Arctic sea level variability from high-resolution model simula- 1 tions and implications for the Arctic observing system

. Two high-resolution model simulations are used to investigate the spatio-temporal variability of the Arctic Ocean sea level. The model simulations reveal barotropic sea level variability at periods <30 days, which is strongly captured by bottom pressure observations. The seasonal sea level variability is driven by volume 10 exchanges with the Pacific and Atlantic Oceans and the redistribution of the water by the wind. Halosteric ef- 11 fects due to river runoff and evaporation minus precipitation (EmPmR), ice melting/formation also contribute in 12 the marginal seas and seasonal sea ice extent regions. In the central Arctic Ocean, especially the Canadian Basin, 13 the decadal halosteric effect dominates sea level variability. The study confirms that satellite altimetric observa- 14 tions and Gravity Recovery and Climate Experiment (GRACE) could infer the total freshwater content changes 15 in the Canadian Basin at periods longer than one year, but they are unable to depict the seasonal and subseasonal 16 freshwater content changes. The increasing number of profiles seems to capture freshwater content changes 17 since 2007, encouraging further data synthesis work with a more complicated interpolation method. Further, in- 18 situ hydrographic observations should be enhanced to reveal the freshwater budget and close the gaps between 19 satellite altimetry and GRACE, especially in the marginal seas.


and the Fram 22
Strait (Polyakov et al., 2017), and an unprecedented freshening of the Canadian Basin especially the Beaufort 23 Gyre (Proshutinsky et al., 2019). The rapid changes potentially impact the weather and climate of the northern 24 hemisphere (Overland et al., 2021). 25 As an integrated indicator, sea level change reflects changing ocean conditions caused by ocean dynamics, 26 atmospheric forcing, and terrestrial processes (Stammer et al., 2013). Satellite altimetry, together with bottom 27 pressure observations from Gravity Recovery and Climate Experiment (GRACE), has been applied to infer 28 ocean temperature and salinity changes that are not measured directly in the Arctic Ocean (e.g., Armitage et al., 29 2016) and in the deep ocean (e.g., Llovel et al., 2014), enhancing our ability to monitor ocean changes. 30 Over the past decades, coupled ocean-sea ice models and observations have advanced our understanding of 31 the Arctic Ocean variability. Proshutinsky and Johnson (1997) demonstrated wind-forced cyclonic/anticyclonic 32 ocean circulation patterns accompanied by dome-shaped sea levels variation using a barotropic model simula-33 tion. Further, in the Canadian Basin, ocean circulation changes result in freshwater accumulation and releasing, 34 very well correlated to sea level changes (Koldunov et al., 2014;Proshutinsky et al., 2002). Given that sea level 35 changes reflect freshwater content changes in the Canadian Basin, Giles et al. (2012) and Morison et al. (2012) 36 proposed to use satellite altimetry observations and GRACE observations to infer freshwater content changes. 37 The method was then applied to explore the freshwater content changes in the Beaufort Gyre (Armitage et al., 38 2016;Proshutinsky et al., 2019) at seasonal to decadal timescales. In the Barents Sea, Volkov et al. (2013) used 39 altimetric sea level observations and the ECCO reanalysis (Forget et al., 2015) to explore seasonal to interannual 40 sea level anomalies, revealing different roles of mass-related changes, thermosteric and halosteric effects on 41 different regions of the Barents Sea. 42 However, the sparseness of in-situ profiles, coarse resolution and significant uncertainties of satellite altim-43 etry and GRACE observations result in large gaps in understanding the spatio-temporal variability of the Arctic 44 sea level and its relations to the thermo/halosteric effects and mass changes (Ludwigsen and Andersen, 2021). 45 Previous studies mainly focus on the decadal sea level variability (e.g., Koldunov et al., 2014;Proshutinsky et al., 46 2007;Proshutinsky and Johnson, 1997), and no study has yet fully explored the Arctic sea level variability at 47 different spectral bands, and its dependence on the mass component and the vertical oceanic variability. Such a 48 study could help identify critical regions and environmental parameters that need to be coordinately observed 49 and point out observational gaps that need to be filled in the future. 