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Circulation and upwelling in Mackenzie Canyon, a dynamically wide submarine canyon in the Beaufort Sea Machuca, Idalia Alicia 2019

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Circulation and Upwelling in Mackenzie Canyon, a Dynamically WideSubmarine Canyon in the Beaufort SeabyIdalia Alicia MachucaB.Sc. Geophysics, The University of British Columbia, 2014A.Sc. Physics and Mathematics, St. John’s College Junior College, 2010A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Oceanography)The University of British Columbia(Vancouver)April 2019c© Idalia Alicia Machuca, 2019The following individuals certify that they have read, and recommend to the Faculty of Graduate andPostdoctoral Studies for acceptance, the thesis entitled:Circulation and Upwelling in Mackenzie Canyon, a Dynamically Wide Submarine Canyonin the Beaufort Seasubmitted by Idalia Alicia Machuca in partial fulfillment of the requirements for the degree of Masterof Science in Oceanography.Examining Committee:Susan Allen, Earth, Ocean and Atmospheric SciencesSupervisorMichael Dunphy, Fisheries and Oceans CanadaSupervisory Committee MemberBrian Hunt, Institute for the Oceans and FisheriesSupervisory Committee MemberStephanie Waterman, Earth, Ocean and Atmospheric SciencesSupervisory Committee MemberRich Pawlowicz, Earth, Ocean and Atmospheric SciencesExternal ExamineriiAbstractMackenzie Canyon, in the southeastern Beaufort Sea, is a site for strong upwelling compared to theadjacent continental shelf and slope and potentially supplies the shelf with significant levels of nitrate.Research regarding the circulation and upwelling mechanisms in submarine canyons has previouslybeen limited to dynamically narrow canyons, and most studies have used numerical models with ideal-ized bathymetry. The main goal of the study presented in this thesis is to describe the circulation andupwelling in Mackenzie Canyon, which is classified as a dynamically wide canyon. This study alsoidentifies key flow features that act as significant modifiers of upwelling, examines differences betweenidealized and realistic model simulations, and estimates the canyon-induced upwelling of nitrate.To address these goals, the circulation and upwelling associated with an upwelling event inducedby an impulsive wind forcing in Mackenzie Canyon was simulated using a nested-grid modelling sys-tem configuration based on the Nucleus for European Modelling of the Ocean framework. Numericalsimulations were conducted using realistic and idealized bathymetry and three cases of wind stress forc-ing. The model performance was evaluated using observational data from Mackenzie Canyon during anupwelling event.This study finds that near-geostrophic flows are topographically steered around the MackenzieCanyon walls. Strong cyclonic vorticity is generated on the upstream corner of the canyon mouthand evolves into a closed, cyclonic eddy, which becomes a site for strong upwelling. A coastal trappedwave (CTW) is induced on the downstream side of the canyon and propagates upstream. It is charac-terized as a shelf wave using a model that searches for the free wave solutions of CTWs along straightcoastlines. An upwelling signal in the canyon exits the canyon and propagates along the slope with theCTW. Unlike narrow canyons, upwelling in Mackenzie Canyon is stronger on the upstream side than onthe downstream side, likely as a consequence of the upstream propagation of the CTW. The nitrate fluxiiiacross the nitracline depth supplied by upwelling in Mackenzie Canyon during the initial 36 hours of anupwelling event is estimated to be twice the seasonal draw-down in the Beaufort Sea.ivLay SummarySubmarine canyons are steep, complex topographic features off the world’s coasts. These regionsare characterized by unique circulation patterns and strong upwelling, which is an oceanographic phe-nomenon whereby water from deeper layers of the ocean is driven upward. Nutrient-rich water deliveredby upwelling to the top layers of the ocean fertilizes photosynthetic organisms near the surface whichsupport coastal populations of fish, mammals, and birds.Research using computer models of the ocean circulation to study the mechanisms driving upwellingin submarine canyons has previously only focused on narrow canyons and mostly used simplifiedcanyon bathymetry. This project studies the different circulation and upwelling patterns in MackenzieCanyon, which is a wide canyon, and compares the results of models which use simplified and realisticbathymetry. This study finds that upwelling in Mackenzie Canyon is sufficiently strong to support highbiological productivity in the region.vPrefaceThis thesis is the original work of the author, Idalia Alicia Machuca. The research project presentedin this thesis was supervised by Susan Allen, who assisted with the model configuration, interpreta-tion of results, and manuscript editing. The numerical experiments were conducted using the NEMO(Nucleus for European Modelling of the Ocean) ocean modelling framework. The AGRIF (AdaptiveGrid Refinement in Fortran) software was used to implement a nested grid, which was primarily config-ured by Michael Dunphy. Model evaluation was conducted using observational data provided by AmyWaterhouse. This work is unpublished, but it is undergoing preparation for future publication.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation for submarine canyons research . . . . . . . . . . . . . . . . . . . . . . . 11.2 Upwelling dynamics in submarine canyons . . . . . . . . . . . . . . . . . . . . . . . 41.3 Circulation and upwelling in the Beaufort Sea and Mackenzie Canyon . . . . . . . . . 91.4 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.1 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Model simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3 Quantification of canyon upwelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23vii2.4 Coastal trapped wave analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.5 Calculations for model result analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1 Circulation patterns influenced by topographic steering . . . . . . . . . . . . . . . . . 313.2 Circulation patterns influenced by coastal trapped wave propagation . . . . . . . . . . 333.3 Coastal trapped wave characterization . . . . . . . . . . . . . . . . . . . . . . . . . . 343.4 Distribution and propagation of the canyon upwelling signal . . . . . . . . . . . . . . 363.5 Nitrate transport across the nitracline depth . . . . . . . . . . . . . . . . . . . . . . . 383.6 Effects of wind forcing on circulation and upwelling . . . . . . . . . . . . . . . . . . 393.7 Model evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.1 General circulation patterns and key features . . . . . . . . . . . . . . . . . . . . . . . 604.2 Distribution and propagation of upwelling signal . . . . . . . . . . . . . . . . . . . . 624.3 Canyon-induced nitrate flux and draw-down . . . . . . . . . . . . . . . . . . . . . . . 644.4 Modelling with idealized and realistic bathymetry . . . . . . . . . . . . . . . . . . . . 654.5 Model considerations and limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . 655 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72A Relevant variables and numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81B Additional details of methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82B.1 Sea surface elevation calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82B.2 Wind stress formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83C Additional figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84C.1 Wave signal at the eastern edge of the model domain . . . . . . . . . . . . . . . . . . 84C.2 Flow speed and direction as 1-hour averages . . . . . . . . . . . . . . . . . . . . . . . 85C.3 Wave propagation on the salinity surface representative of the Atlantic Water . . . . . 86viiiC.4 Structure of the lowest wave mode computed by the coastal trapped wave model . . . . 87C.5 Structure for vertical velocity of the coastal trapped wave in the Mackenzie Canyonmodel simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88D Schematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89D.1 Circulation in narrow canyons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89D.2 Circulation in Mackenzie Canyon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90ixList of TablesTable 2.1 Bathymetry, wind forcing, and stratification cases for all simulations. . . . . . . . . 27Table 2.2 Values for the maximum alongshore wind stress τ pulsex−max, reduced alongshore windstress τrelaxx−const , and cross-shore wind stress τy for all wind forcing cases. . . . . . . . 28Table A.1 Values of relevant variables and numbers for the base wind forcing case. . . . . . . 81xList of FiguresFigure 1.1 Plan view of idealized canyon bathymetry with definitions of the relevant directionsof flow used in this study. The canyon bathymetry is coloured with light greencolours indicating shallow depths and blue colours indicating deeper depths, and theisobaths are labelled in metres. The head, mouth, and axis of a canyon are typicallyused as references for the direction of flows in the region. Flows are considered tobe upwelling-favourable if movement is in the downstream/up-shelf direction. . . . 15Figure 1.2 Cross-section along the axis of the canyon adapted from Ramos-Musalem and Allen(2019). The sketch shows upwelling isopycnals during a canyon-induced upwellingevent and the relevant scales referred to in this thesis. The scales include the up-welling depthZ, depth of the canyon head Hh, depth of the shelf break Hs, depth ofthe canyon at the mouth Hc, canyon length L, and z is the vertical coordinate. Thedeepest isopycnal to be upwelled is depicted by the bold, green line. . . . . . . . . 16Figure 1.3 Plan view of flows over a canyon for small, moderate, and large Rossby numbersRo (Allen, 2004, reprinted with permission of the author). This figure depicts thetendency for flows to either cross or follow the canyon topography depending onRo (which can be defined using the turning radius of the shelf-break isobath on theupstream corner of the canyon R as in Allen (2004) or using the width of the canyonhalf-way along the canyon length RW as in Howatt and Allen (2013)). The thin linerepresents the canyon rim, the thick line shows the flow path, and the arrow pointsin the direction of the flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17xiFigure 1.4 a) Bathymetry of the Arctic Ocean, b) 3-dimensional view of the bathymetry nearMackenzie Canyon, and c) local bathymetry of the southern Beaufort Sea. Panels(a) and (c) show the model domain used in this study outlined by the black rectangle.Panel (c) shows the mooring stations from past observational studies (Carmack andKulikov, 1998; Williams et al., 2006). . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 2.1 a) Realistic and b) idealized model domain and bathymetry. The parent model ex-tends across the full model domain, and the child model covers the area outlined bythe dashed-line rectangle over the canyon bathymetry. The dimensions for canyonwidth and length are identified by the dark, black lines, and the three open bound-aries are labelled according to the corresponding boundary conditions. The directionof mean flow in the model domain is indicated by the upshelf-directed arrow. . . . 29Figure 2.2 a) Alongshore wind stress τx and b) the resulting, alongshore velocity component ofincoming shelf currents for all wind forcing cases (half, base, double). c) Realisticcanyon bathymetry and stations where observation data was collected for stratifi-cation and nitrate concentration. Depth profiles for d) temperature and e) salinityused as initial conditions for the control and evaluation model runs. f) Relationshipbetween salinity and nitrate concentration. . . . . . . . . . . . . . . . . . . . . . . 30Figure 3.1 Characterization of the horizontal circulation on the UHW-representative surfacein the idealized model: Plan views of a-c) flow speed and direction [ms−1] andd-f) relative vorticity [s−1] averaged over three separate days (top row: hours 12-36, middle row: hours 36-60, bottom row: hours 84-108); g) time series of windstress and average alongshore velocity of incoming currents over the upstream sideof the shelf. The blue diamond in plan views (a-c) shows the location of maximumspeeds. The solid, black line outlines the canyon bathymetry at the initial depth ofthe UHW-representative surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 3.2 Characterization of the horizontal circulation on the UHW-representative surface inthe realistic model: Format follows Figure 3.1. . . . . . . . . . . . . . . . . . . . 42xiiFigure 3.3 Characterization of the vertical velocity on and vertical displacement of the UHW-representative surface in the idealized model: Plan views of a-c) vertical velocity[mms−1] 1-hour averages and d-f) vertical displacement [m] averaged over threeseparate days (top row: hours 12-36, middle row: hours 36-60, bottom row: hours84-108); g) time series of wind stress and average alongshore velocity of incomingcurrents over the upstream side of the shelf. The red diamond in plan views (a-c)shows the location of maximum upward displacement. The solid, black line outlinesthe canyon bathymetry at the initial depth of the water mass. Small scale oscillationsin vertical velocity correspond to the steps in the model bathymetry. . . . . . . . . 43Figure 3.4 Characterization of the vertical velocity on and vertical displacement of the UHW-representative surface in the realistic model: Format follows Figure 3.3. . . . . . . 44Figure 3.5 Characterization of the horizontal circulation on the AW-representative surface inthe idealized model: Plan views of a-c) flow speed and direction [ms−1] and d-f)relative vorticity [s−1] averaged over three separate days (top row: hours 12-36,middle row: hours 36-60, bottom row: hours 84-108); g) time series of wind stressand average alongshore velocity of incoming currents over the upstream side ofthe shelf. The blue diamond in plan views (d-f) shows the location of maximumspeeds. The solid, black line outlines the canyon bathymetry at the initial depth ofthe AW-representative surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 3.6 Characterization of the horizontal circulation on the AW-representative surface inthe realistic model: Format follows Figure 3.5. . . . . . . . . . . . . . . . . . . . 46Figure 3.7 Characterization of the vertical velocity on and vertical displacement of the AW-representative surface in the idealized model: Plan views of a-c) vertical velocity[mms−1] 1-hour averages and d-f) vertical displacement [m] averaged over threeseparate days (top row: hours 12-36, middle row: hours 36-60, bottom row: hours84-108); g) time series of wind stress and average alongshore velocity of incomingcurrents over the upstream side of the shelf. The red diamond in plan views (d-f)shows the location of maximum upward displacement. The solid, black line outlinesthe canyon bathymetry at the initial depth of the water mass. Small scale oscillationsin vertical velocity correspond to the steps in the model bathymetry. . . . . . . . . 47xiiiFigure 3.8 Characterization of the vertical velocity on and vertical displacement of the AW-representative surface in the realistic model: Format follows Figure 3.7. . . . . . . 48Figure 3.9 Hovmo¨ller diagrams showing the propagation of the CTW along (a-d) Section Aand (e-h) Section B and (i-l) plan views of vertical velocity [mms−1] on the UHW-and AW-representative surfaces in both idealized and realistic models. The transectsfor Section A and B are outlined by dashed, black lines in the plan views for the cor-responding model and water mass surface. The speed of the CTW as it propagates(b) outside and (f) inside the canyon topography is estimated by tracking the pathof the wave trough (solid, black line with gray diamond markers) on the Hovmo¨llerplots for the AW-representative surface in the idealized model. The green, dashedline in panel (b) has a slope of 0.77 ms−1, which is the speed of the CTW computedby the CTW model based on the wave parameters estimated for the CTW in theMackenzie Canyon model simulations between hours 24 and 36 (Figure 3.11). Theplan views (i-l) show average vertical velocities at hour 36 for UHW-representativesurfaces and at hour 48 for AW-representative surfaces. The shape of the Hovmo¨llerdiagram changes according to the space occupied by the water mass during the up-welling event. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Figure 3.10 Plan views of vertical velocity [mms−1] on the UHW-representative surface at hours24, 48, and 96 in the (a-c) idealized and (d-f) realistic models. . . . . . . . . . . . 50xivFigure 3.11 Characterization of the CTW in the Mackenzie Canyon model as the lowest wavemode calculated by the CTW model. a) Plan view and b) vertical cross-sectionalong the dashed line in (a) of the Mackenzie Canyon model results for verticalvelocity [ms−1] at hour 24; c) dispersion curve of the lowest wave mode calculatedby the CTW model for the cross-shore bathymetry profile outlined by the dashed,black line in (a); d) vertical, cross-shore structure for vertical velocity [ms−1] ofthe lowest wave mode calculated by the CTW model. In panel (c), the green circlemarks the wavenumber and frequency estimated between hours 24 and 36 for theCTW observed in the Mackenzie Canyon model simulations; the yellow diamondmarks the wavenumber and frequency of the lowest wave mode computed by theCTW model. The solid, black line in (a) outlines the canyon bathymetry at theshelf-break depth (80 m). The solid, black contours in (b) and (d) outline wavenodes. The vertical velocity magnitudes calculated by the CTW model (d) havebeen normalized for comparison with the Mackenzie Canyon model results. . . . . 51Figure 3.12 Vertical displacement [m] in the idealized model: Plan views at specific depths a-c) 13 m, d-f) 83 m, and g-i) 162 m averaged over three separate days (top row:hours 12-36, middle row: hours 36-60, bottom row: hours 84-108); j) time series ofmaximum vertical displacement values at depths 13 m, 83 m, 162 m, and 477 m. . 52Figure 3.13 Vertical displacement [m] in the realistic model: Format follows Figure 3.12. . . . 53Figure 3.14 Plan views of a-c) idealized and d-f) realistic model results for nitrate transportacross nitracline depth (∼ 50 m) as estimated from salinity; g) time series of thetotal nitrate transport in the child model domain depicted in panels (a-f). Smallscale structures in nitrate transport correspond to the steps in the model bathymetry. 