In this study, we use a novel pan‐Arctic sea ice‐ocean coupled model to examine the effects of tides on sea ice and the mixing of water masses. Two 30 year simulations were performed: one with explicitly resolved tides and the other without any tidal dynamics. We find that the tides are responsible for a ∼15% reduction in the volume of sea ice during the last decade and a redistribution of salinity, with surface salinity in the case with tides being on average ∼1.0–1.8 practical salinity units (PSU) higher than without tides. The ice volume trend in the two simulations also differs: −2.09 × 10 3 km 3 /decade without tides and −2.49 × 10 3 km 3 /decade with tides, the latter being closer to the trend of −2.58 × 10 3 km 3 /decade in the PIOMAS model, which assimilates SST and ice concentration. The three following mechanisms of tidal interaction appear to be significant: (a) strong shear stresses generated by the baroclinic clockwise rotating component of tidal currents in the interior waters; (b) thicker subsurface ice‐ocean and bottom boundary layers; and (c) intensification of quasi‐steady vertical motions of isopycnals (by ∼50%) through enhanced bottom Ekman pumping and stretching of relative vorticity over rough bottom topography. The combination of these effects leads to entrainment of warm Atlantic Waters into the colder and fresher surface waters, supporting the melting of the overlying ice.

1 Introduction Over the last decade, the Arctic Ocean (AO) has experienced the strongest reduction in sea ice cover seen over the last century. Since the beginning of the satellite record in the late 1970s, mean sea ice extent has declined in all seasons. The most notable change is in September, with a rate of about 13% per decade (National Snow and Ice Data Center, http://nsidc.org/) [Vihma, 2014]. Sea ice volume has also decreased at a rate of about 2.8 × 103 km3/decade during the period 1979–2011, as estimated from the PIOMAS (Pan‐Arctic Ice Ocean Model Assimilating System) model [Schweiger et al., 2011]. The changes in Arctic sea ice have a strong impact on the ocean circulation in the AO through modification of the dynamical and thermohaline surface forcing of the ocean [e.g., Giles et al., 2012], on the Arctic amplification via ice albedo and temperature feedbacks [Pithan and Mauritsen, 2014], and on weather at lower latitudes and, potentially, on the global climate [Francis and Vavrus, 2012; Screen, 2014]. However, these extraordinary changes in sea ice and subsequent feedbacks on the Earth's climate are neither fully understood nor well simulated in global climate models due to their coarse resolution and because they do not represent all key ocean processes. Since continental shelves make up approximately 50% of the AO area, shelf‐sea processes (such as ocean tides, land‐fast ice‐ocean interactions, coastal currents, downslope cascading, up/downwelling, and eddies) [Nurser and Bacon, 2014] have a substantial influence on the entire AO. These processes are generally not accounted for in either global or regional Arctic models, which do not have sufficiently fine horizontal meshes to resolve the required physical scales and sufficiently high vertical resolution to accurately simulate surface and benthic boundary layers. At present, none of the coupled ocean‐atmosphere general circulation models (OA‐GCMs) used in IPCC AR5 and only a few of the global or pan‐Arctic models participating in the Forum for Arctic Ocean Modeling and Observational Synthesis (FAMOS; http://www.whoi.edu/projects/famos/overview) have sufficient resolution to account for shelf‐sea physical processes. Those that do include FVCOM [Chen et al., 2009] with 1–50 km resolution; the global 1/12° NEMO model [Bacon et al., 2014; Duchez et al., 2014], and the HYCOM Group's contribution (http://hycom.org) [Metzger et al., 2014] with 3–5 km resolution in the AO. Of these, only FVCOM explicitly resolves tides and uses terrain‐following coordinates, which are more effective at simulating dense water cascades and benthic boundary layers. Astronomical tides are strong on the Arctic shelf with M2 amplitudes reaching 4.4 m in the Hudson Strait, 2–3 m in the White Sea and >1 m in the Canadian Archipelago (for geographical names see Figure 1). Holloway and Proshutinsky [2007] reviewed the observational and modeling evidence for the role of tides in the Arctic and presented arguments on why the “omission of tides from climate modeling can be particularly troubling.” They hypothesized that tidal‐induced mixing in the AO plays an important role in the global conveyer belt. Holloway and Proshutinsky [2007] included a parameterization of tidal mixing near‐bottom topography and tidal‐induced divergence‐convergence of ice in a coarse resolution (55 km) coupled ocean‐ice general circulation model, and compared the results with and without tides on decadal time scales. Tidal currents in their study were derived from a barotropic ocean‐ice coupled model with a grid spacing of 14 km [Kowalik and Proshutinsky, 1993, 1994]. The authors showed that the regions of strongest tidal dissipation are located along the western opening to the Barents Sea, above Yermak Plateau and over Eurasian continental shelf slopes in the Barents, Kara and Laptev Seas, thus mapping well onto the pathway of the Atlantic Water (AW) inflow in the AO. They suggested that tides can result in AW ventilation and modification via the mixing of this water mass with overlying polar waters, affecting the Arctic extension of the conveyer belt and potentially changing the Arctic and global climate. Figure 1 Open in figure viewer PowerPoint The NEMO model bathymetry (color) along with a schematic of the upper ocean circulation in the Arctic. Red and magenta arrows show Atlantic Water inflow and pathways of the cooled and freshened modified Arctic Atlantic Water; blue arrows show pathways of the polar waters. The lateral boundaries of the regional model domain are in yellow. FB denotes the Foxe Basin; BI, Bear Island; SB, Spitsbergen; YP, Yermak Plateau; NB, Nansen Basin; and SZ, Severnaya Zemlya. In contrast, comparatively low mixing due to double diffusion processes is found in the Canadian Basin [Padman and Dillon, 1987; Timmermans et al., 2008] and in the Eurasian Basin [Perkin and Lewis, 1984; Anderson et al., 1994; Rudels et al., 1999]. This results in very moderate heat fluxes in the AO (0.05–0.3 W m−2) and cannot explain the observed rate of modification of AW along Eurasian shelf break [Lenn et al., 2009; Polyakov et al., 2012]. Padman and Dillon [1991] first identified tides as the main energy source that supports the enhanced dissipation rate of turbulence over steep topography. This is also supported by recent microstructure measurements of turbulent kinetic energy dissipation [Rippeth et al., 2015]; tidal effects have been found to be capable of generating heat fluxes of more than 35–50 W m−2. To our knowledge, with the exception of a regional study by Postlethwaite et al. [2011], there have been no previous modeling studies that consider the effects of tides on the AO by comparing numerical simulations with and without explicitly resolved tides. Although we note that Koentopp et al. [2005] and Makinson et al. [2011] considered similar issues for the Weddell Sea in the Antarctic. In this paper, we focus on ocean tides and their effects on the hydrography and sea ice in the AO using a novel pan‐Arctic sea ice‐ocean coupled model configuration. The configuration is based on the NEMO model (Nucleus for European Modelling of the Ocean) [Madec and NEMO Team, 2008]. It employs realistic high‐frequency atmospheric forcing from a reanalysis and explicitly simulates tidal dynamics and processes in the benthic and ocean‐ice boundary layers. The model resolution (10–15 km) is internal tide and eddy‐“admitting” (i.e., resolving explicitly large eddies) [e.g., Penduff et al., 2007] in the deep AO, but not sufficient to resolve these on the shelf where the baroclinic Rossby radius is of order 1–7 km [Nurser and Bacon, 2014]. The goal of this paper is to identify key tidal‐driven physical mechanisms that affect mixing and water mass transformation in the AO. While this present study does not examine the role of internal tides in full, it contributes to our understanding of the climate scale effects of tides on the water mass formation and ice evolution in the AO. By exploring key dynamical processes and examining the AO variability on decadal time scales (1978–2007), we demonstrate that tides make a significant contribution to the transformation of Arctic water masses and contribute to the reduction in sea ice. The paper is organized as follows. In section 2, we summarize the effects of tides on mixing in the AO and the observational evidence, and formulate the hypotheses addressed in the study. In section 3, we describe the numerical model and experiments. Results from the tidal simulations are presented in section 4. Section 5 discusses the results of 1 year long simulations, demonstrating the immediate effects of tides, with section 6 expanding to the decadal effects of tides. Section 7 concludes the paper and summarizes the findings of the study.

