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The impact of internal tide mixing parameterizations in an eddy-permitting model of the Arctic Ocean Epstein, Jacquie-Lee 2018

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The Impact of Internal Tide MixingParameterizations in anEddy-Permitting Model of the ArcticOceanbyJacquie-Lee EpsteinB.Sc., The University of Alberta, 2015A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Oceanography)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)April 2018c Jacquie-Lee Epstein 2018AbstractThis study considers the impact of enhanced ocean mixing due to the breaking of internal tideson model state in an eddy-permitting numerical model of the Arctic Ocean. The impact of twoenhanced tidal mixing parameterizations each with di↵erent vertical dissipation profiles based onPolzin [2009] and Jayne and St Laurent [2001], respectively, are compared in contrast to a controlrun without the additional tidal mixing parameterization. This study finds that the model runswith implementations of the two internal tide mixing parameterizations have varied and in someinstances, large di↵erences in important model variables indicating that the inclusion of internaltide mixing in a numerical model of the Arctic Ocean will require careful consideration.iiLay SummaryThis study examines the representation of internal tide mixing in a model of the Atlanticand Arctic Oceans and the resulting impact on the Arctic Ocean. Internal tide mixing leads tosignificant changes in the Arctic Ocean model state such as: decreased sea ice cover and surfacecirculation, non-trivial changes to the Arctic Ocean heat budget, redistribution of freshwater in thebasins, and important changes to the temperature, salinity and stratification fields throughout theArctic Ocean. Two di↵erent representations of internal tide mixing were examined from Jayne andSt Laurent [2001] and Polzin [2009] and this study finds that the more physically based internaltide mixing estimation from Polzin [2009] is likely a more realistic representation of the internaltide mixing field in the Arctic Ocean.iiiPrefaceThe results in this thesis utilize the ANHA (Arctic and Northern Hemisphere Atlantic) con-figuration (http://knossos.eas.ualberta.ca/xianmin/anha/model.html) of the NEMO (Nucleus forEuropean Modelling of the Ocean) model as the framework for the model runs. The control run wascompleted by Dr. Paul G. Myers group at the University of Alberta and the JSL and Polzin runsI completed myself with the additional Polzin formulation module coded by X. Hu. Internal tidemixing parameterizations and implementation methods were followed from Jayne and St Laurent[2001] and Melet et al., [2012] for the JSL and Polzin formulations respectively. The data analysisin Chapters 3 and 4 are my original work.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Ocean Mixing and the Role of Internal Tides . . . . . . . . . . . . . . . . . . . . . . 11.3 Arctic Oceanography and Arctic Ocean Mixing . . . . . . . . . . . . . . . . . . . . . 31.3.1 Arctic Ocean Water Masses and Circulation . . . . . . . . . . . . . . . . . . 31.3.2 Arctic Ocean Internal Waves and Mixing . . . . . . . . . . . . . . . . . . . . 51.4 Vertical Mixing in Ocean Models and Internal Tide Mixing Parameterizations . . . 61.5 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1.1 Primitive Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13vTable of Contents2.1.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1.3 Vertical Sub-Grid Scale Physics . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 Internal Tide Mixing Parameterizations . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.1 Jayne and St Laurent Formulation . . . . . . . . . . . . . . . . . . . . . . . . 192.2.2 Polzin Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3 Model Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1 Vertical Di↵usivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Model State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.1 Circulation, Sea Ice, Freshwater & Heat Content, and Fluxes . . . . . . . . . 343.2.2 Hydrography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.3 Atlantic and Arctic Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.2 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70viList of Tables2.1 Model Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.1 Vertical di↵usivity over the Arctic Ocean domain. . . . . . . . . . . . . . . . . . . . . 273.2 Volume, freshwater, and heat fluxes from observational studies (averaging period isshown beneath in brackets) and for the control, JSL, and Polzin model runs (averagedfrom 2012 to 2016) are shown for Fram Strait, Davis Strait, the BSO, LancasterSound (also called Barrow Strait), Nares Strait, and Jones Sound. The OSNAPtransect (see Figure 3.13) is used for the three model runs as an estimation of thetotal flux through Fram Strait, Davis Strait and the BSO. Negative values representfluxes in and positive values represent fluxes out of the Arctic Ocean. . . . . . . . . . 41viiList of Figures1.1 Recent bathymetric map of the Arctic Ocean based on Jakobsson et al. [2008].Abbreviations made on the map are as follows: BS - Barrow Strait, CB - CanadianBasin, DS - Davis Strait, EB - Eurasian Basin, FS - Fram Strait, JS - Jones Sound,NS - Nares Strait. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 ANHA4 mesh grid, where the colour bar shows the resolution in kilometres andoverlying grid shows every tenth model gridline. . . . . . . . . . . . . . . . . . . . . . 122.2 Illustration of the mixing length scale computation. lk is given by Equation 2.15, l✏is given by Equation 2.16, lup and ldwn given by Equations 2.13 and 2.14, respectively. 182.3 Domain values for a) near-bottom buoyancy frequency, b) barotropic tidal speedvariance, c) squared amplitude scale for topographic roughness and d) barotropic tointernal tide energy flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.1 Histograms showing the distribution of vertical di↵usivity in terms of % volume ofthe Arctic Ocean domain averaged from 2012-2016. Vertical di↵usivity for Kvtidedistribution (left) for JSL and Polzin formulations and Kvfull for each of control,JSL and Polzin formulations (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2 Vertical di↵usivity geometrically averaged horizontally over the Arctic domain from2012 to 2016. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3 Vertical di↵usivity geometrically averaged horizontally as a function of height abovebottom for profiles greater than 2000m depth (left) and profiles less than 1000mdepth (right) over the Arctic domain averaged from 2012-2016. Height above bottomprofiles are cut o↵ when there is less than 5000 points to average. . . . . . . . . . . . 29viiiList of Figures3.4 Horizontal slices of vertical di↵usivity at the 186m (top), 1062m (middle) and 2225m(bottom) depth levels over the Arctic domain averaged from 2012-2016 for control(left) JSL (middle), and Polzin (right) configurations. . . . . . . . . . . . . . . . . . 303.5 Transects from Canada Basin to Barents Sea (blue line) and through Canadian ArcticArchipelago (red line). Letters correspond to labels on following transect figures 3.6,3.7, and 3.14-3.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.6 The full vertical di↵usivity averaged from 2012-2016 across the transect from theCanadian Basin to Barents Sea (see Fig. 3.5) for control (top), JSL (middle)and Polzin (bottom) configurations. Regions with di↵usivity values higher than102m2s1 are set to light grey and correspond to where the model convective schemeis activated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.7 The full vertical di↵usivity averaged from 2012-2016 across through the CAA (seeFig. 3.5) for the control (top), JSL (middle), and Polzin (bottom) configurations.As in Fig. 3.6, Regions with di↵usivity values higher than 102m2s1 are set to lightgrey and correspond to where the model convective scheme is activated. . . . . . . . 333.8 Sea surface height averaged from 2012-2016 for control (left), JSL (middle) andPolzin (right) configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.9 Sea ice thickness averaged over the months of March (top) and September (bottom)from 2012-2016 for control (left) JSL (middle) and Polzin (right) configurations. . . 353.10 Average freshwater content over the Arctic domain from 2012-2016 integrated tothe 34.8 isopycnal (top), and corresponding 34.8 isopycnal depth (bottom) for thecontrol (left), JSL (middle) and Polzin (right) configurations. . . . . . . . . . . . . . 363.11 Heat content over the Arctic domain averaged over years 2012-2016 and integratedover the full water column (top) with corresponding anomalies (bottom). . . . . . . 373.12 Air-sea heat flux over the Arctic domain averaged over years 2012-2016 includingboth ice and open ocean fluxes (top) with corresponding anomalies (bottom). . . . . 383.13 Horizontal fluxes of volume, freshwater and heat through major passage ways in theArctic averaged from 2012 to 2016 and integrated over depth for control, JSL andPolzin formulations. Labels on the Arctic map correspond to transects as follows:BS - Barrow Strait, NS - Nares Strait, JS - Jones Sound, OS - OSNAP. . . . . . . . 43ixList of Figures3.14 Depth by along transect distance temperature along the transect CanBar (see Fig.3.5) for the control (top), JSL (middle), and Polzin (bottom) configurations. . . . . . 453.15 Depth by along transect distance temperature anomalies along the transect CanBar(see Fig. 3.5) for control - JSL (top), control - Polzin (middle) and JSL - Polzin(bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.16 Depth by along transect distance salinity along the transect CanBar (see Fig. 3.5)for the control (top) JSL (middle) and Polzin (bottom) configurations. . . . . . . . . 483.17 Depth by along transect distance salinity anomalies along the transect CanBar (seeFig. 3.5) for control - JSL (top), control - Polzin (middle) and JSL - Polzin (bottom). 493.18 Depth by along transect distance buoyancy frequency squared, N2, across the tran-sect CanBar (see Fig. 3.5) for the control (top), JSL (middle), and Polzin (bottom)configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.19 Depth by along transect buoyancy frequency squared, N2, anomalies across thetransect CanBar (see Fig. 3.5) for control - JSL (top), control - Polzin (middle) andJSL - Polzin (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.20 Depth by along transect temperature across the transect through the CAA (see Fig.3.5) for the control (top) JSL (middle) and Polzin (bottom) configurations. . . . . . 533.21 Depth by along transect temperature anomalies across the transect through theCAA (see Fig. 3.5) for control - JSL (top), control - Polzin (middle) and JSL -Polzin (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.22 Depth by along transect salinity across the transect through the CAA (see Fig. 3.5)transect for the control (top) JSL (middle) and Polzin (bottom) configurations. . . . 553.23 Depth by along transect distance salinity anomalies through the CAA (see Fig. 3.5)transect for control - JSL(top), control - Polzin (middle) and JSL - Polzin (bottom). 563.24 Depth by along transect distance buoyancy frequency squared, N2, through the CAAsee Fig. 3.5) transect for control (top) JSL(middle) and Polzin (bottom) configurations. 573.25 Depth by along transect distance buoyancy frequency squared, N2, anomalies throughthe CAA see Fig. 3.5) transect for control - JSL (top), control - Polzin (middle) andJSL - Polzin (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58xList of Figures3.26 Histograms showing the distribution of vertical di↵usivity in terms of % volume ofthe northern hemisphere Atlantic Ocean domain averaged from 2012-2016. Verticaldi↵usivity input from the JSL and Polzin for Kvtide (left) and Kvfull distribution(right) for each of the control, JSL and Polzin formulations. . . . . . . . . . . . . . . 593.27 Vertical di↵usivity geometrically averaged horizontally over the Atlantic Ocean (solidlines) and the Arctic Ocean (dotted lines) from 2012 to 2016 for each of the control,JSL, and Polzin formulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.28 Zonal average of temperature anomalies over the full ANHA4 domain averaged from2012-2016 for control - JSL (top), control - Polzin (middle) and JSL - Polzin (bottom). 613.29 Zonal average of salinity anomalies over the full ANHA4 domain averaged from2012-2016 for control - JSL(top), control - Polzin (middle) and JSL - Polzin (bottom). 