50 Our study systematically explores the Arctic sea level variability as function of timescale and geographic 51 location using daily and monthly outputs of two high-resolution model simulations. Contributions from ba-52 rotropic changes expressed in bottom pressure variations and baroclinic processes represented by ther-53 mo/halosteric changes are quantified at different timescales. We further discuss the existing Arctic Ocean ob-54 serving system's capability to monitor the Arctic freshwater content variability. 55 The structure of the remaining paper is as follows: the numerical models and the observations from the bot-56 tom pressure sensor, GRACE, and satellite altimetry are described in Section 2, together with different compo-57 nents of sea level changes. We compare the model simulations against observations in Section 3. Section 4 ana-58 lyzes sea level variability and associated mechanisms at high frequency (<30 days), at the seasonal cycle and at 59 https://doi.org/10.5194/os-2021-79 Preprint. Here you could cite Solomon et al. (2021;doi: 10.5194/os-17-1081-2021 and summarise briefly. If you discuss freshwater variability estimates for the Arctic, it would be worth mentioning and briefly relating to the following publications: Haine et al. (2015Haine et al. ( , doi: 10.1016Haine et al. ( /j.gloplacha.2014 ) Rabe et al. (2011Rabe et al. ( , doi: 10.1016Rabe et al. ( /j.dsr.20102014, doi: 10.1002/2013GL058121 ) Polyakov et al. (2020, doi: 10.3389/fmars.2020 ). These use various kinds of interpolated products, based on in-situ profiles, to estimate freshwater content variability.     This caption is lacking a clear mention of what model output is used (you mention it somehow at the end of section 3., but would really help to have that here, as well).
The letters a-f are easier to see here, as the gray background is lighter than in Figure 3. However, I'd still think outside labels for rows / columns would speed up understanding this figure.

High-frequency (<30 days) variability 179
With a coarse resolution model simulation, Vinogradova et al. (2007)  The depiction of the phase by vectors is a bit confusing to the non-expert --perhaps remove vectors and add another panel with phase contours / colour ? Need to show lines where correlation coefficients are significant, unless they are significant everywhere. In the latter case, this deserves at least one sentence. The unit vector could be more prominently places at the top left of each figure (gets a bit lost in Greenland, reaching into the EGC). The caption is a bit confusing as to what is c --perhaps clarify by separating into two sentences? (you write it in the text, but should be clear in the caption) Do I understand correctly, that (a) is the correlation of local wind to local sea level, whereas (b) and (c) denote the correlation of each local wind across the Arctic to the averages of the boxes A and B in Figure 5a?
en by the cyclonic/anticyclonic wind pattern in the summer/winter season (Proshutinsky and Johnson, 1997). 262 Mean sea level anomalies from June to August (Fig. 9a) and from December to February (Fig. 9b)   ines the spatial variability of Arctic decadal sea level and addresses its relation to the mass, halosteric, and ther-286 mosteric components. 287 It is revealed that the pronounced decadal sea level variability in the Canadian and Eurasian Basins (Fig. 4c) 288 is mainly due to the halosteric effect (Fig. 10b)   where  is an empirical constant estimated from in-situ profile observations and is set to 35.6. 326 As shown in Fig. 11, freshwater content changes and the two estimates show similar decadal variabilities, 327 but differences remain in the seasonal and long-term trends. Since the halosteric effect dominates the steric 328 effect, estimation using Eq. (6) matches the seasonal freshwater cycle very well (red and black lines), consider-329 ing the amplitude and phase. However, it overestimates the long-term trend (the difference between the black 330 and red dashed lines) since Eq. (6) attributes thermosteric effect (mainly a linear trend) to freshwater changes. 331 Eq. (5) infers a much more substantial seasonal variability of freshwater content, and the phase does not always 332 match the real freshwater content changes (blue and black lines). 333 https://doi.org/10.5194/os-2021-79 Preprint. Regional boxes not clearly labelled --please mark the "d" and "e" in Fig. 10  The method of correcting ITP profilers (WHOI) for drift in the conductivity sensor is analogous to the method used for ARGO floats. "Historical" reference profiles are used in an optimal interpolation approach to compare to in-situ profiles in a certain depth range.
