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Transport through submarine canyons Ramos Musalem, Ana Karina 2020

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Transport Through Submarine CanyonsbyAna Karina Ramos MusalemB.Sc. Physics, Universidad Nacional Auto´noma de Me´xico, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Oceanography)The University of British Columbia(Vancouver)January 2020c© Ana Karina Ramos Musalem, 2020The following individuals certify that they have read, and recommend to the Faculty of Graduateand Postdoctoral Studies for acceptance, the dissertation entitled:Transport Through Submarine Canyonssubmitted by Ana Karina Ramos Musalem in partial fulfilment of the requirements for the degreeof Doctor of Philosophy in Oceanography.Examining Committee:Susan E. Allen, Earth, Ocean and Atmospheric SciencesSupervisorGregory Lawrence, Civil EngineeringSupervisory Committee MemberDouw Steyn, Earth, Ocean and Atmospheric SciencesSupervisory Committee MemberStephanie Waterman, Earth, Ocean and Atmospheric SciencesUniversity ExaminerNeil Balmforth, MathematicsUniversity ExamineriiAbstractExchanges of water, nutrients, and oxygen between coastal and open ocean are key componentsof on-shelf nutrient budgets and biogeochemical cycles. Submarine canyons are underwater topo-graphic features that incise the continental shelf and enhance physical processes such as cross-shelfmass exchanges and mixing. There is a good understanding of the flow around upwelling submarinecanyons; however, the flux of biologically relevant tracers and the collective impact of canyons isless well understood.This dissertation investigates the collective impact of submarine canyons on cross-shelf ex-change of tracers and water and their distribution on the shelf, taking into account the impact oflocally-enhanced mixing within the canyon and the initial geometry of the tracer profile. I per-formed numerical experiments, using the Massachusetts Institute of Technology general circulationmodel (MITGCM), simulating an upwelling event near an idealized canyon. To investigate the roleof mixing I added a passive tracer with an initially linear profile, varying the spatial distribution ofvertical eddy diffusivity and its magnitude. To investigate the impact of the initial tracer profile Iadded 10 passive tracers with initial profiles representing nutrients, carbon and dissolved gasses. Ifound that locally enhanced vertical diffusivity has a positive effect on the tracer that is advectedby the upwelling flow and can significantly increase canyon-upwelled tracer flux; tracer flux alsodepends on the initial vertical tracer gradient within the canyon, the depth of upwelling and theupwelling flux. I identified a pool of low oxygen and high nutrient, methane, dissolved inorganiccarbon and total alkalinity concentrations on the shelf bottom, downstream of the canyon. Thehorizontal extent of the pool depends on the canyon-induced advective fluxes feeding the pool andthe initial background distribution of tracers on the shelf. The interaction between two identicalcanyons during an upwelling event was investigated using a laboratory model on a rotating tank. Ifound that canyons are primarily independent for the parameter regime explored but may interactthrough the arrival of the upstream canyon’s pool to the downstream canyon’s head.iiiLay SummarySubmarine canyons are topographical features that cut across the continental shelves all around theworld. Close to the continental shelf, currents usually flow following the depth contours of theocean bottom. Near submarine canyons, however, currents are bent by the topography and verticalflows occur more readily. This allows deep nutrient-rich, oxygen-depleted water to reach closer tothe surface, making canyons hot spots for marine life.This thesis uses computer simulations and laboratory experiments to investigate the amount ofnutrients and other substances that currents through canyons deliver from deeper to shallower watersof the continental shelf. The main findings are that two canyons behave independently within thelimits of the experiments and that fluxes of a substance depend on the amount of mixing in thecanyon, the initial distribution of the substances in the water column and the strength of the currentsgenerated by the canyon.ivPrefaceChapters 2, 3 and 4 are self contained after reading the Introduction. This may result in minor redun-dancies from chapter to chapter, but the information provided in each chapter is there to serve thepurpose of that specific study. Chapter 2 has been published in very similar form as presented here:Ramos-Musalem, K. and S.E. Allen, 2019: The Impact of Locally Enhanced Vertical Diffusivityon the Cross-Shelf Transport of Tracers Induced by a Submarine Canyon. J. Phys. Oceanogr., 49,561584, https://doi.org/10.1175/JPO-D-18-0174.1; while a version of Chapter 3 has been submittedfor publication as Ramos-Musalem, K. and S. E. Allen, The impact of initial profile on the exchangeand on-shelf distribution of tracers induced by a submarine canyon.I designed the numerical experiments used in Chapters 2 and 3 using the Massachusetts Instituteof Technology General Circulation Model (MITgcm) based on previous work by Jessica Spurgin,with guidance of Susan Allen. I performed all the numerical runs and analysis of model output, aswell as all calculations and metrics. I developed the scaling analysis presented in both chapters incollaboration with Susan Allen. I was responsible for writing and producing the manuscripts andfigures, and received edits and suggestions from Susan Allen.In Chapter 2 I used dissipation data from Eel Canyon and Monterey Canyon provided by AmyWaterhouse and Glenn Carter, respectively to generate the realistic profiles of vertical diffusivity inChapter 2.In Chapter 3 I used bottle measurements, as well as CTD profiles collected during the PathwaysCruise 2013 on board R/V Falkor provided by Susan Allen to initialize all the tracers used in themodel. I also used temperature and salinity from two ARGO float profiles taken close to AstoriaCanyon to generate the initial temperature and salinity conditions of the realistic run ARGO.I designed the experimental set up in Chapter 4 based on previous work by Kate Le So¨uef, AmyWaterhouse and Christian Reuten. I received many suggestions and guidance from Susan Allen. Idesigned the 3D printed canyon inserts with help of Dan Robb and David Feixo Irazabal. AshutoshBudhia and I built and mounted the conductivity probes following instructions by Conduino systemdesigner Paolo Luzzatto-Fegiz. I used the Matlab toolbox PIVlab to analyse the videos for ParticleImage Velocimetry (PIV). The profiler arm was built by Douw Steyn.