623.30 Zonal average of buoyancy frequency squared, N2, anomalies over the full ANHA4domain averaged from 2012-2016 for control - JSL (top), control - Polzin (middle)and JSL - Polzin (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63xiList of SymbolsAvm and AvT Vertical eddy viscosity coecient, computed from the TKEvertical di↵usivity scheme↵CB Craig and Banner’s value Charnock’s constantCk and C✏ Vertical eddy viscosity and di↵usivity coecientsDU, DT , and DS Small scale physical parameterization for momentum, tem-perature and salinity Vector derivative operator in the (i,j,k) directionse Turbulent kinetic energye3 NEMO model grid cell thicknessE Tidal energy flux from barotropic to baroclinic tides✏ Turbulent dissipation rate of the breaking of internal tides⌘ Height of the sea surfacef Coriolis accelerationFU, F T , and FS Surface and bottom forcing termsF (z) Vertical dissipation functiong Gravitational accelerationh2 Topographic amplitude of roughnessH Depth of the ocean bottom(i, j, k) Orthogonal set of unit vectors in the NEMO model suchthat k is the local upward vector and (i,j) are the two vec-tors orthogonal to k and tangent to geopotential surfaces von Karman constantxiiList of Symbols Topographic wavenumber of roughnessKm and K⇢ Vertical eddy viscosity and di↵usivity coecientsKvfull Full model vertical di↵usivity. Depending on the defini-tion of vertical di↵usivity in a model run this could be thesummation of the TKE mixing scheme and tidal mixingparameterization or the TKE scheme only (for the control)Kvtide Vertical di↵usivity from the model run from the tidal mixingparameterization only.l✏ and lk Dissipation and mixing length scalesN Local buoyancy frequencyN2zVertical mean of the buoyancy frequencyNb Near-bottom buoyancy frequency⌦ Earth’s angular velocity vectorp PressurePrt Prandtl number (set to unity)q Average local dissipation eciency⇢ In-situ density⇢0 Reference densityS Salinityt TimeT Potential temperature⌧ Mixing eciency of turbulenceU Vector velocity in the NEMO modelU2 Barotropic tidal speed variancez Vertical coordinatez⇤ Buoyancy scaled vertical coordinatez0Vertical distance from bottom topographyzp WKB-scaled vertical decay scalexiiiAcknowledgementsI am very fortunate to have the support of such professional, and caring mentors throughoutmy time at UBC. My supervisors Dr. Stephanie Waterman and Dr. Paul Myers showed incrediblepatience and foresight as they led me through the completion of this master’s thesis. The excellentteaching and mentorship of Dr. Susan Allen and Dr. Rich Pawlowicz throughout course work andbeyond have helped me to improve my knowledge and overall work by challenging me to do better,and helping me to develop a more focused and scientific point of view. Much appreciation to Dr.Susan Allen for also participating as a committee member, the time and advice given throughoutthis process has been extremely valuable. I would also like to recognize the contributions of Dr.Xianmin Hu, who worked with me to code and develop the tidal mixing module in the numericalmodel, and coached me on using, running, and modifying the model. I have also received muchsupport from the entire Oceanography department at UBC, a special thank you to the individualsin the Waterhole, your help and support was invaluable.xivChapter 1Background1.1 IntroductionIn this chapter, the motivation and background of this study is discussed, leading to a definitionof the main research questions for this thesis. First, the role of internal tides in the global ocean isdiscussed, along with observational and modelling studies describing the current understanding ofthe interactions between the internal wave field and large-scale ocean circulation. Second, propertiesof the Arctic Ocean relevant to this study are presented, along with the motivation for this study’sfocus on internal tide mixing in the Arctic region. Finally, recent research on internal tide modellingstudies is reviewed, and how this work adds to the current knowledge base is explained. The thesisobjectives are stated in the last section of this chapter.1.2 Ocean Mixing and the Role of Internal TidesMixing in the ocean is a consequence of turbulence and occurs either along or across isopycnals.The latter, termed diapycnal mixing, requires displacement that is working against the generallystable stratification of the ocean. For this reason, diapycnal mixing requires more energy thanalong isopycnal mixing and as a consequence, the rate of along isopycnal mixing is typically muchlarger than that of diapycnal mixing. However, diapycnal mixing has a significant role in theglobal ocean’s general circulation as it changes ocean vertical structure which, in turn, controls thevertical transport of heat, salt and dissolved gasses, ultimately influencing the large-scale oceaniccirculation, such as the Meriodonal Overturning Circulation (MOC), and the lateral distribution ofthe ocean’s tracers [Munk and Wunsch, 1998; Huang, 1999]. Diapycnal mixing has large variabilityin space both laterally and vertically [Kunze et al., 2006; Whalen et al., 2012; MacKinnon et al.,2013b]. It has been shown to be enhanced over regions of rough topography [Polzin et al., 1997] and11.2. Ocean Mixing and the Role of Internal Tidesnear sites of internal wave (IW) generation [Dohan and Davis, 2011]. Modelling studies have foundthat oceanic heat transports are very sensitive to variability in the prescription of vertical di↵usivity,an approximation of the diapycnal di↵usivity typically employed in numerical ocean models [Bryan,1987; Marotzke, 1997; Zhang et al., 1999; Saenko and Merryfield, 2005; Zhang and Steele, 2007].Vertical di↵usivity in numerical models has also been shown to significantly impact the uptake andstorage of important tracers that influence the global climate such as carbon [Sokolov et al., 1998].These studies highlight how turbulent mixing plays an important role in determining how heat,salinity and fresh water in the oceans are transported and stored.In the ocean’s interior, away from atmospheric forcing, beneath the surface mixed layer, andoutside the surface and bottom boundary layers, the energy required to produce turbulent mixingis sourced largely from the breaking of internal waves (IW) [Munk and Wunsch, 1998]. Energyinput into the IW field comes primarily from the winds and the tides. Wind forcing generates near-inertial waves with a global power input of 0.2-1.1 TW [Alford, 2001; Plueddemann and Farrar,2006; Furuichi et al., 2008; Rimac et al., 2013], while the flow of barotropic tides in stratifiedregions over rough topography generates internal tides [Egbert and Ray, 2000; Niwa and Hibiya,2001; Garrett and Kunze, 2006], accounting for about 1.0 TW of power input globally [Nycander,2005; Plueddemann and Farrar, 2006; Furuichi et al., 2008; Rimac et al., 2013]. IWs may also begenerated as lee waves in regions of very strong near-bottom flows. It is estimated that lee wavegeneration accounts for 0.2 to 0.7 TW of power input to the internal wave field globally [D’Asaro etal., 1995; Alford 2001, 2003, Nikurashin and Ferrari, 2011; Scott et al., 2011; Wright et al. 2014]. Itfollows that the total power input to the IW field is approximately 2.1±0.7 TW globally [D’Asaro,1995; Alford, 2001,2003], with tides accounting for approximately half of the total power input tothe IW field.Once generated, low-mode internal tides transport their energy as turbulence throughout theglobal ocean by radiating as propagating internal waves (IW) at the tidal frequency. Higher modeinternal tides typically dissipate as turbulence locally near the generation site [Large and Crawford,1995; Klymak et al., 2008]. Local dissipation of higher mode internal tides has been studiedobservationally for the past several decades [Klymak et al., 2006; Polzin et al., 1997], and it has beenfound that turbulent dissipation is elevated by orders of magnitude within hundreds of kilometresof internal-tide generation sites. In deep regions with enhanced high mode internal tide generation,21.3. Arctic Oceanography and Arctic Ocean Mixingelevated turbulent dissipation is typically found over several kilometres above the bottom with amagnitude that typically decreases with increasing height [e.g. Polzin, 1997]. In these environmentsof deep rough topography, measurements indicate that the majority of the energy going into theinternal tide is dissipated locally [Polzin, 2004; Waterhouse et al., 2014]. The internal waves thatare not dissipated locally, propagate away, losing their energy along their ray paths, to a variety ofprocesses such as topographic scattering and reflection [Mu¨ller and Xu, 1992], and to turbulencevia non-linear transfer to smaller scale waves that eventually break [Polzin, 2004; MacKinnon etal., 2013a]. IWs that propagate without losing energy may dissipate by colliding with continentalshelves [Nash et al. 2004, 2007; Zhao and Alford, 2009; Legg, 2013]. In locations with significantlow-mode internal tide generation, the majority of locally generated internal tide energy dissipateselsewhere, propagating across ocean basins in the form of low-mode IWs. This can be seen in in-situflux measurements [Alford, 2003; Althaus et al., 2003; Rudnick et al., 2003; Alford and Zhao, 2007;Zhao et al., 2009], numerical models [Simmons, 2008], and satellite altimetry [Zhao and Alford,2009]. The ratio of energy in the internal tide field that dissipates locally relative to that whichradiates away is almost entirely unconstrained and remains an area of active research.1.3 Arctic Oceanography and Arctic Ocean Mixing1.3.1 Arctic Ocean Water Masses and CirculationThe Arctic Ocean is a semi-enclosed ocean with two major basins, the Eurasian and the Am-erasian (Canadian) basin, and continental shelves making up 53% of its total surface area [Jakobs-son, 2002]. The Eurasian and Canadian basins are ice covered throughout much of the year and areseparated by the Lomonosov Ridge (Fig. 1.1). The Arctic Ocean is connected to the Pacific andAtlantic Oceans through Bering Strait, Fram Strait, Barents Sea, Davis Strait, and the CanadianArctic Archipelago (CAA). These gateways exchange water between the three oceans.Warm and saline Atlantic Water (AW), defined as water above 0C and salinity greater than34.4, enters the Arctic Ocean through Fram strait (350km wide, 2700m deep) and the Barents Sea(mostly via St Anna Trough, 200km wide, 600m deep), where it circulates cyclonically and followsthe topography of the basin due to the boundary currents. Along this pathway, the interfacebetween AW and the overlying waters is continually eroded by mixing [Polyakov et al., 2012;31.3. Arctic Oceanography and Arctic Ocean MixingCarmack and Melling, 2011]. The western slope of the Barents Sea, labelled the Barents SeaOpening (BSO), allows only upper level AW water to enter through a 450m deep passage. The AWcirculating through Barents Sea sees an increase in density due to heat loss to the atmosphere andice formation. By the time AW exits the Barents Sea through St Anna Trough into the EurasianBasin, up to 92% of the heat from the AW inflow through BSO is lost to the atmosphere and itis mostly cooled below 0C [Schauer et al., 2002]. In contrast, Fram Strait is a wide and deeppathway for both AW inflow and Arctic water export into the Nordic Seas (including Greenlandand Norwegian Seas). Compared to AW that flows through Barents Sea which is significantlymodified by the atmosphere, the AW flowing through Fram Strait is transported into the ArcticOcean basins through deeper layers, maintaining its warm temperatures by avoiding significantheat flux to the atmosphere. Inside the Eurasian basin, the Atlantic water is found underneath acold halocline with strong stratification, separating the warm Atlantic water from the sea ice andfresh water at the surface. The density di↵erence here is the main barrier that keeps the heat inthe AW layer isolated from the surface water. The dissipation of IW or double di↵usive mixing arethe primary processes by which the fresh water at the surface can be mixed down and the warmand salty Atlantic water can be mixed up.The western Fram Strait exports cold, fresh water, and sea ice from the Arctic into the NordicSeas and the North Atlantic which accounts for approximately half of the freshwater export out ofthe Arctic [Serreze et al., 2006]. The remainder of the freshwater export goes through the CAA,mainly through Nares Strait, Jones Sound and Barrow Strait. The CAA sees strong tidal flowand enhanced turbulence, resulting in much of the volume flux through this region being carriedby baroclinic flow. The narrow pathways of the CAA empty into Ban Bay, which then flowsto Davis Strait (360 km wide and 650m deep). Fram and Davis Straits together export 84% ofthe freshwater from the Arctic into the North Atlantic. The thermohaline circulation in the NorthAtlantic is sensitive to the balance of freshwater that is exported out of the Arctic, which is acceptedas explaining observed climate variability in the Arctic and North Atlantic [Stau↵er et al., 2015].Exchanges with the North Pacific occur at the relatively narrow Bering Strait (85km wide,50m deep) which brings in one third of the fresh water entering the Arctic Ocean [Serreze et al.,2006]. The fresher Pacific Water (PW), defined as having a temperature maximum less than 0Cand salinity less than 33, enters the Canadian Basin through Bering Strait and lies above the AW,41.3. Arctic Oceanography and Arctic Ocean Mixingaiding in the strong upper ocean stratification by isolating the AW heat from the sea ice at thesurface, especially in the winter. The strong halocline in the Canadian Basin leaves IW dissipationas the dominant process in vertical mixing [Guthrie et al., 2013].1.3.2 Arctic Ocean Internal Waves and MixingIn the Arctic basin interiors, observations indicate very low vertical mixing rates and low levelsof internal wave energy. Central regions of the Arctic with deep bathymetry have been observed tohave dissipation values in the AW thermocline that are too low to drive turbulent mixing able toovercome the surrounding stratification [Fer, 2009; Lenn et al., 2009]. Although the presence of ice-cover in the Arctic Ocean has been speculated at causing the observed low mixing rates [Rainvilleet al., 2011], recent observational studies have found that the upper ocean stratification plays alarge, and possibly dominant role in damping internal wave mixing. In regions of similar IW energyand background mixing, areas of the Arctic with higher upper ocean stratification see a relativeweakening of IW forcing [Guthrie et al., 2013]. Typical di↵usivity values in the Arctic Oceanare O(105m2s1) with di↵usivity values in the deep ocean and interior O(106m2s1) [Rainvilleand Winsor, 2008]. Much of the turbulence observed is thought to be associated with internalwaves generated by flow over topography [D’Asaro and Morison, 1992]. The low levels of mixinghave biochemical and physical implications in the Arctic, limiting the redistribution of oxygen andnutrients. Further, weak mixing serves to maintain the strong stratification in the Arctic Ocean,which e↵ectively traps the heat contained in the AW layer away from the surface [Peralta-Ferrizand Woodgate, 2015].Internal waves and turbulence in the Arctic Ocean are also patchy in space and in time, withenhanced turbulence restricted to steep topography of basin margins, regardless of sea ice cover [Lin-coln et al., 2016], with a strong correlation between shear levels and bottom topography [D’Asaroand Morison, 1992]. Recent observations by Rippeth et al. [2015] show that within the AW ther-mocline, dissipation on the continental slopes of the Arctic Ocean is enhanced by up to two ordersof magnitude compared to the central Arctic. This study also noted that the dissipation rate in theAW thermocline was highly variable with bathymetry across the Arctic but was largely insensitiveto sea ice cover, implying that the source of the internal energy