2 Effects of Tides in the AO: Observations and Hypotheses There is substantial observational evidence of the effects of tides on the hydrophysical fields in the high‐latitude oceans with sea‐ice cover. We separate these effects into four main groups, described in the sections 2.1–2.4. 2.1 High‐Frequency Ice Oscillations High‐frequency fluctuations of ice motion and deformations due to inertial and tidal oscillations were described by Hunkins [1967] and have been identified in drifting buoy data obtained in the AO during summer months [Hibler et al., 1974; Colony and Thorndike, 1980; Pease et al., 1995]. Heil and Hibler [2002] show substantial variability of sea ice at a semidiurnal period during all seasons. Kowalik and Proshutinsky [1994] suggested that the persistent divergence and convergence of sea ice might enhance heat loss from the ocean to the atmosphere, which may in turn lead to increased formation of young ice in the cold seasons. They estimated the young ice formation rate to be 3 cm/d in open leads. Kwok et al. [2003] found a persistent detectable level of oscillatory ice motion in the AO with semidiurnal period in high‐resolution satellite data acquired in winter. They estimated a potential growth of 0.1 m of ice during winter due to the opening and closing of ice. This constitutes approximately 20% of the mean annual basal growth of the thick ice pack in the central Arctic (0.5 m). Padman et al. [1992] estimated the tidal stress divergence at the ice underside as being an order of magnitude greater than the wind stress divergence acting on the top ice surface. Mack et al. [2013] extracted tidal signals from satellite data in the Ross Sea and found tidal amplitudes of ice concentration above 0.2 for diurnal harmonics. Numerical studies (Koentopp et al. [2005] in the Antarctic Ocean and Holloway and Proshutinsky [2007] in the AO) emphasize the competing role of tide‐forced periodic ice divergence: in summertime, the ocean receives higher insolation due to opening/closing of leads, increasing ice melt; in wintertime, the same process leads to growth and ridging of new ice. 2.2 Benthic and Surface Boundary Layer Mixing An increase in shear stress and vertical viscosity/diffusivity in the bottom boundary layer has been commonly observed in strong tidal flows [Robertson et al., 1998]. The presence of ice introduces a second boundary layer at the ice‐ocean interface [e.g., Nøst, 1994]. In the AO, the three most energetic semidiurnal harmonics reach their critical latitudes (hereafter λ cr ), where frequencies of semidiurnal tides equal the inertial frequency (70°58″ for N 2 , 74°28″ for M 2 , and 85°40″ for S 2 ). Observations show that in a water column with near homogeneous viscosity, the tidal current near λ cr becomes strongly depth dependent with strong shear stresses and thick benthic and surface boundary layers [Prandle, 1982; Nøst, 1994; Furevik and Foldvik, 1996; Howarth, 1998]. Observations at the Ronne Ice Front in the Weddell Sea [Makinson et al., 2002, 2006] demonstrated that the combined upper and lower boundary layer in winter can occupy the entire water column within 100–200 km of λ cr . Similar results have been found for the semidiurnal component of currents from observations in the Canadian Arctic in Peel Sound at 73.5°N [Prinsenberg and Bennett, 1989]. These effects are strong even in more southerly latitudes, 1000 km from critical latitudes (in Hudson Bay at approximately 63°N), where differences in tidal and inertial frequencies are about 0.1f. 2.3 Baroclinicity and Internal Tides The baroclinicity of tides relates to both the interaction of stratification with the tidal boundary layers, resulting in seasonal vertical variation in amplitude and phase [Howarth, 1998], and to internal tides. Both mechanisms may contribute to larger tidal shear and enhanced mixing within the pycnocline, although they differ in origin and characteristics. Near the critical latitudes, the Ekman layer tends to span the entire water column in a layer with approximately vertical constant viscosity, K m . Where a pycnocline is present, so K m is depth dependant, an anticyclonic (clockwise in the Northern Hemisphere) component of the tidal current generates an extremely strong shear in the layer of reduced K m [Maas and van Haren, 1987; Souza and Simpson, 1996; Makinson et al., 2006]. Internal tides, generated through interactions between the barotropic tides and bottom topography, result in the vertical displacement of isopycnals. The breaking and shear instability of internal waves also contributes to mixing within the pycnocline [Vlasenko et al., 2003]. Internal waves with diurnal, near‐inertial and quarter‐diurnal periods have been observed near the Yermak Plateau [Padman and Dillon, 1991; Fer et al., 2010], at moorings in the Beaufort and Chukchi Seas [Rainville and Woodgate, 2009; Martini et al., 2014] and in the Canada Basin during the Surface Heat Budget of the Arctic Ocean (SHEBA) Programme [e.g., Pinkel, 2005] and from the Ice‐Tethered Platform (ITPs) [e.g., Dosser et al., 2014]. Internal waves may increase mixing and modification of the AW [Padman et al., 1992; Pinkel., 2005]. In the deep part of AO (about 1000 m), Padman and Dillon [1991] estimated the mean diapycnal heat flux to be about 30 W m−2 above the Atlantic layer core, an order of magnitude larger than that in the surrounding much deeper waters near the Yermak Plateau. Estimates by Fer et al. [2010] for the deep ocean give 15–25 W m−2. Lenn et al. [2011] observed in the shallow, strongly stratified Laptev Sea, a strong tidally induced shear (between 3 × 10−2 and 10 × 10−2 s−1) at the depth of the halocline (20–30 m) and concurrent bursts of intense mixing. They explained these intense bursts of shear and mixing using results from a 1‐D model [Burchard and Rippeth, 2009], where extreme shear was generated when tidal surface currents were aligned with the surface currents, driven by ice motion. Strong baroclinicity of tides and shear in the strongly stratified halocline layer in the eastern Laptev Sea shelf has been detected by Dmitrenko et al. [2012]. They observed sporadic occurrence of a nearly homogeneous layer inside the halocline and consequent reduction of gradient Richardson number. Janout and Lenn [2014] observed an increased dissipation rate at the halocline associated with tides in the Laptev Sea. 2.4 Residual Currents and Rectification Field measurements and laboratory experiments [Vinje et al., 1989; McClimans and Nilsen, 1993] show that the ice floes around Bear Island in the Barents Sea are trapped by clockwise circular motions, which have been explained by Kowalik and Proshutinsky [1995] through the generation of topographically trapped waves and residual circulation (rectification) reaching 8 cm s−1. Rectification refers to the generation of time‐independent currents by tidal flows across depth contours or past coastal headlands [Zimmerman, 2014; Huthnance, 1981]. In the presence of friction at the seabed or an ice interface, periodical motions transfer energy to bottom and ice‐ocean shear stresses with a substantial nonperiodic component and induce a time‐independent component in the Ekman currents. Irregularities in the velocity and bottom shear stresses over a varying topographic relief generate vorticity and vertical motions that result in ageostrophic circulations and either geostrophic upwelling or downwelling of isopycnals. The efficiency of energy transfer from tidal currents to the rectified circulation increases when the characteristic length scales of depth variation match the range of horizontal tidal movement [Zimmerman, 1978, 1980; Loder, 1980; Robinson, 1981] (see also contemporary review Polton [2015]). Kowalik and Proshutinsky [1994, 1995] estimated residual currents of 0.08–0.1 m s−1 in some regions of the Arctic Ocean. MacAyeal [1985] explained the basal melting in the Ross ice shelf through a supply of warmer water by the rectification of currents (as a results of tidal interactions with the topographic and under ice shelf relief). Padman et al. [1992] examining the topographic enhancement of diurnal tides in Yermak Plateau, suggested that rectified along‐slope flow by the combination of cross‐slope tidal currents, planetary vorticity, and bottom friction may explain the filament of the AW current advected clockwise. 