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Supplementary Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxviiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxixList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxxiiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxxiv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Limits on cross-shelf exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.1 Canyon dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.2 Mixing in submarine canyons . . . . . . . . . . . . . . . . . . . . . . . . 91.1.3 Cross-shelf exchange of tracers . . . . . . . . . . . . . . . . . . . . . . . 101.2 Collective effect of submarine canyons on the continental shelf . . . . . . . . . . . 121.2.1 Rotating tanks and the study of submarine canyon dynamics . . . . . . . . 131.3 Objectives and Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 The Impact of Locally-Enhanced Mixing on Canyon-Induced Tracer Transport . . 172.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17vi2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.1 Description of the flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.2 Vertical gradient of density and tracer . . . . . . . . . . . . . . . . . . . . 252.3.3 Cross-shelf transport of water and tracer . . . . . . . . . . . . . . . . . . . 272.3.4 Upwelling flux and upwelled tracer mass . . . . . . . . . . . . . . . . . . 292.3.5 A note on model resolution . . . . . . . . . . . . . . . . . . . . . . . . . . 332.4 Scaling analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.4.1 Advection-diffusion equation in natural coordinates . . . . . . . . . . . . . 352.4.2 Relevant parameter space . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.4.3 Stratification and tracer gradient evolution . . . . . . . . . . . . . . . . . . 382.4.4 Average tracer concentration . . . . . . . . . . . . . . . . . . . . . . . . . 412.4.5 Upwelling and tracer fluxes . . . . . . . . . . . . . . . . . . . . . . . . . 422.5 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.5.1 Implications for internal waves . . . . . . . . . . . . . . . . . . . . . . . . 452.5.2 Extension to other canyons . . . . . . . . . . . . . . . . . . . . . . . . . . 472.5.3 Significance to upwelling nutrients . . . . . . . . . . . . . . . . . . . . . . 483 Cross-Shelf Transport and Distribution of Nutrients and Dissolved Gasses Inducedby a Submarine Canyon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2.1 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.2.2 Tracers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2.3 Transport sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.2.4 Upwelling quantification . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.3.1 Canyon upwelling and circulation . . . . . . . . . . . . . . . . . . . . . . 563.3.2 Cross-shelf transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.3.3 On-shelf tracer distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 613.3.4 Canyon-induced tracer upwelling . . . . . . . . . . . . . . . . . . . . . . 653.4 Scaling considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.4.1 Scaling tracer upwelling flux . . . . . . . . . . . . . . . . . . . . . . . . . 683.4.2 Scaling the pool area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.5.1 Canyon-induced tracer distribution on the shelf . . . . . . . . . . . . . . . 733.5.2 Significance to the near-bottom carbon system . . . . . . . . . . . . . . . 74vii3.5.3 Significance to nutrient upwelling . . . . . . . . . . . . . . . . . . . . . . 754 Dynamical Interaction Between Submarine Canyons . . . . . . . . . . . . . . . . . . 764.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.2.1 Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.2.2 Similarity theory and non-dimensional regime . . . . . . . . . . . . . . . . 834.2.3 Depth of upwelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.2.4 Sources of error and measurement uncertainty . . . . . . . . . . . . . . . . 844.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.3.1 Qualitative description of upwelling in two canyons from dye experiments . 854.3.2 Depth of upwelling from conductivity measurements . . . . . . . . . . . . 864.3.3 Particle image velocimetry and the velocity field . . . . . . . . . . . . . . 924.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.4.1 Differences between upstream and downstream canyon responses . . . . . 1054.4.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.1 Research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.2 Contributions to the field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.3 Research implications and limitations . . . . . . . . . . . . . . . . . . . . . . . . 1115.3.1 Scaling schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115.3.2 Mixing effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125.3.3 Impact of the initial tracer profile . . . . . . . . . . . . . . . . . . . . . . 