must be coming largely from thetides as the exposure of the ocean surface to wind forcing does not have a measurable e↵ect. This51.4. Vertical Mixing in Ocean Models and Internal Tide Mixing Parameterizationsconclusion initially seems counter to the fact that much of the Arctic is above the critical latitudeof the semidiurnal lunar (M2) tide, which restricts this tide from generating an internal tide at thisfrequency [Simmons et al., 2004; St. Laurent et al., 2002]. However, a recent study by Rippeth etal. [2017] points out that even though internal tides are not generated by theM2 tide in much of theArctic Ocean, internal lee waves are still generated by the tidal flow. Increased internal tide drivenmixing on the continental slopes could have important implications for the vertical movement ofAtlantic water heat beneath the thermocline. Following this, if the regions of enhanced dissipationare largely due to internal tide energy, then knowledge its spatial variability and distribution couldgive indication of the regions where enhanced mixing is expected.1.4 Vertical Mixing in Ocean Models and Internal Tide MixingParameterizationsMixing that results from the breaking of internal tides is important to be included in OceanGeneral Circulation Models (OCGMs) for realistic simulation of many aspects of the ocean’s vari-ability. Examples include enhanced mixing over regions of rough topography and the verticaldistribution of model tracers such as temperature and salinity [Melet et al., 2012]. The breakingof internal tides occurs on spatial scales too small to be represented explicitly by current globaland regional numerical ocean models as it requires grid resolution on the order of metres in thevertical throughout the water column and 1-10 kilometres in the horizontal. This resolution is gen-erally inaccessible to global climate models creating the need for a parameterization of the e↵ectof internal tide breaking for more accurate simulations. Parameterizations of this e↵ect need toincorporate the key dynamics of where internal tides generate geographically, and the process bywhich the internal tides break and dissipate causing mixing [St. Laurent and Garrett, 2002]. Itis also important that they are physically based to allow them to react to varying model fieldsand evolve with a changing climate as would be expected in reality. Representing the mixing dueto internal tide breaking is important as a wide range of processes that vary in time scales frommonths to millennia such as the strength of the MOC and equatorial upwelling, are sensitive tohow diapycnal mixing is represented in OCGMs [Friedrich et al., 2011; Melet et al., 2015].Parameterizations of mixing due to the breaking of internal tides are generally added in addition61.4. Vertical Mixing in Ocean Models and Internal Tide Mixing Parameterizationsto other parameterizations of mixing such as a constant di↵usivity or a laterally uniform di↵usivityprofile used to represent diapycnal mixing [Bryan and Lewis, 1979; Huang, 1999]. Spatially dynamicrepresentations of vertical mixing and the inclusion of internal tide driven mixing is a relativelyrecent improvement to OCGMs of the last two decades. Parameterizations of internal tide-drivenmixing to date, first require an estimate of the amount of energy transferred from the barotropic tothe baroclinic tides, which is based on the linear theory of Bell [1975]. The uncertainty of where thetidally sourced IWs dissipate and the fraction of their energy that dissipates locally versus radiatesaway is still very uncertain, and the focus of current modelling as well as observational work.A commonly implemented parameterization by Jayne and St. Laurent [2001] (hereafter the JSLformulation), uses observations made in the Brazil Basin [Ledwell et al., 2000] to develop a semi-empirical and energetically constrained parameterization where the internal tide driven turbulentdissipation is bottom enhanced with a prescribed exponential vertical decay scale. The fraction oflocal to remote dissipation is set uniformly to 1/3 to match the Brazil Basin observations. Morerecently, a dynamic approach taken by Polzin [2009] uses the radiation balance equation [Polzin,2004] to determine a vertical dissipation profile that is linked to the internal wave shear producingthat dissipation. The Polzin formulation has the advantage of allowing for temporal variability inthe prescribed internal tide driven dissipation and mixing, and could theoretically change with achanging model state.Jayne and St Laurent [2001] implemented the JSL parameterization of internal tide mixingplus a background vertical di↵usivity of 105m2s1 into a course resolution global ocean modeland reported the range of vertical di↵usivities that were realized in their model at various depthlevels in the Atlantic, Pacific and Indian Ocean basins. They found significant spatial variationof vertical di↵usivity over the model domain ranging mostly from 105 to 103m2s1 with thehighest concentration di↵usivities that exceeded 103m2s1 at the seafloor covering only 16% ofthe model domain. Simmons et al. [2004] also implemented the JSL parameterization into a globalocean model plus a constant background di↵usivity, setting all areas north of 72N to the constantbackground di↵usivity, and compared this run to two runs with fully uniform and horizontallyuniform di↵usivity prescriptions, respectively. They found that the tidal mixing run had morerealistic temperature and salinity structure compared to the other two runs, indicating that thewater mass transformations essential to establishing a more realistic global scale thermohaline71.5. Thesis Objectivesstructure, are a result of spatially variable vertical di↵usivities which cannot be captured by anyone globally averaged profile of mixing. Saenko and Merryfield [2005] found a contrary result.In their study, the JSL formulation, implemented in a coarse resolution 10,000 year model run,had a very small impact on the circulation of deep water formed in the North Atlantic and itsassociated heat transport. However, they did find that the additional abyssal mixing from the tidalmixing parameterization was essential to diapycnal upwelling in the Southern and Pacific Oceansand thus in the southern arm of the MOC. Jayne [2009] implemented the JSL parameterizationand compared it to a horizontally uniform vertical profile of di↵usivity in 3 and 1 resolutions ofa global ocean model. He found that the tidal mixing parameterization strengthens the deep cellof the MOC compared to the ad hoc specified vertical profile of di↵usivity, with the poleward heattransport being a weak function of the abyssal mixing parameterization.Melet et al. [2012] was the first study to examine model experiments that implement both thePolzin and JSL formulations. They consider a coarse resolution 1000 year global simulation withthe diapycnal di↵usivity defined only by the tidal mixing parameterization and resolved shear andbottom friction with no background mixing added. Thus, the runs in this study had comparativelylow values of mixing to other similar studies. They found there is induced warming in the Atlanticocean in the Polzin formulation relative to the JSL with stronger di↵erences of 0.5-1C found locallyin the averaged last year of the model run. They focused primarily on the Pacific Ocean, and foundthat the Indo-Pacific MOC was sensitive to the prescription of internal tide parameterization. Whencomparing the structures of the di↵usivity, they found that the vertical decay scale in the Polzinrun tended to be smaller in regions of strong barotropic to baroclinic tide energy conversion, withmore dissipation occurring higher in the water column compared to JSL. This resulted in tidallyinduced vertical di↵usivities being weaker in the deep ocean and stronger in the thermocline in thePolzin run relative to the JSL. They concluded that not only the energy input to the internal tidesmatters but also where in the vertical it is dissipated.1.5 Thesis ObjectivesIn all previous studies examining the impact of internal tide mixing parameterizations, nonehave reported on the impact of these parameterizations to the Arctic Ocean. Yet, the impact in the81.5. Thesis ObjectivesFigure 1.1: Recent bathymetric map of the Arctic Ocean based on Jakobsson et al. [2008].Abbreviations made on the map are as follows: BS - Barrow Strait, CB - Canadian Basin, DS -Davis Strait, EB - Eurasian Basin, FS - Fram Strait, JS - Jones Sound, NS - Nares Strait.91.5. Thesis ObjectivesArctic Ocean is of significant interest owing to its unique properties such as strong stratification,AW heat, sea ice cover, and low internal wave energy levels. Currently, it remains unclear if theparameterizations for mixing that are used in numerical models of mid-latitude regions are stillvalid in the Arctic region due to the low mixing and patchiness of the vertical di↵usivity field.In this study we explore the impact of internal tide mixing parameterizations in an eddy-permitting model of the Arctic Ocean. Specifically we compare and contrast the impact of the JSLversus Polzin formulations, noting the potential for the latter to deviate significantly and in uniqueways in the Arctic Ocean given its strong and uniquely structured stratification profile and lowinternal wave energy levels. In this study we aim to:1. Quantify the impact that the JSL and Polzin internal tide driven mixing parameterizationshave on the magnitude and spatial variability of the vertical di↵usivity field in an eddy-permitting model of the Arctic Ocean.2. Explore the impact that the addition of these parameterizations has on the Arctic modelstate.3. Compare and contrast the impacts of these two internal tide mixing parameterizations inboth the Arctic and North Atlantic Ocean domains, potentially identifying ways in whichthese impacts may be unique to the Arctic Ocean.10Chapter 2Methods2.1 Model DescriptionThe model runs considered in this study are completed with NEMO (Nucleus for EuropeanModelling of the Ocean) [Madec et al., 2015]. It is a numerical model which solves the primitiveequations on a three dimensional Arakawa C-type staggered grid. We used the ANHA4 (Arctic andNorthern Hemisphere Atlantic) regional configuration of NEMO with a 1/4 resolution [Fig. 2.1](http://knossos.eas.ualberta.ca/xianmin/anha). The ANHA4 configuration is based on the 1/4tripolar grid taken from the NEMO ORCA025 configuration developed within the MERCATOR-ocean and DRAKKAR collaboration [Barnier et al., 2006]. This model has 50 vertical levels witha 1m thick top level and decreasing resolution with increasing depth. The ANHA4 domain hastwo open boundaries at 20S and Bering Strait in the Arctic Ocean with horizontal resolution ofapproximately 30km at the equator and 10km in the Canadian Arctic Archipelago. Sub-grid scalevertical physics is represented using a Turbulent Kinetic Energy (TKE) closure model [Madec etal., 1998; Axell, 2002; Holdsworth and Myers, 2015] with additional parameterizations of internaltide mixing in experimental runs [Jayne and St Laurent, 2001; Polzin 2009]. Sea ice is representedusing the Louvain-la-Neuve sea-ice model (LIM2) [Fichefet and Morales-Maqueda, 1997] with anelastic-viscous-plastic ice rheology [Hunke and Dukowicz, 1997].Initial conditions for these model runs are taken from GLORYS2 (Global Ocean Reanalyses andSimulations) [Ferry et al., 2012] output including three dimensional temperature, salinity, lateraland zonal velocity, and two dimensional sea surface height and sea ice cover. The model runs areforced with monthly river runo↵ from Dai et al. [2009] and inter-annual atmospheric data de-rived from the Canadian Meteorological Centre’s Global Deterministic Prediction System (CGRF)[Smith et al., 2013] with an hourly resolution in time and a spatial resolution of 0.45 longitude112.1. Model DescriptionResolution(km)Figure 2.1: ANHA4 mesh grid, where the colour bar shows the resolution in kilometres andoverlying grid shows every tenth model gridline.122.1. Model Descriptionand 0.3 latitude for: surface wind stress, air temperature, humidity, downward shortwave andlongwave radiation, and total precipitation. From the total precipitation, snowfall is representedwhen temperature at the surface is less than 0C, and rain otherwise.2.1.1 Primitive EquationsNEMO uses the Navier-Stokes equations with a nonlinear equation of state which couples tem-perature and salinity (active tracers) to the fluid velocity. There are six additional assumptionsmade using rational scaling [Madec et al., 2015]:1. Spherical Earth approximation: Local vertical gravity is parallel to the Earth’s radius byassuming geopotential surfaces are spheres.2. Thin-shell approximation: The ocean depth is very small compared to the thickness of theEarth and is neglected when considering the Earth’s radius.3. Turbulent closure hypothesis: The turbulent fluxes (which represent the impact of sub-gridscale processes on the large scale) are expressed in terms of the large-scale features.4. Boussinesq hypothesis: Density variations are only considered when they contribute to thebuoyancy force.5. Hydrostatic hypothesis: Vertical momentum equations are simplified to be a balance be-tween the vertical pressure gradient and the buoyancy force. This disconnects convectiveprocesses from the Navier-Stokes equations so that convective processes must be representedby parameterizations in the model.6. Incompressibility hypothesis: The divergence of the velocity vector is assumed to be zero inthree dimensions. This is e↵ectively a statement of the conservation of mass for an incom-pressible fluid.Using these six assumptions, the primitive equations for the NEMO model are produced. Anorthogonal set of unit vectors is used (i,j,k) and linked such that k is the local upward vector and(i,j) are two vectors orthogonal to k and tangent to the geopotential surfaces. This is useful in theequations of large-scale geophysical motions as the gravitational force is so dominant. Now lettingU132.1. Model Descriptionrepresent the vector velocity where U=Uh+wk (h is the local horizontal vector), T the potentialtemperature, S the salinity, and ⇢ is the in-situ density. The vector form of the Navier-Stokesequations gives the following six governing equations (momentum balance, hydrostatic