54Figure 3.15 Comparison metric representing the response of CTW amplitude (through verticalvelocity) to wind forcing for idealized and realistic models and normalized withrespect to the ‘base’ wind forcing case. The metric is the mean positive verticalvelocity on the slope just upstream of the canyon. . . . . . . . . . . . . . . . . . . 55xvFigure 3.16 Comparison metric representing the response of upwelling (through vertical dis-placement) to wind forcing for idealized and realistic models and normalized withrespect to the ‘base’ wind forcing case. The metric is the maximum positive valueof vertical displacement in the canyon region. . . . . . . . . . . . . . . . . . . . . 56Figure 3.17 Comparison metric representing the response of nitrate transport for idealized andrealistic models and normalized with respect to the ‘base’ wind forcing case. Themetric is the total transport of nitrate in the child model domain. . . . . . . . . . . 57Figure 3.18 Model-to-observations comparison for currents in Mackenzie Canyon. Model re-sults for flow speed and direction are represented by the coloured background andthe light blue arrows populating the domain. Observational data for flow speed anddirection are represented by dark blue arrows along three transects indicated by thin,black lines: 1) across the canyon mouth, 2) across the canyon near mid-length, and3) cross-shore at the downstream slope. The length and angle of the arrows repre-sent the horizontal components of velocity for both model results and observationalmeasurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Figure 3.19 Model-to-observations comparison for salinity in Mackenzie Canyon. Model resultsfor salinity are represented by the coloured background. Observational data forsalinity is represented by the coloured diamonds along three transects: 1) acrossthe canyon mouth, 2) across the canyon near mid-length, and 3) cross-shore at thedownstream slope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Figure C.1 Plan view of horizontal speeds [ms−1] on the AW-representative surface at hour 96in the idealized model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Figure C.2 Plan views depicting horizontal speed [ms−1] and direction of flows on the UHW-representative surface at hours 24, 48, and 96 in the (a-c) idealized and (d-f) realisticmodels. Speed is depicted by the colouring and direction is depicted by the flowlines on the surface. The flow lines shown in this figure are not streamlines. Theflow lines show flow direction only; these do not show flow speed. . . . . . . . . . 85Figure C.3 Vertical velocity 1-hour averages showing the propagation and modification of thecoastal trapped wave on the AW-representative surface between hours 18 and 84. . 86xviFigure C.4 Structure of the lowest wave mode calculated by the CTW model. a) Disper-sion curve and vertical, cross-shore structure for b) u-velocity component [ms−1],c) v-velocity component [ms−1], d) w-velocity component [ms−1], e) pressure[kgm−1 s−2], and f) density [kgm−3] of the lowest wave mode as calculated by theCTW model for the cross-shore bathymetry profile outlined by the dashed, blackline in Figure 3.11. In panel (a), the green circle marks the wavenumber and fre-quency estimated between hours 24 and 36 for the CTW observed in the MackenzieCanyon model simulations; the yellow diamond marks the wavenumber and fre-quency of the lowest wave mode computed by the CTW model. The magnitudes forall values (b-f) have been normalized for comparison with the Mackenzie Canyonmodel results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Figure C.5 Evolution of the cross-shore structure for vertical velocity [ms−1] of the CTW in theMackenzie Canyon model simulations. The wave structure becomes more complexin time, as depicted by the 1-hour averages for hours a) 12, b) 24, c) 36, and d) 48. 88Figure D.1 Schematic of general circulation and upwelling in narrow canyons. Shelf and slopecurrents flow past the upstream side of the canyon mouth before being deflected on-shore near the downstream wall. At the downstream wall, flows either upwell ontothe shelf, continue towards the head, or turn offshore to exit the canyon. Cycloniccirculation in the canyon evolves into a cyclonic eddy at the canyon rim depth thatspans the canyon width. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Figure D.2 Schematic of general circulation and upwelling in Mackenzie Canyon. Flows aretopographically steered around the canyon walls. An onshore-directed jet encoun-ters the canyon topography at the head, and upwelled flows are advected down-stream. Along-slope flows separate from the topography on the upstream corner ofthe canyon mouth, resulting in the generation of high vorticity flows and the sub-sequent formation of a cyclonic eddy. The attached cyclonic eddy on the upstreamcorner of the canyon mouth becomes a site for strong upwelling. A coastal trappedwave is generated on the downstream side of the canyon and propagates the canyonupwelling signal upstream along the upstream wall and slope. . . . . . . . . . . . 90xviiAcknowledgmentsI extend my heartfelt gratitude and appreciation to everyone who has been a part of my journey ingraduate school. Susan, you have been not only a supportive and encouraging supervisor and mentor,but also an incredible role model. Your dedication to fostering an inclusive, empowering, and caringenvironment for your students has enriched my experience in the Waterhole. Stephanie, Michael, Brian,thank you for your guidance and enthusiasm throughout the completion of this project.Folks of the Waterhole, I am truly lucky to have you all in my life! Thank you for the hugs, wordsof encouragement, mid-afternoon chats and coffee breaks, and Friday evening excursions around Van-couver. Special thanks to my fellow colleagues from the Submarine Canyons - Arctic group, Karina,Birgit, Saurav, and Gonzalo, who have been like family away from home.Rob, thank you for your unwavering confidence that this day was just around the corner and forreminding me of a bright future.Thank you to my family, and especially to my abuelitos, for tirelessly cheering me on over the yearsand nurturing the curiosity and dedication that has proven invaluable for this endeavour.Finally, I dedicate this thesis to my mother, who is my hero, inspiration, and pillar of strength.Everything that has led to this moment would not have been possible without you.xviiiDedicationPor tus esfuerzos, sacrificios, y valentı´a.Por tus consejos y oraciones.Y sobre todo, por el amor y apoyo incondicional que me has brindado.Te la dedico, mami. Lo logramos!xixChapter 1Introduction1.1 Motivation for submarine canyons researchSubmarine canyons are “relatively narrow, deep depressions with steep sides” (Bouma, 1990) thatincise the shelves and slopes of all continental margins. The origin and evolution of submarine canyonsis attributed to mass wasting events, erosive turbidity currents, tectonic activity, and subaerial erosionby rivers and glaciers during the last ice age. A comprehensive database of the topographic features ofthe world’s major oceans called the Global Seafloor Geomorphic Features Map (Harris and Whiteway,2011) identifies 9477 individual canyons. Submarine canyons are classified as either shelf-incising(2,076 of the total, often associated with a major river system) or blind (7,401 of the total, confined tothe continental slope). On average, the areas (777 km2 vs. 375 km2) and lengths (54.8 km vs. 37.3 km)are greater for shelf-incising canyons than for blind canyons. In total, canyons make up 1.21% of theglobal ocean area and 11.2% of the global continental slope area. The pervasiveness and coverage ofsubmarine canyons along the world’s continental slopes draw attention to their role in local physical,sedimentary, and ecological dynamics.The knowledge network related to submarine canyons has been mapped using information retrievaltechniques on a large volume of relevant publications, and it shows that submarine canyon research con-sists of various knowledge clusters spanning geology, oceanography, and ecology (Matos et al., 2018).The largest cluster, Geology and Geophysics, arises early in the history of submarine canyon researchand deals with the geomorphology, sediment dynamics, and geological survey and sampling of subma-rine canyons. Biology and Ecology is the second largest cluster and initially focused on community1composition and trophic structure of benthic ecosystems in canyon systems. Technological develop-ments and the use of multidisciplinary data from observatory networks have further expanded this fieldto include environmental and conservation work. Oceanographic Processes, which includes work onoceanographic phenomena, seasonal variability, and particle transport, is found at the core of the sub-marine canyons research network as it shares many connections with the other clusters. For example, aModelling cluster, which has emerged recently and shares a strong connection with Oceanographic Pro-cesses, includes topics that range from currents and internal waves to distribution patterns of whales andlarvae, all addressed via modelling approaches. Technological advancements in both sampling and com-puting have led to growing interdisciplinarity in research regarding not only canyons but also coastal anddeep-ocean environments. The work presented in this thesis explores oceanographic processes in onesubmarine canyon region and considers the resulting biological implications using numerical modelling.Although submarine canyon research is conducted by many institutions and researchers in over 50countries, the work has been focused on a limited number of canyons (Matos et al., 2018). The 11 moststudied canyons account for 48% of the research effort and have more than 50 associated publicationseach. These canyons are, in descending order of publications, Monterey, Baltimore, Hudson, Gully,Nazare, Lacaze-Duthiers, Cap de Creus, Blanes, Gaoping, La Jolla, and Alaminos, and are locatedalong the Pacific and Atlantic coasts of North America, the South China Sea coast of Taiwan, andthe Mediterranean. The interest in these canyons may be derived from their proximity to researchinstitutions, scientific or economic interest in their geology and/or ecology, or continual effort buildingupon previous data collection. It is crucial to acknowledge, however, that the shortage of studies onsubmarine canyons in other major regions, such as the Arctic, South Atlantic, South Pacific, Indian,and Southern Oceans, may compromise our understanding of the variability of canyon dynamics andprocesses. The role of submarine canyons on oceanic processes in the Arctic region may be of particularinterest since the largest and longest shelf-incising canyons, with an average size of 2160 km2 and meanlength of 99.6 km, are located along the Arctic shelves and slopes (Harris and Whiteway, 2011). In fact,compared to the other major ocean regions, the Arctic Ocean has the highest percentage (16.1%) of theslope area covered by canyons (Harris and Whiteway, 2011). The subject of this study is MackenzieCanyon, a shelf-incising canyon associated with the Mackenzie River and located in the southeasternBeaufort Sea in the Arctic Ocean. As such, this work will provide insight into the oceanic processes ina region that has yet to be adequately studied.2Submarine canyons have been described as “keystone structures” (Vetter et al., 2010) because theyprovide social and economic services that impact human wellbeing (Fernandez-Arcaya et al., 2017; Job-stvogt et al., 2014). Services provided by canyons can be classified as provisioning (the direct productsderived from an ecosystem), regulating (the benefits offered by an ecosystem’s regulatory processes),or supporting (the underlying processes that support these services). Supporting services include watercirculation and exchange by up/downwelling, turbidity currents, hyperpycnal flows, dense shelf watercascading, and mixing (Jobstvogt et al., 2014; Puig et al., 2014). These processes support regulatingservices, such as nutrient and sediment cycling, carbon sequestration, and removal of pollutants fromshelf areas. Canyons also contribute to the biodiversity of coastal regions by acting as nurseries fordemersal fish and other mobile species (Johnson et al., 2013), recruitment grounds for juvenile fish andcrustaceans (Sarda` et al., 1994), and refugia from predation and anthropogenic disturbances (Huvenneet al., 2011). Consequently, canyons offer provisioning services as prime locations for commercial fish-ing (Martı´n et al., 2014; Puig et al., 2012) and several form Marine Protected Areas (Hooker et al.,1999; Sanchez et al., 2013). Research on the various elements involved in these services plays a criti-cal role in not only increasing our understanding on these dynamic regions, but also supporting propermanagement and protection measures through science-based decision-making.Submarine canyons are sites for strong down-canyon and up-canyon flows, mixing, and internalwave generation and breaking. Downwelling and other down-canyon currents are known as “concen-trating processes” (Moors-Murphy, 2014) since these processes supply organic matter derived from sur-face primary production over the canyon to the benthic community on the seabed (Leduc et al., 2014).Other down-canyon currents include turbidity currents, which are high-velocity, turbulent, sediment-laden plumes that flow down-slope as a result of having higher density than the surrounding water dueto their high particle concentration. These currents are triggered by shelf sediment resuspension inducedby storms, sediment slumping and submarine slides along canyon walls, failures of sediments recentlydeposited by fluvial sources, and sediment resuspension induced by bottom-trawling (Puig et al., 2012,2014; Sanchez-Vidal et al., 2012). Canyons associated with river mouths may also experience hyperpyc-nal flows, which are gravity flows driven by the density contrast caused by excess sediments supplied byhigh river discharge during floods (Liu et al., 2009; Puig et al., 2014). In contrast, dense shelf water cas-cading involves currents that are driven by the density contrast of the water itself. As shelf waters coolor evaporate, they may become dense enough to sink and initiate a down-slope current (Canals et al.,32006; Pasqual et al., 2010). These down-canyon flows export high amounts of resuspended sedimentscontaining aged (eroded from the shelf and canyon head) and new (derived from any coinciding phy-toplankton blooms) organic carbon at higher sedimentation rates than the adjacent slope (Canals et al.,2013; Masson et al., 2010; Zu´n˜iga et al., 2009). The accumulation of organic material on the canyonfloor not only promotes high abundance and diversity of demersal and benthic organisms (Brodeur,2001; De Leo et al., 2012), such as detritivores and suspension feeders (Moors-Murphy, 2014; Vetteret al., 2010), but also reveals canyons as significant sinks for organic carbon (Masson et al., 2010).In contrast, upwelling and mixing are considered “enrichment processes” (Moors-Murphy, 2014)that transport nutrient-rich water from the deep ocean to the euphotic zone (Allen et al., 2001). Episodesof canyon upwelling involve up-canyon flows that are driven by an unbalanced cross-shelf pressuregradient associated with currents flowing with the shallower side to the left in the Northern Hemisphere,and vice versa in the Southern Hemisphere (Allen and Durrieu De Madron, 2009; Freeland and Denman,1982). Other enrichment processes in canyons include the elevated levels of mixing and turbulenceproduced by the generation and breaking of internal waves and the focusing of internal tides on canyontopography (Gardner, 1989; Gordon and Marshall, 1976; Hall et al., 2017). Altogether, the increasedsupply of nutrients to the euphotic zone by these processes stimulates primary production (Bosley et al.,2004; Hickey and Banas, 2008; Ryan et al., 2005), which in turn supports high zooplankton abundanceand attracts large pelagic fish and cetaceans (Allen et al., 2001; Brodeur, 2001; Hooker et al., 1999;Moors-Murphy, 2014; Rennie et al., 2009). The dynamics involved in canyon upwelling are describedin Section 1.2.1.2 Upwelling dynamics in submarine canyonsIn this thesis, the alongshore and cross-shore directions refer to the movement of flows or windsalong or across the shelf or shore isobaths. In the cross-shore direction, flows can be onshore or offshore(i.e. towards or away from the coast). Alongshore flows are described as up-shelf /downstream whenthe shallower side (or coast) is to the left of the flow in the Northern Hemisphere, and vice versa in theSouthern Hemisphere. Conversely, down-shelf /upstream refer to the opposite direction. In the NorthernHemisphere, flows are considered left-bounded if movement is in the downstream/up-shelf direction,and vice versa in the Southern Hemisphere. In canyons, the cross-canyon and along-canyon directionsare taken across the canyon width (i.e. alongshore) and along the canyon length (i.e. cross-shore),4respectively. Additionally, the sides of a canyon are referred to as upstream or downstream based onthis vocabulary. These terms are summarized in Figure 1.1.Coastal upwelling is associated with an alongshore, up-shelf wind stress, which induces offshore-directed Ekman transport of the surface layers. As surface water moves offshore, the sea level lowerstowards the coast and creates an onshore pressure gradient. The pressure gradient is generally balancedby the Coriolis force, and a geostrophic current is initiated in the up-shelf direction. Due to massconservation, deeper water is upwelled to replace the surface water that was carried offshore. Althoughinitiated by similar forcing, canyon upwelling involves a more complex series of processes and producesstronger upwelling compared to its adjacent shelf (Allen, 1996).The response of a submarine canyon to shelf currents is largely dependent on the canyon widthand stratification (Allen, 2000; Hickey, 1997; Hyun, 2004; Klinck, 1996). Canyons are considered dy-namically narrow, intermediate, or wide depending on the ratio between the canyon width W and theinternal Rossby radius of deformation a (Klinck, 1988, 1989). The internal Rossby radius of defor-mation a = NHc/ f (Hickey, 1997; Klinck, 1996; Williams et al., 2006) characterizes the horizontalscale at which rotation and gravity (in this format, through stratification) are equally significant. Forthese expressions, N is the Brunt-Va¨isa¨la¨ or buoyancy frequency where N2 = −g/ρo∂ρ/∂ z, Hc is thedepth of the canyon at the mouth, f is the Coriolis parameter, g is the gravitational acceleration, ρ isthe density, ρo is a reference density, and z is the vertical coordinate. Flows with length scales greaterthan the deformation radius are generally geostrophic. Canyons with widths W smaller than 2a are con-sidered “narrow” (Hyun, 2004), and have been extensively studied (Allen and