1125.3.4 Laboratory models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135.4 Future research directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115A Notes on Body Forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122B Supplementary Results for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 126C Advection-Diffusion Equation in Natural Coordinates . . . . . . . . . . . . . . . . . 129D Effect of Diffusivity Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131E Supplementary Results for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 134viiiF Notes on Laboratory Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139F.1 Density measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139F.1.1 Probe calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139F.1.2 Density profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141F.2 Near-inertial oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143F.3 Canyon inserts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144F.4 Surface deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144G Additional Laboratory Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146G.1 Recovery stage of upwelling experiments . . . . . . . . . . . . . . . . . . . . . . 146G.2 Lag between upwelling depth maxima . . . . . . . . . . . . . . . . . . . . . . . . 146G.3 Azimuthal velocity from PIV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146ixList of TablesTable 2.1 All runs in the Dynamical Experiment have a corresponding no-canyon run andconstant vertical diffusivity as in the base case in Table 2.2. For all runs, pa-rameters N0, f and U were chosen to represent realistic oceanic conditions forcanyons (within values in Table 1 in Allen and Hickey (2010)) while satisfyingthe dynamical restrictions imposed by Allen and Hickey (2010) and Howatt andAllen (2013). Only values changed from the base case (bold face entries in firstrow) are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Table 2.2 All runs in the Mixing Experiment have the same dynamical parameters as thebase case in Table 2.1. All runs reported have a corresponding no-canyon run.Only values changed from the base case (bold face entries in first row) are shown.Values of RL and RW for these runs slightly vary from the base case values withRL between 0.42 and 0.44, and RW between 0.28 and 0.30. . . . . . . . . . . . . 23Table 2.3 Mean vertical (VTT), advective (VATT) and total (TTT) tracer transport anoma-lies through cross sections CS1-CS5 and LID as well as vertical water (VWT)and total (TWT) water transport anomalies throughout the advective phase withcorresponding standard deviations calculated as 12 hour variations for selectedruns. Results for all runs are available in Appendix B. . . . . . . . . . . . . . . 29Table 2.4 Mean water and tracer upwelling fluxes (F (2.4) and FTr (2.5)) for selected runsduring the advective phase, reported with 12 hour standard deviations. All otherquantities are evaluated at day 9: Volume of upwelled water (Vcan), upwelledtracer (Mcan) for the canyon case and fractional canyon contributions to thesequantities calculated as the canyon case minus the no-canyon case divided bythe canyon case, and total tracer mass anomaly on shelf (M-Mnc (2.6)) in kg ofNO−3. Results for all runs are available in Appendix B. . . . . . . . . . . . . . 32xTable 2.5 Non-dimensional groups constructed for the tracer scaling. To calculate thesescales, I took geometric parameters reported by Allen et al. (2001) for BarkleyCanyon (L=6400 m,R=5000 m ,Wm=13000 m), stratification and incoming ve-locity values reported by Allen and Hickey (2010) (N0= 10−3 s−1,U = 0:1ms−1).Although not measured for Barkley Canyon, we used the diapycnal diffusivity(KD = 3:90× 10−3 m2s−1 (Gregg et al., 2011) and isopycnal diffusivity KI =2 m2s−1 (Ledwell et al., 1998). . . . . . . . . . . . . . . . . . . . . . . . . . . 37Table 3.1 All experiments were initialized with 10 passive tracers (Table 3.2). Activetracer profiles, temperature and salinity, vary between runs. Stratification forARGO and PATH experiments corresponds to the mean stratification throughthe upwelling depth (about 100 m below head depth) following Allen and Hickey(2010). For every run there is a corresponding no-canyon case. . . . . . . . . . 52Table 3.2 Initial concentration (Cs) and vertical gradient at shelf break depth (¶zC) for alltracers initialized in the four runs analysed in this chapter. . . . . . . . . . . . . 54Table 3.3 In columns 2-4: Mean net transport (NT), Mean NT relative to AST transportand canyon contribution to Mean NT for selected tracers; in columns 5-7: Sameas 2-4 but for Maximum net transport (Max NT). Tracer transport units (TU) aremMm3s−1, mmol kg−1m3s−1, mMm3s−1, nMm3s−1, mmol kg−1m3s−1, whereM=mol/L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Table 3.4 Pool area normalized by canyon area at day 9, maximum pool area, mean andmaximum pool concentration, and maximum change in concentration (%) frominitial concentration for selected tracers. Concentration units are mM, mmol/kg,mM, nM, mmol/kg. Results for other tracers are available in Table E.2. . . . . . 64Table 3.5 In column 2: Mean tracer upwelling flux [FTr in 3.2] for selected tracers dur-ing the advective phase (days 4-9), reported with 12-h standard deviations. Incolumns 3 and 4: Tracer inventory or anomaly of total tracer mass on shelf [see(3.3)] and percentage relative to no-canyon case. Results for other tracers areavailable in Table E.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Table 4.1 Geometrical parameters of the tank canyons and Astoria Canyon and BarkleyCanyon for comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Table 4.2 List of laboratory experiments. Names starting with T correspond to experimentswith two canyons, names starting with S to experiments with a single canyonand DYE to experiments with dye visualizations. Most two-canyon experimentshave replicate runs. For those experiments the buoyancy frequency N is the meanof the replicates and the error corresponds to the standard deviation (Same forBurger number Bu and radius of deformation a.) . . . . . . . . . . . . . . . . . 