equilibrium,incompressibility equation, the heat and salt conservation equations, and an equation of state):@Uh@t= (5⇥U)⇥U+ 125 (U2)h f k⇥Uh  1⇢0 5h p+DU + FU (2.1)@p@z= ⇢g (2.2)5 ·U = 0 (2.3)@T@t= 5 ·(TU) +DT + F T (2.4)@S@t= 5 ·(SU) +DS + FS (2.5)⇢ = ⇢(T, S, p) (2.6)where 5 is the vector derivative operator in the (i,j,k) directions, t is time, z is the verticalcoordinate, ⇢ is the in-situ density given by Equation 2.6, ⇢o is the reference density, p is thepressure, g is the gravitational acceleration, and f = 2⌦ · k is the Coriolis acceleration (⌦ is theEarth’s angular velocity vector). DU, DT , and DS are small scale physical parameterizations formomentum, temperature and salinity, and FU, F T , and FS are surface and bottom forcing terms.2.1.2 Boundary ConditionsThere are numerous boundaries to define and consider in a model ocean such as coastlines,bottom topography, air-sea and ice-sea. All of these boundaries can be defined with two surfaces,z = H(i, j) and z = ⌘(i, j, k, t), where H is the depth of the ocean bottom and ⌘ is the heightof the sea surface. At these boundaries, fluxes of heat, fresh water, salt, and momentum can be142.1. Model Descriptionexchanged with land, sea ice and the atmosphere. Some of these fluxes occur on very long timescales and are neglected in this model. Listed below are the major flux exchanges at the oceanboundaries.Land-ocean interfaceThe major flux represented here is the exchange of fresh water through river run-o↵. This isimportant in long term simulations and for regions of high latitude like the Arctic Ocean as thereis a large amount of river runo↵ during the melt season modifying waters close to river mouths.Solid earth-ocean interfaceThe heat and salt fluxes exchanged between the ocean and solid earth are neglected in thisconfiguration of the model on the basis that their timescale is much longer than those of interest,and there is no flow across solid boundaries (meaning bottom velocity is parallel to solid boundaries).There is momentum exchanged through friction which transfers at small scales in a boundary layer.It is parameterized in terms of turbulent fluxes.Atmosphere-ocean interfaceThis interface considers kinematic surface conditions, the mass flux of fresh water and pre-cipitation minus the evaporation budget. Surface tension is neglected (which removes capillarywaves) which results in continuity of pressure across the atmosphere-ocean interface. Horizontalmomentum is also exchanged in the form of wind stress and heat.Sea ice-ocean interfaceThe ocean and sea ice exchange heat, salt, fresh water and momentum. The melting and freezingcycles of sea ice are associated with freshwater and salt fluxes.2.1.3 Vertical Sub-Grid Scale PhysicsThe model resolution is larger than the scale of the processes responsible for vertical turbulence(such as shear instability, internal wave breaking, etc.). Thus, turbulent motions cannot be explic-152.1. Model Descriptionitly solved and are parameterized. The vertical momentum and tracer di↵usive operators are ofsecond order and represented as:DvU =@@z(Avm@Uh@z), DvT =@@z(AvT@T@z), DvS =@@z(AvT@S@z) (2.7)where Avm and AvT are the vertical eddy viscosity and di↵usivity coecients, respectively. Thevertical eddy viscosity and di↵usivity coecients are computed from the TKE turbulent closurescheme using a prognostic equation for the turbulent kinetic energy, e¯, and a closure scheme forturbulent length scales [Bougeault and Lacarrere, 1989, Gaspar et al., 1990, Blanke and Delecluse,1993, Madec et al., 1998]. The time evolution of e¯ is the result of the production of kinetic energythrough vertical shear, destruction through stratification, its vertical di↵usion and its dissipation:@e¯@t=Kme32⇣@u@z⌘2+⇣@v@z⌘2K⇢N2 + 1e3@@zAvme3@e¯@z c✏ e¯32l✏(2.8)Km = Cklkpe¯ (2.9)K⇢ = Avm/Prt (2.10)here N is the local bouyancy frequency, e3 being the grid cell thickness, and l✏ and lk are thedissipation and mixing length scales, Km and K⇢ are the vertical eddy viscosity and di↵usivitycoecients with constants Ck = 0.1 and C✏ =p2/2. The constants are determined from laboratoryand oceanic observations to calibrate the TKE parameterization. The Prandtl number, Prt, is setto unity.At the surface e¯ is prescribed by the wind stress field and the bottom value is assumed to beequal to the value just above. A minimum cuto↵ value of 106m2s2 is used to ensure that thisparameter is positive since this is not ensured in the numerical scheme. A cuto↵ is also applied toKm and K⇢ to ensure that numerical instabilities do not occur due to too weak vertical di↵usionand is set by the cuto↵ value 106m2s1.162.1. Model DescriptionTurbulent length scaleThe turbulent length scale (TLS) describes the size of the energy-containing eddies in a turbulentflow. In this parameterization the TLS is based the following first order approximation from Blankeand Delecluse [1993]:lk = l✏ =p2e¯/N (2.11)with an additional constraint on the vertical gradient of the length scale:1e3 @l@z  1 with l = lk = l✏ (2.12)meaning that vertical changes to the length scale cannot be larger than changes in depth. Twoadditional length scales are introduced lup and ldwn which represent the upward and downwardlength scales, defined as (using numerical indexing):l(z)up = min⇣l(z), l(z+1)up, e(z)3t⌘from z = 1 to jpk (2.13)l(z)dwn = min⇣l(z), l(z1)dwn, e(z1)3t⌘from z = jpk to 1 (2.14)where l(z) is computed using equation 2.11, e3t is the vertical coordinate, z represents an arbitrarydepth level, and jpk is the number of vertical grid cells in the model configuration. Next thedissipation and mixing TLS are determined using Gaspar et al. [1990]:lk =plupldwn (2.15)l✏ = min(lup, ldwn) (2.16)This is illustrated in Figure 2.2.Surface wave breaking parameterizationThe TKE turbulence closure scheme also includes the e↵ects of surface wave breaking energeticsfollowing Mellor and Blumberg [2004]. These e↵ects are represented by a boundary condition on172.2. Internal Tide Mixing ParameterizationsFigure 2.2: Illustration of the mixing length scale computation. lk is given by Equation 2.15, l✏ isgiven by Equation 2.16, lup and ldwn given by Equations 2.13 and 2.14, respectively.surface TKE values following Craig and Banner [1994] as:e¯0 =12(15.8↵CB)2/3 |⌧ |⇢0(2.17)where ↵CB = 100 is the Craig and Banner’s value and ⌧ is the wind stress. The boundary conditionfor the turbulent length scale comes from the Charnock relation as:l0 = |⌧ |g⇢0(2.18)where  is the von Karman constant set to 0.40 and  is the Charnock’s constant set to 2.105,suggested by Mellor and Blumberg [2004], the value chosen by Stacey [1999] from observationalevidence.2.2 Internal Tide Mixing ParameterizationsThe essential goal of internal tide mixing parameterizations is to represent the momentumexchange between the barotropic tides and the unrepresented internal waves induced by tidal flowover rough topography in a stratified ocean and the processes by which these internal waves break182.2. Internal Tide Mixing Parameterizationsand dissipate. Here we describe two di↵erent parameterizations that will be implemented in separatemodel runs in our study. Both parameterizations use the estimate for turbulent di↵usivity due tothe breaking of internal tides following the Osborn [1980] relation for the mechanical energy budgetof turbulence as follows:Kv =T ✏N2(2.19)here T is the mixing eciency of the turbulence generally assumed to be T = 0.2 [Osborn, 1980]and ✏ is the dissipation rate which has a di↵erent description for each of the two parameterizations.2.2.1 Jayne and St Laurent FormulationFirst implemented in global ocean models by Simmons et al. [2004], the JSL parameterizationis commonly used in oceanographic models to simulate the breaking of internal tides close to theirgeneration site. This parameterization uses the idea of an internal tide energy flux generated from abarotropic tide moving over regions of rough topography, generating internal waves. The turbulentdissipation rate of the breaking of internal tides is expressed as:✏(x, y, z) =qE(x, y)⇢F (z) (2.20)where ⇢ is the density and q represents the average local dissipation eciency which expressesthe fraction of wave energy that is dissipated locally by turbulent processes relative to that whichis radiated away as internal waves. It is estimated at q = 0.3 ± 0.1 [St Laurent et al., 2002],however, other applications of this parametrization have stated this value as q = 1 [Polzin, 2009]or otherwise. In general, this variable is largely unconstrained and can vary widely throughout theocean [Gries et al., 2013]. In this study, it is set to 1/3. F (z) is the vertical dissipation function,which is assumed to be exponential, and is represented as:F (z) =e(H+z)/⇣⇣(1 eH/⇣) (2.21)192.2. Internal Tide Mixing Parameterizations(a) Nb (s1) (b) U2(m2s2)(c) h2 (m2) (d) E ( Wm2 )Figure 2.3: Domain values for a) near-bottom buoyancy frequency, b) barotropic tidal speedvariance, c) squared amplitude scale for topographic roughness and d) barotropic to internal tideenergy flux.202.2. Internal Tide Mixing Parameterizationswhere ⇣ is set to 500m. E(x, y) in Equation 2.20 is the tidal energy flux from barotropic to baroclinictides with the form:E(x, y) ' 12⇢Nbh2hU2i (2.22)where Nb is the near-bottom buoyancy frequency taken from World Ocean Atlas 2013 version 2(WOA13 V2) climatology from National Oceanic and Atmospheric Administration (NOAA) (Fig.2.3a) [Locarnini et al., 2013; Zweng et al, 2013], and (h2,) are the topographic amplitude andwavenumber scales of roughness. h2 is calculated from two bathymetric datasets: The InternationalBathymetric Chart of the Arctic Ocean (IBCAO) [Jakobsson et al., 2012] with 500m resolution,was used to calculate h2 in the Arctic region above 64N latitude and the Smith and SandwellGlobal Topography dataset [Smith and Sandwell, 1997] horizontal resolution of 1 to 12 kilometres,was used for the North Atlantic portion of the domain. Over each grid cell a plane is fit to thebottom topography (given by H = Ax+By +C) and the residual heights are used to compute h2[Jayne and St Laurent, 2001]. Figure 2.3a shows the values of h2 over the model domain. Highervalues of h2 are seen in areas where topography is rougher, such as over the mid-Atlantic ridge,and lower values are seen over smooth topography such as the Canadian Basin, indicating that thismethod of calculating roughness is e↵ective at capturing some of the variability in roughness overthe model domain.  is a tuning parameter set to 2⇡/1.5 km to match the baroclinic tide powerinput taken from Green and Nycander [2012]. U2 is the barotropic tidal speed variance calculatedfrom the Carre´re and Lyard [2003] hydrodynamic global tide model, MOG2D-G (Fig. 2.3b). Theresulting distribution of energy flux (E) over the model domain is shown in Figure 2.3d.2.2.2 Polzin FormulationThe parameterization from Polzin [2009] is a dynamic parameterization which links the dissi-pation to the internal wave shear producing that dissipation. An idealized internal wave verticalwavenumber energy spectrum is used to produce analytic solutions to a radiation balance equation[Polzin, 2004]. These solutions yield a dissipation profile ✏(z):✏(z) =✏0[1 + (z/zp)]2 (2.23)212.2. Internal Tide Mixing Parameterizationswhere the magnitude ✏0 and scale height zp can be expressed in terms of the spectral amplitudeand bandwidth of the idealized vertical wavenumber energy spectrum in uniform stratification[Polzin, 2009]. To extend the formulation to nonuniform stratification, Polzin [2009] applied abuoyancy scaling using the Wentzel-Kramers-Brillouin (WKB) approximation. This causes thevertical wavenumber of a wave packet to vary in proportion to the buoyancy frequency, whichimplies additional transport of internal wave energy to smaller scales where the buoyancy frequencyis large, and thus potentially enhanced mixing in regions where the stratification is strong. Thise↵ect is captured by buoyancy scaling the vertical coordinate z as:z⇤(z) =Z z0N2(z0)Nb2dz0 (2.24)with z0 being distance from the bottom topography. The turbulent dissipation rate then becomes✏ =✏0[1 + (z⇤/zp)]2N2(z)Nb2 (2.25)The variability of N(z) is suciently small in the bottom most 1500 m that fit parameters are nota↵ected (z0 = 150m, ✏0 = 1⇥ 108 W/kg). At shallower depths, however, increasing stratificationcoupled to nonlinearity serves to transport the remaining energy eciently to small scales.Model implementationWhen implementing the Polzin formulation into the numerical model, steps from Melet et al.