For that reason it's not useful to consider the deeper part of the profile (deeper than about 500 m) to analyse long-term variability / trends, as they would likely not show up. The analysis by Rabe et al. (2011;2014) and others thus only considered observational data shallower than 500 m, or even limited the analysis to the layer shallower than the lower halocline (practical salinity < 34 Please use a couple of sentences to discuss the potential error by assuming a standard density profile or estimating this constant, in the SSH-based estimate of freshwater content. What area did you consider --e.g. "Arctic" bounded by what? Figure 11. Freshwater content anomalies (10 3 km 3 ) and approximated based on Eq. (5) in blue and Eq. (6) in red 335 using the monthly output. The thick dashed lines are the annual mean values. 336 Eq. (5) assumes the isopycnal adjusts simultaneously with sea level anomaly, which may not apply in the 337 presence of baroclinic effects. In order to illustrate the limitation of Eq. (5) we take the differences between Feb. 338 2003 andSep. 2002 (in which Eq. (5) fails to reproduce the phase and the amplitude of freshwater content 339 changes) and between 1994-1996and 2008-2010 reproduces the freshwater changes well). 340 From Sep. 2002to Feb. 2003 (Fig. 12a), anticyclonic wind stress anomalies occur in the Beaufort Sea, re-341 sulting in positive SLA through Ekman transport. However, freshwater content is reduced during this period. 342 The salinity difference averaged over the central Arctic Ocean reveals that salinity increases in the top 30 m 343 caused by ice formation. At the same time, the isopycnal (27.9 kg m -3 ) does not deepen (Fig. 12c) as predicted 344 by Eq. (5). The assumption that freshwater content changes are captured by freshwater column thickness chang-345 es • (1 + 1 2 − 1 )(red dashed lines in Fig. 12c) fails to infer freshwater content changes in this case. 346 From 1994From -1996From to 2008From -2010, anticyclonic wind stress anomalies appear in the Canadian Basin, accom-347 panied by positive SLA and freshwater content anomalies (Fig. 12b). During that period, Ekman pumping deep-348 ens the isopycnals (blue and red lines in Fig. 12), accumulating more freshwater and reducing the local salinity 349 over the top 300 m (Fig. 12d). In this scenario, the water column thickness change dominates the freshwater 350 content variability, which is approximated by • (1 + 1 2 − 1 ) (red dashed lines in Fig. 12d). Therefore, Eq. (5) 351 captures the interannual freshwater content changes using the satellite altimetry observations. Therefore, caution 352 needs to be taken when inferring Arctic Ocean freshwater content changes using satellite altimetry observations 353 and GRACE measurements. In addition, Figs. 12b and 12c also indicate that Eq. (5)  wind stress(vectors) between (a) Feb. 2003and Sep. 2002, (b) 1994-1996and 2008-2010 and (d)

In-situ profilers 364
In-situ profilers measure salinity directly, but they are limited by sea ice presence. The endeavor of polar 365 expeditions and the evolving measurement techniques (e.g., ITP) have generated a large number of hydrograph-366 ic data in the central Arctic and subarctic seas (e.g., Behrendt et al., 2018). This section examines to what extent 367 existing hydrographic observations could help reveal Arctic freshwater content changes and identify observa-368 tional gaps. Based on the spatiotemporal distribution of profiles in the study of Behrendt et al. (2018) and an 369 ensemble optimal interpolation (EnOI) scheme (Evensen, 2003;Lyu et al., 2014) Please define "difference" --is it the latter period MINUS the former, or vice versa? (b) suggests that it 's 2008-2010MINUS 199-1996. Units are missing on the colorbars ! What you are plotting in colour are the FW inventories (presumeable in "m"), not the content (that being a volume quantity, i.e. "m^3"). This is a nice study making use of the model runs presented here. However, this section deserves reference to existing works. For example, Rabe et al. (2014, doi:10.1002/2013GL058121 ) do not resolve the seasonal cycle, using data from 1992 to 2012, but instead use a 6-year moving window to weigh data in time and space using an optimal interpolation method. The final interpolated product showed high error for the annual mean estimate of Arctic Basin freshwater content, indicating that shorter than interannual / multi-year variability is not adequately resolved by those observations. IT's at least worth a paragraph of discussion. Again, much work has been done, e.g. by Rabe..., Polyakov... and also Haine... --please cite appropriately here and/or above (see prior comments). plot) from the background state, the "truth", and the optimal interpolation reconstructed state (see legend). 