79xiTable B.1 Mean vertical (VTT), advective (VATT) and total (TTT) tracer transport anoma-lies through cross sections CS1-CS5 and LID as well as vertical water (VWT)and total (TWT) water transport anomalies throughout the advective phase withcorresponding standard deviations calculated as 12 hour variations for all runs. . 127Table B.2 Mean water and tracer upwelling fluxes (F (4) and FTr (5)) for all runs duringthe advective phase, reported with 12 hour standard deviations. All other quan-tities are evaluated at day 9: Volume of upwelled water (Vcan), upwelled tracer(Mcan) for the canyon case and fractional canyon contributions to these quantitiescalculated as the canyon case minus the no-canyon case divided by the canyoncase, and total tracer mass anomaly on shelf (M-Mnc (6)) in kg of NO−3. . . . 128Table E.1 Tracer transport units (TU) for each tracer are mMm3s−1, mMm3s−1, nMm3s−1and kg−1m3s−1, respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . 136Table E.2 Pool area normalized by canyon area at day 9, maximum pool area, mean andmaximum pool concentrations and maximum change in concentration from ini-tial concentration. Concentration units are: PSU, mM, mM, nM, mmol/kg. . . . 137Table E.3 Column 2: Mean tracer upwelling flux for selected tracers during the advectivephase (days 4-9), reported with 12-h standard deviations. Columns 3 and 4:Tracer inventory or anomaly of total tracer mass on shelf and percentage relativeto no-canyon case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138xiiList of FiguresFigure 1.1 Schematics of the advection-driven phase of upwelling in a submarine canyonfollowing Allen and Hickey (2010). The figure represents a canyon where theshelf and slope currents flow equatorwards (left to right) and mixing is locally-enhanced within the canyon. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Figure 1.2 Bathymetry of a portion of the Pacific Northwest shelf including the south-ern Vancouver Island and north of Washington State. The approximate shelfbreak (solid gray line) corresponds to the 200 m depth contour. In this the-sis I focus on short, narrow canyons like all canyons identified in the map ex-cept for Juan de Fuca Canyon, which is a long canyon. Note the high densityof canyons incising all the continental shelf. Bathymetric data for this fig-ure was provided by GEBCO Compilation Group (2019) GEBCO 2019 Grid(doi:10.5285/836f016a-33be-6ddc-e053-6c86abc0788e). . . . . . . . . . . . . 8xiiiFigure 2.1 (a) Cross-shelf section through the canyon axis, the dashed line marks the shelfbottom, which can be identified with the canyon rim. The red arrows indicatedirections of transports calculated through CS and LID sections. (b) Top view ofthe canyon. The shaded area corresponds to the LID section across which verti-cal transport was calculated. The solid black line is the shelf-break at 149.5 m.Canyon dimensions: L = 8:3 km is the length along the axis,Ws = 12:3 km isthe width at mid length at the shelf-break isobath,W = 21:1 km is the width atmid-length at rim depth,Wm = 24:4 km is the width at the mouth at shelf-breakdepth, and R = 5:5 km is the radius of curvature of the shelf-break isobath,upstream of the canyon. (c) Top view of the domain. The shelf volume isbounded by the wall that goes from shelf-break (black contour) to surface in theno-canyon case (sections CS1-CS6), alongshelf wall at northern boundary andcross-shelf walls at east and west boundaries. (d) Example of initial vertical dif-fusivity profiles at a station in the canyon with Kcan = 10−2 m2s−1 and differentvalues of e . Note that e = 5 m corresponds to a step profile. The dashed redline indicates the depth of the canyon rim. Initial profiles of (e) temperature andsalinity for the base case, and (f) tracer concentration with maximum and mini-mum values of 45 and 2 mM, respectively, and shelf-break depth concentrationCs = 7:2 mM. The dashed gray line corresponds to the shelf-break depth. . . . 19Figure 2.2 Main characteristics of the flow during the advective phase. Average days 3-5contours of tracer concentration (color) and sigma-t (solid black lines, units ofkgm−3) at an alongshelf section close to canyon mouth (b) and along the canyonaxis (a). (c) Along-shelf and (d) cross-shelf components of velocity. (e) Evolu-tion of alongshelf component of incoming velocityU , calculated as the mean inthe gray area delimited in (c). The dashed line marks the beginning of the ad-vective phase. (f) Speed contours and velocity field at 127.5 m depth with shelfbreak in white. (g) Evolution of average bottom concentration on the down-stream shelf, bounded by the yellow rectangle in (h). (h) Tracer concentrationon the shelf bottom averaged over days 3-5. . . . . . . . . . . . . . . . . . . 24xivFigure 2.3 Concentration contours averaged over days 4 and 5 are plotted along canyonaxis for the base case (a) and locally enhanced diffusivity cases with Kcan =10−3 m2s−1 (b), Kcan = 10−2 m2s−1 (c) and Kcan = 10−2 m2s−1, e = 50 m (d).The dotted line indicates the location of the shelf downstream (rim depth). (e)Profiles of vertical diffusivity at a station in the canyon indicated by the dashedline in (a-d). (f, g, h) Vertical profiles of vertical tracer gradient divided byinitial tracer gradient (¶zC=¶zC0), concentrationC, and stratification divided byinitial stratification N2=N20 taken on day 5 at same station as (e). Horizontal,dotted, grey lines correspond to the rim depth. . . . . . . . . . . . . . . . . . . 