2.5 In This Study We Consider the Following Hypotheses Periodic ice motions induced by ice‐ocean shear stresses result in the opening and closing of leads, thus affecting the ice formation and heat fluxes between the ocean, ice, and atmosphere. The clockwise component of tidal currents result in thicker surface and bottom boundary layers and so enhance the exchange between the halocline and the warm Atlantic layer. Critical latitude effects result in strong baroclinicity of tides and generate layers with strong shear in the interior at or below the base of the mixed layer. Residual tidal circulation induced by nonlinear advection or tidal shear stresses leads to intense quasi‐steady vertical motions and contributes to modification of water mass properties. Our model does not resolve internal tides on the shelf, so we restrict our consideration of the baroclinicity of tides to that due to the interaction of boundary layers and stratification.

3 Model Setup and Numerical Experiments We use the NEMO ocean model [Madec and NEMO Team, 2008], which is a nonlinear primitive equation, three‐dimensional model, coupled to the Louvain‐la‐Neuve Ice Model version 2 ice model (LIM2). LIM2 employs Semtner's thermodynamics [Fichefet and Maqueda, 1997] and dynamics with elastic‐viscous‐plastic sea ice rheology (EVP) [e.g., Hunke and Dukowicz, 1997], implemented on a C‐grid [Bouillon et al., 2009]. The global 1/4° configuration of NEMO with LIM2‐EVP has been extensively tested in the FAMOS project to verify model skill in simulating the AO circulation and sea ice [e.g., Jahn et al., 2012; Johnson et al., 2012]. NEMO has been adapted to include shelf‐sea and shelf‐break processes [O'Dea et al., 2012], providing a realistic application to broad tidally active continental shelf regions. These adaptations include a nonlinear free surface formulation with variable volume, mode‐split explicit time stepping, the Generic Length Scale turbulence model [Umlauf and Burchard, 2003], a semiimplicit scheme for bottom friction and generalized vertical coordinates. The global NEMO configuration has a tripolar model grid, with the model poles at the geographical South Pole, in the Canadian Arctic and Siberia, with a “seam” or “north fold” between the latter two. In the regional, pan‐Arctic configuration considered here (Figure 1), we use an extraction of the mesh and topography from the global 1/4° NEMO configuration [Madec and NEMO Team, 2008]. In this model setup, the northernmost part of the tripolar grid is used, with a reindexing of the grid to a rectangular model domain without the “north fold,” thus creating a seamless model grid. As a result, there are two open liquid boundaries: in the Bering Sea, located at 57°N and in the Atlantic Ocean near 48°N (Figure 1). The nominal 1/4° resolution corresponds to 15 km in the central basin, 10 km on the Siberian shelf, and down to about 6 km and finer in the Canadian Arctic Archipelago. The model uses a new generalized hybrid vertical coordinate [Shapiro et al., 2013] with 50 vertical levels: 20 terrain‐following s‐levels in the upper 300 m and 30 partial‐step z‐levels below. The s‐levels are evenly distributed in shallow regions (shallower than 50 m) and stretched in the central water column in deeper water while maintaining high resolution in the upper and lower boundary layers. Vertical mixing in the AO is an order of magnitude smaller than elsewhere in the global ocean, with a significant fraction of total diapycnal mixing in the AO being attributed to double‐diffusive processes that are not currently present in this model. To guarantee the small background vertical mixing (artificial and modeled), we employ the Piecewise Parabolic Method [Colella and Woodward, 1984; James, 2000] for vertical advection for tracers and set a background vertical diffusivity of ∼10−6 m2 s−1. For vertical diffusivity/viscosity parameterization we used (k‐e) model with Kantha and Clayson [1994] structural functions, which we found less diffusive between Generic Length Scale options, available in NEMO module. The lateral mixing is set by a Laplacian geopotential operator and uses the Smagorinsky parameterization. Exchanges of momentum, heat, and freshwater/salt fluxes at the ice‐ocean interface are computed every baroclinic time step, which is 600 s in the model. Initial and open boundary conditions include temperature, salinity, and slow‐varying component of sea surface elevation derived from 5 day mean fields from a global 1/4° NEMO simulation without tides [Johnson et al., 2012]. We add tides by specifying geopotential tidal forcing with 15 constituents and lateral boundary conditions for 9 tidal harmonics (barotropic velocities and sea surface elevations) from the 1/4° resolution inverse tidal model TPX07.2 [Egbert and Erofeeva, 2002]. Surface air‐ice and air‐ocean fluxes are calculated from the Common Ocean‐Ice Reference Experiments (CORE) atmospheric boundary layer formulae [Large and Yeager, 2004] using atmospheric fields from the DRAKKAR Forcing Set v5.1.1 (DFS5.1.1). These are supplied at 3 h intervals and 0.7° spatial resolution [Brodeau et al., 2010]. Climatological (mean seasonal cycle) continental river runoff is used, as described by Barnier et al. [2006]. Two numerical simulations, one with, and another without tides (hereafter “T” and “NT”) are performed. Both the simulations begin on the 15 January 1978 and have a “spin‐up” for 1 year forced with the DRAKKAR Forcing Set (DFS) v4.1 atmospheric forcing [Brodeau et al., 2010]. Then, the integrations continued for 1979–2007 using DFS v5.1.1 forcing. This period is used for the analysis. Water masses of the AO change significantly during the 29 years of simulation, and nonlinear interaction of advection, mixing, currents, and ice formation takes place. This makes attribution of the dominant processes difficult. To isolate the immediate effects of the tides, we consider an additional 1 year long spin‐down model experiment. In this experiment, the model is run for 1 year (1978) with tides and then run through 1979 without tides. The tidal energy completely dissipates after a month and then we compare the results with the original solution with tides for 1979. We use these to explore the four hypotheses identified in section 2.5.