Hickey, 2010; Hickey,1997; Klinck, 1988, 1996). The details regarding the circulation and upwelling response associated withnarrow canyons are described below.Geostrophic currents upstream of a canyon are supported by an onshore, barotropic pressure gradi-ent produced by the tilted free surface. The pressure gradient is balanced by the Coriolis force and theresulting geostrophic flow is constrained to follow isobaths, thereby inhibiting transport up the steep to-pography. In a narrow canyon, however, alongshore flow is prevented by the canyon walls and the effectof the Coriolis force is secondary compared to other terms in the momentum balance (Allen, 2004). Asa result, flow inside the canyon is driven down the unbalanced, onshore pressure gradient and is allowedto move along-canyon and up the topography (Allen, 1996; Freeland and Denman, 1982; Klinck, 1988,1989; She and Klinck, 2000). Thus, the enhanced upwelling observed in narrow submarine canyons is5driven by the onshore, barotropic pressure gradient over the shelf which is unbalanced due to the canyontopography (Allen, 2004).Throughout an upwelling event, the continuous tilting of isopycnals associated with the upwellingtransport inside the canyon generates an offshore, baroclinic pressure gradient to compensate for theonshore, barotropic pressure gradient above the canyon rim (Klinck, 1996; She and Klinck, 2000).The baroclinic pressure gradient force due to the tilting isopycnals eventually balances the barotropicpressure gradient force associated with the offshore surface transport, inhibiting further upwelling insidethe canyon (Howatt and Allen, 2013). The upwelling depth Z (Figure 1.2) is considered an importantcharacteristic of upwelling in submarine canyons (Allen and Hickey, 2010; Howatt and Allen, 2013).Assuming upwelling occurs mostly near the head with little or none at the mouth, the upwelling depthis defined as the change in depth of the deepest isopycnal that is upwelled onto the shelf over the rimof the canyon at the canyon head. In other words, this isopycnal is upwelled from a depth Z+Hh tothe head at depth Hh (Figure 1.2). At the depth of this isopycnal at the canyon mouth (i.e. Z+Hh),where upwelling is minimal, a balance is expected between the barotropic pressure gradient force dueto the tilting free surface and the baroclinic pressure gradient force due to the tilting isopycnals insidethe canyon (Allen and Hickey, 2010; Howatt and Allen, 2013). An estimate for the barotropic pressuregradient, which drives the upwelling event, can be made by first considering the directionality of flowover the canyon.The Rossby number characterizing flows over a canyon is typically based on the width of the canyonat half-length and is defined as RW∗ =U/ fRW , where U is the velocity scale upstream of the canyonand RW is the width of the canyon taken half-way along the canyon length and measured across the shelfbreak isobath (Howatt and Allen, 2013). A Rossby number quantifies the relative scales of the inertialacceleration of a flow to the magnitude of the Coriolis force deflecting the flow and, in the case of theRossby number RW∗, indicates the degree to which the incoming shelf currents will follow the canyontopography or flow across it (Figure 1.3). For narrow canyons (large RW∗), the inertial acceleration willbe large enough for the shelf currents to flow past the upstream side of the canyon mouth before beingdeflected onshore (Allen, 2004). If the flow crosses the canyon without significant onshore deflection,then the cross-shelf pressure gradient will be similar to that on the shelf away from the canyon (Allenand Hickey, 2010). Therefore, for a narrow canyon, the pressure gradient force over the canyon isapproximated to be on the order of ρo fUFW∗(RW∗) (Allen, 2004; Howatt and Allen, 2013), while the6pressure gradient force due to the tilting isopycnals is on the order of ρoN2Z2, where ρo is a referencedensity, f is the Coriolis parameter, U is the velocity of the incoming shelf currents, and N is the Brunt-Va¨isa¨la¨ buoyancy frequency. Here, FW∗ = RW∗/(0.9+RW∗) is a function of the Rossby number RW∗and ranges between 0 and 1 (Howatt and Allen, 2013). The function FW∗, therefore, shows the role ofthe Rossby number RW∗ in describing the ability of the canyon flow to generate the pressure gradientthat drives upwelling.In contrast, flows over wide canyons (low RW∗ and W > 2a) are expected to be steered by and aroundthe canyon topography (Allen, 2004), and the cross-shelf pressure gradient considered to be the maindriver for upwelling in narrow canyons is expected to be negligible (Allen and Hickey, 2010). For thisreason, it was originally assumed that wide canyons would only distort flows to move along the canyonisobaths without generating any substantial upwelling (Klinck, 1988, 1989). Numerical experimentsvarying canyon width (Hyun, 2004), however, show that upwelling does occur in canyons wider thantwice the internal radius of deformation. The characteristics of the circulation and upwelling observedin both narrow and wide canyons are detailed below.Circulation inside a canyon during an upwelling event is typically thought to evolve in three stages(Waterhouse et al., 2009, Figure 5) based on the response of the flow to the influence of the canyontopography (Allen and Durrieu De Madron, 2009). The initial, transient stage of upwelling is referredto as the acceleration phase since it covers the period during which upwelling-favourable winds producean offshore Ekman transport which removes water from the upper Ekman layer at a constant rate (Allen,1996). As such, the amount of water removed near the coast increases linearly, and the horizontal ve-locity of the shelf currents increases in time. The momentum balance describing this stage is:∂~u∂ t+ f kˆ×~u = −1ρo∇p (1.1)where the first term on the left hand side represents the acceleration of shelf currents, the second termrepresents the Coriolis acceleration, the term on the right hand side represents the onshore pressuregradient force per unit mass, ~u is the horizontal velocity, t is time, f is the Coriolis parameter, ρo isa reference density, and p is the pressure. As the upwelling event progresses and flows over the shelfreach constant velocity, advection replaces time-dependence as the dominant process for upwelling(Allen, 1996, 2004). The quasi-steady, advection-driven stage is described by:7~u ·∇~u+ f kˆ×~u = −1ρo∇p (1.2)where the first term on the left hand side represents the non-linear, advection of momentum per unitmass. The third and final stage, the relaxation stage of upwelling, occurs once the shelf current velocitiesdecrease towards the end of the event (Allen and Durrieu De Madron, 2009).During the time dependent stage of upwelling in a narrow canyon, currents along the slope enterthe canyon through the mouth and move towards the downstream wall. At the downstream wall, flowseither upwell onto the shelf, continue towards the head or turn offshore to exit the canyon. Flows insidenarrow and long canyons are typically slow and form a weak cyclonic circulation (Waterhouse et al.,2009). Notably, there is a narrow band of downwelling along the upstream wall (Klinck, 1996) as theonshore flux upstream of the canyon is redirected through the canyon (Allen, 1996). As velocities insidethe canyon continue to decrease into the advection-driven stage, the cyclonic circulation evolves into acyclonic eddy at the canyon rim depth and cyclonic vorticity develops deeper inside the canyon (Allen,1996; Waterhouse et al., 2009). Flows are advected into the canyon and upwelled onto the shelf overthe downstream wall near the canyon head. At the downstream wall, anticyclonic vorticity develops(Allen et al., 2001; Allen, 2004) and upwelled flows over the shelf turn offshore towards the shelf break(Waterhouse et al., 2009).The generation of the cyclonic vorticity inside narrow canyons has been attributed to flow separationfrom the topography on the upstream corner of the canyon mouth (Pe´renne et al., 2001; She and Klinck,2000) and to vortex stretching due to shelf flows dipping into the canyon on the upstream side (Hickey,1997; She and Klinck, 2000). Vortex stretching, however, is found to be the dominant mechanism(Waterhouse et al., 2009). Shelf flows passing over the canyon rim plunge into the canyon and stretchthe water column. Due to the conservation of potential vorticity, stretching the water column generatescyclonic vorticity on the upstream side of the canyon (Hickey, 1997). Similarly, stretching due to tiltingisopycnals generate cyclonic vorticity deeper in the canyon (Allen, 2004; Klinck, 1996; She and Klinck,2000). Conversely, anticyclonic vorticity is generated on the downstream side of the canyon by the fluidcolumn being compressed as upwelling flows are advected onto the shelf (Allen, 2004; Klinck, 1996;She and Klinck, 2000).Wide (e.g. W/a ∼ 3) and intermediate-sized (e.g. W/a ∼ 1.5) canyons exhibit similar circulation8features as narrow canyons, but the coverage, shape, strength of, and dynamics behind such features aredifferent (Hyun, 2004). In wider canyons, the surface elevation is higher in the centre of the canyoncompared to either side since the canyon walls are sufficiently far apart to only weakly interact (ibid.).This pressure distribution most likely allows flows entering the canyon on the upstream side to movearound the canyon walls and form an anticyclonic circulation. The mean flow inside the canyon hasbeen found to weaken as the canyon becomes wider (ibid.). During the initial stage of the upwellingevent, flows are directed onshore along the upstream wall, downstream around the canyon head, andoffshore along the downstream wall (ibid.). With increasing wind-stress forcing, the incoming currentsalong the upstream slope strengthen and separate from the upstream corner of the canyon mouth (ibid.).It should be noted that, while the cyclone (i.e. the rim depth eddy) spans the width of a narrow canyon,the cyclone produced in a wide canyon is attached to the upstream wall of the canyon (ibid.). Whileupwelling inside wide canyons also occurs along the downstream wall, the isopycnals are displacedhigher inside narrow canyons (ibid.). Furthermore, the transport per unit width is larger in narrowcanyons than in wide canyons (ibid).The deformation radius a = NHc/ f of Mackenzie Canyon is ∼ 23.6km, where N is the Brunt-Va¨isa¨la¨ frequency and Hc is the depth of the canyon at the mouth, f is the Coriolis parameter, andthe width W is 62km. If the ratio between the canyon width W and radius of deformation a is usedto define the dynamical width of a canyon, Mackenzie Canyon would be classified as a marginallywide (or intermediate) canyon (Carmack and Kulikov, 1998; Williams et al., 2006). The known detailsconcerning the circulation patterns and upwelling in Mackenzie Canyon are summarized in Section 1.3.1.3 Circulation and upwelling in the Beaufort Sea and MackenzieCanyonThe Mackenzie Shelf (Figure 1.4) is in the southeastern Beaufort Sea and is bordered by the Macken-zie River delta to the south, Mackenzie Canyon to the west, and the Amundsen Gulf to the east (Carmacket al., 1989). The shelf is shallow (average depth of 35 m) and flat (average bottom slope of 10−4), andit extends 530 km along the coast and 120 km offshore to the shelf break at 80 m depth (Carmack et al.,1989; Forest et al., 2007; Hill et al., 1991). The shelf bottom is mostly regular, with the exception ofMackenzie Canyon and Kugmallit Canyon (Carmack et al., 1989). Mackenzie Canyon is a U-shapedtrough which incises the shelf nearly perpendicular to the coast and is topographically associated with9the Mackenzie River (Hill et al., 1991; Moors-Murphy, 2014). It is 98 km long (cross-shore or along-canyon direction), 62 km wide (along-shore or cross-canyon direction), and 372 m deep at the mouth.Given a depth-averaged buoyancy frequency N ∼ 8.7×10−3 s−1 (averaged between the ocean surfaceand 500 m depth from the salinity and temperature profiles used to define the stratification for the con-trol experiments conducted in this study), the maximum depth of the canyon bottom Hc = 372m, anda Coriolis parameter f = 1.37×10−4 s−1, the canyon’s radius of deformation is a = NHc/ f ∼ 23.6km,making Mackenzie Canyon a wide canyon.The Canada Basin is characterized by a two-layer circulation system (Lique et al., 2015): the anticy-clonic Beaufort Gyre at the surface, which is driven by the Beaufort atmospheric high-pressure systemcentred north of Alaska (Serreze and Barrett, 2011), and the cyclonic, topographically steered Beaufortshelf-break current (an extension of the Alaskan Coastal Current), which is 20 km wide and spans 150 mand 200 m depth over the Atlantic Water (Pickart, 2004). In Mackenzie Canyon, diurnal tidal currentsare negligible (<0.3 cms−1) and semidiurnal tidal currents are relatively weak (for example, the M2tidal constituent which dominates semidiurnal tides in the region has maximum velocities ∼0.7 cms−1in Mackenzie Canyon compared to ∼6.5 cms−1 in the Amundsen Gulf) (Kulikov et al., 2004). Addi-tionally, the Mackenzie River plume extends offshore throughout Mackenzie Bay and is predominantlyforced eastward along the Tuktoyaktuk Peninsula and into the Amundsen Gulf (Carmack and Macdon-ald, 2002; Dunton et al., 2006; Forest et al., 2007).Six main water masses (Carmack et al., 1989; Lansard et al., 2012; Macdonald et al., 1989) can beidentified in the southeastern Beaufort Sea: 1. Sea Ice Melt (SIM) 2. Meteoric Water (MW), 3. WinterPolar Mixed Layer (PML), 4. Upper Halocline Water (UHW), 5. Atlantic Water (AW), and 6. CanadaBasin Deep Water (CBDW). The MW (Mackenzie River outflow and precipitation) has been detectedin the upper 10 m (Lansard et al., 2012) to the upper 50 m (Williams et al., 2006) beyond the shelf breakand along Mackenzie Canyon during periods of strong runoff from the Mackenzie River. The MWhas a characteristic salinity of 0 gkg−1 and low nutrient concentrations. The UHW, which is derivedfrom Pacific water that flows into the Arctic Ocean through the Bering Strait (Pickart, 2004), typicallyextends from 120 m to 180 m depth in the interior ocean, but it has also been found at 50 m depth alongMackenzie Canyon, potentially as a consequence of canyon upwelling (Williams and Carmack, 2008;Williams et al., 2006). It has a characteristic salinity of 33.26 gkg−1 (Macdonald et al., 1989) and highnutrient concentrations (Carmack et al., 2004; Macdonald et al., 1989). The AW, which is formed by10water entering the Arctic Ocean through the Fram Strait and Barents Sea, is found between 200 m and800 m depth and has a characteristic salinity of 34.99 gkg−1 and relatively low nutrient concentrations(Macdonald et al., 1989).Primary productivity in the southern Beaufort Sea is controlled by nutrient supply through riverineinput and mixing and/or upwelling of deep waters and by light availability through ice cover (Macdon-ald et al., 1987). In the winter, nutrients in the inner shelf are supplied by the Mackenzie River andcontain high nitrate, high silicate, and low phosphate levels (Macdonald et al., 1987). At this time, iceand snow cover inhibit light penetration, resulting in low primary productivity (Carmack et al., 2004).In the spring, while there are sufficient nutrients for primary production, light is still limited due toincreased turbidity from river outflow and lingering ice (Carmack and Macdonald, 2002). Additionally,the water column becomes more stratified as a result of ice melt and river discharge, thereby preventingnutrient exchange between the nutrient-rich UHW and the photic zone (Carmack et al., 2004). Pro-ductivity increases in the summer, but it remains phosphate-limited over the inner shelf (onshore of the20 m isobath) as these levels remain low while nitrate levels rise (Carmack et al., 2004). Over the mid-dle (between the 20 m and 80 m isobaths) and outer shelf (beyond the 80 m isobath, which defines theshelf break), however, nitrate values are lower, indicating nitrate limitation (Carmack and Macdonald,2002). In the autumn, stratification weakens due to reduced river outflow, sea ice formation, and in-creased wind-driven mixing. Overall, primary production in the southern Beaufort Sea is characteristicof oligotrophic waters (Carmack et al., 2004; Martin et al., 2010).Canyon-driven upwelling in Mackenzie Canyon was first observed through the tilting of nitrate anddensity isolines (Macdonald et al., 1987). It was suggested that this upwelling signal plays a critical rolein nutrient supply to the shelf given the low productivity typical of the Beaufort Sea (Macdonald et al.,1987). Since then, there have been two published, observational studies on the circulation and upwellingin Mackenzie Canyon, namely Williams et al. (2006) and Carmack and Kulikov (1998). Carmack andKulikov (1998) uses temperature, salinity, and current observations from moorings deployed at stationsSS1, SS2, SS3, and SS4 (Figure 1.4) between spring 1987 and spring 1988. Williams et al. (2006)uses temperature, salinity, and current observations from moorings deployed at stations A, B, C, andD (Figure 1.4) from August 1993 to September 1996 and Conductivity-Temperature-Depth (Williamset al., 2006, Figure 8) and Acoustic Doppler Current Profiler (Williams et al., 2006, Figure 9) datacollected for along-canyon and cross-canyon transects in September 2002. The main findings of these11studies are outlined below.Currents along the Mackenzie Shelf, as observed at stations B (Williams et al., 2006), SS3, and SS2(Carmack and Kulikov, 1998), are strongly aligned in the along-shore direction and are topographicallysteered by the slope. In contrast, currents on the downstream slope, specifically at station A, do not showany preferential directionality. Along the upstream slope, upstream flows (towards the northeast) aregenerally stronger than downstream flows (towards the southwest) and show seasonal variability, withmaximum velocities occurring in October and November (Williams et al., 2006). Additionally, unlikethe circulation for narrow canyons, near-surface flows over Mackenzie canyon are deflected around thecanyon head, indicating that the influence of this canyon extends to the surface (Williams et al., 2006).Upwelling in Mackenzie Canyon is significantly correlated with easterly winds and southwestwardcurrents (Carmack and Kulikov, 1998). Upwelling flows are observed at station C for downstream-directed currents at station B, but there is no correlation between flows at station C and station A(Williams et al., 2006). Furthermore, there is a stronger correlation between upwelling and mean dailywind stress compared to hourly wind stress, implying a stronger relationship to the cumulative effect ofshort but intense wind events (Carmack and Kulikov, 1998). In addition, ice motion during the winterhas also been observed to produce upwelling (Williams et al., 2006). Time series for the vertical dis-placement of water masses, temperature anomaly, and alongshore velocity show that approximately 6-7upwelling events occur in Mackenzie Canyon over the course of a year (Carmack and Kulikov, 1998;Williams et al., 2006), which is similar to the 9-10 upwelling events per year identified for the BeaufortShelf west of Mackenzie Canyon (Pickart et al., 2013a).During an upwelling event, isohalines in Mackenzie Canyon have been observed to tilt upwardstowards the upstream side of the canyon and towards the head (Williams et al., 2006, Figure 8). Aftera series of easterly winds over the preceding weeks in the autumn, upwelling has been recorded toproduce a maximum isopycnal displacement of 600 m, with water being displaced from a depth of600 m to about 50 m (Carmack and Kulikov, 1998). Measurements at 200 m depth from station C and90 m depth from station D show upwelling flows towards the canyon head (Williams et al., 2006). Infact, it has been suggested that even weaker upwelling events are likely to produce a flux of nitrates, forwhich the concentration peak lies between 100 m to 200 m depth, to the shelf (Williams et al., 2006). Asupwelling relaxes, flows inside the canyon are directed offshore from the head to the mouth and travelalong the isobaths on the upstream side of the canyon (Williams et al., 2006, Figure 9). Additionally,12eddy-like oscillations are observed not only for outgoing flows on the upstream side of the canyon, butalso at station A on the downstream slope and at 100 m depth in the centre of the canyon near station C(Williams et al., 2006).Notably, the upwelling signal initially observed in Mackenzie Canyon at station SS4 has been ob-served to propagate eastward along the shelf break (Carmack and Kulikov, 1998, Figure 12). It is sug-gested that, given the propagation speed, this disturbance is likely the first mode of an internal Kelvinwave (Carmack and Kulikov, 1998). Indeed, it has been shown that irregular bathymetric features, suchas submarine canyons, can induce coastal trapped waves under upwelling-favourable wind conditions(Zhang and Lentz, 2017); however, the dynamics involved in this phenomenon require further attention.Mackenzie Canyon is an interesting subject for the study of circulation patterns and upwelling dy-namics inside wide canyons. While previous work on both narrow and wide canyons show that up-welling typically occurs on the downstream side of the canyon, observations in Mackenzie Canyonshow the strongest upwelling occurring on the upstream side. The influence of a canyon also generallydoes not reach near-surface layers, while flows well above shelf break depth in Mackenzie Canyon re-gion still display significant distortion due to the canyon. The upwelling signal propagating upstreamof Mackenzie Canyon also offers the possibility to examine a relatively unstudied mechanism for up-welling around submarine canyons. With this context in mind, we define the scope of this thesis in thefollowing section.1.4 Research objectivesUnderstanding the oceanic processes that play a role in the recirculation of nutrients is critical,especially for oligotrophic regions such as the Arctic Ocean. Bathymetric features, such as submarinecanyons, have been found to produce enhanced upwelling in coastal regions. Initiated by shelf currentsflowing in the direction opposite to that of coastal trapped waves, upwelling in dynamically narrowcanyons is driven by an unbalanced cross-shore pressure gradient over the canyon. Questions remainregarding the mechanisms driving upwelling in dynamically wide canyons. Using a numerical model,this study aims to simulate the circulation and upwelling inside Mackenzie Canyon during a wind-drivenupwelling event and consider the implications for nutrient delivery to near-surface waters. Idealized andrealistic models are used to investigate the various processes inside and near Mackenzie Canyon duringthe upwelling event. To evaluate the performance of the model, the simulated circulation and upwelling13patterns are compared to real-world observations. Owing to the dearth of studies on the upwellingdynamics in wide and realistic canyons, this study contributes to our understanding of the influence ofcanyon geometry and bathymetric details on canyon upwelling. Understanding the physical mechanismsinvolved in circulation and upwelling in Mackenzie Canyon supplements the current knowledge onthe numerous interlinked processes supporting the complex ecological systems in the Beaufort Sea.Specifically, this study aims to answer the following research questions.1. What are the circulation patterns inside and near Mackenzie Canyon during an upwelling event?2. What flow features are significant modifiers of the upwelling in Mackenzie Canyon?3. What differences in upwelling are caused by smoothing the topography to make an idealizedcanyon?4. Are the model results for circulation and upwelling in Mackenzie Canyon supported by observa-tional evidence?5. Does upwelling in Mackenzie Canyon produce significant upward transport of nitrate across thenitracline depth and, if so, how much?14Figure 1.1: Plan view of idealized canyon bathymetry with definitions of the relevant directions offlow used in this study. The canyon bathymetry is coloured with light green colours indicat-ing shallow depths and blue colours indicating deeper depths, and the isobaths are labelledin metres. The head, mouth, and axis of a canyon are typically used as references for the di-rection of flows in the region. Flows are considered to be upwelling-favourable if movementis in the downstream/up-shelf direction.15Figure 1.2: Cross-section along the axis of the canyon adapted from Ramos-Musalem and Allen(2019). The sketch shows upwelling isopycnals during a canyon-induced upwelling eventand the relevant scales referred to in this thesis. The scales include the upwelling depth Z,depth of the canyon head Hh, depth of the shelf break Hs, depth of the canyon at the mouthHc, canyon length L, and z is the vertical coordinate. The deepest isopycnal to be upwelledis depicted by the bold, green line.16Figure 1.3: Plan view of flows over a canyon for small, moderate, and large Rossby numbers Ro(Allen, 2004, reprinted with permission of the author). This figure depicts the tendency forflows to either cross or follow the canyon topography depending on Ro (which can be definedusing the turning radius of the shelf-break isobath on the upstream corner of the canyon R asin Allen (2004) or using the width of the canyon half-way along the canyon length RW as inHowatt and Allen (2013)). The thin line represents the canyon rim, the thick line shows theflow path, and the arrow points in the direction of the flow.17Figure 1.4: a) Bathymetry of the Arctic Ocean, b) 3-dimensional view of the bathymetry nearMackenzie Canyon, and c) local bathymetry of the southern Beaufort Sea. Panels (a) and (c)show the model domain used in this study outlined by the black rectangle. Panel (c) showsthe mooring stations from past observational studies (Carmack and Kulikov, 1998; Williamset al., 2006).18Chapter 2Methods2.1 Model descriptionThis study uses numerical simulations of circulation and upwelling in Mackenzie Canyon producedusing a nested-grid modelling system. The modelling system is configured based on version 3.6 of theocean component (OPA) (Madec et al., 1998) of the Nucleus for European Modelling of the Ocean(NEMO) (Madec, 2008) framework, and it uses the Adaptive Grid Refinement in Fortran (AGRIF) (De-breu et al., 2008) software to implement a nested grid. The NEMO ocean general circulation modelsolves the three-dimensional primitive equations (i.e. the Navier-Stokes equations under the Boussinesqand hydrostatic approximations) discretized on the Arakawa C-grid. The prognostic variables of themodel are the three-dimensional velocity fields, sea surface height, conservative temperature, and abso-lute salinity. Furthermore, the AGRIF software is used to embed a high-resolution child model within acoarse-resolution parent model, the details of which are described below.The coarse-resolution parent model encompasses the entire modelled region and employs a 2.26 kmhorizontal grid resolution and 120 s baroclinic time step. The high-resolution child model encompassesonly the submarine canyon bathymetry (Figure 2.1). Implementing horizontal grid and temporal refine-ment by a factor of 3, the child model has a ∼754 m horizontal grid resolution and 40 s baroclinic timestep. The parent domain is arranged into nx = 270 by ny = 174 grid cells, extending 610 km and 393 kmin the alongshore (x) and cross-shore (y) directions, respectively. The child domain is arranged into nx= 274 by ny = 244 grid cells, extending 207 km and 184 km in the alongshore (x) and cross-shore (y)directions, respectively. The full model domain covers an area extending from 150.8◦ W to 132.9◦ W19and from 68.4◦ N to 72.7◦ N (Figure 1.4). Given that the area of the Beaufort Sea is approximately447000 km2 (Jakobsson, 2002), the parent and child model domains occupy 0.5 and 0.09 times the areaof the Beaufort Sea, respectively. Both parent and child models have 80 vertical z-levels with a constantvertical resolution of 9 m between the surface and 500 m depth, increasingly coarser vertical resolutionbetween 500 m and 790 m depth, and a constant 43 m vertical resolution from 790 m to a maximumdepth of 1300 m. Partial z-levels are applied to allow the thickness of the bottom grid cells to vary fora more detailed representation of the bottom topography. The barotropic time step in both parent andchild models is set to respect the Courant-Friedrichs-Lewy condition with a maximum Courant numberof 0.5.Numerical simulations were conducted using either realistic or idealized bathymetry (Figure 2.1;Table 2.1). The realistic bathymetry was extracted from a 500 m horizontal resolution, polar stereo-graphic dataset of the International Bathymetric Chart of the Arctic Ocean (IBCAO) (Jakobsson et al.,2012), version 3.0, which is a compilation of bathymetric data for the Arctic region north of 64◦N.The idealized bathymetry was constructed so as to closely resemble the realistic bathymetry. The ide-alized bathymetry features a simplified profile for the continental slope, a sloping continental shelf,and a secant-shaped submarine canyon with the approximate dimensions of Mackenzie Canyon (Fig-ure 2.1 b.): length (cross-shore) L = 98km, width (alongshore) W = 62km, depth at the canyon mouthHc = 372m.The AGRIF package (Debreu et al., 2008) is composed of a set of routines for adaptive mesh refine-ment and time integration of embedded grids (Berger and Oliger, 1984) over regions where complex dy-namics require enhanced resolution for increased accuracy. The coupled NEMO-AGRIF model config-uration was implemented using a set of pre-processing algorithms available at http://www.nemo-ocean.eu/Using-NEMO/SetupNewConfiguration/AGRIF-nesting-tool. In this study, the child and parent gridsshare a connection zone that has a width of 9 child grid cells in the realistic model and 3 child grid cellsin the idealized model. This connection zone serves as both a “seam” over which the parent and childbathymetry are interpolated and a dynamical interface between parent and child models. The modellingsystem in this study uses two-way nesting (Debreu and Blayo, 2008; Debreu et al., 2012), which allowsresults from the parent model to serve as boundary conditions for the child model while updating theparent model with results from the child model at every parent time step. Additionally, a sponge layerwith enhanced diffusivity (100 m2 s−1) and viscosity (100 m2 s−1) was applied at the boundaries of the20child model. Diffusivity and viscosity were set to 125 m2 s−1 in the parent model and 12.5 m2 s−1 in thechild model for both realistic and idealized models.The numerical simulations are forced with an easterly (westward) wind stress at the surface (Sec-tion 2.2), which induces a westward mean flow in the domain. In the parent model, the eastern (i.e.down-shelf/upstream) and western (i.e. up-shelf/downstream) boundaries are treated as periodic bound-aries. To reduce dynamical inconsistencies between these two boundaries, the western side of the real-istic model bathymetry was modified to match the bathymetry at the eastern boundary. Additionally, therealistic model domain was oriented at an angle (Figure 2.1) that allowed the coastline near the bound-aries to be aligned parallel to the direction of the mean flow. At the northern (i.e. offshore) boundary,the model adopts Flather open boundary conditions (Flather, 1976) for barotropic velocities and seasurface height, Orlanski radiative open boundary conditions (Orlanski, 1976) for baroclinic velocities,and Neumann conditions for tracers. The Orlanski boundary conditions are used in conjunction witha sponge layer with a maximum viscosity of 500 m2 s−1 to dampen reflections from outgoing waves.Baroclinic and barotropic velocities are prescribed at the northern boundary from calculations for theEkman and geostrophic currents produced by the given wind forcing. Sea surface height was also sup-plied at the northern boundary, and it was calculated using the solution (Section B.1) for the barotropicRossby adjustment over a shelf (Allen, 1996).At the solid lateral and bottom boundaries (i.e. the coastline and bottom topography), boundary con-ditions are set for the normal and tangential components of velocity. A masking array with elements setas 1 in the ocean and 0 elsewhere is used to define normal velocities at the solid boundaries as zero. Thetangential component of velocity at the solid boundaries is managed by slip boundary conditions. Theparent model uses partial slip boundary conditions, which allows for a dampened, non-zero tangentialvelocity, while the child model uses the free-slip condition, which implies no shear in tangential flowsalong the solid boundaries. A quadratic bottom friction parameterization with log-layer enhancement isused and initialized with a drag coefficient bounded by CminD = 7.5× 10−3 and CmaxD = 2 and a bottomroughness length of 0.07 m in both parent and child models. The model was tested with the variousbuilt-in schemes for tracer advection available for the NEMO model (Madec, 2008). The MonotoneUpstream Scheme for Conservation Laws (MUSCL) scheme was chosen for this study since it was theonly scheme to not produce spurious salinity maxima in the simulations.212.2 Model simulationsSeven numerical experiments were conducted for this study (Table 2.1). All simulations were ini-tialized from rest with wind forcing at the surface for a run duration of 6 days. This run duration waschosen to avoid canyon-induced disturbances from propagating across the periodic boundaries and in-fluencing the canyon circulation and upwelling in the later stages of the simulation (Figure C.1). Eachsimulation was run with a unique combination of bathymetry type (classified as idealized or realistic),strength of wind forcing (classified as base, half, or double), and stratification (classified as control orevaluation). This study mainly focuses on the results of the 6 simulations with the control stratificationprofile. The evaluation stratification case is used to evaluate model performance against observations.The simulations are forced by wind stress at the surface with varying degrees of intensity. The forc-ing cases (base, half, and double) are defined by the strength of the wind event that induces upwellingin the modelled region (Figure 2.2 (a) and Table 2.2). Easterly (westward) winds were generated bymodifying the analytical formulation for wind stress in the NEMO model code. The modified windstress (Section B.2) is composed of a spatially constant but temporally variable alongshore componentτx (Equation B.4) and zero cross-shore component τy (Table 2.2). The alongshore component τx fea-tures a strong wind pulse τ pulsex (Equation B.2) during the initial 25.5 hours of the simulation with amaximum wind stress value τ pulsex−max (Table 2.2). For the remainder of the run duration, τx features a re-duced, constant wind stress τrelaxx (Figure 2.2 (a) and Equation B.3) with a wind stress value of τrelaxx−const(Table 2.2). The wind stress remains at a reduced, non-zero value until the end of the simulation in orderto maintain alongshore flows in the domain at near-constant velocities, which support the quasi-steadystage of upwelling in the canyon.The model stratification is set by using an observed vertical profile of temperature and salinity col-lected near Mackenzie Canyon (Figure 2.2 (c-e)). The stratification for the control experiments wasderived from temperature and salinity measurements collected in August 2009 (dataset for 2009) by theCanadian research icebreaker CCGS Amundsen and made available by the Amundsen Science program,which was supported by the Canada Foundation for Innovation and Natural Sciences and EngineeringResearch Council of Canada, as well as by ArcticNet, a Network of Centres of Excellence of Canada(Rail et al., 2011). The stratification for the evaluation experiment (RBE) was derived from temperatureand salinity measurements collected on a cruise in September 2015 on the American research vessel22RV Sikuliaq and funded by the National Science Foundation Division of Polar Programs. The tem-perature and salinity data was collected using shipboard and towed Conductivity-Temperature-Depthinstruments, and the horizontal velocity data for currents was collected using a shipboard AcousticDoppler Current Profiler. The observational data was provided by Amy Waterhouse through personalcommunication (Waterhouse, in prep), and readers are referred to Waterhouse et al. (2017) for detailsregarding data processing techniques that were also used to process the observational data collected inMackenzie Canyon.The performance of the model was evaluated by comparing observational data for horizontal ve-locity and salinity (Waterhouse, in prep) against model results for the simulation RBE, which uses therealistic bathymetry, base case of wind forcing, and the stratification near Mackenzie Canyon at thetime when the observational data was collected. The comparisons between observations and model re-sults are made specifically for RBE because the base case of wind forcing produces horizontal velocitymagnitudes more similar to those in the observations compared to the other wind forcing cases. Themodel-observation comparisons presented in this study use observations collected over the course ofthree days (September 5-7, 2015) along two cross-canyon transects and one cross-shore transect at thedownstream slope (Section 3.7). While this was a period of shifting winds, easterly winds dominatedthe first two days, likely causing the upwelling-favourable westward flows along topography.2.3 Quantification of