26Figure 2.4 Base case (a) tracer and (b) water cross-shelf and vertical transport anomaliesduring the simulation through cross-sections defined in Figure 2.1. The hor-izontal, cross-shelf tracer transport anomaly through sections CS2, CS3 andCS4 and averaged over days 4 to 9 is plotted in (c). A full-depth version is plot-ted in (d) to include cross-shelf transport anomaly through the canyon. Verticaltracer transport averaged over days 4 to 9 is plotted in (e). . . . . . . . . . . . 27Figure 2.5 (a-b) Vertically-integrated upwelled water volume and tracer at day 3.5 along-shelf. Dashed lines show the position of the canyon. (c, d, e) Volume of wateron the shelf with concentration values initially below shelf-break depth. (f, g,h) Upwelled tracer mass on shelf. (c) and (f) canyon cases, (d) and (g) no-canyon cases, and (e) and (h) the difference between these. The boundaries ofthe shelf box are the wall that goes from shelf-break to surface in the no-canyoncase, alongshelf wall at northern boundary and cross-shelf walls at east and westboundaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Figure 2.6 (a) Comparison between the mean flux of water and the mean flux of tracerupwelled through the canyon during the advective phase of upwelling for allruns. Error bars correspond to standard deviations. (b) Upwelled tracer fluxincreases (darker, larger markers) with increasing Rossby number RW and de-creasing Burger number Bu. The size and color of the markers are proportionalto the tracer flux, and the red-edged markers correspond to runs with locally-enhanced Kcan. Locally-enhanced diffusivity weakens the stratification belowrim depth and allows more tracer to upwell. . . . . . . . . . . . . . . . . . . . 33xvFigure 2.7 The coordinate system (t , h , b) corresponds to the trihedron that moves alongthe upwelling current (blue line) and (s, z, n) corresponds its horizontal projec-tion (natural coordinate system). So s⃗ is the projection of t⃗ in the x− y plane(horizontal) and z is the usual vertical coordinate (s, z, n). In our derivation, weassume that the coordinates n and b are the same and moreover, they lie on theisopycnal plane. This means that the difference between the coordinate systemsis a single rotation a around the n=b axis. . . . . . . . . . . . . . . . . . . . . 35Figure 2.8 (a) Isopycnals (gray lines) tilt towards the canyon head during a canyon-inducedupwelling event. This tilt is proportional to the upwelling depth Z, defined asthe displacement of the deepest isopycnal to upwell onto the shelf (heavy, greenline). Locally enhanced vertical diffusivity Kcan compared to the backgroundvalue Kbg further squeezes isopycnals above rim depth (canyon rim representedby the dashed line) and in turn, further stretches isopycnals below rim depth.The squeezing effect is proportional to the characteristic length Zdi f (2.19). (b)Zoom in of the red square keeping only two isopycnals: the heavy, dark greenline is the deepest isopycnal that upwells onto the shelf and the grey one is areference isopycnal. The light green line represents the deepest isopycnal thatupwells when diffusivity is homogeneous everywhere (base case). The extradisplacement of this isopycnal when diffusivity is locally-enhanced is the scaleZdi f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 2.9 Scaling estimates of maximum stratification Nmax above the canyon (a), min-imum stratification below rim depth Nmin (b), tracer concentration just aboverim depth Hr (c), and effective stratification Ne f f = 0:75Nmax + 0:25Nmin (d).Dashed lines correspond to ± one mean squared error. . . . . . . . . . . . . . 42Figure 2.10 Scaling estimates of upwelling flux of water (a) and upwelling flux of tracer (b)through a submarine canyon. Dashed lines correspond to ± one mean squarederror. Run legend same as for Figure 2.9. . . . . . . . . . . . . . . . . . . . . 44Figure 2.11 Schematics of tracer transport through a submarine canyon: 1) The upwellingcurrent (blue arrow) brings tracer-rich water onto the shelf, generating an areaof relatively higher tracer concentration than the upstream shelf (4). Enhancedvertical diffusivity within the canyon (2 and 3) increases the tracer concentra-tion near rim depth and weakens the stratification. These two effects enhancecanyon-induced tracer flux onto the shelf. . . . . . . . . . . . . . . . . . . . . 46xviFigure 3.1 (a) Cross-shelf section showing depth profiles of the shelf (dashed) and canyonaxis (solid) for Astoria-like (black) and Barkley-like (orange) bathymetries.Gray and peach lines correspond to the location of cross-sections CS3 and LIDfor Astoria-like and Barkley-like bathymetries, respectively. (b) Top view ofAstoria-like (colormap) and Bakley-like (orange contours) bathymetries withshelf break isobaths in black. Dimensions of Astoria-like bathymetry in pur-ple correspond to the cross-shelf length of the canyon from head to mouthL=21.8 km; Ws=8.0 km and Wm=15.7 km the alongshelf widths at mid-lengthat shelf break depth and mouth, respectively; and R=4.5 km, the upstreamradius of curvature. Barkley Canyon dimensions are L=6.4 km, Ws=8.3 km,Wm=13.0 km and R=5.0 km. (c) Top view of the Astoria-like domain withdepth contours 20, 100, 200, 400, 600, 800, 1000, 1200 m. The solid black linecorresponds to the shelf break isobath along which I defined the cross-sectionsCS1-CS6 to calculate cross-shelf transport. The horizontal section LID wasused to calculate vertical transport through the canyon. (e, f) Temperature andsalinity profiles for all runs. Gray and black dotted lines indicate the shelf breakdepth for Barkley-like and Astoria-like bathymetries, respectively. . . . . . . . 51Figure 3.2 (a-e, g-k) Initial tracer profiles for all tracers used in the simulations. Dotted anddashed gray lines correspond to the shelf-break depth for the Astoria Canyonand Barkley Canyon bathymetries, respectively. (f) Initial density sq and (l)buoyancy frequency N profiles for the four runs analysed in this chapter. . . . . 