5 Effects of Tides on the Arctic Upper Ocean and Ice on Seasonal to Annual Time Scales To examine the integrated effects of tides on ice and ocean on the seasonal to annual time scales, we analyze year long runs with and without tides in 1979. We spin‐up the model over 1978 with tides for both runs; then, in one of the runs, tides are turned off and dissipate over a day‐month time scale, for simplicity we again use “T” and “NT” to identify these runs. Figure 10 shows the differences in properties between T and NT integrated over the AO under ice cover, where the concentration of ice is larger than 0.1. There are no significant changes in ice volume during the T and NT runs until April (Figure 10a). It is only then that the difference starts to grow, reaching around 6% in September and December, with a 2–5 cm reduction in the mean ice thickness. There are also changes in the turbocline depth (Figure 10b) at the start of winter, but these only become prominent during the next cold period, November–December 1979 (5% of total; mean depth difference of 1 m). Figure 10 Open in figure viewer PowerPoint (a) Ice volume with time for T and NT simulations; (b) mean turbocline depth below the ice cover; (c) differences in heat fluxes between T and NT integrated below the ice cover: solar radiation, ocean to ice (OI) heat flux, and upward total nonradiative heat flux to ocean; (d) relative changes in the mean concentration, ice extent, and ice volume between T and NT simulations under the ice cover; (e) downward and upward cumulative vertical Ekman bottom mass fluxes under the ice cover and difference between T and NT cases; and (f) the same for the surface boundary layer. The difference in the total nonsolar heat flux from the water and in the heat flux from ocean to ice is negligible, except in December 1979 (Figure 10c). Hence, we conclude an increase in heat flux from the ocean to atmosphere due to opening/closing of polynyas and leads is relatively small in this model. This is not surprising given that the model's comparatively course resolution does not resolve polynyas. However, the ice model is capable of generating grid‐scale tidal variations in ice concentration (see section 4.1), thus, some effects of leads/polynyas are present in the model. In wintertime, the heat flux from the ocean to ice (OI) increases in the T run by ∼5% in January–March (+20–30 × 1012 W compared with 400–600 × 1012 W in total) and 10–12% in November–December (+50 × 1012 W compared with 400–600 × 1012 W in total) (Figure 10c). In summer, the incoming solar radiation gained by the water increases by up to 5% in run T with a peak in May (Figure 10c). This leads to a small decrease in ice extent by 1% in June (Figure 10d) and mean ice concentration by 0.01 (Figure 10d). A much larger decrease in ice volume is also seen, by up to 3% in July–September, with a peak of 6% in September, and a general trend of 3.9%/year. The former is explained by a secondary peak in the heat flux from the ocean during July in run T, following a peak in the difference in solar radiation flux between T and NT simulations in spring to early summer (Figure 10c). As a consequence, an opening and closing of ice takes place, resulting in an increase in the fraction of open water in summer and a decrease in the albedo in the T simulation. These effects have been discussed by Koentopp et al. [2005] in their modeling study of the Weddell Sea, where they found that a “combination of lower ice concentration, i.e., mainly enhanced absorption of radiation, and additional entrainment of warmer waters into the mixed layer by tidal currents, are responsible for an accelerated melting process in spring and a retarded expansion of the ice cover in early fall.” In section 4.3, we discussed the sources of persistent quasi‐steady motions induced by tides through surface and bottom Ekman pumping in the base of the boundary layers and internal sources due to nonlinear stretching of tidal vorticity over bottom topographic anomalies. To estimate the net role of quasi‐steady vertical motions, produced by tides, we calculate net upward and downward bottom Ekman mass fluxes separately, following equation 1. Figure 10e shows the integral near‐bottom Ekman mass fluxes for T and NT runs and their difference (under ice cover), using shear stresses averaged over 3 days. Upward and downward bottom mass fluxes are of the same order for each simulation, but with a net upwelling, and these exhibit strong seasonal and synoptic variability (the latter is evident from the NT run, green and red curves). The difference in the mass fluxes, due to tides, reaches 50% and is well correlated with the heat flux difference. Periodic oscillations in the mass fluxes of 14.04–14.6 days (roughly 25–26 oscillations per year) are also evident, which are absent in NT simulations. This period is close to = 14.35 days, the period of low frequency M2–S2 interaction (i.e., the spring‐neap tidal variation), as both constituents contribute to the bottom shear. There are no significant differences in the area average subsurface Ekman mass fluxes in T and NT simulations (Figure 10f), but local differences may well be important (not shown here). At the base of the surface boundary layer, downwelling Ekman pumping under the ice dominates over upwelling by 2 Sv. This is consistent with the general anticyclonic atmospheric circulation over the AO [Proshutinsky and Johnson, 1997]. Conversely, the situation is reversed at depth, where bottom Ekman pumping exhibits a net upwelling of 0.6 Sv. The surface Ekman pumping is acting over the entire basin, since it relates to the atmospheric circulation, while bottom shear stresses are prominent only over the shelf and slope, where bottom currents are strongest. Thus, the upwelling generated by bottom shear stress over varying topographic relief is amplified by 40–50% by tides and results in the penetration of AW into the surface layer. After a year of simulation, the effects of tides lead to a decline in ice thickness of ∼0.05 to ∼1 m almost everywhere, except Baffin Bay (Figure 11a) and corresponds to a much deeper turbocline depth (TD) (Figure 11c). The strongest reduction in ice thickness is observed around Spitsbergen (Svalbard), north of Greenland, in the Laptev Sea, Foxe Basin, and Canadian Archipelago. These changes are well correlated with both the spatial pattern of OI heat flux increase and the decrease of turbocline depth (Figures 11b and 11c). The OI heat flux increases by 10–30 W/m2 near the Yermak Plateau and Storfjord Channel; the former is in agreement with the observations of Padman and Dillon [1991] and Fer et al. [2010]. Comparing this with Figure 9a, we find that locations of intense vertical bottom Ekman pumping correspond to locations of increased OI heat flux and TD variation. Figure 11 Open in figure viewer PowerPoint (a) Ice thickness difference in T and NT simulations after a year of simulations in December 1979; (b) ocean to ice heat flux difference OND 1979; and (c) turbocline depth difference, December 1979. Contours show ice concentrations (0.15, 0.75, and 0.9). Tides intensify quasi‐steady vertical motions and mixing in the Fram Strait which produce changes in the AW inflow properties (Figures 12a and 12b). Monthly mean (December 1979) temperature and quasi‐steady vertical velocity on the transect C (shown in Figure 9a) are mostly the same in the Barents Sea, while across Fram Strait, there are intense vertical motions in both the warm core (off Spitsbergen coast) and the cold core (from Greenland side). The Atlantic core in the T run is much closer to the surface and intense vertical motions (>10−5 m s−1) penetrate to depths of 10–20 m from the surface. Figure 12 (bottom) demonstrates the increase of vertical diffusivities in T run versus NT case in the Atlantic layers by up to 2 orders and by 2–10 times in the most of pycnocline regions. This figure is a good illustration of the interaction between two mechanisms capable of transforming water masses: increased mixed layer depth due to tidal shear and thick Ekman depth (2.2) and vertical motions associated with tidally driven residual currents (2.4). Figure 12 Open in figure viewer PowerPoint (a, b) Monthly mean temperature and vertical velocity for T and NT simulations for the transect C shown in Figure 9a; dashed line: −1 × 10−5 m s−1 and solid line: 1 × 10−5 m s−1. (c) The ratio of monthly mean vertical diffusivities A., in T and NT simulations in logarithmic scale (December 1979). Contour shows temperature for T simulations and dashed lines denote negative values. Transect D is located north of transect C (see Figure 9 for location) shows the effects of ice‐ocean shear stresses on the formation of quasi‐steady vertical motions and tidal coupling between the surface and bottom layers (Figure 13). The area of intense vertical motions is located above the north side of the Yermak Plateau and extends from the bottom (depth of 800–1000 m) upward to a depth of 200–300 m. The maximum vertical velocity reaches 1–2 × 10−4 m s−1 at a depth of 300–400 m (not shown here). These large vertical velocities can be formed by the vorticity stretching of the tidal currents (Figure 9d). In October (Figure 13a), ice just starts to form, and there is little vertical motion in the subsurface layer at this location. With ice forming during November and December, the appearance of vertical motions in the subsurface upper layer becomes evident (Figure 13b) and is collocated with intense vertical motions in the deeper layer, which are absent in NT simulations (Figure 13c). We attribute the formation of strong subsurface vertical motions in December to the appearance of the second solid boundary at the surface and hence the generation of vorticity by ice‐ocean shear stresses. In December, we detect substantial changes in AW due to tidal effects. Figure 13 Open in figure viewer PowerPoint Monthly mean temperature and vertical velocity for the transect D shown in Figure 9a. (a, b) T simulations for October and December, (c) NT case, December (−1; −0.5; 0.5; 1) × 10−5 m s−1. Vertical velocity contours are shown and dashed lines denote the negative values.