[2012] were used for ease of implementation, readability and to maintain as much consistency aspossible between the two parameterizations. First, to satisfy energy conversion and ensure that theintegral of the vertical structure for the turbulent dissipation over depth is unity the dissipationrate is rewritten as:✏(x, y, z) =e0zp[1 + (z⇤/zp)]2N2(z)Nb21z⇤(z=H)+1zp(2.26)This requires that the total energy dissipated by both this and the JSL parameterization are equal.Second, Polzin [2009] assumed that the total dissipation was locally in balance with the barotropicto baroclinic energy conversion rate (q = 1), q here will be set to 1/3 for consistency between the222.2. Internal Tide Mixing Parameterizationstwo parameterizations and the implementation in Melet et al. [2012]. zp is also reformulated to bemore readable as:zp = µ(Nbref )2 Uh22Nb3 (2.27)where µ is a non-dimensional number based on reference values from Jayne and St Laurent [2001](µ = 0.06970) and Nbref = 9.6⇥ 104s1 is the reference value of the bottom buoyancy frequency.Lastly a di↵erent WKB scaling is used to allow easier implementation into the model. Since thedissipation here is expressed as a function of the ratio z⇤/zp, by modifying zp accordingly, the WKBscaling can be changed. This modifies the scaled height coordinate, z⇤, to bez⇤(z) =1N2zZ z0N2(z0)dz0 (2.28)and the WKB-scaled vertical decay scale, zp becomes:zp⇤ = µ(Nbref )2 Uh22NbN2z (2.29)where N2zis the vertical mean of the buoyancy frequency. With these modifications, the Polzinparameterization of the dissipation rate becomes:✏ =qE(x, y)⇢[1 + (z⇤/zp⇤)]2N2(z)N2z1H+1zp⇤(2.30)Comparing to the expression for dissipation rate in JSL shows that the di↵erence lies in the verticaldissipation profile, so the places in the water column where the energy is being dissipated (and whereturbulent mixing is occurring) can be di↵erent between the two formulations. Note the energy input(E) into both parameterizations is equal. Now the vertical dissipation depends on model variables,allowing the vertical profiles of dissipation to vary both across the model domain and with time asit reacts to changes in stratification.232.3. Model Runs2.3 Model RunsThis study consists of three model runs using the ANHA4 configuration each with a di↵erentprescription of vertical di↵usivity described in Table 3.1. The control run is taken from Dr. PaulG. Myers’ Geophysical Fluid Dynamics Ocean Modelling Group at the University of Alberta inthe Earth and Atmospheric Sciences Department (http://knossos.eas.ualberta.ca/xianmin/anha),which defines di↵usivity using the TKE turbulent closure scheme described in Section 2.1.3 withminimum values set by the cut o↵ di↵usivity. Two additional experimental runs add vertical di↵u-sivity due to the breaking of internal tides. The first implements the tidal mixing parameterizationof Jayne and St Laurent [2001], the JSL formulation (Table 3.1). The second uses the parame-terization from Polzin [2009], implemented as in Melet et al. [2012], which will be referred to asthe Polzin formulation. The added vertical di↵usivity due to the breaking of internal tides in theJSL and Polzing formulations have a maximum value of 102m2s1. This cuto↵ value was chosenconsidering the distribution of vertical di↵usivity in the control run and aiming to keep a similarrange of di↵usivity values in the two tidal mixing model runs. All three configurations are run from2002 to 2016. We choose to focus on time-mean fields in the model output and thus, all resultspresented in the analysis average the model fields from 2012 to 2016. This removes seasonal andyearly fluctuations in the model output.Table 2.1: Model RunsANHA4 Run Kv PrescriptionControl TKEJayne and St Laurent TKE + Jayne and St Laurent formulationPolzin TKE + Polzin formulation24Chapter 3Results3.1 Vertical Di↵usivityFigure 3.1 shows the distribution of the vertical di↵usivities added by the tidal mixing parame-terizations (Kvtide) and of full vertical di↵usivity (Kvfull), TKE added to tidal mixing di↵usivitiesin the Arctic Ocean domain (area above 60N) for each run. The Kvtide distribution shows somevery significant di↵erences between the additional vertical di↵usivity added by the JSL and Polzinformulations, exemplifying how each vertical distribution of internal tide energy dissipation man-ifests di↵erently into vertical di↵usivity addition in the model. Kvtide values are generally smallwith 43% and 62% of values below 106m2s1, the minimum cuto↵ value prescribed by the TKEscheme, for the JSL and Polzin formulations respectively. Despite this, there is also a significantpercentage of Arctic Ocean volume that experiences large values of Kvtide and further, there areimportant di↵erences in the high end distribution of Kvtide between the two tidal mixing runs.Although the two runs have a similar range of Kvtide from O(1014) to O(102)m2s1, the Polzinformulation shows an approximately log normal distribution of Kvtide centred around 106m2s1,while the JSL formulation shows a skewed log distribution with a peak at O(105m2s1), plus anadditional significant peak at 102m2s1, which is the cuto↵ maximum value for Kvtide. The peakfor JSL around 102m2s1 is apparent in both the Kvtide and Kvfull distributions, indicating thatthis spike in di↵usivities is due to the added tidal di↵usivity and not from an altered model statedue to the enhanced mixing but rather from the constant addition of high di↵usivity values overthe averaging period. For Kvfull, all model runs see a range of di↵usivity values from 106 to102m2s1 with peak and median values of O(105) (see Table 3.1), matching previously observedtypical Arctic Ocean di↵usivity values [Rainville and Winsor, 2008]. However, Kvfull values below2000m are 1-2 orders of magnitude larger than observed values of the deep ocean and interior. The253.1. Vertical Di↵usivityKvtide (m2s ) Kvfull (m2s )Figure 3.1: Histograms showing the distribution of vertical di↵usivity in terms of % volume of theArctic Ocean domain averaged from 2012-2016. Vertical di↵usivity for Kvtide distribution (left) forJSL and Polzin formulations and Kvfull for each of control, JSL and Polzin formulations (right).changes to the distribution of Kvfull in the high end tails shows a significant increase in modelvolume with di↵usivity values greater than 105m2s1 for both the JSL and Polzin model runscompared to the control. The JSL formulation has over 10% volume in the Arctic Ocean domainwith Kvfull values above 103m2s1 which is consistent with previous modelling studies using thesame parameterization over a global domain [St Laurent et al., 2002], however these values arelikely to be unphysical for the Arctic region. JSL Kvfull also shows a large peak around 102m2s1which relates to large di↵usivity values in the bottom most cells of the model in regions of highenergy conversion due to the exponentially decaying vertical distribution function (F (z)). ThePolzin formulation has a similar range of values as the control run, however, it maintains a portionof the domain with values elevated to that of the control between 104 and 103m2s1, with 5%volume in the Arctic Ocean domain with Kvfull values above 103m2s1.The average depth profile of vertical di↵usivity (Fig. 3.2), over the Arctic region for each modelrun, shows increased values of Kvfull in the experimental runs compared to the control at everydepth level. The Kvfull in the JSL has the highest vertical di↵usivity values at each depth level,and Kvfull in the Polzin formulation remains larger than the control run but less than full Kvfull inthe JSL run, on average. This is further evident in Figure 3.3, showing the full vertical di↵usivityas a function of height above bottom (HAB) for deep (greater than 2000m depth) and shallow (less263.1. Vertical Di↵usivitythan 1000m depth) profiles in the Arctic domain. In the shallow profiles, there are large di↵erencesranging one to two orders of magnitude in Kvfull between the three model runs at every depth levelon average. This indicates the significant impact that the tidal mixing parameterizations have onshallow profiles by adding di↵usivity at each depth level. The shallow averages for HAB includesthe Arctic domain shelves where tidal mixing is expected to have a larger impact [Rippeth et al.2015]. Deep profile HAB averages display bottom intensification in the JSL and Polzin mixingschemes with elevated near bottom and similar near surface Kvfull values compared to the control.This shows that near to the surface in deep profiles (in areas of the domain that are over deepbasins, for example), the parameterizations do not have much impact with respect to the controlwhere lower di↵usivity values would be expected.Table 3.1: Vertical di↵usivity over the Arctic Ocean domain.Depth ANHA4 Run Kvfull Geometric Mean (m2s1) Kvfull Median (m2s1)FullControl 1.0⇥105 1⇥105Jayne and St Laurent 2.7⇥105 1.2⇥105Polzin 1.5⇥105 1.2⇥105> 2000mControl 4.1⇥105 3.8⇥105Jayne and St Laurent 1.0⇥104 5.1⇥105Polzin 1.6⇥104 4.1⇥105Horizontal slices of the full vertical di↵usivity in the Arctic region (Fig. 3.4), show how theadded di↵usivity from the two experimental formulations enhance Kvfull over regions of roughtopography such as the Lomonosov and Gakkel Ridges in the Eurasian basin. The spatial patternsof Kvfull for both experimental formulations are similar with di↵usivity values one to two ordersof magnitude larger than the control run in the 1062 and 2225m depth levels corresponding toregions where the baroclinic energy transfer is large. The patchy high values of Kvfull in theexperimental runs contribute disproportionately to the averages seen in Figures 3.2 and 3.3, dueto the order of magnitude range in values, meaning that although the averages are much higher atdepth, there is large spatial variability in where the tidal mixing scheme adds mixing to the TKEscheme. The increased Kvfull values in the 1062 and 2225m depth slices in the experimental runsare consistent with the average vertical profiles and HAB profiles (Figures 3.2 and 3.3) which showlarger di↵erences inKvfull at depth (for deep HAB profiles). Vertical di↵usivity values from the JSLformulation are larger in magnitude than in the Polzin formulation in the particular regions where273.1. Vertical Di↵usivityKvfull (m2s )Depth(m)Figure 3.2: Vertical di↵usivity geometrically averaged horizontally over the Arctic domain from2012 to 2016.tidal mixing is enhanced over bottom topography, such as ridges in the Eurasian basin. The tidalmixing experimental runs are adding more mixing on average into the model, however, the addedmixing is localized to regions where enhanced mixing is expected due to the underlying bottomtopography. A further connection here to the HAB shallow profiles, the 186m slices in (Fig. 3.4),show similar values of Kvfull over the Eurasian and Amerasian Basins, but on the Arctic shelves,there is elevated values of di↵usivity, two to three orders of magnitude compared to the controlfor both experimental runs, all around the shelf edges, rather than the localized mixing seen indeeper slices. This shows the di↵erent impact that the parameterizations have in shallow and deepprofiles.Depth-distance sections of full Kvfull along transects across the Arctic from the Canadian Basinto Barents Sea (CanBar) and through the CAA (see Fig. 3.5) show the enhancement of near bottommixing in the experimental runs. In the CanBar transect (Fig. 3.6) the water column above theLomonosov and Gakkel ridges is characterized by di↵usivity values of two orders of magnitudehigher in the JSL and Polzin model runs relative to the control, with the JSL run having higher283.2. Model StateKvfull (m2s ) Kvfull (m2s )Figure 3.3: Vertical di↵usivity geometrically averaged horizontally as a function of height abovebottom for profiles greater than 2000m depth (left) and profiles less than 1000m depth (right)over the Arctic domain averaged from 2012-2016. Height above bottom profiles are cut o↵ whenthere is less than 5000 points to average.di↵usivity values that persist throughout most of the water column above these regions of roughertopography. In the CAA (Fig. 3.7), the shallow depths combined with large roughness valuesresults in large changes in Kvfull throughout most of the transect in the JSL run relative to thecontrol, as well as more instances of the convective scheme being activated (indicated by a valueof Kvfull of 102m2s1), particularly between points C and D. Moving from the Canadian Basininto the CAA between points A to B, Kvfull is up to three orders of magnitude larger in the JSLcompared to the control and Polzin runs, indicating that in this shallow and rough region, theJSL formulation adds more mixing compared to the Polzin. In both the CanBar and the CAAtransects we can see how the prescription of vertical di↵usivity in the Polzin formulation can resultin smaller, but localized changes to the Kvfull field compared to JSL.3.2 Model StateThe changes made to the vertical di↵usivity by the addition of the internal tide mixing pa-rameterizations impacts the model state. In the following we discuss the changes in select modeloutputs to analyze the impacts on the Arctic Ocean model domain state.293.2. Model StateKvfull (m2s )Figure 3.4: Horizontal slices of vertical di↵usivity at the 186m (top), 1062m (middle) and 2225m(bottom) depth levels over the Arctic domain averaged from 2012-2016 for control (left) JSL(middle), and Polzin (right) configurations.303.2. Model StateFigure 3.5: Transects from Canada Basin to Barents Sea (blue line) and through Canadian ArcticArchipelago (red line). Letters correspond to labels on following transect figures 3.6, 3.7, and3.14-3.25.313.2. Model StateKvfull (m2s )Figure 3.6: The full vertical di↵usivity averaged from 2012-2016 across the transect from theCanadian Basin to Barents Sea (see Fig. 3.5) for control (top), JSL (middle) and Polzin (bottom)configurations. Regions with di↵usivity values higher than 102m2s1 are set to light grey andcorrespond to where the model convective scheme is activated.323.2. Model StateKvfull (m2s )Figure 3.7: The full vertical di↵usivity averaged from 2012-2016 across through the CAA (see Fig.3.5) for the control (top), JSL (middle), and Polzin (bottom) configurations. As in Fig. 3.6,Regions with di↵usivity values higher than 102m2s1 are set to light grey and correspond towhere the model convective scheme is activated.333.2. Model StateSSH (m)Figure 3.8: Sea surface height averaged from 2012-2016 for control (left), JSL (middle) and Polzin(right) configurations.3.2.1 Circulation, Sea Ice, Freshwater & Heat Content, and FluxesSea surface height (SSH), can be used as a proxy to interpret surface circulation patterns.In general, flow circulates cyclonically around the Arctic Ocean basins with the exception of theBeaufort gyre, which has anticyclonic surface circulation. SSH patterns in all 3 runs (Fig. 3.8),show a gradient across the Canadian Basin; the strength of the gradient can be used as a proxyfor the strength of the circulation around the basin. The magnitude of this basin scale gradient issignificantly reduced in both experimental runs. In the control run, the maximum di↵erence in SSHacross the Canadian Basin is ⇠0.6m, in JSL ⇠0.35m and Polzin ⇠0.5m. This indicates a reductionin the strength of the surface circulation in the runs with tidal mixing, which has implications onthe transport of freshwater and heat through the Arctic Ocean domain.The ice thickness output fields also show significant impacts from the the addition of internaltide mixing parameterizations (Fig. 3.9). The extent of the sea ice coverage is similar for all threemodel runs for both the March and September monthly averages, however there are significantdi↵erences in the sea ice thickness. The JSL run shows a very large reduction in the amount of seaice that is 3m thick or greater; this result is seen more strongly in the September average wherethe area of sea ice at least 3m thick is reduced by nearly half compared to the control run. Sea icethickness in the Polzin run shows smaller changes from the control run and, compared to JSL, has343.2. Model StateFigure 