53Figure 3.3 Advective phase (days 4-9) averages of (a, e) vertical velocity in color and hor-izontal velocity vectors at rim depth (mid-length depth), every 6th quiver isshown; (b, f) cross-shelf velocity in color (positive onto the shelf) and sq con-tours every 0.1 kg m−3 at the canyon mouth; (c, g) alongshelf velocity at thecanyon axis with positive velocities in the upwelling-favourable direction and(d, h) linear tracer concentration (color) and sq contours every 0.1 kg m−3 alongthe canyon axis. Top and middle rows correspond to AST and BAR runs, re-spectively. (i) Along shelf velocity averaged over the yellow rectangles in c andg. (j, k) Water transport across sections CS1-CS6 and net CS water transportfor Astoria Canyon (j) and Barkley Canyon (k) runs, note the difference in scale. 57xviiFigure 3.4 Mean cross-shelf (a1-e1) and vertical (a2-e2) transport of linear tracer, oxygen,nitrate, methane and DIC (top to bottom) during the advective phase. (a3-e3)Canyon effect on the net cross-shelf transport of tracer during the simulationfor all runs with the same units as given in left panel of each row. (f1-f6) Lin-ear tracer transport through cross-sections CS1+CS2, CS3,CS4,CS5+CS6, LID,and net transport for all runs. Tracer transport onto the shelf occurs mostlyabove the canyon and through the canyon lid (canyon induced) and right abovethe shelf break (shelf-break upwelling). . . . . . . . . . . . . . . . . . . . . . 59Figure 3.5 (a,b) The pool of upwelled linear tracer (contour value 1) shown as the meanbottom concentration of linear tracer during advective phase, Cbottom, normal-ized by the initial concentration at shelf break Cs. (c1-4, d1-4) Linear tracerprofiles at days 0 through 8 at virtual stations S1-S4 (black triangles) showthe near-bottom impact of the pool. (e, f) The pool boundaries for 5 differenttracers (contour 1 Cbottom=Cs) show the dependence on the initial tracer pro-file. (g1-4, h1-4) Mean profiles showing changes from initial concentration(∆C(z) =C(z)−C0(z)) at virtual stations S1-S4 during the advective phase. . . 63Figure 3.6 (a and c) Pool area normalized by canyon area increases faster during the timedependent phase (days 0-4) and is larger for AST and ARGO runs. (b and d)The mean pool concentration normalized by initial concentration at shelf-breakdepth Cs is maximum (minimum for oxygen) around day 2.5 but stays higherthanCs through out the simulation. . . . . . . . . . . . . . . . . . . . . . . . . 65Figure 3.7 Flux of water (a) and flux of linear tracer (b) upwelled onto the shelf. The cor-responding canyon contribution is calculated as the difference between canyonand no-canyon runs in (c) and (d). The dotted line marks the beginning of theadvective phase of upwelling. (e) Upwelling flux of tracer from model outputcompared to the modelled water upwelling flux multiplied by the initial tracerconcentration at shelf break depth FCs. Note that the marker for DIC is behindthe marker for alkalinity. (f) Percentile error between quantities in (e) calcu-lated as (FTr−FCs)=FTr is a function of the tracer gradient near shelf break(local average 10 m) normalized by the averaging length ∆Z =10 m overCs. . . 66xviiiFigure 3.8 (a) The cross-shelf section at the canyon axis shows the tilting of isopycnals(gray solid lines) and iso-concentration lines (lines in shades of green) towardsthe canyon head during the upwelling event. Tracer upwelled by the upwellingflux (tracer flux) comes from depths between Hh and Hh+Z and has a concen-tration between C(Hh) and C(Hh+Z). (b) Length scales used to scale the poolarea are shown in a cross-shelf section of the shelf downstream of the canyon.The background pool, shown in tracer contours (shades of green, increasingwith depth), has a cross-shelf length L and associated vertical scale H. Theshelf slope is given by q << 1. . . . . . . . . . . . . . . . . . . . . . . . . . 69Figure 3.9 Scaling estimates for (a) tracer upwelling flux and (b) maximum pool area,equations (3.8) and (3.13), respectively. Tracer upwelling flux is proportionalto upwelling flux and the initial tracer distribution within the canyon. The max-imum pool area is a function ofP, a non-dimensional number given by the ratiobetween on-shelf canyon-induced tracer flux and the initial background tracerdistribution on shelf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Figure 3.10 Mean bottom 20 m (a, b) and top 10 m (c, d) salinity and temperature valuesat CTD stations sampled around Barkley Canyon during 1997 cruise. Salinity(e) and potential temperature (f) profiles at stations upstream and downstreamof Barkley Canyon marked by pink and purple circles in maps, respectively.Bottom data shows a patch of higher salinity and lower temperature at stationson the downstream side of the canyon relative to stations on the upstream sideof the canyon head. Surface data shows canyon influence more strongly abovethe canyon head. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 4.1 Top row: Side and top views of the experimental set up. Bottom row: Top viewof a tank bathymetry slice showing the two canyons annotated with geometricdimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Figure 4.2 Example of density profiles fromwater samples taken before experiments DYE01and DYE02 at 7 different depths marked on the tank’s sloping bottom. Both ex-periment runs happened on the same day, one after the other. Note the thelinearity of the density profile, especially above shelf break depth. . . . . . . . 80xixFigure 4.3 Dye visualizations of the flow during two upwelling experiments DYE01 (firstand third rows) and DYE02 (second and fourth rows). Strong oscillations alongthe canyon axis. Red dye, originally in the canyon is upwelled onto the shelf andadvected downstream of the canyons. These plumes are larger and spread fasterfor larger forcing (DYE02). Eventually, the upstream canyon plume reaches thehead of the downstream canyon. An eddy trapped within the canyon can beseen at around 80 s close to downstream side of the canyons for DYE02. Bluedyed water in DYE01 frames is lighter (shallower) than the red dyed water. . . 