6 Multiyear Effects of Tides on Ice and Ocean The 1 year simulations with and without tides, discussed in section 5 demonstrate prominent changes due to tides. Here we consider the effects of tides integrated over three decades (1978–2007). The 30 year T and NT simulations both show a negative trend in September sea ice volume (month of minimum ice volume, Figure 14a), but with a significantly stronger decrease in the T simulation: ∼2.49 × 103 km3/decade compared with 2.09 × 103 km3/decade in the NT simulations. During March (the month of maximum ice volume), over this period, the negative trend increases to −2.54 × 103 km3/decade in T case and decreases to −2.05 × 103 km3 in NT simulations. In total, tides are responsible for about 15–17% of the modeled ice volume reduction (Figure 14a) by the end of 30 year simulations, with an average difference over this period of ∼11%. We have performed four additional simulations with different “ice strength” parameter, P*, in the range: 1 × 104 to 2 × 104 N m−2. In all these simulations, the rate of ice volume reduction differs slightly, but with the same effect of the tides being apparent: tides accelerate the ice volume decrease by 12–17% over 30 years. Figure 14 Open in figure viewer PowerPoint (a) Ice volume anomaly in September over 30 years of simulations for T and NT runs and IC‐SST PIOMAS simulations; (b) ice volume in September 2007; (c) ice volume difference between T and NT simulations in September 2007; (d–f) SSS winter (March–April) 2007 for NT and T simulations and their difference (T) − (NT); and (g–i) the same as Figures 14d–14f but for September 2007; Figure 14d also shows domain for calculations of mean salinity and heat content, Figure 14g shows the region of fresh water content calculation as in Jahn et al. [2012], in Figure 14e location of main rivers are shown. Schweiger et al. [2011] compared ice volume anomalies for three different PIOMAS simulations with different ice models: with assimilation of ice concentration and SST (IC‐SST run), ice concentration assimilation only (IC), and without any assimilation (NA). Their model was run from 1958 to 2010, with a comparison period from 1979 to 2010. All these simulations showed good statistics for ice thickness compared with submarine‐based sonar measurements. They found ice thickness trends to be −0.15, −0.19, and −0.20 m decade−1 in March and −0.25, −0.33, and −0.37 m decade−1 in October for IC‐SST, IC, and NA runs, respectively. For ice volume anomaly, PIOMAS gives trends of (−2.8, −3.5, and −3.8) × 103 km3/decade, respectively, with estimated uncertainty to be 1 × 103 km3/decade. For March, our study predicts ice thickness trends −0.146 and −0.124 m decade−1 for T and NT simulations, respectively. The equivalent rates for October are − 0.230 and −0.194 m decade−1. The T run is very close to the IC‐SST estimate both for ice volume (−2.53 × 103 versus −2.8 × 103 km3/decade) and thickness (−0.146 versus −0.15 m decade−1 in March and −0.230 versus −0.25 m decade−1 in October, respectively) and in the range of the uncertainty of the mean value (−3.4 × 103 km3/decade) of the three PIOMAS runs. Thus, including tides in the model increases the downward trend in the sea ice volume and therefore improves the agreement with PIOMAS. However, PIOMAS trend takes into account the faster decline of ice during 2008–2010, whereas our model stops in 2007. Recalculating the IC‐SST PIOMAS ice volume trend for the period of 1979–2007 in September, as shown in Figure 14a, demonstrates an even better agreement with T runs: IC‐SST PIOMAS: −2.58 × 103 km3/decade versus T simulations: −2.49 × 103 km3/decade and NT simulations: −2.09 km3/decade. While our model here overestimates total ice volume compared with PIOMAS, it predicts the trends well. Thus, including tides reduces the error in ice volume and ice thickness trend from 20% (NT) to 4% (T). The ∼10% excess ice volume is a common bias in this configuration with the LIM2 model [e.g., Popova et al., 2013]. It is caused by using sea ice thermodynamics with a simplified sea ice thickness distribution function, which assumes that the ice thicknesses is uniformly distributed between zero thickness and twice the mean ice thickness value in the ice‐covered part of model the grid cell [Fichefet and Maqueda, 1997]. The bias is not detrimental for the present analysis. Spatial differences between the T and NT runs in September (ice extent minimum) in 2007 (Figure 14c) show a decline of ice thickness of generally 20–50 cm and up to 1 m in the Canadian Archipelago. Tides significantly change the surface salinity on multidecadal time scales; on average surface salinity at the end of the 30 year run is ∼1 PSU higher across the whole model domain (including Atlantic and Bering Sea regions) in the tidal case and 1.8 PSU higher across the deep (>500 m) part of the AO (see domain in Figure 14d) with anomalies reaching 8 PSU (Figure 14f). The surface salinity exhibits strong annual variability with the differences of about 2 PSU between winter (March–April, Figures 14d and 14e) and summer (September) (Figures 14g and 14h). In winter, the spatial mean difference between T and NT run reaches a maximum of 2 PSU, decreasing to 1.46 PSU in September and 1.3 PSU in January. A further decrease of surface salinity in the deeper part of the basin is as a lagged response to the signal from fresh river runoff. In both simulations, surface salinity decreases with time, but the rate of decrease is lower in the tidal case. For both the T and NT simulations, we calculate the mean 1992–2001 total liquid freshwater content (FWC) in the upper 250 m of the Arctic Ocean for the area marked in Figure 14d. Hereafter, all the FWC calculations are referenced to the mean Arctic salinity of 34.8 PSU. In these runs, FWC is similar, being 