Assessment of 21 years of Arctic Ocean Absolute Sea Level Trends (1995-2015)

The Arctic Ocean is at the frontier of the fast changing climate in the northern latitudes. As the first study, we assess the different mass and steric components of the observed sea level trend from both absolute sea level (ASL) from altimetry and tide gauges, without using gravimetric observations from GRACE. This approach permits a longer time series and avoids problems with errors from leakage effects in GRACE-products. ASL is equal to mass-driven sea level added with steric sea level, while tide gauge based sea level are also corrected with novel estimates of vertical land movement. Calculations of the 5 mass component from present-day deglaciation, shows that deglaciation rises Arctic sea level with more than 1 mm y−1, while the steric contribution is between -5 and 15 mm y−1 with large spatial variability, with the halosteric signal dominating the pattern. A dynamic mass contribution is derived from the Estimating Circulation and Climate of the Oceans (ECCO)-model (version 4 release 4), which varies between -1 and 2 mm y−1. The combined mass and steric product agrees (within uncertainty) with ASL-trends observed from altimetry in 99% of the Arctic, although large uncertainties originate from poor data coverage 10 in the steric data and large variability in the dynamic product. A comparison with ASL trends observed at tide gauges agrees with mass+steric at 11 of 12 tide gauge sites.

and is corrected for VLM by using the VLM-model (Ludwigsen et al., 2020b) or, as in the case for Ny-Alesund and Reykjavik, using nearby GNSS for VLM (see figure 1). Reykjavik (64.2°N), Nome (64.5°N), and Rorvik (64.9°N) are located off the edge of the DTU/TUM Arctic altimetry dataset (Rose et al., 2019), which only extends to 65°N, but are nevertheless included to extend the spatial distribution of the TG-sites.
TG-trends are determined with least-squares method using months with data between 1995 and 2015 and the VLM-correction 60 is interpolated onto the monthly TG-time series. From figure 2, we see that trends in the Arctic vary with nearly +/-1 cm y −1 , with Ny-Ålesund on Svalbard having a negative sea level trend of -7.45 mm y −1 , while Kostelnyi Island between the Laptev and East Siberian Sea shows a positive trend of 7.67 mm y −1 . The VLM-model utilizes the Caron2018 GIA-model (Caron et al., 2018) which is added to an annual elastic VLM-model from 1995-2015 change in present-day ice loading (PDIL). As shown in Ludwigsen and Andersen (2020), Ny-Ålesund and Depth profiles from the temperature and salinity grids are used for computing the right-hand side of equation 3: where H denotes the minimum height (maximum depth (z)). S and T are defining salinity and temperature anomalies, with reference values used in Ludwigsen and Andersen (2020) are 0 C°and 35psu. β is the saline contraction coefficient and α is the thermal expansion coefficient. The opposite sign of η S is needed since β represents a contraction (opposite to thermal expansion). α and β are functions of absolute salinity, conservative temperature and pressure, and is determined with help from the freely available TEOS-10 software (Roquet et al., 2015). Map ofη S andη T from 1995-2015 is shown in figure 3. Maps of the individual contributions to change in ocean mass is shown in figure 4. We divide the mass contributions into changes caused by changes in surface loadingṄ , from GreenlandṄ GRE , Northern Hemisphere glaciersṄ GN H , Antarcticȧ N AN T and GIAṄ GIA , and atmospheric pressure (IB) and a dynamic contribution (Ḋ M ).
Similar to the VLM-product (Ludwigsen et al., 2020a), the Regional Elastic Rebound Calculator (REAR) (Melini et al., 2015) is used to estimate elastic gravitational changes,Ġ, while gravitational changes from GIA is derived from the Caron2018model.Ṅ is retrieved by adding the spatially constant c to the change of the geoid,Ġ, c is equal to the contribution to global mean sea level (Spada, 2017), and is defined as The used ice model with mass M I , is a combined high resolution model for glacial estimates (Marzeion et al., 2012;Ludwigsen et al., 2020a) and Greenland ice caps and is here an extended version of the model used for calculations of VLM, U , in (Ludwigsen et al., 2020a). A O is the global area of the ocean, while ρ w is the average density of ocean water. ... , denotes the average of the ocean surface.

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The geoid perturbation of non-tidal ocean loading (NOL) (van Dam et al., 2012) and rotational feedback (RF) (King et al., 2012) is not shown since it is below 0.05 mm y −1 , but is included inṄ GN H . The change in surface mass, M I , is zero for GIA, RF and NOL. The GIA contribution to global mean sea level (c) is 0.3 mm y −1 consistent with other studies (Peltier, 2009;Spada, 2017).
In figure 6 and table 1, we quantify the contributions to sea level change explained in this chapter at each of the 12 tide gauge locations using a surrounding average of 100 km radius (5 km for GIA and elastic VLM). This radius ensures, that Rorvik, Nome and Reykjavik reaches the altimetric data, but few data points, might cause the data to be more variable and hence increase the uncertainty.