3.9: Sea ice thickness averaged over the months of March (top) and September (bottom)from 2012-2016 for control (left) JSL (middle) and Polzin (right) configurations.better maintained the sea ice cover and thickness seen in the control run.Fresh Water Content (FWC) is defined as the integrated salinity fraction above the 34.8 isopy-cnal [Woodgate et al., 2006, 2012], where 34.8 is estimated to be the average salinity in the Arctic[Aagaard and Carmack, 1989]. FWC in the Arctic domain, (Fig. 3.10) shows a decrease in fresh-water in the Canadian Basin and an increase in both freshwater and the depth of the 34.8 isopycnalin the Eurasian Basin in the experimental runs. This result is more pronounced in the JSL for-mulation compared to the Polzin which can be related to the increased strength of the circulationin the Polzin compared to the JSL run. Generally, freshwater run o↵ from the strong and largeSiberian rivers is advected into the Canadian Basin following the cyclonic flow. Figure 3.8 showedweakened circulation in the experimental runs, implying that less freshwater will be advected o↵ ofthe Siberian shelves, leading to larger freshwater content in the East Siberian Sea compared to the353.2. Model StateFigure 3.10: Average freshwater content over the Arctic domain from 2012-2016 integrated to the34.8 isopycnal (top), and corresponding 34.8 isopycnal depth (bottom) for the control (left), JSL(middle) and Polzin (right) configurations.control run accompanied by an increase in the depth of the 34.8 isopycnal in this region. The JSLformulation showing increased freshwater compared to the Polzin formulation reflects the relativelysmaller SSH gradients in JSL. Bering Strait is a model boundary thus having the same forcing offreshwater input for all three model runs, similarly, river run o↵ is forced with the same data foreach run, so these sources do not have an impact on variations of FWC. The amount of sea icemelt varies between model runs, as we do see a further reduction in sea ice extent and thicknessin the JSL and Polzin runs. Thus, it is possible there is net freshwater input from ice melt in theexperimental runs.Significant changes are seen in the Heat Content (HC) field (Fig. 3.11) between the three modelruns. HC is defined as:HC = ⇢0cpZ z=0z=HT (z)dz (3.1)where ⇢0 is the reference density, cp is the heat capacity of sea water, and T (z) is the temperatureprofile, integrated over the full water column. Anomaly plots show a decrease in HC in the JSL and363.2. Model State(a) Control (b) JSL (c) Polzin(d) Control - JSL (e) Control - Polzin (f) JSL - PolzinFigure 3.11: Heat content over the Arctic domain averaged over years 2012-2016 and integratedover the full water column (top) with corresponding anomalies (bottom).Polzin runs compared to the control in the Eurasian and Canadian Basins. The sources and sinksfor the HC in the Arctic Ocean come from heat flux through the main Arctic pathways (see Figure3.13) and air-sea fluxes. Relating the heat content field to the sea ice concentration indicates thatthe added Kvtide may decreases stratification in the upper ocean and increase the amount of AWheat mixed higher in the water column, which then melts sea ice, resulting in reduced heat content,however, additional ice melt could also come from increased heat fluxed into the Arctic Ocean fromthe Atlantic Ocean, interacting with sea ice at the surface combined with an increased heat flux tothe atmosphere also resulting in reduced HC.The air-sea fluxes show increased heat fluxed into the atmosphere in the experimental runscompared to the control. Over the Barents Sea, the heat loss to the atmosphere is the strongest,with the control run fluxing more heat than both JSL and Polzin. Through the CAA, the basinmargins, and a large proportion of the Nordic Seas the experimental runs are fluxing more heatthan the control. In the Arctic Ocean overall, more heat is fluxed to the atmosphere in the two373.2. Model State(a) Control (b) JSL (c) Polzin(d) Control - JSL (e) Control - Polzin (f) JSL - PolzinFigure 3.12: Air-sea heat flux over the Arctic domain averaged over years 2012-2016 includingboth ice and open ocean fluxes (top) with corresponding anomalies (bottom).tidal mixing runs compared to the control run. The JSL run shows the strongest deviations fromthe control run. This validates the result seen in the HC field, as there is more heat fluxed to theatmosphere in the tidal mixing runs, there is less HC in the Arctic Ocean.Large scale fluxes show how the addition of tidal mixing changes the transport of volume,freshwater and heat in and out of the Arctic (Fig. 3.13). Observational measurements of masstransports are more common and can be easily compared to model results. Observations show aninflow of about 2.0 Sv through the BSO (based on measurements between 1997 and 2007, fromSmedsrud et al., 2013; Skagseth et al., 2008). This input is balanced by a net outflow through theFram Strait of 2.0±2.7 Sv (1997 to 2007, from Schauer et al., 2008) and through the Davis Straitof 1.6±0.2 Sv (2004 to 2010, Curry et al., 2013). We use the sum of BSO, Fram Strait and DavisStrait observations to evaluate the fluxes through the OSNAP (Overturning in the Sub-polar NorthAtlantic Program) (see Figure 3.13) transect which shows a net flux out of the Arctic through thistransect of about 1.8 Sv for each model run averaged from 2012 to 2016. Adding the observational383.2. Model Statevalues for BSO, Fram Strait and Davis Strait gives 1.6±2.9 Sv. Assuming a steady flux and smallchanges over the past decade through these transects, all three model runs are consistent withobservations and the addition of tidal mixing parameterizations does not significantly impact thesummed mass transport through this region. Observations of freshwater flux in and out of theArctic Ocean show 55 to 60 mSv freshwater inflow through BSO (1997-2007, from Smedsrud etal., 2010). Freshwater outflow is observed through Fram Strait as 66 to 80 mSv (1997-2008, deSteur et al., 2009; Rabe et al., 2009) and Davis Strait with 92±34 mSv (1987 to 1990, Cuny et al.,2005) or 116±41 mSv (2004-2005, Curry et al., 2010). Freshwater through the OSNAP transect issimilar for all three model runs, as expected from the similar mass transport outputs, with 46-48mSv freshwater flux out of the Arctic and sub-polar gyre domain. Observed summed outflow is 98to 117±34 or 122 to 141±41. This result means that model outputs of freshwater flux are on thelow end of the error estimate in the observations. Heat fluxes from observations show 50 to 70 TWheat flux in for BSO (1997-2007, reference temperature of -0.1C, Smedsrud et al., 2013; Skagsethet al., 2008), 36±6 TW flux in for Fram Strait (1997 to 2009, Schauer and Beszczynska-Mo¨ller,2009), and 20±9 TW (2004-2005, reference temperature of -0.1C, Curry et al., 2011) for DavisStrait influx. Again, adding together the three transects gives 108 to 126±23. The model runs allhave much higher heat flux values ranging 480 to 500 TW across the OSNAP transect. One reasonfor this discrepancy may be that the the OSNAP line is to the south of the Nordic Seas where thereis increased heat fluxed to the atmosphere, the change to the heat flux would be captured in theobservational results causing lower heat flux values. It is likely the placement of the OSNAP linerelative to the observations that is causing the largest discrepancy.Transects in the CAA, Barrow Strait, Jones Sound, and Nares Strait are relatively narrowand account for much smaller amounts of volume, freshwater and heat flux. Fluxes through theseregions are dicult to model due to the small scale, shallow and varied topography, and a moredominant tidal signal. The addition of the tidal mixing parameterizations in the JSL and Polzinruns resulted in significant changes to the fluxes through these regions, reflecting the impact thatthe mixing parameterizations had on Kvfull through the CAA (see Figure 3.7). Observations arenot available for every metric across these transects. Observed volume fluxes across Barrow Strait(also Lancaster Sound) are 0.7 Sv out of the Arctic Ocean, freshwater fluxes are 48±15 mSv out ofthe Arctic Ocean, and heat flux is 4⇥107 TW out of the Arctic Ocean (1998-2006, Prinsenberg393.2. Model Stateet al., 2009). Model output from the control and JSL are closer to observations for volume andfreshwater fluxes through Barrow strait compared to Polzin, and all three model runs vastly overestimate the heat flux into the Arctic. Jones Sound has observed volume flux out of the ArcticOcean of 0.3 Sv (2000-2002, Melling et al., 2008) and has no measurements available for freshwateror heat flux. Model output for volume flux through Jones Sound, shows improvement for Polzinand JSL runs, with JSL closer larger and Polzin smaller by a similar magnitude. Volume fluxfor Nares Strait has been observed to be 0.71±0.09 to 1.03±0.11 Sv (2003-2009, Mu¨nchow, 2016)out of the Arctic Ocean. Model results show closer values to observations for the Polzin run andincreasing di↵erences in the JSL run compared to the control. Freshwater flux observations acrossNares Strait show 32±5.7 to 54±9.3 mSv (2003-2009, Mu¨nchow, 2016) out of the Arctic. All threemodel runs are within a reasonable range compared to the observations with Polzin showing adecrease and JSL an increase on average compared to the control run. Comparing the three modelruns, we see that the tidal mixing runs flux 20 to 30 TW more heat into the Arctic through OSNAPcompared to the control, but volume and freshwater fluxes are consistent across all three modelruns with similar values. In the CAA, Polzin shows the best match to observations and eitherimproved or maintains the control run estimate in Nares Strait and Jones Sound, but does a worsejob estimating fluxes across Barrow Strait. The JSL run in the CAA either does a worse job or ormaintains the same as the control run estimate.In general, the experimental runs are inputting more heat into the Arctic, and fluxing moreheat into the atmosphere resulting in less heat being contained in the Arctic Ocean. Volumeand freshwater fluxes are reasonably consistent with observations in the three model runs and aresimilar between the three runs over the OSNAP transect. Considering heat flux through OSNAPin context with the air-sea fluxes and HC, gives a full hypothesis of how the heat budget has beenchanged by the tidal mixing runs in the Arctic Ocean domain. More heat is fluxed into the Arcticvia the OSNAP transect, however, more heat is also being fluxed into the atmosphere, resulting ina net decrease in HC overall.403.2. Model StateTable 3.2: Volume, freshwater, and heat fluxes from observational studies (averaging period isshown beneath in brackets) and for the control, JSL, and Polzin model runs (averaged from 2012to 2016) are shown for Fram Strait, Davis Strait, the BSO, Lancaster Sound (also called BarrowStrait), Nares Strait, and Jones Sound. The OSNAP transect (see Figure 3.13) is used for thethree model runs as an estimation of the total flux through Fram Strait, Davis Strait and theBSO. Negative values represent fluxes in and positive values represent fluxes out of the ArcticOcean.Observational FluxesNet Volume Flux (Sv) Liquid Freshwater Flux (mSv) Heat Flux (TW)Fram Strait 2.3±4.312 66 to 8034 -36 ±65?(1997-2007) (1997-2008) (1997-2009)Davis Strait 1.6±0.22 92±346 or 116±412 -20±92??(2004-2010) (1997-2008) (2004-2005)BSO -2.078 -55 to -607 -507 8?? to -707?(1997-2007) (1997-2007) (1997-2007)Lancaster Sound 0.469 329 4⇥107,9??(1998-2006) (1998-2006) (1998-2006)Nares Strait 0.71±0.09 to 1.03±0.1110 32±5.7 to 54±9.310(2003-2009) (2003-2009)Jones Sound 0.311(2000-2002)Control RunOSNAP 1.8 46.2 -490.2Barrow Strait 0.6 19.8 1.91Schauer et al., 20082Curry et al., 20103de Steur et al., 20094Rabe et al., 20095Schaur and Beszczynska-Moller, 2009?heat flux for closed volume budget6Cuny et al., 2005??heat flux calculated with reference temperature -0.1C7Smesdrud et al., 20108Skagseth et al., 20089Prinsenberg et al., 200910Munchow, 201611Melling et al., 2008413.2. Model StateNares Strait 0.98 32.5 3.3Jones Sound 0.13 4.8 0.4JSL RunOSNAP 1.8 48.0 -495.0Barrow Strait 0.6 20.1 0.7Nares Strait 1.1 37.2 2.4Jones Sound 0.4 12.6 0.5Polzin RunOSNAP 1.8 46.2 -499.0Barrow Strait 0.4 13.1 0.6Nares Strait 0.9 30.4 2.9Jones Sound 0.2 7.0 HydrographyThis next section we use first CanBar then CAA transects (see Figure 3.5), to examine temper-ature, salinity and buoyancy frequency squared in the Arctic Ocean and how these properties areimpacted by the addition of the tidal mixing parameterizations.Canadian Basin to Barents SeaThe CanBar temperature transects (Fig. 3.14) show AW (defined as temperature greater than0C and salinity greater than 34.4) inflow from Barents Sea and Fram Strait (between points H andI). The AW layer can be seen across the Arctic Ocean as it circulates around the basins between theapproximate depths 500m to 1500m, losing heat as it circulates the Arctic Ocean. PW can be seenat the surface of the transect (defined as temperature less than 0C and salinity less than 33) fromapproximately 0 to 200m; it enters at Bering Strait (point G) and circulates the Canadian Basin,finally exiting through the CAA or Fram Strait. The di↵erence plots for this field (Fig. 3.15)423.2. Model StateFigure 3.13: Horizontal fluxes of volume, freshwater and heat through major passage ways in theArctic averaged from 2012 to 2016 and integrated over depth for control, JSL and Polzinformulations. Labels on the Arctic map correspond to transects as follows: BS - Barrow Strait,NS - Nares Strait, JS - Jones Sound, OS - OSNAP.433.2. Model Stateshow where the experimental runs have less heat compared to the control run. In the AW andPW layers there is less heat in the Polzin formulation (0.25-0.5C) compared to the control acrossthe Arctic Ocean, except for the Canadian basin at the surface near Bering Strait where there isincreased heat by up to 0.25C. The JSL formulation has much larger changes in the PW layer of0.5 to 1C lower temperatures in the Eurasian Basin and increased temperatures in the CanadianBasin and, in general, less heat in the AW layer (0.25 to 0.5C), relative to the control run. Higherheat in the PW in the Canadian Basin for JSL and Polzin compared to the control, relates to