376 As shown in Fig. 13, the sparse in-situ profiles help bring the freshwater content in the background state 377 close to the "truth" state. However, it is not until 2007 that the reconstructed state reproduces the seasonal to 378 inter-annual freshwater content variability in the Canadian Basin, benefiting from the increasing number of 379 research activities and international collaborations. In Fig. 14 The regional selection is somewhat arbitrary --best use either the topographic basin boundaries (e.g. denoted by continental slope isobath and Alpha-Mendeleyev Ridge). The Beaufort Gyre follows dynamics that may show variability in this box that is not related to FW content changes in the whole gyre.  Figure 14. Root mean square errors of freshwater content between the reconstructed state and the "truth". 385 The above results highlight that the increase of hydrographic observations have enhanced our ability to re-386 construct the Arctic freshwater content changes since 2007. A lack of hydrographic observations in the coastal 387 areas results in significant errors in the marginal seas, which require extensive international collaborations. 388

Summary and conclusions 389
Sea level variability reflects changes in ocean dynamics, atmospheric forcing, and terrestrial runoff pro-390 cesses (Stammer et al., 2013). In particular, sea level observations have been applied to infer freshwater content 391 changes (Armitage et al., 2016;Giles et al., 2012;Proshutinsky et al., 2019) in the central Arctic Ocean. To com-392 plement our understanding of the Arctic sea level variability and its mechanisms, we use two high-resolution 393 ATLARC model simulations to investigate the Arctic sea level variability at different timescales and the relation 394 with bottom pressure and thermo/halosteric effects, identifying critical observational gaps that need to be filled. 395 Both the model simulations and mooring observations reveal very high-frequency bottom pressure varia-396 tions. The model simulations confirm that the bottom pressure anomaly is equivalent to sea level anomaly in 397 most areas of the Arctic Ocean at periods <30 days, reflecting the barotropic nature of this high-frequency vari-398 ability. Correlation analyses show that the high-frequency sea level variability is caused by wind-driven Ekman 399 transport and propagations of these barotropic signals. Here we have a mixture of 1--regional observation density in time and space 2--variance of regional observations Due to 1 we would expect high errors on the shelves, whereas due to 2 we see errors in the well-sampled Canada Basin. Please discuss in a couple of sentences....
Number: 2 Author: brabe Subject: Highlight Date: 12/10/2021, 10:38:09 this discussion ignores all the estimates of FW content based on in-situ observations. Please include this in your discussion, as you specifically look at the use of those observations in your analysis. (see my prior comments for references) Arctic Archipelago (Fig. A1d). However, only slight improvements are observed in the central Arctic Ocean, 476 and errors in the Kara Sea are slightly increased. Since we focus on the Arctic freshwater content variability, 477 we use a 1000 km influencing radius throughout this study. 478 479 480 Figure A1. Example of sea surface salinity difference between (a) the background and the truth, (b) the analysis 481 with an influencing radius of 300 km and the truth, (c) the analysis with an influencing radius of 1000 km and 482 the truth, and (d) the analysis with an influencing radius of 2400 km and the "truth". Black dots in panel (a) 483 denote the locations of synthetic observations, sampled using sites of the observations from year 2008. 484