69 × 103 and 70 × 103 km3, respectively, for T and NT, and is in a good agreement with the FWC of 74 × 103 km3, obtained by Jahn et al. [2012] from the University of Washington Polar Hydrography Center (PHC) climatology [Steele et al., 2001]. Our results are also within the FWC range of 56 × 103 to 87 × 103 km3, simulated in the Arctic Ocean Model Inter‐comparison Experiment (AOMIP) [Jahn et al., 2012, Table 3]. Differences in the AOMIP models are due to differences in model physics and resolution [Jahn et al., 2012]. Spatial distribution of the fresh water in our simulations is similar to the global ORCA25 AOMIP simulations and climatology [cf. Jahn et al., 2012, Figure 2a]. Similar to most of the models in Jahn et al. [2012], T and NT runs show a high FWC in the Beaufort Sea, in agreement with observations in the 1990s from Proshutinsky et al. [2009] and Rabe et al. [2011]. The differences in spatial distributions of FWC between T and NT runs are much smaller than the spread in the AOMIP models. In the upper layer (0–100 m), the freshwater content (calculated in the rectangle shown in Figure 14d) exhibits natural variability in phase with the atmospherically forced circulation [e.g., Proshutinsky and Johnson, 1997]. It is, however, lower in the T case than NT by 6–7% in 2007 (36.3 × 103 versus 42.26 × 103 km3 NT) partly at the expense of the intermediate layer of 100–500 m depth, which gains 1.81 × 103 km3 more freshwater in the T case (18.4 × 103 km3 in T versus 16.6 × 103 km3 in NT). Thus, a deficit of 1.06 × 103 km3 of freshwater in the upper 100 m in the tidal case can be explained by changes in shelf‐deep ocean exchange or by exchange with the Atlantic Ocean. Indeed, in Figures 14d and 14g, we see a longer tongue of freshwater outflowing along the East Greenland coast. The deep AW layer (500–1000 m) in the AO continuously freshens, but with a weaker trend in the tidal case (1.29 × 103 km3 less freshwaters in T than NT over 30 years) with little change to the salinity in the deepest layer (1000–4000 m). Adding tides also result in strong changes in the surface freshwater signal along the East Siberian coast (Figures 14d–14i). The surface freshwater signal from the Lena and Yenisey estuaries propagates counter clockwise with increased salinity along the coastline and shelf break, and a negative salinity anomaly in the outer part of the Canadian Basin. Tides result in the dilution of riverine freshwater with surrounding saltier waters, which changes stratification, baroclinic pressure gradients and modifies the surface circulation in AO. In the NT case, the fresh water signal penetrates much further to the south along the east Greenland coast in comparison with the tidal case (Figures 14d and 14e). The origin of the salinity anomaly signal is very well correlated with tidally increased shear in the intermediate layers, as shown in Figure 6. As shown previously by Holloway and Proshutinsky [2007], we also find that tidal effects slow down the strong warming trends in the central AO that are seen in many ocean models. However, we find a weaker effect in the current model than reported by Holloway and Proshutinsky [2007]. Surface to seabed depth integrated heat content trend (calculated in the rectangular box shown in Figure 14d relative to temperature 0°C) in our model is positive, reducing from 6.3 × 1020 J/year in NT case to 5.7 × 1020 J/year in T. In the upper 100 m, heat content (negative due to average negative temperature) grows in the upper 0–100 m layer from −0.3 × 1022 to −0.05 × 1022 J in T case and from −0.3 × 1022 to +0.062 × 1022 in NT case with about a 30% difference in trends. The strong changes in the water mass properties in the AO due to tidal effects can be seen in transects of yearly mean salinity and temperature in 2007 (Figure 15) for T and NT. Transect A (location shown in Figure 6b) crosses the entire AO near the Pole from the Greenland coast to the East Siberia Sea. Similar to the results of Holloway and Proshutinsky [2007], which demonstrate a cooling of the AO in the comparison with nontidal simulations, our model predicts a thinner AW layer and a much colder and saltier upper 100 m in run T compared with NT. Near the Pole, a colder saltier core forms in the upper 100 m in the T run (see also Figure 14e). Figure 15 Open in figure viewer PowerPoint Yearly mean temperature and salinity along transect A shown in Figure 6b for simulations with and without tides. Figure 16 shows yearly mean temperature and salinity in the transect B (location marked in Figure 6b), which crosses the Eurasian shelf and the Barents/Kara Seas openings, intersecting three areas of potential tide‐induced Ekman bottom vertical pumping (see Figure 9a, in Figure 16 these zones are marked by arrows). In general, AW in the AO is colder and shallower in T simulations than in NT. We find the T case is characterized by much sharper isotherms and isohalines with multiple outcroppings from the surface to the bottom at the locations of strong tidal vertical Ekman pumping. Outcroppings of isopycnals in the NT case also take place but are shallower and never reach the seabed. Figure 16 Open in figure viewer PowerPoint The same as Figure 15 but for transect B. Arrows mark the areas of strong vertical bottom pumping due to tides (see Figure 9a). These results are relevant to the results from section 5, where we find that tidal effects are particularly important on the ocean to ice heat fluxes, with a much smaller effect on the ocean‐atmosphere exchange. Since ice melting is stronger in the tidal simulations, but the surface salinity is higher, we conclude that tidally induced mixing is a more important effect than ice formation due to the convergence‐divergence of ice. This is not surprising given the comparatively coarse resolution of the model.