thereduction in sea ice concentration seen in the two experimental runs. The AW entering the Arcticdomain between points H and I corresponding to the Fram Strait transect is over 1C warmer inthe control run compared to JSL and 0.75-1C warmer than the Polzin formulation, however, alongthe BSO (point I), both experimental runs are warmer than the control. This connects the HC andheat flux results, where the experimental runs are fluxing more heat into the Arctic through theOSNAP line, however, in the Nordic Seas there is stronger air-sea fluxes in the experimental runscompared to the control, resulting in the experimental runs showing a net heat loss, compared tothe control for the AW entering the Eurasian Basin. Not only is the AW modified in the Arctic asit circulates around the basin, but the AW entering the Arctic from the Greenland and LabradorSeas has already been cooled compared to the control run.Salinity across this transect (Fig. 3.16) also highlights the entrance of the AW between points Hand I with high salinity values at about 200 to 500m depth. The salinity di↵erence plots in Figure3.17 clearly show the depths where the experimental runs are increasing salinity or freshening. PWlayer at the surface shows increased salinity of 0.4 to 1 for both the JSL and Polzin formulations,with much stronger changes in the Canada Basin (point G) in JSL compared to Polzin. In the AWlayer (approximately 200-1500m), the tidal mixing runs show a freshening of this layer comparedto the control run. Similarly to the temperature field, the AW entering the Arctic between pointsH and I is impacted by the tidal parameterizations and is already fresher than the control run forboth the JSL and Polzin runs. The basins below about 1500m are largely unchanged in both thetemperature and salinity transects. This is expected considering the short run from 2002-2016.Very generally, we see in the Polzin run, PW is saltier and colder (except for surface waters nearBering Strait), and AW is is fresher and colder, compared to the control. For JSL, PW is saltierand colder, similar to changes seen in the Polzin run, and AW is fresher and warmer compared to443.2. Model StateTemperature (C)Figure 3.14: Depth by along transect distance temperature along the transect CanBar (see Fig.3.5) for the control (top), JSL (middle), and Polzin (bottom) configurations.453.2. Model StateTemperature Anomaly (C)Figure 3.15: Depth by along transect distance temperature anomalies along the transect CanBar(see Fig. 3.5) for control - JSL (top), control - Polzin (middle) and JSL - Polzin (bottom).463.2. Model Statethe control.The changes to the salinity and temperature fields are reflected in the changes to N2 and thestratification across this transect (Fig. 3.18). In the top 500m stratification is very strong, from103 to 104s2, with decreasing stratification with depth, and weak stratification through much ofthe deep basins. Stratification in the top 1000m is impacted by the tidal mixing parameterizationswith increased stratification at the very surface and decreased levels of stratification just below at200-500m depth. In general the changes to the stratification are at or smaller than the order ofmagnitude of the value (Fig. 3.19). Anomaly plots show similar di↵erences from the control runin both Polzin and JSL formulations, with the JSL run having changes further down in the watercolumn than the Polzin run. There is weakened stratification at the surface in the Eurasian Basin,at 200-500m depth level in the Canadian Basin and at the surface near Bering Strait. Increasedstratification is seen in the 200-1000m depth range in the Eurasian Basin and most of the surface ofthe Canadian Basin. This implies an erosion of the stratification through the Arctic cold halocline,which separates PW and AW, explaining the increased heat seen at the surface in the CanadianBasin, heat loss in the AW layer, and increased salinity of the PW layer.Canadian Arctic ArchipelagoThe transect through the CAA shows Kvtide increases of several orders of magnitude in theexperimental runs compared to the control (see Figure 3.7), consequently, the temperature, salinityand buoyancy frequency fields are significantly impacted by this enhanced vertical mixing. In thetemperature field (Fig. 3.20) both JSL and Polzin runs show cooling from 0 to 1000m from pointsB to E from 0.5 to 3C (Fig. 3.21) with the largest temperature changes between points D to Fcorresponding to the Ban Bay. This suggests that the water moving through the CAA is largelymodified by the tidal mixing parameterizations from the Canada Basin at point A. JSL maintainscolder temperatures across the CAA transect except in the Canada Basin (A to B) portion of thetransect. Salinity through the CAA (Fig. 3.22) and corresponding anomalies (Fig. 3.23), show anet increase in salinity of the surface waters of up to 1.25 through the CAA transect for the JSLrun. Below about 200m, the experimental runs are fresher than the control, with very small changesto Canada Basin from 200-1000m. This indicates that the water exiting the CAA through BarrowStrait, is colder and saltier at the surface and colder and fresher at depth in the experimental runs473.2. Model StateSalinityFigure 3.16: Depth by along transect distance salinity along the transect CanBar (see Fig. 3.5)for the control (top) JSL (middle) and Polzin (bottom) configurations.483.2. Model StateSalinity AnomalyFigure 3.17: Depth by along transect distance salinity anomalies along the transect CanBar (seeFig. 3.5) for control - JSL (top), control - Polzin (middle) and JSL - Polzin (bottom).493.2. Model StateN2 (s2)Figure 3.18: Depth by along transect distance buoyancy frequency squared, N2, across thetransect CanBar (see Fig. 3.5) for the control (top), JSL (middle), and Polzin (bottom)configurations.503.2. Model StateN2 Anomaly (s2)Figure 3.19: Depth by along transect buoyancy frequency squared, N2, anomalies across thetransect CanBar (see Fig. 3.5) for control - JSL (top), control - Polzin (middle) and JSL - Polzin(bottom).513.3. Atlantic and Arctic Comparisoncompared to the control. Looking at how the changes to temperature and salinity impacts N2(Figures 3.24 and 3.25), for both the JSL and Polzin runs there is a weakening of stratificationat the surface, however for JSL, there is weakened stratification throughout the first 400m of thetransect compared to the control. Below 400m and in patches throughout the transect for thePolzin formulation, the stratification is increased in the experimental runs. This has impacts onthe water that is being exported out of the Arctic Ocean into Ban Bay and into Labrador Sea asit overlies stronger stratification and is colder and fresher.3.3 Atlantic and Arctic ComparisonA comparison of the impacts of the tidal mixing parameterizations in the North Atlantic andthe Arctic is of interest as it highlights the ways that the Arctic responds uniquely to these param-eterizations given its low internal wave energy levels and strong stratification.Comparing the Arctic to the northern hemisphere Atlantic Ocean distribution of the Kvfull field(Figures 3.1 and 3.26) shows that each region experiences a similar range of values but with di↵erentdistributions. In the Atlantic Ocean, the Polzin Kvtide has a smaller % volume with values from109 to 103m2s1 but in the Arctic Ocean there is a significant percentage of volume with valuesin the range 1013 to 109m2s1, which do not impact the values generated from the TKE closurescheme. For Kvfull the Atlantic region has a larger proportion of the total volume with verticaldi↵usivity values above 105m2s1 compared to the Arctic region for the JSL formulation, thePolzin formulation has a similar distribution of Kvfull values to the Arctic region. One dimensionalaverages of Kvfull over the Arctic and Atlantic Ocean domains (Figures 3.2 and 3.27) show that theAtlantic domain has the same ordering of the model runs in terms average di↵usivity strengths (JSLhas the largest values at every depth level and Polzin is less than JSL but larger than the control)however, the Atlantic region has much larger JSL values at depth compared to the Arctic domainof up to an order of magnitude. The Polzin formulation shows a clear bottom enhancement inAtlantic compared to the control, indicating that higher internal tide energy in the Atlantic causesthe Polzin formulation to behave more similarly to the JSL which shows clear bottom enhancementin both regions.Zonally averaged temperature, salinity and stratification (N2) anomaly sections along the full523.3. Atlantic and Arctic ComparisonTemperature (C)Figure 3.20: Depth by along transect temperature across the transect through the CAA (see Fig.3.5) for the control (top) JSL (middle) and Polzin (bottom) configurations.533.3. Atlantic and Arctic ComparisonTemperature Anomaly (C)Temperature Anomaly (C)Figure 3.21: Depth by along transect temperature anomalies across the transect through theCAA (see Fig. 3.5) for control - JSL (top), control - Polzin (middle) and JSL - Polzin (bottom).543.3. Atlantic and Arctic ComparisonSalinityFigure 3.22: Depth by along transect salinity across the transect through the CAA (see Fig. 3.5)transect for the control (top) JSL (middle) and Polzin (bottom) configurations.553.3. Atlantic and Arctic ComparisonSalinity AnomalyFigure 3.23: Depth by along transect distance salinity anomalies through the CAA (see Fig. 3.5)transect for control - JSL(top), control - Polzin (middle) and JSL - Polzin (bottom).563.3. Atlantic and Arctic ComparisonN2 (s2)Figure 3.24: Depth by along transect distance buoyancy frequency squared, N2, through the CAAsee Fig. 3.5) transect for control (top) JSL(middle) and Polzin (bottom) configurations.573.3. Atlantic and Arctic ComparisonN2 Anomaly (s2)Figure 3.25: Depth by along transect distance buoyancy frequency squared, N2, anomaliesthrough the CAA see Fig. 3.5) transect for control - JSL (top), control - Polzin (middle) and JSL- Polzin (bottom).583.3. Atlantic and Arctic ComparisonKvtide (m2s ) Kvfull (m2s )Figure 3.26: Histograms showing the distribution of vertical di↵usivity in terms of % volume ofthe northern hemisphere Atlantic Ocean domain averaged from 2012-2016. Vertical di↵usivityinput from the JSL and Polzin for Kvtide (left) and Kvfull distribution (right) for each of thecontrol, JSL and Polzin formulations.ANHA4 domain shows how the addition of the internal tide mixing parameterizations impactsthe model state di↵erently in the Atlantic vs the Arctic Ocean. The temperature anomaly field(Fig. 3.28) in the Atlantic for control-JSL, shows the JSL formulation warming the majority ofthe Atlantic domain relative to changes in the Arctic region, which are small except at the surface,where waters are much cooler in the JSL run, as has been already commented on. The Polzin runhas very small di↵erences from the control run beneath 1000m across the full domain, however, atthe surface there net warming in the Atlantic and cooling in the Arctic regions. This is consistentwith the JSL and Polzin runs fluxing more heat into the Arctic Ocean across the OSNAP line, asthere is more heat in the North Atlantic in the two tidal mixing runs (see Figure 3.13).Salinity anomalies (Fig. 3.29) in the Atlantic region show increased salinity in the top 1000mand decreased at the surface for both the JSL and Polzin configurations compared to the control.The Arctic shows the opposite trends, with increased salinity at the surface and decreased from200-2000m. While JSL and Polzin show similar patterned changes to the salinity field compared tothe control run, the JSL configuration again shows much stronger magnitude changes that penetratedeeper. N2 anomalies (Fig. 3.30), show larger changes to the upper ocean stratification in the Arcticcompared to the Atlantic in the experimental runs. Zonal averages allow changes to stratificationin the Arctic to be seen more visibly, with a decrease in stratification in the upper 200 to 500m593.3. Atlantic and Arctic ComparisonKvfull (m2s )Depth(m)Figure 3.27: Vertical di↵usivity geometrically averaged horizontally over the Atlantic Ocean (solidlines) and the Arctic Ocean (dotted lines) from 2012 to 2016 for each of the control, JSL, andPolzin formulations.and stronger stratification in the majority of the basin compared to the control run. This is incontrast to the Atlantic portion of the domain which shows a general increase in stratification in theexperimental run above about 3000m compared to the control. The decreased surface stratificationin the Arctic Ocean in the experimental runs can be connected to the increased air-sea fluxes (seeFigure 3.12). With lower stratification, more vertical mixing can occur causing increase heat fluxfrom the AW layer. Oppositely, in the Atlantic Ocean, the increased surface stratification leadsto a decrease in vertical mixing, keeping heat in the ocean, leading to higher temperatures in theexperimental runs compared to the control. In general, we see that the Atlantic and Arctic regionsof the domain are impacted di↵erently by the addition of internal tide mixing parameterizations,indicating that the unique properties of the Arctic, namely low internal wave energy and highstratification, causes opposite trend deviations from the control run, as well as higher magnitudeanomalies, particularly for the JSL run.603.3. Atlantic and Arctic ComparisonTemperature Anomaly (C)Figure 3.28: Zonal average of temperature anomalies over the full ANHA4 domain averaged from2012-2016 for control - JSL (top), control - Polzin (middle) and JSL - Polzin (bottom).613.3. Atlantic and Arctic ComparisonSalinity AnomalyFigure 3.29: Zonal average of salinity anomalies over the full ANHA4 domain averaged from2012-2016 for control - JSL(top), control - Polzin (middle) and JSL - Polzin (bottom).623.3. Atlantic and Arctic ComparisonN2 Anomaly (s2)Figure 3.30: Zonal average of buoyancy frequency squared, N2, anomalies over the full ANHA4domain averaged from 2012-2016 for control - JSL (top), control - Polzin (middle) and JSL -Polzin (bottom).63Chapter 4Summary and Discussion4.1 Summary of ResultsInternal tide mixing parameterizations from Jayne and St Laurent [2001] and Polzin [2009]were added in separate experimental runs of the ANHA4 regional configuration of the NEMOmodel. There were three runs