canyon upwellingCanyon upwelling has been quantified by the upwelling depth in numerical and laboratory studiesof idealized canyons (Allen, 2004; Allen and Hickey, 2010; Howatt and Allen, 2013; Jaramillo Uribe,2005; Ramos-Musalem and Allen, 2019) and by the effective depth in observational studies of Macken-zie Canyon (Carmack and Kulikov, 1998; Williams et al., 2006). The upwelling depth is defined as thechange in depth of the deepest isopycnal to be upwelled to the canyon rim at the head (Figure 1.2). Theeffective depth, as used to quantify upwelling in Mackenzie Canyon, is an estimate for the depth throughwhich a water mass has been displaced given salinity measurements at a fixed location and depth in theupwelling region and a reference salinity profile. In the Beaufort Sea, the reference salinity profile istypically taken from an offshore location where water properties can be assumed to vary slowly. Salinityis the preferred property for estimating upwelling in the Arctic region since salinity is the primary de-terminant of density and salinity values typically increase monotonically with depth while temperature23values may not necessarily map onto a single depth.In this study, canyon upwelling is quantified using a metric which we simply refer to as “verticaldisplacement”. Similar to effective depth, vertical displacement is defined as the depth across which awater mass has been displaced during an upwelling event. In this case, however, the reference salinityprofile used to estimate the original depth of a water mass is the initial salinity profile used at thestart of the numerical simulation (Figure 2.2 (e)). Vertical displacement is expressed such that upwardexcursions of water via upwelling are represented by positive values.This study considers the vertical displacement both at particular depths and on salinity surfacesrepresentative of specific water masses. The salinity surfaces represent the Upper Halocline Water(UHW) and Atlantic Water (AW) water masses with characteristic salinities of 33.26 gkg−1 (Macdonaldet al., 1989) and 34.99 gkg−1 (Macdonald et al., 1989), respectively. Given an initial salinity profile,these methods of visualization are beneficial in identifying areas of upwelling and downwelling andtracking the temporal and spatial evolution of these excursions.2.4 Coastal trapped wave analysisThe model simulations show the generation and propagation of a coastal trapped wave (CTW) inMackenzie Canyon. The wave signal has also been identified in observational studies documenting flowvariability inside Mackenzie Canyon and along the Mackenzie Shelf (Carmack and Kulikov, 1998). Thestructure of this wave is investigated in this study using a model that searches for the free wave solu-tions of Boussinesq, hydrostatic, linearized CTWs along straight coastlines (Brink, 2018). The CTWmodel is packaged as Matlab software called Bigr∗.m available at the Woods Hole Oceanographic In-stitution website http://www.whoi.edu/page.do?pid=23361. The model calculates the dispersion curvesand cross-shore vertical structures for pressure, along-shore and cross-shore velocities, vertical veloc-ities, and density for wave modes possible under the specified conditions. To simulate the conditionsused in the Mackenzie Canyon model, the CTW model was given the cross-shore profiles for the ide-alized bathymetry at the upstream side of domain away from the canyon. The CTW model also usesthe same Coriolis parameter f and vertical profile for the Brunt-Va¨isa¨la¨ buoyancy frequency squaredN2 as the Mackenzie Canyon model. The CTW model domain is discretized into 220 and 15 grid cellsin the cross-shore and vertical directions, extending 280 km and 1300 m, respectively. The boundariesare closed at the coast and open at the offshore edge of the domain. Wave solutions are sought in the24absence of a mean flow and with a nominal accuracy of 0.01% for the absolute value of frequency.The wave parameters and the cross-shore structure of the vertical velocity of the coastal trappedwave observed in the Mackenzie Canyon model simulation (idealized bathymetry, base case for windforcing) were compared to those calculated by the CTW model using the same idealized bathymetry.The alongshore propagation of the CTW in the Mackenzie Canyon model simulations was trackedbetween hours 24 and 36 using the vertical velocity signal averaged over all model depths to estimatethe wave parameters. The wavenumber was calculated using the wavelength estimated as the distancebetween two consecutive crests of the simulated CTW. The frequency was calculated using the wavespeed estimated using the alongshore distance travelled by the CTW between hours 24 and 36. TheCTW model was then used to calculate the cross-shore structure of vertical velocity for a CTW with thewavenumber and frequency estimated for the CTW in the Mackenzie Canyon model simulations.2.5 Calculations for model result analysisA number of quantitative metrics were calculated using the model results to characterize the circula-tion and upwelling in Mackenzie Canyon and to compare the different simulation cases. These metricsare described below.Relative vorticityThe vertical component of relative vorticity ζ is calculated as:ζ =∂v∂x− ∂u∂y(2.1)where u and v are the horizontal components of velocity and x and y are the horizontal coordinates. Forvisualization purposes, the values for relative vorticity are normalized by the local Coriolis parameterf =1.37×10−4 s−1.Nitrate transportThe nitrate advection in the modelled domain was estimated using the average relationship betweensalinity and nitrate concentration in the Mackenzie Canyon region. Geochemistry and salinity datafrom the Beaufort Gyre Exploration Project was obtained from the Woods Hole Oceanographic Insti-25tution website http://www.whoi.edu/page.do?pid=66521. Three stations inside and near the MackenzieCanyon were chosen and data from September 2009 was considered. The mean relationship betweensalinity and nitrate concentration from this data is illustrated in Figure 2.2. To calculate the total nitratetransport in units of mmols−1 in the region, the nitrate concentration in units of mmolm−3 is multipliedby the vertical velocity and horizontal area of each grid cell, and the product is then integrated over thecanyon region defined by the child model domain.Comparisons for wind forcing casesThree metrics were defined to compare the response of the the flow near the canyon to the threewind forcing cases (base, half, double). The first metric describes the CTW amplitude and is definedas the mean positive vertical velocity on the slope just upstream of the canyon. The small area atthe upstream slope over which the calculation was made was strategically chosen to avoid the effectsof canyon upwelling on vertical velocities while still capturing the vertical velocities of the CTW asit propagates upstream along the slope. The second metric considers the maximum positive value ofvertical displacement in the canyon region, thereby describing the strength of upwelling. The thirdmetric is the total transport of nitrate in the canyon region. All metrics consider model results for thefull simulation duration and all depth levels.26Simulation name Bathymetry Wind Forcing StratificationIBC idealized base controlIHC idealized half controlIDC idealized double controlRBC realistic base controlRHC realistic half controlRDC realistic double controlRBE realistic base evaluationTable 2.1: Bathymetry, wind forcing, and stratification cases for all simulations.27Wind forcing case τ pulsex−max [Nm−2] τrelaxx−const [Nm−2] τy [Nm−2]Base -0.8 -0.1 0Half -0.4 -0.05 0Double -1.6 -0.2 0Table 2.2: Values for the maximum alongshore wind stress τ pulsex−max, reduced alongshore wind stressτrelaxx−const , and cross-shore wind stress τy for all wind forcing cases.28Figure 2.1: a) Realistic and b) idealized model domain and bathymetry. The parent model extendsacross the full model domain, and the child model covers the area outlined by the dashed-line rectangle over the canyon bathymetry. The dimensions for canyon width and length areidentified by the dark, black lines, and the three open boundaries are labelled according tothe corresponding boundary conditions. The direction of mean flow in the model domain isindicated by the upshelf-directed arrow.29Figure 2.2: a) Alongshore wind stress τx and b) the resulting, alongshore velocity component ofincoming shelf currents for all wind forcing cases (half, base, double). c) Realistic canyonbathymetry and stations where observation data was collected for stratification and nitrateconcentration. Depth profiles for d) temperature and e) salinity used as initial conditions forthe control and evaluation model runs. f) Relationship between salinity and nitrate concen-tration.30Chapter 3Results3.1 Circulation patterns influenced by topographic steeringThe influence of Mackenzie Canyon on local circulation patterns is examined by tracking the evo-lution of horizontal and vertical flows on salinity surfaces representing two water masses, namely theUpper Halocline Water (UHW) and the Atlantic Water (AW), which have depths of 119 m and 470 m,respectively, throughout the domain when the simulation is initialized from rest. The flow patterns atdepths cut by the canyon topography (between 40 m and 372 m) are largely represented by the horizon-tal and vertical flows on the UHW-representative surface (Figures 3.1–3.4). The few key differencesin circulation at greater depths within the canyon topography are reviewed by considering flows on theAW-representative surface (Figures 3.5–3.8 and Section 3.2), especially in regards to the propagation ofthe coastal trapped wave (Figure 3.9).Generally, flows in Mackenzie Canyon are steered by and around the canyon topography. Duringthe time-dependent stage of upwelling, which occurs within the initial 36 hours of the simulation (Fig-ures 3.1 and 3.2 (g)), high-speed alongslope currents (∼0.57 ms−1) slightly overshoot the upstreamcorner of the canyon mouth and move towards the canyon head and downstream wall (Figures 3.1and 3.2(a)). Flows along the upstream wall reach the canyon head with high speeds (∼0.25 ms−1), whileflows farther downstream inside the canyon reach the downstream wall with lower speeds (∼0.05 ms−1).Near the mid-length of the canyon along the downstream wall, low-speed flows turn offshore and exitthe canyon on the downstream side of the canyon mouth. At the downstream corner of the mouth, out-going flows slightly separate from the topography before turning westward, parallel to the downstream31slope.The rest of the simulation represents the quasi-steady stage of upwelling since the alongshore ve-locity of the incoming shelf flows is near-constant (Figures 3.1 and 3.2 (g)). Two distinct circulationfeatures related to the canyon topography develop during the advection-driven stage of upwelling. Thefirst feature is a high-speed onshore jet that moves along the upstream wall from the mouth to the headof the canyon (Figures 3.1 and 3.2 (b-c)). At the canyon head, high-speed flows from the jet encounterthe topography, and the water mass experiences a strong upward excursion (Figures 3.3 and 3.4 (d-f)and Section 3.4). The UHW-representative surface extends farther onshore as it is upwelled, and flowsclosest to the shore are redirected westward (Section 3.2). Concurrently, flows inside the canyon con-tinue to turn offshore along the downstream wall and exit the canyon on the downstream side of themouth.The second circulation feature that develops during the advection-driven stage of upwelling is aregion of strong cyclonic vorticity on the upstream corner of the canyon mouth in both idealized andrealistic models (Figures 3.1 and 3.2 (d-f)). This vorticity anomaly evolves into a closed cyclonic eddymore readily in the realistic simulations than in the idealized simulations (Figure 3.2 (d-f)). Throughoutthe simulation, the flow separation at the upstream side of the canyon mouth gradually increases (Fig-ures 3.1 and 3.2 (a-c)) and allows for strong cyclonic vorticity to develop at this location (Figures 3.1and 3.2 (d-f)). The highest speeds on the UHW-representative surface always occur near the upstreamcorner of the canyon mouth where incoming flows turn into the canyon (Figures 3.1 and 3.2 (a-c)).These speeds are higher in the idealized model (∼ 0.7 ms−1) than in the realistic model (∼ 0.5 ms−1).The average magnitude for relative vorticity on the upstream side of the canyon mouth, whether posi-tive or negative, is higher in the idealized model (4×10−4 s−1 and −1×10−4 s−1) than in the realisticmodel (3×10−4 s−1 and −8×10−5 s−1). The formation of a closed cyclonic eddy thus appears to bedependent on the interaction between incoming flows and the shape of the topography at the upstreamcorner of the canyon mouth. Reminiscent of rotational flows around headlands, the incoming currentsalong the upstream slope separate from the topography at the upstream corner of the canyon mouth,resulting in the generation of high vorticity flows and the subsequent formation of a cyclonic eddy onthe lee side of the topography, especially in the realistic bathymetry case which resembles a sharp cape.323.2 Circulation patterns influenced by coastal trapped wavepropagationIn addition to being influenced by topographic steering, the circulation patterns near MackenzieCanyon are also influenced by the generation and propagation of a coastal trapped wave. This wavefeature, which is most clearly seen in the vertical velocity results, is induced by the interaction of thealongshore flows with the canyon topography. The CTW is generated on the downstream side of thecanyon mouth within the first day of the simulation (Figure 3.10), and it propagates in the upstream di-rection around the canyon topography (Figure 3.9 (e-h)) and along the upstream slope (Figure 3.9 (a-d)).The CTW is bottom-intensified, exhibiting a stronger vertical velocity signal on the AW-representativesurface (Figures 3.7 and 3.8 (a-c)) compared to the UHW-representative surface (Figures 3.3 and 3.4(a-c)). Throughout the simulation, the CTW is scattered by the bathymetry, especially in the realisticmodel (Figures 3.4 and 3.8 (c)). On the UHW-representative surface, the signal has mostly degeneratedas a consequence of this scattering by the end of day 2 in the realistic model and by the end of day 4 inthe idealized model (Figure 3.10). On the AW-representative surface, the signal in the idealized modelis more persistent and reaches the eastern edge of the domain by the end of day 4 (Figure C.1), whereasthe signal in the realistic model has significantly dissipated before reaching the edge of the domain (notshown).The horizontal velocity field on both UHW- and AW-representative surfaces is affected by the pas-sage of the CTW along the canyon and slope topography. Anticyclonic and cyclonic vorticity developsat the CTW wave nodes leading troughs and crests, respectively (Figure 3.9 (i-l), Figure 3.10). Giventhat both the size of the canyon topography and the strength of the propagating wave signal differ be-tween the UHW- and AW-representative surfaces, the influence of the CTW on the circulation for eachsurface is described separately.On the UHW-representative surface, incoming currents induce a region of positive vertical velocities(upwelling) at the downstream side of the canyon head during the initial stage of the upwelling event(Figures 3.3 and 3.4 (a)). Throughout the simulation, strong upward currents persist at the downstreamside and centre of the canyon head (Figures 3.3 and 3.4 (b-c)). The generation of the CTW is evidentat ∼ hour 18 of the simulation by a region of negative vertical velocities (representing the wave trough)extending from the mouth to the mid-length of the canyon along the downstream wall (Figure 3.10 (a,33d)). As this signal propagates towards the head, the wavelength of the CTW decreases. By the secondday of the simulation, multiple wave troughs and crests can be observed along the downstream wallof the canyon (Figure 3.9 (i, k), Figure 3.10 (b, e)). The CTW signal is mostly suppressed along theupstream wall of the canyon by the strong onshore jet (Figure 3.9 (e, g)), and only a weak signal can beobserved propagating along the upstream slope outside of the canyon (Figure 3.9 (a, c)).During the first two days of the simulation, before the CTW has been significantly scattered, strongvorticity is generated at the nodes of the wave. For the UHW-representative surface in the idealizedmodel, an anticyclonic eddy forms near the canyon head and cyclonic vorticity develops near the mid-length of the canyon (Figure 3.9 (i), Figure 3.10 (a-b)). The CTW-induced anticylonic eddy interactswith the onshore jet to support onshore and westward flows at the canyon head. Concurrently, the CTW-induced cyclonic vorticity near the mid-length of the canyon contributes to the steering of outgoingflows. The generation of vorticity at the wave nodes is much less pronounced in the realistic model dueto higher levels of wave scattering (Figure 3.9 (k), Figure 3.10 (d-e)).On the AW-representative surface, the CTW signal has a stronger influence than topographic steer-ing on the local circulation since the size of the canyon is much smaller at the depths occupied bythis water mass. In both idealized and realistic model simulations, incoming currents flow around thecanyon topography during the first day of the simulation (Figures 3.5 and 3.6 (a)), similar to currentson the UHW-representative surface. At the same time, the CTW propagates upstream along the canyonwalls and exits the canyon on the upstream side of the mouth (Figure 3.7 (a), Figure C.3). During thesecond and third days of the simulation, the structure of the CTW is modified (Section 3.3), likely as aconsequence of the difference in bottom slope within the canyon topography compared to that offshoreof the canyon and along the upstream slope. As the CTW propagates along the topography in bothidealized and realistic models, it distorts the horizontal velocity field and induces an eddy at the wavenode which travels upstream with the CTW (Figure 3.9 (j, l)). After the third day of the simulation, thewave signal has degenerated and no longer produces pronounced distortions in the horizontal velocityfield (Figure 3.10 (c, f)).3.3 Coastal trapped wave characterizationThe propagation of the CTW in the Mackenzie Canyon model simulation was tracked from hour 24to hour 36 using the depth-averaged vertical velocity signal to estimate the wave parameters (Figure 3.1134(a), Section 2.4). The wavelength, wavenumber, speed, and frequency of the CTW estimated fromthe Mackenzie Canyon model results are 81 km, 7.8×10−5 radm−1, 0.78 ms−1, and 6.1×10−5 rads−1(Figure 3.11 (c)), respectively. The modal structure of a wave with the approximate frequency andwavenumber estimated from the Mackenzie Canyon model