87Figure 4.4 Density change from initial value at the upstream (orange) and downstream(blue) probes. The grey line corresponds to the difference between upstreamand downstream probes. Most experiments were performed covering the down-stream canyon, so only the upstream canyon is active (a-i), and three experi-ments were performed with the opposite configuration (j-l), upstream coveredand downstream uncovered. Note how the canyon probe has a larger responseto the forcing and reaches its maximum faster than the shelf probe. . . . . . . 88Figure 4.5 Comparsion between the depth of upwelling derived from density measure-ments and the scaling estimate proposed by Howatt and Allen (2013). Thereis good agreement between both quantities with a root mean squared error of0.27 cm. Depth of upwelling measured in the downstream canyon (blue dots)tends to be lower than the scaling estimate while depth of upwelling in the up-stream canyon (orange dots) tends to be larger. . . . . . . . . . . . . . . . . . 90Figure 4.6 Density change from initial value at the upstream canyon (orange) and down-stream canyon (blue) head probes. The grey line corresponds to the differencebetween upstream and downstream probes. Each line is the mean time seriesof 3 repeats per experiment (except f, g,h, l that don’t have repeats).The shadedareas around the lines correspond to the largest between the standard deviationand the uncertainty, calculated as in Section 4.2.4. . . . . . . . . . . . . . . . 91Figure 4.7 Depth of upwelling derived from density change at the upstream canyon (or-ange) and downstream canyon (blue) head probes. The grey line is the differ-ence between upstream and downstream probes. Each line is the mean timeseries of 3 repeats per experiment (except f, g, h, l that don’t have repeats). Theshaded areas correspond to the maximum of the standard deviation and the un-certainty. The depth of upwelling evolves similarly in both canyons, but Zlab=Zis larger in the upstream canyon and there is a lag between the maximums ingeneral. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93xxFigure 4.8 Comparsion between the depth of upwelling derived from density measure-ments and the scaling estimate proposed by Howatt and Allen (2013). Bothcanyons follow the scaling estimate well but the depth of upwelling measuredin the upstream canyon (orange dots) has a better fit with a root mean squareerror (rmse) of 0.14 cm while the downstream canyon has a rmse of 0.23 cm(blue dots). Error bars correspond to the maximum of the standard deviationand the uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Figure 4.9 The difference in depth of upwelling between the upstream and downstreamcanyons is not significantly correlated to the Burger number Bu (a) and it isproportional to the Rossby number as 2:2RW −0:28 with correlation coefficientof r=0.52 (b) for all two-canyon experiments. Error bars correspond to themaximum of the standard deviation and the uncertainty. Panel (c) shows thedifference in upwelling depth as a function of both RW and Bu. The colours ofthe markers are proportional to Zupslab −Zdnslab and their sizes are proportional to themagnitude of Zupslab −Zdnslab . The dependence of Zupslab −Zdnslab on Bu and RW definestwo regimes: upstream depth of upwelling larger or lower than downstream. . 94Figure 4.10 Difference between the maximum and minimum of the depth of upwellinganomaly (upstream-downstream) max(Zanomlab )−min(Zanomlab ) is inversely propor-tional to the Burger number Bu as−0:54Bu+1:18 with a correlation coefficientof -0.83 (a) while the Rossby number RW is not significantly correlated (b)for all two-canyon experiments. Panel (c) shows max(Zanomlab )−min(Zanomlab ) asa function of both Bu and RW with marker colours and sizes proportional tomax(Zanomlab )−min(Zanomlab ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Figure 4.11 Mean 5 second velocity direction field (arrows) and radial speed (color map) forthe first 45 seconds of experiment T02 (RW = 0.2, Bu= 1:18) at three differentdepths: shelf break depth at 2.8 cm, 3.8 cm and 4.8 cm. The velocity vectors arenormalized to show only the direction of the flow and only every second arrowis plotted. Radial or cross-shelf velocities are green when going up-canyonor on-shelf and red when going down-canyon or off-shelf. Flow is up-canyonduring time dependent phase and circulation is cyclonic during advective phase.Flow is stronger at shelf break depth than deeper. . . . . . . . . . . . . . . . . 96xxiFigure 4.12 Mean 5 second velocity direction field (arrows) and radial speed (color map) forthe last 50 seconds of experiment T02 (RW = 0.2, Bu = 1:18) at three differentdepths: shelf break depth at 2.8 cm, 3.8 cm and 4.8 cm. The velocity vectors arenormalized to show only the direction of the flow and only every second arrowis plotted. Radial or cross-shelf velocities are green when going up-canyon oron-shelf and red when going down-canyon or off-shelf. After the advectivephase, the up-canyon flow relaxes and an oscillating flow up and down canyontakes over the circulation in the canyons. . . . . . . . . . . . . . . . . . . . . 97Figure 4.13 Mean 5 second velocity direction field (arrows) and radial speed (color map)for the first 35 seconds of experiment T04, T12, T11 and T07 (RW = 0.20, 0.18,0.14, 0.12 and Bu =1.67, 1.34, 1.34, 1.07, respectively) at shelf break depth.The velocity vectors are normalized to show only the direction of the flow andonly every second arrow is plotted. Up-canyon velocities are green and down-canyon velocities are red. Radial velocities are larger for lower Bu and largerRW and up-canyon flow is stronger in the downstream canyon for all runs. . . . 