7 Conclusions In this work, we have explored four hypotheses (A–D), formulated in the introduction (section 2.5). Hypothesis (A) considers the role of opening and closing of leads, produced by tidal convergence‐divergence, on the heat exchange between ocean and atmosphere and ice production. Our model reproduces the tidal motions of ice, tidal stresses, and levels of ice concentration variability that are consistent with available observations (section 4.1). We have found that in this particular model (NEMO/LIM2) and with this particular resolution (10–15 km), the open and closing of leads affects heat exchange with the atmosphere: however, the sign of this flux differs between the summer and wintertime. In summer, this process reduces the net surface albedo, resulting in an increase in short‐wave radiation flux to the ocean, while in winter, there is an increase in heat loss (long‐wave, sensible, and latent heat fluxes) from ocean to atmosphere (see Figure 10). However, these changes in heat fluxes are secondary in comparison with the net increase in heat flux from ocean to ice, resulting in the acceleration of ice decline due to tides. We note that the magnitude of this effect will be subject to improvements in model resolution and in ice model physics (e.g., embedding of ice in the ocean, using a multicategory ice model, and including ice‐ocean roughness drag variability). Hypotheses (B) and (C) both consider the role of tidal shear at latitudes close to critical. In section 4.2, we demonstrate that, in accordance with the theory and observations, anticyclonic (clockwise) component of tidal current generates very thick boundary layers in a weakly stratified fluid (point X in Figure 7) with nearly constant shear in the water column. In contrast in strongly stratified layers, very strong shear is generated at or below the base of the mixed layer (Figures 6d–6f). The areas of strong shear for M2 and S2 harmonics are situated in the Laptev Sea and near the entrances to the Arctic Ocean, Yermak Plateau, and the Barents Sea (see Figures 6b and 6c). The locations, variability, and the form of the tidal profiles are consistent with observations in the Laptev Sea [Dmitrenko et al., 2012; Lenn et al., 2011; Janout and Lenn, 2014]. These studies considered different hypotheses for the sporadic increase in mixing in intermediate strongly stratified layers: ice‐tide interaction, spring‐neap tidal shear enhancement, and interaction with mean currents. Our multidecadal simulations reveal some of the strongest tidal effects on the AO circulation in the Laptev Sea (Figure 14), where mixing of fresh water river runoff with ambient saltier waters results in the modification of water masses. Another important region of tidal mixing effects is the Yermak Plateau north of Svalbard, where internal tides of diurnal, semidiurnal, and quarter‐diurnal periods have been observed [Padman and Dillon, 1991, 1992; Fer et al., 2010]. Our model does produce strong shear in this region, which cannot be explained by internal tides. Internal tides at latitudes above critical are thought to have properties of nonlinear mixed lee waves with the length scales of about 1.5 km [Vlasenko et al., 2003], which are not resolved by this model. In these simulations, we find the strongest changes in the turbocline depths, ocean to ice heat flux and resulting changes in the ice thickness both in the short‐term (see Figure 11) and the long‐term (Figure 14) simulations occurring between the critical latitudes of M2 and S2. In hypothesis (D), we suggested that rectified tidal currents can significantly affect water mass exchange and ice in the AO. Typically being localized over variations in topographic relief, this process is characterized by intense quasi‐steady vertical motions of isopycnals that can push warm AW toward the surface or bottom boundary layers and cause further entrainment of AW into the mixed layers. The regions of strongest bottom vertical Ekman pumping resulting in geostrophic motions of isopycnals and ageostrophic quasi‐steady motions due to tidal vorticity stretching correspond to the gateways of AW to the Arctic Ocean and concentrate at the shelf break regions (Figure 9) and colocate with the regions of strong tidal shear. In the 1 year runs with and without tides, we find that tides are responsible for an increase in the magnitude of the vertical displacement of isopycnals by 50% near the seabed (Figure 10e). The model also demonstrates stronger vertical monthly mean motions in the tidal case (Figures 12 and 13). When ice forms, additional tidal‐induced surface Ekman vertical motions arise at the ice‐ocean interface, due to horizontal variations of tidal currents and ice‐ocean shear stresses over rough topography (see Figure 13). Polyakov et al. [2012] and Lenn et al. [2009] argue that observed transformation of AW along Eurasian shelf break could not be explained by relatively low double‐diffusive mixing. Rippeth et al. [2015] observed an enhanced dissipation rate of turbulent kinetic energy in several isolated locations: in the vicinity of the Yermak Plateau and above the shelf‐break of the Laptev and East‐Siberian Seas. That study suggested tides as a main mechanism for the turbulent energy dissipation. All the observed regions in the above studies were characterized by steep seabed topography, and the high level of dissipation rate was strongly correlated with the bathymetric slopes and tidal dissipation rates. Therefore, it has been proposed that short and nonlinear internal tides are responsible for the enhanced turbulence and dissipation rate. While our model does not resolve internal tides, these locations (Yermak Plateau, shelf‐break of the Laptev Sea and Siberian Seas) correspond to the area of both strong shear in the tidal currents (Figures 6b and 6c) and tidally induced quasi‐steady vertical motions (Figures 9c and 9d). A combination of these effects could provide an alternative mechanism (to internal tides), explaining the strong modification of Atlantic Waters along the Eurasian shelf break. Comparing the long‐term simulations with and without tides shows stronger fronts, relatively colder AW, sharper isotherms/isohalines and outcropping of isopycnals in the simulation with tides at the locations of strong vertical bottom Ekman pumping. These processes, i.e., thicker mixed layers, lateral and vertical rectified currents, concentrated at the shelf break can significantly modify shelf edge‐deep ocean exchange, including dense water cascades, modification of AW by cold and saltier Barents Sea waters, and cascading processes. Simulations with tides (see Figure 16) show significantly colder, and slightly fresher near‐bottom waters across the Barents and Kara Sea shelves. The observed locations of cascading [Ivanov et al., 2004, Figure 32] correspond to the locations of vertical bottom pumping and tidally induced rectified currents, shown in Figures 9a–9d. We conclude that tidal shear stresses at the bottom and the ice‐ocean interface facilitate the transport of warmer and saltier AW to the surface layers, while the effects of tides along the Siberian shelf result in mixing of fresh river runoff waters with saltier water below the eroding halocline. Mixed layers, being much thicker due to the effects of the critical latitude on the clockwise component of tidal currents, entrain saltier waters to the surface boundary layers. Along the Siberian coast with strong river runoff, thicker boundary layers result in mixing in halocline and penetration of freshened waters to depth. Finally we find that, in this particular model, tides are responsible for ∼15% of the ice volume reduction and the presence of more salt waters at the surface in average by ∼1–1.7 PSU (Figure 14). Tides significantly modify the freshwater pathways along the Siberian shelf, resulting in saltier water along the Greenland coast. Tides affect the fresh water and heat content in the AO, with a reduction in the former by 7% in the upper 100 m. Some coarse resolution global ocean models already include the effect of unresolved tides [e.g., Canuto et al., 2010] through the application of the Monin‐Obukhov law in a stratified fluid, and shear stresses and enhanced bottom drag calculated from tidal velocities. However, the Monin‐Obukhov law does not contain the inertial and tidal frequencies as governing parameters. Our study shows that effect of tides on mixing and mixed layer depths is strong at high latitudes near to the critical latitudes of semidiurnal tides. Similar effects are also observed at midlatitudes near to the critical latitudes of diurnal tides (∼30°). Souza [2013] has explored a way to parameterize the effects of thick Ekman layer depth on the clockwise component of currents (i.e., combined effect of rotation and tidal frequency) and stratification on the water column structure in shallow shelf seas. However, the accurate representation of mixing processes in global models requires additional efforts to develop observation‐based or model‐based parameterization of mixed layer in the tidal seas. In principle, the effect of baroclinic tides can also be accounted for in coarse resolution models by incorporating seasonally calculated 3‐D amplitudes and phases of tidal shear from a fine‐resolution tidal baroclinic model into the mixing parameterization. Moreover, several of the climate models under development for future IPCC assessments have similar resolution to that used in the present study. For example, the ocean component of the new UKESM1 model uses the 1/4° global model that forms the basis for the model used in this study. This opens the possibility for tidal effects to be simulated directly in coupled ocean‐atmosphere climate models, accepting the need to explore their impact more widely than the AO in such a model. In summary, this study demonstrates that including tidal dynamics has an impact on the sea ice and water masses in AO and improves the modeling of the current state of the Arctic sea ice. This study provides evidence that including key shelf‐sea physical processes, currently absent in climate models, either explicitly or as parameterizations will improve the fidelity of the forward simulations and, therefore, increasing our confidence in future climate projections.