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The Norwegian tide gauges (Rorvik, Tromso, Vardo) are considered the most stable. The derived product is in good agreement with the tide gauge and has for Tromso and Vardo better alignment with the TG-data than altimetry. This is also the region with highest density of hydrographical data and thus most reliable. We see that for Vardo and Rorvik, the sea level change is split between a steric and mass contribution of roughly the same size, which is similar to the share of the global sea level trend (Church and White, 2011;Group, 2018). At Tromso a negative halosteric signal (more saline water) is lowering the sea level 150 trend.
Along the Siberian coast, multiple river outlets contributes to a freshening of the Arctic Ocean (Morison et al., 2012;Armitage et al., 2016), which is reflected by the positive halosteric trend. At Amderma TG, which is located on the coast between the Barents and Kara Sea, there is however no nearby major river outlet, but a significant halosteric signal is still present which matches the tide gauge-measured sea level. Ice loss from Novaya Zemlya contributes with over 1 gigaton of freshwater to the Kara Sea every year (Melkonian et al., 2016), but it is unclear if this is the reason for the halosteric sea level rise at Anderma, or if the halosteric signal is (falsely) extrapolated from the gulf of Ob which has mayor river outlets and the match with tide gauge is accidental. The altimetric signal reflects the mass contribution, which together with low hydrographic data density in the region, could indicate that both the tide gauge and halosteric sea level trends are overestimated.
The four other tide gauges along the Siberian coast all show a pattern, where mass+steric has a negative trend, altimetry has 160 a slight negative or positive trend and the tide gauge has a clear positive trend. Due to poor hydrographic coverage along the Siberian coast (Ludwigsen and Andersen, 2020) it is difficult to estimate the 'true' sea level. The positive trend among tide gauges in the Siberian Seas is however consistent and has been recognized in other studies using an extended set of Siberian tide gauges (Proshutinsky et al., 2004;Henry et al., 2012). Remarkably is that the TG-trend at Kotelnyi and Kigiliah differ with almost 6 mm y −1 despite being less than 250 km apart. This difference is only realistic if local circumstances is affecting the 165 RSL.
Nome and Prudhoe Bay in Alaska both show a positive steric trend which is not reflected in sea level trends from altimetry or the tide gauge. The strong halosteric trend of the Beaufort Gyre, might be extrapolated towards the Alaskan coastline. Altimetry agrees reasonably well with the tide gauge trend.
Few hydrographic data around Reykjavik, makes the steric sea level rather uncertain as well. A negative halosteric contribu-170 tion causes the steric+mass product to be to low compared to TG-data and altimetry.
At Ny-Ålesund on Svalbard, which like the other Norwegian TG-sites has good hydropgraphic data density, is the mass + steric contribution in agreement with the TG-trend. Ny-Ålesund is dominated by a large VLM caused by deglaciation in recent years and after the Little Ice Age that ended in the 19th century (Rajner, 2018;Ludwigsen et al., 2020a). This uplift completely mitigates the large sea level fall measured by the tide gauge. A small mass upward trend is countered by a smaller 175 steric downward trend, which in total agrees with the tide gauge measured sea level trend. Altimetry shows a slightly higher trend.
Generally the largest uncertainties (estimated as standard error of the trend) are found along the Siberian coast and in the interior of the Arctic where the largest sea level trend is present (see figure 7). The steric uncertainty, which in most cases is the largest source of uncertainty, is computed as the standard deviation of the detrended and deseasoned time series, which naturally 180 reflects if steric heights are unstable and poorly constrained. This method requires in principal temporal independence, which is not entirely true, since data from adjacent years are used instead of outliers. Furthermore, large influence by the non-periodic and non-linear Arctic Oscillation, would enhance the uncertainty, even though this is a real physical signal.
The mass contribution and VLM has naturally the largest uncertainties close to glaciated areas. Glacial ice loss on Baffin Island is poorly constrained in the ice model, which is reflected in large uncertainties in this area. A significant uncertainty also 185 originates in the dynamic mass loss, which probably also can be attributed to the Arctic Oscillation, which significantly changes wind patterns. Since no uncertainties are associated with the ECCO-product, we also here assume no temporal correlation, and calculate the standard deviation of the time series, even though the model likely has inter-annual correlations.