simulation was calculated using the CTWmodel (Brink, 2018). The wavelength, wavenumber, speed, and frequency calculated by the CTWmodel are 81 km, 7.8×10−5 radm−1, 0.77 ms−1, and 6.0×10−5 rads−1 (Figure 3.11 (c)), respectively.The cross-shore structure for vertical velocity of the wave in the Mackenzie Canyon model results(Figure 3.11 (b)) is well represented by that of the lowest wave mode computed by the CTW model(Figure 3.11 (d)). However, a few differences in the wave structure for vertical velocity do exist be-tween the results of the Mackenzie Canyon model and CTW model, such as a band of negative velocityapproximately 250 km offshore (Figure 3.11 (b)). Further work using the CTW model could investigatethe contribution of higher wave modes in producing the more complex cross-shore structure for verti-cal velocity observed in the Mackenzie Canyon model simulations, especially as the wave structure ismodified and becomes more complex throughout the simulation (Figure C.5). Overall, the results of theCTW model for the lowest wave mode can be used to understand the general structure of the CTW inthe Mackenzie Canyon model results.The dispersion curve and cross-shore structure of the lowest wave mode calculated by the CTWmodel are used to determine if the CTW exhibits gravity wave characteristics, as would be the casefor Kelvin waves, or topographic Rossby wave characteristics, as would be the case for shelf waves.The CTW in the Mackenzie Canyon model results can be characterized as a shelf wave. Shelf wavesare right-bounded coastal trapped waves which require both rotation and depth variations along theshelf. The dispersion curve of a shelf wave shows that frequency increases monotonically for smallwave numbers, and the group speed tends to zero for high wavenumbers (Mysak, 1980). The dispersioncurve calculated by the CTW model (Figure 3.11 (c)) is, therefore, consistent with that of a shelf wave.Furthermore, the modal structure calculated by the CTW model shows that alongshore and cross-shorevelocity components have similar magnitudes (Figure C.4), which is also consistent with the structureof a shelf wave as opposed to that of a Kelvin wave. Finally, the ratio of the wave kinetic and potentialenergies, which is also provided by the CTW model, could be used as a diagnostic of whether the natureof a wave is more similar to that of a Kelvin wave or a shelf wave (Brink, 1982). The energy ratio forthe CTW is 1.1, which indicates that the CTW could exhibit attributes of both Kelvin and shelf waves.35Given the dispersion curve and modal structure of the wave, however, the nature of the CTW appearsto be more similar to that of a shelf wave. Further work is required to definitely determine the nature ofthis CTW and build a comprehensive understanding of its dynamics. Altogether, the characterization ofthe CTW observed in the Mackenzie Canyon model results supports future investigation regarding theinfluence the CTW on the propagation of the upwelling signal observed along the Mackenzie Shelf afteran upwelling event.The structure of the CTW in the Mackenzie model simulations is modified as it propagates along thecanyon walls and, eventually, along the upstream slope. The evolution of the wave is examined furtherusing the AW-representative surface in the idealized model since the amplitude of the wave is larger atgreater depths (and, therefore, the signal is more distinct) and scattering is considerably lower than thatin the realistic model. The average phase speed of the CTW throughout the simulation is estimated fromthe Hovmo¨ller diagrams showing the wave signal inside (Figure 3.9 (f)) and offshore of (Figure 3.9 (b))the canyon. The average phase speed of the CTW is ∼ 0.14 ms−1 inside the canyon topography (i.e.along Section B) and 0.49 ms−1 offshore of the canyon (i.e. along Section A). Further work using theCTW model (Brink, 2018) is required to examine changes to the wave characteristics as a consequenceof differences in bottom slope between the canyon and upstream slope.3.4 Distribution and propagation of the canyon upwelling signalMackenzie Canyon shows enhanced upwelling compared to the adjacent shelf and slope. Thestrongest upwelling induced by the canyon displaces water upward by 175 m in the idealized modeland 248 m in the realistic model compared to less than 40 m on the downstream slope away from thecanyon in the idealized and realistic models (Figures 3.12 and 3.13). The spatial distribution of up-welling in Mackenzie Canyon is influenced by the interaction between the onshore jet and the canyontopography, the cyclonic eddy on the upstream side of the canyon mouth, and the propagation of theCTW along the canyon walls and upstream slope.The UHW-representative surface in the idealized model (Figure 3.3 (d-f)) demonstrates the influenceof the onshore jet, upstream cyclonic eddy, and CTW on upwelling. During the initial, time-dependentstage of upwelling, the strongest upward displacement occurs near the head and along the downstreamwall of the canyon. Flows turning into the canyon travel to the head and downstream wall of the canyon(Figure 3.1 (a)), resulting in upward excursions as this water encounters the topography. During the36quasi-steady stage of upwelling, however, the strongest upwelling occurs near the head and along theupstream wall of the canyon. At the head, the onshore jet reaches the topography with high speeds(Figure 3.1 (b-c)), generating upwelling that extends the coverage of the water mass farther onshore.Upwelled flows at the head are directed downstream by a combination of topographic steering andthe influence of the anticyclonic eddy induced by the CTW (Figure 3.9 (i)). Additionally, the strongupwelling observed along the upstream wall is likely a consequence of the upwelling signal propagatingalong the canyon walls with the CTW (Figure 3.3 (a-c)). Notably, the strongest upwelling along theupstream wall occurs in the region of high cyclonic vorticity (Figure 3.1 (d-f)). The influence of theupstream cyclonic eddy on upwelling is more apparent in the realistic model, as described below.The UHW-representative surface in the realistic model shows the the influence of the shape of thetopography on the distribution of upwelling throughout the canyon. Topographic steering around thecanyon walls is relatively unaffected by the propagation of a CTW (Figure 3.2 (a-c)) in the realisticmodel, resulting in an upwelling signal that is mostly balanced around the canyon walls (Figure 3.4(d-f)). Generally, the spatial distribution of upwelling and the values for vertical displacement are com-parable between the upstream and downstream sides of the canyon, with two exceptions. First, the watermass exhibits strong upwelling at the centre and downstream side of the canyon head (Figure 3.4 (d-f)),which is induced by onshore flows inside the canyon flowing over the topography instead of turningin the offshore direction to exit the canyon (Figure 3.2 (a-c)). Second, the strongest upwelling alongthe upstream wall is centred over the closed cyclonic eddy nestled on the lee side of the topography atcanyon mouth (Figure 3.4 (a-c)). Notably, the region of strong upwelling expands as the cyclonic eddywidens throughout the simulation (Figure 3.2 (d-f)).In both idealized and realistic models, the upwelling signal on the AW-representative surface prop-agates along the slope topography with the CTW (Figures 3.7 and 3.8 (d-f)). The strongest upwellingoccurs immediately adjacent to the slope topography, and some downwelling occurs farther offshore.Notably, downwelling coincides with regions with cyclonic vorticity, including the cyclonic eddy in-duced by the CTW (Figure 3.9 (j, l)). This is in stark contrast with the strong upwelling observed atthe cyclonic eddy generated by flow separation on the UHW-representative surface (Figures 3.3 and 3.4(d-f)).Upwelling at specific depths shows the main features observed on the UHW- and AW-representativesurface (Figures 3.12 and 3.13). The strongest upwelling is initially focused at the canyon head and37downstream wall, but it shifts toward the upstream wall, especially around the cyclonic eddy at theupstream side of the mouth, throughout the simulation. As expected, the upwelling signal is strongeralong the upstream slope at greater depths due to the propagation of the CTW. Additionally, strongupwelling is also evident near the surface (Figures 3.12 and 3.13 (a-c)). Throughout the simulation,upwelling is typically stronger at greater depths and occurs within the initial 2.5 days of the upwellingevent (Figures 3.12 and 3.13 (f)).3.5 Nitrate transport across the nitracline depthIn the Beaufort Sea, the nitracline occurs at∼ 50 m depth (Ardyna et al., 2017; Monier et al., 2015).In this study, the nitrate transport across this depth (henceforth referred to as the nitracline depth) isestimated using both nitrate concentrations and vertical velocities at this depth (∼ 50 m). The highestvalues, whether positive or negative, of nitrate transport either occur within the canyon topography atthe nitracline depth or show the influence of the topography at greater depths. In the idealized model(Figure 3.14 (a-c)), upward transport occurs at the canyon head and downward transport occurs overthe downstream wall of the canyon. In the realistic model (Figure 3.14 (d-f)), upward transport mostlyoccurs along the downstream wall of the canyon and covers a smaller region compared to the idealizedmodel.Throughout the simulation, the nitrate transport integrated over the child domain is positive, indicat-ing canyon-induced upwelling of nitrate across the nitracline depth (Figure 3.14 (g)). The time series fortotal nitrate transport (Figure 3.14 (g)) shows a sharp increase just after the peak in wind stress is appliedat the surface and around the same time as the maximum alongshore velocities of shelf currents. For theremainder of the simulation, the total transport remains fairly steady at a reduced value. Notably, eventhough the idealized model shows higher downward transport than the realistic model, it also producesupward transport over a larger area (Figure 3.14 (a, d)), resulting in overall higher upward transportthroughout the simulation (Figure 3.14 (g)).During the initial 36 hours of the simulation, when the strongest transport is observed, the total trans-port across the nitracline depth is 1.65×108 mmols−1 in the idealized model and 1.02×108 mmols−1.Additionally, the maximum transport estimated for any given hour during the initial 36 hours of the sim-ulation is 1.11×107 mmols−1 in the idealized model and 7.59×106 mmols−1 in the realistic model.383.6 Effects of wind forcing on circulation and upwellingThe response of Mackenzie Canyon to wind forcing was examined by comparing metrics represent-ing key features in the canyon across the three wind forcing cases (‘half’, ‘base’, and ‘double’). It isimportant to note that these metrics have been normalized relative to the respective ‘base’ case. There-fore, linear processes are considered to be dominant for a given metric if the response of the canyon isrepresented by a 2:1 ratio between base:half and/or double:base wind cases.For all metrics (Figures 3.15–3.17), the ratio between the base and half cases is approximately 2:1,indicating a linear response of the canyon to wind forcing. Non-linear processes, however, appear totake a more dominant role with increasing wind forcing given that the ratio between the double andbase cases is not precisely 2:1 for any of the features represented. The effect of increased wind forcingis especially pronounced for processes contributing to the estimate for CTW amplitude in the realisticmodel (Figure 3.15). A closer look at the model results (Figures 3.4 and 3.8) shows small, isolatedregions of anomalous vertical velocities in areas with high bottom roughness along the upstream slopein the realistic model that do not appear to correspond with the CTW propagation. Unlike verticaldisplacement (Figure 3.16), nitrate transport (Figure 3.17) shows a distinct deviation from linearity duein part to the non-linear relationship between salinity and nitrate concentration (Figure 2.2 (f)).3.7 Model evaluationThe model’s ability to reproduce key circulation features and upwelling patterns in MackenzieCanyon was evaluated by conducting a simulation using realistic bathymetry and a stratification pro-file collected near the canyon (i.e. model run RBE). This study benefitted from access to observationaldata (Waterhouse, in prep) for currents, salinity, temperature, and winds in Mackenzie Canyon. Themodel results show remarkable qualitative agreement with both current (Figure 3.18) and salinity (Fig-ure 3.19) observations. The general circulation inside the canyon and cyclonic eddy feature on theupstream side of the canyon mouth are well represented in both model results and observations. Themodel appears to underestimate the velocities of the high-speed jet separating from the topography onthe upstream side of the canyon (as represented by the length of the arrows in Figure 3.18), indicatingthat future work should consider intentionally adjusting the wind stress applied to the surface in order toreproduce matching velocities for the incoming along-slope flows for evaluation simulations. Salinity39measurements in the canyon show that the model reproduces the site of upwelled, high-salinity water onthe upstream side of the canyon. The observational data also corroborates the unexpected finding thatupwelling is stronger on the upstream side of the canyon compared to the downstream side.40Figure 3.1: Characterization of the horizontal circulation on the UHW-representative surface inthe idealized model: Plan views of a-c) flow speed and direction [ms−1] and d-f) relativevorticity [s−1] averaged over three separate days (top row: hours 12-36, middle row: hours36-60, bottom row: hours 84-108); g) time series of wind stress and average alongshorevelocity of incoming currents over the upstream side of the shelf. The blue diamond in planviews (a-c) shows the location of maximum speeds. The solid, black line outlines the canyonbathymetry at the initial depth of the UHW-representative surface.41Figure 3.2: Characterization of the horizontal circulation on the UHW-representative surface inthe realistic model: Format follows Figure 3.1.42Figure 3.3: Characterization of the vertical velocity on and vertical displacement of the UHW-representative surface in the idealized model: Plan views of a-c) vertical velocity [mms−1]1-hour averages and d-f) vertical displacement [m] averaged over three separate days (toprow: hours 12-36, middle row: hours 36-60, bottom row: hours 84-108); g) time series ofwind stress and average alongshore velocity of incoming currents over the upstream sideof the shelf. The red diamond in plan views (a-c) shows the location of maximum upwarddisplacement. The solid, black line outlines the canyon bathymetry at the initial depth of thewater mass. Small scale oscillations in vertical velocity correspond to the steps in the modelbathymetry. 43Figure 3.4: Characterization of the vertical velocity on and vertical displacement of the UHW-representative surface in the realistic model: Format follows Figure 3.3.44Figure 3.5: Characterization of the horizontal circulation on the AW-representative surface in theidealized model: Plan views of a-c) flow speed and direction [ms−1] and d-f) relative vorticity[s−1] averaged over three separate days (top row: hours 12-36, middle row: hours 36-60,bottom row: hours 84-108); g) time series of wind stress and average alongshore velocity ofincoming currents over the upstream side of the shelf. The blue diamond in plan views (d-f)shows the location of maximum speeds. The solid, black line outlines the canyon bathymetryat the initial depth of the AW-representative surface.45Figure 3.6: Characterization of the horizontal circulation on the AW-representative surface in therealistic model: Format follows Figure 3.5.46Figure 3.7: Characterization of the vertical velocity on and vertical displacement of the AW-representative surface in the idealized model: Plan views of a-c) vertical velocity [mms−1]1-hour averages and d-f) vertical displacement [m] averaged over three separate days (toprow: hours 12-36, middle row: hours 36-60, bottom row: hours 84-108); g) time series ofwind stress and average alongshore velocity of incoming currents over the upstream side ofthe shelf. The red diamond in plan views (d-f) shows the location of maximum upward dis-placement. The solid, black line outlines the canyon bathymetry at the initial depth of thewater mass. Small scale oscillations in vertical velocity correspond to the steps in the modelbathymetry. 