Acknowledgments The authors thank Laurie Padman (Earth and Space Research) and anonymous reviewers for their very important and valuable comments that allow us significantly to improve this paper. The authors acknowledge the National Capability funding provided by the UK Natural Environment Research Council (NERC) and the NERC Ocean Acidification Programme (ROAM, NERC grant NE/H01732/1). The study is also a contribution to the TEA‐COSI Project of the UK Arctic Research Programme (NERC grant NE/I028947/), the Forum for Arctic Ocean Modeling and Observational Synthesis (FAMOS), funded by the National Science Foundation Office of Polar Programs, awards PLR‐1313614 and PLR‐1203720. Model data from this work will be made available from the British Oceanographic Data Centre (BODC, http://www.bodc.ac.uk/). The ORCA simulations use as a boundary and initial conditions were completed as part of the DRAKKAR collaboration [Barnier et al., 2006]. We also acknowledge the use of the UK National High Performance Computing resource.

Appendix A: Estimate of the Mean Ice Tidal Shear Kowalik and Proshutinsky [ 1994 D, of ice velocity as a measure of ice cover deformation expressed through the tensors of horizontal tension/compression strain rate D T and of shear strain rate D S . (A1) ] proposed to use a maximal shear,, of ice velocity as a measure of ice cover deformation expressed through the tensors of horizontal tension/compression strain rateand of shear strain rate D2 over all n = (1:m) harmonics: (A2) x n } denote averaging of variable, x n , over tidal period, T n , n denotes a tidal constituent. In the curvilinear coordinates (A3) e 1 and e 2 and are horizontal scale factors in the x and y directions of coordinate system and u, v are the components of velocity. Substituting the expressions for tidal velocities: t is time, is frequency of tidal constitute, φ u , φ v are phases of the velocity components) to (A1), (A2) and integrating over tidal period 2π/ω we get the expression for the mean squared ice velocity shear: (A4) However, from their paper, it is not clear how they estimated the integral effect over all the tidal harmonics. In this study, we estimate mean maximal ice velocity shear by the summation of tidal meanover all n = (1:) harmonics:where curled brackets {} denote averaging of variable,, over tidal period,denotes a tidal constituent. In the curvilinear coordinateswhereandand are horizontal scale factors in theanddirections of coordinate system andare the components of velocity. Substituting the expressions for tidal velocities:(whereis time,is frequency of tidal constitute,are phases of the velocity components) to (A1), (A2) and integrating over tidal periodwe get the expression for the mean squared ice velocity shear:

Appendix B: Equations for Mean Ocean Velocity, Vorticity, and Estimates of Tidal‐Induced Vertical Motions in the Tidal Sea B1. Equation for Mean Velocity in the Tidal Seas τ and t denote “mean” and tidal components, respectively, {} denotes averaging over tidal period T. Averaging the equations of motion over tidal period we obtain (B1) f is a Coriolis parameter, KE = (u τ 2 + v τ 2)/2 and KET = {u t 2 + v t 2}/2 are kinetic energy of the mean and tidal currents, DIFF H denotes lateral mixing term, K m and K mt are time mean and fluctuating components of vertical turbulent viscosity, is the unit vector in vertical direction, η is surface height, P is baroclinic pressure, f is Coriolis acceleration, and is horizontal gradient operator. Additional terms I and II are the effects of tidal Reynolds stresses: due to vorticity, generated over topographic anomalies and the potential term. Terms III and IV are the effects of tidal shear and tidally induced mixing. Mean diffusivity K m itself contains tidally induced component due to enhance of shear production of turbulent kinetic energy due to tides. Let us decompose velocity components in to the slow‐varying (synoptic, seasonal, etc.) and high‐frequency tidal components of motion:where subscriptsanddenote “mean” and tidal components, respectively, {} denotes averaging over tidal period. Averaging the equations of motion over tidal period we obtainwhereis a Coriolis parameter,= ()/2 and= {}/2 are kinetic energy of the mean and tidal currents,denotes lateral mixing term,andare time mean and fluctuating components of vertical turbulent viscosity,is the unit vector in vertical direction,is surface height,is baroclinic pressure,is Coriolis acceleration, andis horizontal gradient operator. Additional terms I and II are the effects of tidal Reynolds stresses: due to vorticity, generated over topographic anomalies and the potential term. Terms III and IV are the effects of tidal shear and tidally induced mixing. Mean diffusivityitself contains tidally induced component due to enhance of shear production of turbulent kinetic energy due to tides. (B2) C db is seabed drag coefficient and is the density of water. At the bottom of the ocean, the boundary conditions for velocity are set by a quadratic friction law (in this particular model with an asymptotic of the logarithmic boundary layer):whereis seabed drag coefficient andis the density of water. is correspondingly: (B3) u i = u iτ + u it is ice velocity, which contains both tidal u it and slow‐varying components u iτ , is the drag coefficient between sea ice and ocean, subscript “s” denotes surface values. Tidal mean ice‐ocean and bottom shear magnitude and direction cannot be found analytically in a general case. At the ice‐ocean interface, shear stressis correspondingly:whereis ice velocity, which contains both tidaland slow‐varying componentsis the drag coefficient between sea ice and ocean, subscript “” denotes surface values. Tidal mean ice‐ocean and bottom shear magnitude and direction cannot be found analytically in a general case. B2. Equation for the Mean Vorticity and Estimates of Tidal‐Induced Vertical Motions Gill, 1982 (B4) Similarly, using the equation of vorticity [see e.g.,] and again decomposing variables into tidal and mean (i.e., slow‐varying component) components we get in comparison with planetary, and smallness of the mean component of current in comparison with the tidal component, we get the equation for the estimation of vertical velocity: (B5) (B6) (B7) In a steady state case on an f‐plane and with assumptions of smallness of time‐mean relative vorticityin comparison with planetary,and smallness of the mean component of current in comparison with the tidal component,we get the equation for the estimation of vertical velocity:where in absence of tides, the left‐hand side corresponds to the Ekman balance at steady state. Terms I–III are production terms due to advection of relative vorticity of tidal currents, stretching and tilting of horizontal relative vorticity into vertical, IV is tidally induced Ekman pumping term. Term IV is important only near seabed and at the ocean‐ice boundary layers and gives the following estimates of vertical velocity production. Integrating over the Ekman bottom and surface depth, we get the Ekman vertical fluxes to the interior: (B8) (B9) (B10) Estimates of tilting and stretching terms are (B6)–(B10) are only approximations of the actual strength of vertical motions, or production terms of vertical velocity. However, tidally induced persistent vertical motions can be reconstructed using, for example, omega‐type [Sanz and Viúdez, 2005; Giordani et al., 2006] or Sawyer‐Eliassen [Clayson et al., 2008] semigeostrophic equations with corresponding tidally induced source terms included on the right‐hand side of the equation. B3. Estimates of Vertical Velocity Induced by Stretching Term as (B11) Let us estimateas Substituting to (B11) expressions for tidal velocity as (B12) We get Finally, is found as a sum of all tidal harmonics.