of greenhouse gas upon permafrost thaw and terrOC mobilization in the circum-Arctic.

### Synthesis

This study provides a large-scale receptor-based assessment of carbon releases from potentially climate-sensitive terrestrial deposits around the entire circum-Arctic. Dual-carbon isotope source apportionment and recipient fluxes in the circum-Arctic shelf seas reveal large differences in propensity for terrOC remobilization both from different source compartments and between the different Arctic Ocean drainage basins. The release of terrOC from the Eurasian-Arctic sector is about five times larger than from the American-Arctic sector. Most of the released terrOC originates from Surface Soil (61 ± 39%), with Ice Complex Deposit permafrost as the second largest source (30 ± 10%). The index metric of receptor-based terrOC fluxes to inland terrOC stocks (I-CRI) provides a perspective on the relative terrOC release propensity along the entire circum-Arctic. The geographical patterns of the I-CRI suggest that one driver of terrOC release may be Arctic warming and the progressive permafrost thawing over the past half century, which broadly shows a spatial pattern similar to normalized terrOC release in the circum-Arctic. However, the normalized terrOC release varies by a factor of five between larger and smaller catchments, which also suggests efficient degradation of terrOC as part of long-distance freshwater transport and underway remineralization of terrOC to greenhouse gases. Taken together, this large-scale perspective on terrOC release patterns informs about the functioning of climate-relevant carbon remobilization across the circum-Arctic, and provides a benchmark for future investigations of terrOC release in the Arctic during climate change.

## Methods

### Organic carbon in surface sediments

Total OC concentrations as well as δ13C and Δ14C values of OC were taken from CASCADE20,21 (https://bolin.su.se/data/cascade). Only data from surface sediments was considered in this study, which are here defined as the surface layer at the water-sediment interface and not deeper than 5 cm.

### Source apportionments of OC

This study employs a dual-isotope (13C, 14C) mixing model55 to distinguish fractions derived from the major OC sources (i.e., SurfSoil-OC, ICD-OC, Peat-OC, Petrogenic-C and marine phytoplankton) using the δ13C and Δ14C values of OC from 260 stations distributed across the Arctic Ocean (Fig. 2). This method simulates mixing of three end members using a Bayesian Markov chain Monte Carlo script55, run in Matlab R2018a with 1,000,000 runs and a burn-in period of 10,000 runs per sample. The end members vary between the shelf seas depending on their occurrence in the catchment areas of the shelf seas. Of all end members, SurfSoil-OC, ICD-OC and peat OC were considered terrOC, while highly matured petrogenic OC released from, e.g., rock weathering or bituminous coal, abundant in the drainage areas of the Canadian Arctic Archipelago, Beaufort and Barents Seas36,56 is unlikely to be a substantial contributor of greenhouse gases and was therefore excluded from the terrOC budget. For all shelf seas, mixing from three sources was thus assumed, consisting of two terrestrial and one marine end member, respectively. The end member definition was based on an extensive database, which has been utilized by a number of previous studies focusing on Siberian permafrost systems5,17,57. For this study, the database was substantially enhanced both geographically and numerically with additional and recently published data for previously unstudied regions. The end member definition for each shelf sea is described in detail in Supplementary Methods 1. A summary of the end members is given in Supplementary Table 4 and the full end member database is accessible in the Supplementary Data 1 spreadsheet.

### Cross-shelf transport correction

Previous studies have demonstrated that cross-shelf transport causes considerable aging of terrOC26, which needs to be accounted for in the definition of the 14C end member. Accordingly, our source apportionment script includes an approach described previously26 to estimate OC aging with increasing cross-shelf distance for all terrOC end members. For transported SurfSoil-OC and peat OC, we assumed predominant transport by rivers and thus considered the distance between each Δ14C-location and the nearest river outlet (Supplementary Fig. 3a). For transported ICD-OC we used coast line compartments with active erosion34 to measure the cross-shelf transport distance (Supplementary Fig. 3b). For both transport pathways the shortest distance between the sampling location and (i) the river outlet, or (ii) eroding coast line was considered, which is a conservative estimate and does not account for coast-parallel transport.

The effect of the cross-shelf transport correction was largest for the SurfSoil-OC end member. For instance, SurfSoil-OC transported to a location in the outer Laptev Sea 500 km away from the Lena river mouth would be affected by aging 2750 years26, leading to a final Δ14C value of transported SurfSoil-OC −433.9‰ (compared to the mean surface soil Δ14C of −201.1‰). We also tested the sensitivity of the source apportionment and the OC accumulation rates to the cross-shelf transport correction. Source fractions calculated without considering cross-shelf transport revealed terrOC fractions 2 ± 4% larger (of the total OC; mean ± s.d.), while the relative uncertainties of the OC source fraction estimates were 11% higher. As this mostly affected samples at outer shelf locations with low mass accumulation rates there was no acknowledgeable effect to the mass accumulation budget. We further tested the effect of any post-depositional OC aging to the source apportionment. Based on 210Pbxs sedimentation rates in circum-Arctic shelf sediments (0.21 ± 0.22 cm/yr average for this study; n = 164), and the corresponding 14C depletion of marine OC over the 0–2 cm depth interval, we find resulting OC fractions to shift <1% (of the total OC) compared to source fractions for which the end member remained unchanged. Even under very low sedimentation rates (0.004 cm/yr), the (oldest) petrogenic OC fraction in Beaufort and Barents seas sediments is only around 1% smaller, which is much lower than the uncertainty estimates of this fraction. Hence, any post-depositional OC aging can be ruled out and will not significantly affect the source apportionment.