47Figure 3.8: Characterization of the vertical velocity on and vertical displacement of the AW-representative surface in the realistic model: Format follows Figure 3.7.48Figure 3.9: Hovmo¨ller diagrams showing the propagation of the CTW along (a-d) Section A and(e-h) Section B and (i-l) plan views of vertical velocity [mms−1] on the UHW- and AW-representative surfaces in both idealized and realistic models. The transects for Section A andB are outlined by dashed, black lines in the plan views for the corresponding model and watermass surface. The speed of the CTW as it propagates (b) outside and (f) inside the canyontopography is estimated by tracking the path of the wave trough (solid, black line with graydiamond markers) on the Hovmo¨ller plots for the AW-representative surface in the idealizedmodel. The green, dashed line in panel (b) has a slope of 0.77 ms−1, which is the speed of theCTW computed by the CTW model based on the wave parameters estimated for the CTWin the Mackenzie Canyon model simulations between hours 24 and 36 (Figure 3.11). Theplan views (i-l) show average vertical velocities at hour 36 for UHW-representative surfacesand at hour 48 for AW-representative surfaces. The shape of the Hovmo¨ller diagram changesaccording to the space occupied by the water mass during the upwelling event.49Figure 3.10: Plan views of vertical velocity [mms−1] on the UHW-representative surface at hours24, 48, and 96 in the (a-c) idealized and (d-f) realistic models.50Figure 3.11: Characterization of the CTW in the Mackenzie Canyon model as the lowest wavemode calculated by the CTW model. a) Plan view and b) vertical cross-section along thedashed line in (a) of the Mackenzie Canyon model results for vertical velocity [ms−1] athour 24; c) dispersion curve of the lowest wave mode calculated by the CTW model for thecross-shore bathymetry profile outlined by the dashed, black line in (a); d) vertical, cross-shore structure for vertical velocity [ms−1] of the lowest wave mode calculated by the CTWmodel. In panel (c), the green circle marks the wavenumber and frequency estimated be-tween hours 24 and 36 for the CTW observed in the Mackenzie Canyon model simulations;the yellow diamond marks the wavenumber and frequency of the lowest wave mode com-puted by the CTW model. The solid, black line in (a) outlines the canyon bathymetry atthe shelf-break depth (80 m). The solid, black contours in (b) and (d) outline wave nodes.The vertical velocity magnitudes calculated by the CTW model (d) have been normalizedfor comparison with the Mackenzie Canyon model results.51Figure 3.12: Vertical displacement [m] in the idealized model: Plan views at specific depths a-c)13 m, d-f) 83 m, and g-i) 162 m averaged over three separate days (top row: hours 12-36,middle row: hours 36-60, bottom row: hours 84-108); j) time series of maximum verticaldisplacement values at depths 13 m, 83 m, 162 m, and 477 m.52Figure 3.13: Vertical displacement [m] in the realistic model: Format follows Figure 3.12.53Figure 3.14: Plan views of a-c) idealized and d-f) realistic model results for nitrate transport acrossnitracline depth (∼ 50 m) as estimated from salinity; g) time series of the total nitratetransport in the child model domain depicted in panels (a-f). Small scale structures in nitratetransport correspond to the steps in the model bathymetry.54Figure 3.15: Comparison metric representing the response of CTW amplitude (through verticalvelocity) to wind forcing for idealized and realistic models and normalized with respect tothe ‘base’ wind forcing case. The metric is the mean positive vertical velocity on the slopejust upstream of the canyon.55Figure 3.16: Comparison metric representing the response of upwelling (through vertical displace-ment) to wind forcing for idealized and realistic models and normalized with respect to the‘base’ wind forcing case. The metric is the maximum positive value of vertical displacementin the canyon region.56Figure 3.17: Comparison metric representing the response of nitrate transport for idealized andrealistic models and normalized with respect to the ‘base’ wind forcing case. The metric isthe total transport of nitrate in the child model domain.57Figure 3.18: Model-to-observations comparison for currents in Mackenzie Canyon. Model resultsfor flow speed and direction are represented by the coloured background and the light bluearrows populating the domain. Observational data for flow speed and direction are repre-sented by dark blue arrows along three transects indicated by thin, black lines: 1) across thecanyon mouth, 2) across the canyon near mid-length, and 3) cross-shore at the downstreamslope. The length and angle of the arrows represent the horizontal components of velocityfor both model results and observational measurements.58Figure 3.19: Model-to-observations comparison for salinity in Mackenzie Canyon. Model resultsfor salinity are represented by the coloured background. Observational data for salinity isrepresented by the coloured diamonds along three transects: 1) across the canyon mouth, 2)across the canyon near mid-length, and 3) cross-shore at the downstream slope.59Chapter 4DiscussionThis study aims to describe the circulation and upwelling patterns in Mackenzie Canyon duringan upwelling event, identify the flow features that act as significant modifiers of upwelling, comparethe results of idealized and realistic simulations, and quantify the flux of nitrate across the nitraclinedepth induced by canyon upwelling. This section provides a review of the modelled patterns and timeevolution of circulation and upwelling in Mackenzie Canyon and compares these findings to those fornarrow, intermediate, and wide canyons from previous numerical, scaling, and observational studies.The effects of CTW propagation on the distribution of the upwelling signal in Mackenzie Canyon isalso discussed. This section also provides further context on the influence of canyon upwelling on thetransport and flux of nitrate across the nitracline depth, specifically as it relates to the seasonal draw-down in the Beaufort Sea. Finally, this section discusses the significance of having used both idealizedand realistic models in this study and outlines the limitations of the model.4.1 General circulation patterns and key featuresFlows are topographically steered around Mackenzie Canyon. In stark contrast to the circulationaround narrow canyons (with widths less than twice the radius of deformation), incoming, along-slopeflows (between the depth of the canyon head Hh = 40m and the maximum depth of the canyon Hc =372m) turn into Mackenzie Canyon near the upstream side of the mouth, move along the canyon walls,and exit the canyon on the downstream side of the mouth. Flows above the head of Mackenzie Canyon,up to a depth of ∼ 4m, are also deflected over the canyon, showing a similar pattern as the circulationinside the canyon. In narrow canyons, near-surface, along-slope, and shelf flows cross the canyon with60little onshore deflection and support a cross-shore pressure gradient between the canyon head and mouth.The model results for Mackenzie Canyon, however, show lower pressure values around the canyonwalls compared to the centre of the canyon (not shown), which is consistent with near-geostrophic flowsfollowing the canyon walls.During the initial, transient stage of upwelling (within ∼36 hours from the start of the simulation),flows crossing Mackenzie Canyon encounter the downstream wall near the canyon mid-length. Duringthe quasi-steady stage of upwelling (the remainder of the simulation), flows inside the canyon are morestrongly steered around the topography and turn offshore closer to the canyon head. A stagnation (Hyun,2004) or separation (Waterhouse et al., 2009) point is defined as the location where currents crossingthe canyon reach the downstream wall and either turn onshore and flow around the canyon head orturn offshore and exit the canyon topography. The separation point is expected to be located closer tothe canyon head for wider canyons and farther offshore for narrow canyons (Hyun, 2004). If the ratiobetween the canyon width W and radius of deformation a is used to define the dynamical width of acanyon, Mackenzie Canyon would be classified as marginally wide (or intermediate) with W/a ∼ 2.6.The separation point in Mackenzie Canyon is near the canyon mid-length, as expected for intermediatecanyons, only during the initial stage of upwelling when incoming currents are accelerating. For theremainder of the simulation, however, the separation point is at the canyon head like that expected forwider canyons.The average alongshore velocity of shelf currents upstream of Mackenzie Canyon (between depths13 m and 56 m) is∼0.1 ms−1, and the Rossby number RW∗ =U/ fRW (Howatt and Allen, 2013), whichuses the width of the canyon taken half-way along the canyon length and measured across the shelfbreak isobath, is ∼0.02. As expected for canyons with low Rossby number RW∗ (Allen, 2004; Howattand Allen, 2013), flows inside Mackenzie Canyon follow the topography. In contrast, flows in nar-row canyons with higher Rossby numbers RW∗, such as Astoria (RW∗∼0.21) and Barkley canyons(RW∗∼0.11), cross the canyon and form a cyclonic eddy over the canyon (Allen et al., 2001; Allenand Hickey, 2010; Hickey, 1997).Along-slope flows turning into Mackenzie Canyon separate from the topography and, in the case ofrealistic bathymetry, readily form a closed cyclonic eddy on the upstream corner of the canyon mouth.In narrow canyons, a cyclonic eddy forms at rim depth and spans the canyon width as along-slopecurrents cross the canyon and turn onshore at the downstream wall near the mouth and flows above the61rim descend into the canyon, generating vortex stretching (Allen et al., 2001; She and Klinck, 2000;Waterhouse et al., 2009). Interestingly, however, previous experiments with intermediate and widecanyons (Hyun, 2004) show the formation of a cyclonic eddy with a width of approximately twice thedeformation radius and extending across the length of the canyon. In Mackenzie Canyon, however, andspecifically in the realistic model, the canyon eddy is approximately 10-15 km wide for the simulationwith base wind forcing, and the region with strong cyclonic vorticity does not extend farther onshorethan the mid-length of the canyon. In the idealized model, the region with strong cyclonic vorticityextends farther onshore, and the upstream eddy only forms at greater depths. Even when the cycloniceddy forms in the idealized model, however, it only occupies a small area on the upstream side of thecanyon like in the realistic model but unlike previous studies.The conceptual model proposed for processes associated with the flow patterns around headlandsmay be partially analogous to the development of the cyclonic eddy attached to the upstream side ofMackenzie Canyon. The separation of alongshore flows and formation of a cyclonic eddy on the lee sideof headlands have been attributed to friction associated with complex bottom topography and variationsin vorticity resulting from the curvature of the topography (Castelao and Barth, 2007; Penven et al.,2000). Granted, other factors, such as orographic effects on wind stress, that have also been attributed tothese circulation patterns (Castelao and Barth, 2007) are not applicable to those in submarine canyons,at least within the scope of this project. Conditions favourable to the formation of a headland eddy havebeen related to the Burger number Bu =(NH/ f Lchar)2, where N is the Brunt-Va¨isa¨la¨ frequency, H isthe water depth, f is the Coriolis parameter, and Lchar is a characteristic length scale, such as the sizeof the cape (Penven et al., 2000). Using the maximum canyon depth Hc=372 m and canyon width atthe mouth W=62.7 km as the characteristic length scale, the Burger number of Mackenzie Canyon is∼0.14. The low Burger number for Mackenzie Canyon indicates that the flow is expected to generate anattached cyclonic eddy (Penven et al., 2000) as advection and bottom friction become more dominant inthis region compared to the adjacent slope where flows are more geostrophic.4.2 Distribution and propagation of upwelling signalSimilar to narrow canyons, the location of the strongest upwelling in Mackenzie Canyon duringthe initial, transient pulse is associated with the interaction of accelerating, onshore flows inside thecanyon with the topography. Like narrow canyons, the strongest upwelling in Mackenzie Canyon dur-62ing the initial stage of upwelling occurs near the canyon head and downstream wall. For the remainderof the simulation, however, the strongest upwelling in Mackenzie Canyon shifts to the upstream wall,while it typically remains along the downstream wall in narrow canyons. Notably, at greater depths,the upwelling signal initially near the canyon head clearly shifts upstream, exits the canyon topography,and propagates along the upstream slope with the canyon-induced CTW. The upstream (northeastward)propagation of the upwelling signal has been identified in observations along the Mackenzie Shelf (Car-mack and Kulikov, 1998). While the dynamics involved in the propagation of a canyon-driven upwellingsignal by a canyon-induced CTW have not yet been studied, strong upwelling events in canyons havepreviously been associated with the passage of remotely-forced CTWs (Sobarzo et al., 2016). The cur-rent existing literature on upwelling generated in canyons as a result of CTWs focuses on stationary, leewaves that are induced by the canyon bathymetric perturbation and arrested by incoming flows (Zhangand Lentz, 2017). These stationary, canyon-induced waves have been linked to the formation of isolated,alternating zones of upwelling and downwelling (Kaempf, 2012). In Mackenzie Canyon, and specifi-cally on the AW-representative surface, temporary, localized zones of upwelling and downwelling areindeed observed, but these regions occur at the nodes of the CTW and move upstream with the CTW.With a phase speed of ∼0.78 ms−1 (as estimated between hours 24 and 36, Section 3.3), the CTW inMackenzie Canyon propagates upstream since it is not arrested by incoming slope currents, which reacha maximum speed of only ∼0.2 ms−1 on the AW-representative surface in the idealized model duringthe initial stage of upwelling (Figure 3.5 (a)).Model results showing the strongest upwelling near the head and along the upstream wall are cor-roborated by observational studies in Mackenzie Canyon (Macdonald et al., 1987; Williams et al., 2006)and numerical experiments with intermediate and wide canyons (Hyun, 2004). Compared to field mea-surements in Mackenzie Canyon (Carmack and Kulikov, 1998), the realistic model produces a slightlystronger upwelling signal in the canyon compared to adjacent slopes. Between ∼ 30m and ∼ 214m,the model results for vertical displacement and field observations show that upwelling inside the canyonis approximately 3-4.5 times and 2-3 times as strong as the upwelling along the adjacent slope, respec-tively. Near the canyon head at a depth of ∼90 m, the realistic model results for vertical displacementshow water upwelled from a depth of ∼171 m, which is similar to that measured in Mackenzie Canyon,∼180 m, for the same depth (Williams et al., 2006). The upwelling depth Z, which is defined as thechange in depth of the deepest water to be upwelled onto the shelf, is estimated to be ∼37.3 m for63Mackenzie Canyon using the scaling in Howatt and Allen (2013).The model results for depths betweenthe canyon head (∼40 m) and shelf break (∼80 m) show a maximum vertical displacement of ∼88 m,which is higher than that predicted by the scaling for upwelling depth Z. Since Mackenzie Canyon isneither short nor narrow, this scaling is not likely to be appropriate. Indeed, model results for verticaldisplacement show a linear dependence on incoming velocity, which is inconsistent with the non-linear,advection processes considered for the scaling ofZ.4.3 Canyon-induced nitrate flux and draw-downIn the Beaufort Sea, the base of the euphotic zone is typically below the nitracline, where the formeris located between 60-70 m depth and the latter occurs at ∼ 50 m depth (Ardyna et al., 2017; Monieret al., 2015). The model results for Mackenzie Canyon show sustained transport of nitrate across thenitracline depth and significant upwelling to the shelf. This finding supports previous suggestions thatcanyon-induced upwelling is likely to produce a flux of nutrient-rich water to the shelf that may supportincreased productivity (Macdonald et al., 1987; Williams et al., 2006).The total nitrate flux across the nitracline depth in the model can be estimated using the diagnosednitrate transport (Figure 3.14 and Section 3.5) over the canyon region (encompassed by the child domain,which extends 207 km and 184 km in the alongshore and cross-shore directions) and compared to theseasonal nitrate draw-down in the Beaufort Sea. For the canyon region in the realistic model, the totalnitrate flux for the initial 36 hours is ∼ 348mmolm−2. In the southern Beaufort Sea, the seasonal draw-down of nitrate is∼5×10−3 molm−3 over a depth of∼30 m (Codispoti et al., 2013), resulting in a totaldraw-down of ∼150 mmolm−2. Therefore, the total nitrate supplied by Mackenzie Canyon over thefirst 36 hours of the upwelling event per unit area is ∼232% the seasonal draw-down. Considering thatthe area of the child domain is 0.09 times the area of the Beaufort Sea, this is a contribution of ∼21%of the seasonal drawdown in one canyon upwelling event. Approximately 6-7 upwelling events occurin Mackenzie Canyon over the course of a year (Carmack and Kulikov, 1998; Williams et al., 2006).Since draw-down (or net nutrient consumption) can be used to characterize net community production(Bergeron and Tremblay, 2014), Mackenzie Canyon can be considered a region of significant nutrientsupply, which indicates the potential for high primary production.The nitrate flux presented in this study accounts for the advection processes affecting the distributionof nitrate in the region. Submarine canyons, however, are regions of enhanced mixing due to the fo-64cusing of internal waves and tides. The effect of locally-enhanced mixing inside canyons on tracer fluxhas previously been studied with numerical experiments prescribing higher values for diffusivity to themodel grid cells inside the canyon topography (Ramos-Musalem and Allen, 2019). Locally-enhanceddiffusivity in canyons has been found to increase the tracer flux via upwelling by a maximum of 27%,and it results in larger tracer concentrations near the canyon rim (Ramos-Musalem and Allen, 2019).4.4 Modelling with idealized and realistic bathymetryThe general circulation and upwelling patterns are similar in the idealized and realistic models.In both models, incoming along-slope currents separate from the topography and generate cyclonicvorticity on the upstream corner of the canyon mouth. The cyclonic eddy on the upstream side of thecanyon mouth develops more readily and is more persistent in the realistic canyon. As a consequence,the onshore jet arrives at the canyon head with lower speeds, and therefore produces weaker upwelling,in the realistic model compared to the idealized model. The propagating signal of the CTW is morepersistent in the idealized model since there is less scattering by the topography compared to the realisticmodel. As such, the propagation of the upwelling signal by the CTW is more distinct in the idealizedmodel.At present, only a few studies have conducted numerical experiments with both idealized and re-alistic bathymetry (Connolly and Hickey, 2014; Liu and Gan, 2015). Studies that have conducted nu-merical experiments with realistic canyon bathymetry have evaluated model performance using eitherobservational data from the same canyon when data is available (Ardhuin et al., 1999) or results of pre-vious laboratory and numerical experiments (Skliris et al., 2002). Other studies have noted that specialcare should be taken when considering open boundary conditions since models using realistic canyonbathymetry may produce unstable solutions (Dinniman and Klinck, 2002). This study finds that 1) a sta-ble, numerical model with realistic bathymetry and stratification can largely reproduce the circulationand upwelling features observed in a real canyon and 2) idealized models capture the main circulationand upwelling features that develop in realistic models.4.5 Model considerations and limitationsThe numerical simulations conducted in this study are forced with a simplified analytical formula-tion for wind stress. Upwelling events in Mackenzie Canyon have been associated with the cumulative65effect of a series of brief, but intense, wind pulses (Carmack and Kulikov, 1998). Therefore, while themodel provides results suitable for a process study, it does not necessarily exhibit all elements of anupwelling event in Mackenzie Canyon induced by realistic winds. Additionally, this project focusessolely on upwelling driven by wind stress at the surface, even though studies have