examined in total, the two experimental runs, the Jayne and StLaurent (JSL) and Polzin implementations, as well as a control run without any parameterizationfor internal tide mixing. All three calculated sub-grid scale vertical mixing using the TurbulentKinetic Energy (TKE) closure scheme, with the experimental runs adding additional di↵usivityprescribed by the tidal mixing parameterizations to the calculated vertical di↵usivity values fromthe TKE mixing scheme. The runs were integrated from January 2002 to 2016, and analysis wasdone on the time-averaged fields from 2012 to 2016 in the Arctic Ocean domain, with comparisonsmade to the Atlantic Ocean domain as well.The distribution of the full time-averaged vertical di↵usivity (Kvfull) and the time-averagedvertical di↵usivity from the internal tide mixing parameterizations only (Kvtide) over all modelgrid cells in the Arctic Ocean domain were examined using histograms, as well as via one and twodimensional spatially averaged views of Kvfull. The addition of the tidal mixing parameterizationsresulted in enhanced vertical di↵usivity over the regions of rough topography in the Arctic Oceanas has been previously observed [Rainville and Winsor, 2008]. The two internal tide mixing runsadded vertical di↵usivity values to the model field that are above the minimum value of the TKEscheme to a large proportion of the volume of the Arctic Ocean region, thus, despite the low tidalenergy levels of the Arctic Ocean, the internal tide mixing parameterizations still had a significantimpact on the vertical di↵usivity field and largely alters the model state. The most significantdi↵erence between the two parameterizations was that the magnitudes of vertical di↵usivity added644.1. Summary of Resultsby the JSL formulation were up to two orders of magnitude larger over rough topography and inregions of high internal tide energy compared to those added by the Polzin formulation. Kvfull inthe JSL run frequently reached values of 102m2s1, which have not been observed in the ArcticOcean region and are likely unrealistic.This study has shown that in the low internal wave energy and highly stratified Arctic Oceanenvironment, the choice of internal tide parameterization in a coarse resolution model has significantimpact on the model fields. Sea surface height (SSH), sea ice thickness and freshwater content(FWC), were compared between the three runs. This showed that the elevated rates of mixing inthe JSL run and to a lesser extent in the Polzin run, reduced the SSH gradient across the CanadianBasin, its related gyre circulation, and decreased the amount of thick (3m or greater) sea ice.Changes in the JSL run were generally of much larger magnitudes compared to the Polzin run.The changed patterns of FWC shows the consequence of the decreased circulation in the CanadianBasin seen in the SSH fields, with freshwater distributed throughout the Canadian Basin and notadvected as far in the JSL run particularly. The heat content (HC) field showed a decrease in theamount of heat in the Arctic Ocean in both the JSL and Polzin runs, and a small area where HCwas larger for the tidal mixing runs in the Greenland Sea. This result was linked to a significantincrease in the ocean-air heat fluxes in the experimental runs. Presumably, increased tidal mixingfluxed more heat to the ocean surface where it was lost to the atmosphere in these runs. Thisis consistent and proportional with the respective loss in sea ice thickness seen in the JSL andPolzin runs. Fluxes of volume, freshwater, and heat were calculated across the OSNAP transectand through the CAA (see Figure 3.13) and the sum of observations from commonly observedlines to the north of the OSNAP line were used to evaluate the exchange between the Atlanticand Arctic Oceans. For all three model runs, volume and freshwater fluxes were within reasonableagreement with observed values, however the heat flux is much larger compared to the observations,reflecting the large amount of heat loss in the Nordic Seas that is missed by the choice of a moresouthern transect. In the CAA, fluxes through Barrow Strait, Jones Sound and Nares Strait werecompared to observations where available. Comparisons to observed values of volume flux throughJones Sound and volume and freshwater flux through Nares Strait, showed that the Polzin runperformed the best of the three runs overall, whereas, through Barrow Strait, the JSL and thecontrol runs were closer to observations for volume and freshwater flux. All three model runs vastly654.2. Discussion and Conclusionsoverestimated the heat flux through Barrow Strait, observations for heat flux through Nares Straitand Jones Sound were not available.Two transects were chosen to examine the spatial structure of temperature, salinity and strati-fication for each model run. The first was across the Arctic Ocean from the Canadian Basin to theBarents Sea (CanBar), and the second through the CAA (see Figure 3.5). The CanBar transectshowed important changes to the major water masses (PW and AW) across the Arctic Ocean inboth tidal mixing runs. The two experimental runs changed the PW to be colder and more salinecompared to the control similarly, with larger magnitude changes seen in the JSL run, howeverthe changes to the AW layer di↵ered between the two, particularly in the Canadian Basin wherethe JSL run increased the temperature of the AW, and the Polzin run decreased AW temperaturerelative to the control. Through the relatively shallow CAA, changes to the salinity, temperatureand N2 fields in the experimental runs persisted throughout the whole water column, resultingin the water exiting Barrow Strait into Ban Bay being significantly colder and fresher than thecontrol run in both runs employing tidal mixing formulations.In the last section, a first order comparison between the Atlantic and Arctic Oceans highlightedhow the tidal mixing parameterizations impacted the two regions di↵erently, indicating that theunique environment of the Arctic Ocean causes the two mixing parameterizations to manifestdi↵erently then they would in a higher energy environment such as the North Atlantic Ocean.Significant changes to the temperature, salinity and N2 fields were seen at greater depths in theAtlantic Ocean compared to the Arctic Ocean, showing how the unique stratification structure ofthe Arctic Ocean impacts how the changes to the model fields due to increased tidal mixing aredistributed.4.2 Discussion and ConclusionsOne of the key findings of this study, which contrasted the impact of two di↵erent formulationsof an internal tide mixing parameterization, was that the JSL formulation prescribed significantlylarger values of mixing rate than the Polzin formulation and, as such, had a significantly largerimpact on the model fields. To understand this result, it is helpful to take a closer look at theparameterizations to draw some insight on how the Polzin and JSL formulations distribute mixing664.2. Discussion and Conclusionsdi↵erently. In the prescription of dissipation, the two formulations input the same baroclinic tidalenergy and have the same total dissipation integrated over the full water column. The Polzin for-mulation relates where in the vertical profile dissipation is placed to the stratification, placing moredissipation where the stratification is higher. However, the places where stratification is stronger isalso where mixing is inhibited by the strength of the stratification according to the assumed Osborn[1980] relation. In contrast, the JSL formulation places dissipation in the vertical profile accord-ing to an exponentially decaying scale, regardless of the overlying stratification. Therefore, if thePolzin formulation is systematically placing dissipation where mixing more inhibited by the highstratification, then it is reasonable to expect it to produce less mixing than the JSL formulationoverall, even though the total dissipation is the same. Furthermore, because the JSL formulationis bottom intensified, where the stratification tends to be weaker compared to the surface and thehalocline, especially in the Arctic Ocean, one further expects that the prescribed dissipation willresult in mixing compared to the Polzin formulation for the same profile. This provides a plausibleexplaination why, even though the two parameterizations have the same input of baroclinic tidalenergy and the same dissipation integrated over depth, the Polzin formulation has lower mixingthan the JSL overall.It is also worthwhile to evaluate how physical both the varying Kvfull values and their impacton the model state for each of the runs are, for these values and impacts can vary significantlyacross the three model runs. In the experimental runs, up to 10% of the Arctic Ocean volume hasKvfull values greater than 103m2s1, which are likely unphysical, as they are higher than observedvalues. Despite this, for Kvfull, all model runs have average values of O(105m2s1), matchingpreviously observed typical Arctic Ocean di↵usivity values [Rainville and Winsor, 2008]. Thus,although a lot of mixing is being added in the experimental runs, on average, the average verticaldi↵usivity is not unrealistic. However, Kvfull values below 2000m in these runs are typically 1-2orders of magnitude larger than observed values of vertical di↵usivity in the deep ocean. Thislarge average value is strongly influenced by a small number of very large values that are patchy inspace and generally found right near the bottom topography as is prescribed by the tidal mixingformulations. A large proportion of the deep Kvtide values in the Eurasian and Canadian Basinsare O(106m2s1), which does match with previous estimated averages of vertical di↵usivity inthe deep Arctic Ocean. Due to the vertical di↵usivity field being patchy in space and time, it is674.2. Discussion and Conclusionsdicult to say whether the places where enhanced mixing is placed in the Arctic Ocean from thetidal mixing parameterizations is accurate. The observations from Rippeth et al. [2015] indicatedthere to be enhanced mixing on the continental slopes, a feature which is captured by the tidalmixing runs and not by the control run.The changes from the control run for temperature, salinity and stratification fields were largerin magnitude in the JSL run relative to the Polzin run, indicating that the former has a larger andmore immediate impact on model fields, not surprising considering the larger Kvfull values in JSLrun overall. The larger magnitude temperature and salinity anomalies at depth in the JSL runcompared to the Polzin run indicates that the increased vertical di↵usivity, on average, allows forchanges to temperature and salinity to permeate into the model domain at a faster rate. However,there are much smaller changes to salinity and temperature at depth in the Arctic Ocean comparedto the Atlantic Ocean. Regardless of the vertical profile of di↵usivity used in the tidal mixingformulation, the higher levels of stratification in the Arctic Ocean serves to reduce vertical transferof heat and salt. This accounts for the significant di↵erence in the zonal anomalies found in theAtlantic and the Arctic Oceans.It is useful to focus in on the heat budget in the Arctic Ocean as a particular point of interestto show that the implications of increased mixing are not straight forward, and have a complicatedand multifaceted e↵ect. The HC was lower in the two experimental runs, particularly for the JSLformulation, which was counterintuitive considering that there is more heat fluxed into the ArcticOcean through the OSNAP transect, however, there is also more heat fluxed to the atmosphere inthe two experimental runs. This motivated a comparison of all terms in the heat budget in thethree model runs. Specifically, the HC integrated over the full depth in the Arctic Ocean region,the heat fluxed into the Arctic Ocean through the OSNAP transect and the air-ocean heat flux.These three metrics need to be considered together in order to attain a balanced heat budget, asthe heat fluxed to the atmosphere is large enough to counter the additional heat fluxed into theArctic Ocean via the OSNAP transect and result in an overall reduction in HC for the two tidalmixing runs. This result also needs to be considered in context of the changes seen in the AtlanticOcean. This study did not look at the Arctic Ocean as a closed system, instead the results in theArctic Ocean also include an influence of the changes in the Atlantic Ocean due to enhanced tidalmixing which input into the Arctic Ocean domain. This makes teasing apart the source of some of684.2. Discussion and Conclusionsthe Arctic Ocean results challenging.Considering all of the results in this study and the observational evidence examined, it is likelythat the representation of additional tidal mixing for the Polzin formulation is closer to expected inthe Arctic Ocean. Despite the uncertainty of how realistic the magnitudes of the vertical di↵usivityvalues are, both parameterizations successfully add a spatial variability to the model’s mixing fieldthat is realistic, and the consideration of the importance of representing this mixing geographyin realistic models such as NEMO is an important exercise. The way that the two tidal mixingparameterizations manifest in the Arctic Ocean represents an interesting study of adding spatiallydynamic mixing, but also of adding more mixing in general to the Arctic Ocean. This study exploresthe concern many oceanographers have in regards to seeing increased mixing in the Arctic Oceandue to sea ice reduction and resulting increased exposure to atmospheric forcing. We have found adecrease in halocline stratification, ice concentration and increased freshwater outflow in the tidalmixing runs, which can have impact in the global climate through reduced albedo e↵ect, and reducedopen ocean convection, the driving process in the Northern Atlantic arm of the MOC. The workpresented here highlights the usefulness of internal tide parameterizations in representing the spatialvariability observed in vertical di↵usivity values in the Arctic Ocean. Areas over rough topographyshow enhanced mixing using both formulations, which have significant impacts on the Arctic Oceanstate and functioning. 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