The results of the final source apportionments for all stations are provided in Supplementary Table 5.

### Estimation of mass accumulation rates (MAR)

To estimate the circum-Arctic accumulation of sediments we collected published MAR data based on 210Pb dating of 152 shallow sediment cores. In addition, we performed gap-filling 210Pb dating for 12 cores, of which ten were located in the Laptev and East Siberian seas, and two in the Kara Sea (Supplementary Table 7). A few studies provided information about sedimentation rates based on 210Pb dating but no MAR was reported, in which cases a dry bulk density of 0.8 g cm−3 was assumed to estimate the MAR4. Other cases reported OC fluxes only, which were converted into MAR using information about the OC concentration: MAR = OC flux (g m−2 yr−1) / OC (wt%) / 100. In total, our flux calculations are based on 164 cores dated using 210Pb profiles (Supplementary Fig. 2; Supplementary Table 6). All MAR will also be included in the next version of CASCADE.

### Spatial interpolation and calculation of OC accumulation in circum-Arctic shelf seas

Calculated source fractions, total OC values from CASCADE and the MAR data were interpolated using Empirical Bayesian Kriging to an Arctic Ocean wide grid at 5 × 5 km resolution (EBK; ArcGIS, ESRI). For calculating fractional accumulation rates, OC fractions were interpolated and projected to the North Pole Lambert Azimuthal Equal Area coordinate system, which is a projection that is area conservative across the latitudes. The resulting interpolated layers were multiplied with interpolated total OC concentrations from CASCADE as well as with the gathered and interpolated MAR data.

### Calculation of carbon stocks in terrestrial deposits

To compare circum-Arctic accumulation of OC from terrestrial sources we calculated the stock of OC stored in surface soils (of both permafrost and non-permafrost soils), ICD and peatlands for each shelf sea watershed. Surface soils were defined as soils to a depth of 1 m. The calculation of the stock of OC in permafrost surface soils was facilitated by the NCSCD22 using spatial OC densities for the active layer and permafrost to a depth of 100 cm. This dataset was amended by the Harmonized World Soil Database (HWSD)23, which also includes non-permafrost soils at a vertical extent of 0–100 cm depth. To calculate the OC stock in ICD permafrost in northeastern Siberia, Alaska and northwestern Canada, we calculated the ICD stock for each drainage basin using the fraction of the spatial coverage of ICD in the whole circum-Arctic and then allocated the total ICD-OC stock of 212 Pg C according to that distribution3. The OC stocks in circum-Arctic peatlands were calculated using the maps provided by Hugelius et al.6. It should be mentioned that peat overlaps with the surface soil 0–100 cm depth interval in areas of high peat coverage, such as for the Kara and Beaufort seas. All mapping was carried out in ArcGIS 10.6 (Esri, USA) and calculations were done in Matlab R2018a.

### Comparing accumulation of carbon in shelf seas with land-based carbon stocks I-CRI

Comparing the fractional OC accumulation in shelf sediments with the partitioning of the OC stored in the respective catchment in each of the circum-Arctic shelf seas informs about the tendencies of OC stores to be laterally released to the coastal sediments. The Integrated Carbon Release Index (I-CRI) per terrOC fraction (f, i.e., SurfSoil, ICD, Peat) represents the percentage (%) of the respective terrOC stock that is translocated to the shelf receptor per century (100 years). Hence, it is used to reflect the efficacy of terrOC release relative to the inland terrOC stock:

$${{{{{{\rm{I}}}}}}{{{{{\rm{-}}}}}}{{{{{\rm{CRI}}}}}}}_{f}[\%\,{{{{{\rm{terrOC}}}}}}\,{{{{{\rm{translocated}}}}}}\,{{{{{\rm{per}}}}}}\,100\,{{{{{\rm{yrs}}}}}}]=\frac{{{{{{{\rm{MAR}}}}}}}_{f}[{{{{{\rm{Tg}}}}}}\,{{{{{{\rm{yr}}}}}}}^{-1}]}{{{{{{{\rm{OC}}}}}}}_{f}[{{{{{\rm{Pg}}}}}}]}\times \frac{100\,{{{{{\rm{yrs}}}}}}}{1000\,{{{{{\rm{Tg}}}}}}}\times 100\%$$
(1)

Where MARf is the mass of the fraction (of surface soil or ICD) accumulated to the sediments of each shelf sea, and OCf is the corresponding land-based OC inventory (of OC in surface soil or ICD). We also calculated the I-CRI for total terrOC using the sum of surface soil, ICD, and peat for MAR, and the total terrOC pool as OC inventory.

### Statistical analysis

Linear regression analysis was used to investigate the correlation between the I-CRI and the environmental characteristics of the drainage basins.