found that ice-relatedstress at the surface not only produces but also amplifies the upwelling response in Mackenzie Canyon(Williams et al., 2006). Furthermore, the numerical model was not configured to include tides. Thisdecision was made since diurnal and semidiurnal tidal currents reach a maximum of ∼0.3 cms−1 and∼0.7 cms−1 (Kulikov et al., 2004), respectively, while alongshore currents upstream of the canyon havebeen observed with velocities of up to ∼40 cms−1 during an upwelling event (Williams et al., 2006).Finally, the results presented in this study typically show larger horizontal and vertical velocities in thechild model compared to the parent model. Future studies using nested modelling grids should carefullyconsider the values used for diffusivity, viscosity, and slip boundary conditions in the parent and childmodels in order to reduce differences in horizontal and vertical velocities between nested domains.66Chapter 5ConclusionsSubmarine canyons are sites for enhanced upwelling and distinct flow patterns compared to adja-cent continental slopes and are associated with high biological productivity and nutrient and sedimentcycling. Generally, currents in geostrophic balance over the shelf and slope are constrained to followisobaths, inhibiting transport up the steep topography along coastlines. Ageostrophic flow dynamics insubmarine canyons, however, permit strong deep ocean to shelf exchange. Numerical experiments offera medium through which the various complex elements involved in the dynamics of canyon upwellingcan be individually and systematically explored. Numerical models have significantly contributed toour understanding of flows over and near submarine canyons under both steady and transient forcing, aswell as of the effects of stratification and canyon width on upwelling dynamics. Great strides have beenmade towards an ultimate goal of understanding and simulating the response of temporally and spatiallyvariable flows with realistic stratification over realistic canyon topography with complex bottom rough-ness. Despite this progress, however, most numerical studies to date have employed idealized canyonbathymetry, and our current understanding of upwelling dynamics is largely limited to dynamicallynarrow canyons. As such, the goal of this study was to improve our understanding of the circulationpatterns and upwelling mechanisms in a dynamically wide submarine canyon using numerical modelswith idealized and realistic bathymetry and to evaluate the model results with real-world observations.The following research questions were addressed.1. What are the circulation patterns inside and near Mackenzie Canyon during an upwelling event?Flows are topographically steered around Mackenzie Canyon. Along-slope, incoming currents67turn into the canyon on the upstream side of the mouth, move along the canyon walls, exit thecanyon on the downstream side of the mouth, and continue downstream along the slope. At theupstream corner of the canyon mouth, incoming currents turning into the canyon separate from thetopography. This produces strong cyclonic vorticity on the lee side of the topography at the up-stream side of the canyon and eventually generates a closed, cyclonic eddy in the realistic model.Furthermore, a coastal trapped wave is induced as incident flows interact with the canyon topog-raphy. The nature of this wave was examined using a model that calculates the modal structureand dispersion curve of coastal trapped waves possible for a given topographic profile and strat-ification. The results of the CTW model for the vertical velocity structure of the wave stronglyresembled that of the wave produced in the Mackenzie Canyon model. As such, the results ofthe CTW model were used to identify the wave in the Mackenzie Canyon model simulations as ashelf wave.2. What flow features are significant modifiers of the upwelling in Mackenzie Canyon?During the initial, transient stage of the upwelling event, the strongest upwelling occurs at the cen-tre and downstream side of the canyon head. Throughout the remainder of the simulation understeady forcing, the strongest upwelling occurs at the canyon head and along the upstream wall,especially over the region with strong cyclonic vorticity near the corner of the canyon mouth.Pressure values are higher closer to the centre of the canyon than along the walls, indicating thatthe enhanced upwelling observed in Mackenzie Canyon occurs under near-geostrophic condi-tions. The upwelling at the head and downstream wall of the canyon, especially during the initialstage of upwelling is likely a response to high-speed, accelerating flows encountering the canyontopography. As the CTW propagates upstream along the canyon walls, the upwelling signal shiftsto the upstream side of the canyon. The influence of the CTW is especially evident along thesalinity surface representative of the Atlantic Water, for which a strong upwelling signal clearlypropagates upstream, exits the canyon, and continues along the upstream slope. The propagationof an upwelling signal has been identified by observational studies along the Mackenzie Shelf.Furthermore, upwelling over the area with strong cyclonic vorticity on the upstream side of thecanyon is strongest for cases where the closed, cyclonic eddy forms.683. What differences in upwelling are caused by smoothing the topography to make an idealizedcanyon?There are three key differences between the idealized and realistic modelled results for circu-lation features that act as significant modifiers of upwelling in Mackenzie Canyon. While theflow separation of incoming currents and resulting cyclonic vorticity is simulated by the idealizedmodel, the sharp topographic change on the upstream side of the realistic canyon facilitates theformation of a closed, cyclonic eddy. The realistic model, therefore, shows stronger eddy-inducedupwelling than the idealized model. Additionally, flows that separate from the canyon topographyin the idealized model maintain the high speeds required to support a strong onshore jet that pro-duces strong upwelling at the canyon head. Therefore, upwelling at the canyon head is stronger inthe idealized model compared to the realistic model. Finally, the rougher topography of the real-istic model dissipates the signal of the CTW as it propagates upstream. As a result, the upwellingsignal on the upstream side of the canyon and along the upstream slope is more persistent in theidealized model.4. Are the model results for circulation and upwelling in Mackenzie Canyon supported by observa-tional evidence?The numerical model configured for this project successfully reproduces the key circulation andupwelling features of an observed upwelling event in Mackenzie Canyon. In-situ observations offlow speed and direction in the canyon corroborate the general anticyclonic circulation simulatedby the realistic model. On the upstream side of the observational velocity transects, high-speedonshore-directed flows adjacent to low-speed outgoing flows corroborate model findings of thegeneration of a cyclonic eddy in that region of the canyon. Additionally, a strong upwelling sig-nal is observed on the upstream side of the canyon near the mouth in both salinity observationsand model results. While observations for currents and salinity were not available near the canyonhead, previous observational studies in Mackenzie Canyon support the patterns simulated by theMackenzie Canyon model.695. Does upwelling in Mackenzie Canyon produce significant upward transport of nitrate across thenitracline depth and, if so, how much?Model results show that upwelling in Mackenzie Canyon produces significant upward transport ofnitrate, especially near the head and on the downstream side of the canyon. In a single hour duringan upwelling event, Mackenzie Canyon can supply one fifth of the seasonal nitrate draw-down inthe Beaufort Sea. Over the initial 36 hours of an upwelling event, the total nitrate flux induced byMackenzie Canyon is twice the seasonal draw-down in the Beaufort Sea.This study makes three significant contributions to the scientific landscape of coastal oceanographyresearch. The first and most critical contribution of this work is to the field of submarine canyons re-search, especially as it relates to physical processes in these coastal regions. Research of the upwellingdynamics in submarine canyons has been focused on canyons that are dynamically narrow (Figure D.1).This study is, in essence, a case study improving the current understanding of the circulation patternsand upwelling dynamics in wide canyons (Figure D.2). Such differences include topographic steeringof flows under near-geostrophic conditions, the formation of a cyclonic eddy, the generation and prop-agation of a coastal trapped wave, and strong upwelling at the head and along the upstream side ofthe canyon. Future efforts in modelling, laboratory, or observational research should consider furthercharacterizing the key circulation features explored in this study in order to develop our understandingon wide canyons further. Additionally, while previous studies show that the transport per unit width islarger in narrow canyons compared to wide canyons (Hyun, 2004), this study shows that the verticaldisplacement in Mackenzie Canyon is higher than that predicted using the established scaling for up-welling depth in narrow canyons. Future comparisons of upwelling metrics, such as upwelling depthand transport, should account for the aforementioned circulation features acting as significant upwellingmodifiers in order to determine if either narrow or wide canyons produce more efficient upwelling.The second key contribution of this study is to modelling efforts of the physical processes in sub-marine canyon regions. Previous studies on the upwelling dynamics in submarine canyons have mostlyused idealized bathymetry. This study, however, finds that the mechanisms supporting enhanced up-welling in Mackenzie Canyon can be heavily impacted by the nature of the topography. Future workshould continue to explore the differences in circulation and upwelling patterns between idealized andrealistic models, especially for canyons with more complex geomorphology. Additionally, this work70shows value in comparing model results with in-situ observations.Finally, this study investigates one of the many hydrodynamic mechanisms that modulate primaryproductivity, and by extension, impact the food supply that supports biological populations in the south-eastern Beaufort Sea. In this region, nutrient (and specifically nitrate) supply controls the magnitudeof phytoplankton productivity, while irradiance levels determine its timing (Carmack and Macdonald,2002; Carmack et al., 2004; Macdonald et al., 1987). The strong stratification maintained by sea-icemeltwater in this region, however, hampers the vertical exchange of nutrients and limits primary pro-duction. Consequently, increased phytoplankton biomass is associated with the delivery of nitrate to theeuphotic zone by shelf-break upwelling, mixing, advection from adjacent shelves, and riverine outflow(Carmack and Chapman, 2003; Pickart et al., 2013b; Tremblay et al., 2011, 2014). Therefore, and espe-cially in view of the environmental stressors associated with climate change, continual research effortsare required for a comprehensive understanding of the physical mechanisms and biological pathwayssupporting coastal communities.Future work is required to evaluate the response of the physical mechanisms studied here to therapidly changing environmental conditions in the Arctic Ocean. For example, the ongoing trend ofreceding sea-ice (Ardyna et al., 2017; Carmack and Chapman, 2003; Carmack and Macdonald, 2002;Carmack et al., 2004; McLaughlin and Carmack, 2010; Williams and Carmack, 2015) results in in-creased meltwater, which supports a stronger stratification and further curtails the vertical transport ofnutrients to the euphotic zone. Additionally, increased sea-ice melt intensifies aragonite undersaturationand acidity in the Arctic Ocean by enhancing carbon dioxide uptake as a result of increased open wa-ters and decreasing the alkalinity and concentration of dissolved inorganic carbon in the water columnthrough mixing with meltwater (Yamamoto-kawai, 2009). Increased aragonite undersaturation has beenfound to impair ability of calcifying organisms in high-latitude oceans to form calcium carbonate shells.On the other hand, longer periods of open water allow for increased wind-driven upwelling and higherlight availability, both of which support primary productivity. Still, increased upwelling could bringaragonite undersaturated water to the shelves. 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ISSN 00796611. doi:10.1016/j.pocean.2009.07.002. → page 480Appendix ARelevant variables and numbersNotation Definition Valuea radius of deformation (a = NHcf ) 2.38×104 mBu Burger number Bu =(NHcfW)2 0.144Dh depth scale Howatt and Allen (2013) (Dh =f LNs) 5.19×102 mf Coriolis parameter 1.37×10−4 s−1FW∗ function of RW∗ (FW∗ = RW∗(0.9+RW∗) ) 0.0193Hc depth of the canyon at the mouth 372 mHh depth of the canyon at the head 40 mHs depth at shelf break 79.6 mHw depth of the coast 39.6 mL length of the canyon 9.87×104 mLsw distance between the coast and shelf break 1.15×105 mN Brunt-Va¨isa¨la¨ frequency (averaged from surface to500 m depth)8.76×10−3 s−1Ns Brunt-Va¨isa¨la¨ frequency (averaged from surface toshelf break depth)2.61×10−2 s−1RW∗ Rossby number (RW∗ = UfRW ) 0.0177RL canyon length-based Rossby Number (RL = Uf L ) 0.00836RW width of the canyon at half-length 4.65×104 ms continental shelf slope (s = Hs−HwLsw ) 3.48×10−4SE slope effect ( sNsf (FW∗RL)1/2) 0.101U upstream (along-slope) velocity 0.113 ms−1W width of the canyon at the mouth 6.27×104 mZ upwelling depth of the deepest isopycnal to reachthe canyon head Howatt and Allen (2013) (Z =Dh[1.8(FW∗RL)1/2(1−0.42SE)+0.05])37.3 mTable A.1: Values of relevant variables and numbers for the base wind forcing case.81Appendix BAdditional details of methodologyB.1 Sea surface elevation calculationThe solution for the barotropic Rossby adjustment over a shelf Allen (1996) referred to in Sec-tion 2.1 is:η =−∫ t ft0 τdtfρas(1α sinh(S/as)+ cosh(S/as))exp[−(y−S)ad](B.1)where η is the surface elevation, τ is a steady and uniform wind stress in the alongshore direction, fis the Coriolis frequency, g is the gravitational acceleration, ρ is density, S is the distance to the shelfbreak, HS is the depth of the shelf break, HD is the maximum depth of the domain, aS =√gHSf is thebarotropic Rossby number over the shelf, aD =√gHDf is the barotropic Rossby radius off the shelf, andα =√HS/HD.82B.2 Wind stress formulationThe modified formulation for wind stress used to force the model referred to in Section 2.2 is:τ pulsex = τpulsex−max×12(1− cos( f × k×∆t2))(B.2)τrelaxx = τrelaxx−const ×12(1+ tanh(k− krelax/2krelax/6))(B.3)τx =τ pulsex + τrelaxx , if k ≤ krelaxτrelaxx , otherwise(B.4)krelax =trelax∆t(B.5)where τx is the alongshore component for wind stress, τ pulsex is a strong wind pulse with a maximumwind stress value τ pulsex−max, τrelaxx is a reduced constant wind stress with a wind stress value τrelaxx−const , f isthe Coriolis parameter, k is the model time step counter, ∆t is the baroclinic time step in seconds, trelaxis the time in seconds when τ pulsex switches to τrelaxx , and krelax is the time step that corresponds to thetime trelax.83Appendix CAdditional figuresC.1 Wave signal at the eastern edge of the model domainFigure C.1: Plan view of horizontal speeds [ms−1] on the AW-representative surface at hour 96 inthe idealized model.84C.2 Flow speed and direction as 1-hour averagesFigure C.2: Plan views depicting horizontal speed [ms−1] and direction of flows on the UHW-representative surface at hours 24, 48, and 96 in the (a-c) idealized and (d-f) realistic models.Speed is depicted by the colouring and direction is depicted by the flow lines on the surface.The flow lines shown in this figure are not streamlines. The flow lines show flow directiononly; these do not show flow speed.85C.3 Wave propagation on the salinity surface representative of theAtlantic WaterFigure C.3: Vertical velocity 1-hour averages showing the propagation and modification of thecoastal trapped wave on the AW-representative surface between hours 18 and 84.86C.4 Structure of the lowest wave mode computed by the coastal trappedwave modelFigure C.4: Structure of the lowest wave mode calculated by the CTW model. a) Dispersion curveand vertical, cross-shore structure for b) u-velocity component [ms−1], c) v-velocity com-ponent [ms−1], d) w-velocity component [ms−1], e) pressure [kgm−1 s−2], and f) density[kgm−3] of the lowest wave mode as calculated by the CTW model for the cross-shorebathymetry profile outlined by the dashed, black line in Figure 3.11. In panel (a), the greencircle marks the wavenumber and frequency estimated between hours 24 and 36 for theCTW observed in the Mackenzie Canyon model simulations; the yellow diamond marks thewavenumber and frequency of the lowest wave mode computed by the CTW model. Themagnitudes for all values (b-f) have been normalized for comparison with the MackenzieCanyon model results.87C.5 Structure for vertical velocity of the coastal trapped wave in theMackenzie Canyon model simulationsFigure C.5: Evolution of the cross-shore structure for vertical velocity [ms−1] of the CTW in theMackenzie Canyon model simulations. The wave structure becomes more complex in time,as depicted by the 1-hour averages for hours a) 12, b) 24, c) 36, and d) 48.88Appendix DSchematicsD.1 Circulation in narrow canyonsFigure D.1: Schematic of general circulation and upwelling in narrow canyons. Shelf and slopecurrents flow past the upstream side of the canyon mouth before being deflected onshore nearthe downstream wall. At the downstream wall, flows either upwell onto the shelf, continuetowards the head, or turn offshore to exit the canyon. Cyclonic circulation in the canyonevolves into a cyclonic eddy at the canyon rim depth that spans the canyon width.89D.2 Circulation in Mackenzie CanyonFigure D.2: Schematic of general circulation and upwelling in Mackenzie Canyon. Flows aretopographically steered around the canyon walls. An onshore-directed jet encounters thecanyon topography at the head, and upwelled flows are advected downstream. Along-slopeflows separate from the topography on the upstream corner of the canyon mouth, resultingin the generation of high vorticity flows and the subsequent formation of a cyclonic eddy.The attached cyclonic eddy on the upstream corner of the canyon mouth becomes a site forstrong upwelling. A coastal trapped wave is generated on the downstream side of the canyonand propagates the canyon upwelling signal upstream along the upstream wall and slope.90

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