99Figure 4.14 Mean 5 second velocity direction field (arrows) and radial speed (color map)for the last 15 seconds of experiment T04, T12, T11 and T07 (RW = 0.20, 0.18,0.14, 0.12 and Bu = 1.67, 1.34, 1.34, 1.07, respectively) at shelf break depth.The velocity vectors are normalized to show only the direction of the flow andonly every second arrow is plotted. Cross-shelf velocities are green when goingup-canyon and red when going down-canyon. For all runs, oscillations of periodsimilar to the inertial period take over the circulation. Oscillations are not inphase between upstream and downstream canyons. . . . . . . . . . . . . . . . 100Figure 4.15 Mean 5 second velocity direction field (arrows) and radial speed (color map) forthe first 50 seconds of experiments S03 and S12 (RW = 0.18, Bu = 1.21, 1.18) atshelf break depth (2.8-3 cm). The velocity vectors are normalized to show onlythe direction of the flow and only every second arrow is plotted. Cross-shelfvelocities are green when going up-canyon and red when going down-canyon.Both canyons respond consistently to the same forcing and their circulation issimilar to the circulation with two canyons (Figure 4.11). . . . . . . . . . . . . 102Figure 4.16 Mean 5 second velocity direction field (arrows) and radial speed (color map) forthe last 20 seconds of experiments S03 and S12 (RW = 0.18, Bu = 1.21, 1.18) atshelf break depth (2.8-3 cm). The velocity vectors are normalized to show onlythe direction of the flow and only every second arrow is plotted. Cross-shelfvelocities are green when going up-canyon and red when going down-canyon.In both canyons an oscillatory flow takes over in the same way as in the two-canyon experiments (Figure 4.12). . . . . . . . . . . . . . . . . . . . . . . . . 103xxiiFigure 4.17 The three stages of the flow around two submarine canyons during an upwellingevent are illustrated in four panels where the stream plots show the direction ofthe flow and the color map shows the cross-shelf component of velocity for 15second means of experiment T02 at shelf break depth. From top left to bottomright: During the time dependent phase the flow is up-canyon and increasesfrom rest. Then, cyclonic circulation develops in both canyons that lasts whilethe current is steady (panels in top right and bottom left). After the forcing stops,the cyclonic circulation is weaker and the flow within the canyons is dominatedby up and down canyon oscillations. . . . . . . . . . . . . . . . . . . . . . . . 104Figure 5.1 Schematic of tracer transport through two submarine canyons. (1) The up-welling current, which is similar for both canyons (blue arrow), brings tracer-rich water onto the shelf, generating an area of relatively higher tracer con-centration than the upstream shelf (4). Enhanced vertical diffusivity within thecanyons increases the tracer concentration near rim depth and weakens the strat-ification (2). These two effects enhance canyon-induced tracer flux onto theshelf. Initial tracer gradient at shelf-break depth determines the upwelling fluxof tracer (3) and the size of the pool (4). Canyons may interact via the upstreampool (5). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Figure A.1 The left panel shows the body forcing (units ms−2) applied to the alongshore ve-locity tendency at 5 different cross-shore locations (indicated in the right panel)at all depths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123xxiiiFigure A.2 The main reason to choose simulations no longer than 9 days is that the timescale of upwelling events near the short canyons on the west coast of Vancou-ver Island, BC are on this order. To illustrate this, we show ADCP data at theslope on the west coast of Vancouver Island near Barkley Canyon. Alongshelfand cross-shore velocities were provided by the Neptune Observatory operatedby Ocean Networks Canada at Pod 2 of the upper slope station of the BarkleyCanyon network, taken from the 75kHz ADCP located at 400 m depth, up-stream of Barkley Canyon, during upwelling conditions. The alongshore veloc-ity was filtered using a Doodson filter (39 hours) to remove the tides. Althoughsummer 2014 was not particularly upwelling favourable, we see two longerevents, one from May 29th to June 17th and the second one from July 29th toAugust 15th (b). Each one lasts no more than 20 days each. This is consistentwith evidence reported by Mirshak and Allen (2005) and Hickey (1997). Alsonote that the flow is nearly-uniform in the vertical between 50-250 m depth dur-ing the two periods of canyon-driven upwelling favourable flow, supporting theuse of body forcing to generate a deeper shelf current than wind stress would(a). Negative (upwelling-favourable) flows are directed southwards. . . . . . . 125Figure D.1 (a-c) Tracer concentration difference from the initial profile for runs from the1D diffusion model varying (a) Kcan, (b) t and (c) e . (d-f) Corresponding tracerprofile gradients. (g) Minimum tracer gradient for 1D model runs coveringthe parameter space e = 1 to 50 m (e runs), Kcan = 10−5 to 1:2× 10−2 (Kcanruns) and t = 1 to 12 days (t runs). The orange line corresponds to the fitteddecreasing exponential function relating the stretching and Zdi f =∆z. . . . . . . 132xxivFigure D.2 Diffusivity profiles from observations in Monterey (Carter and Gregg, 2002), Eel (Waterhouse et al., 2017) and Ascension (Gregg et al., 2011) Canyons.Green lines correspond to individual profiles along the canyon axis and blacklines correspond to the mean profile. For comparison, the vertical coordinate isnormalized in two different ways: by bottom depth, z′ = z=zbottom where zbottomis the depth of the canyon at each particular station; or using the rim depth,z′rim = (z− zrim)=(zbottom− zrim). We run simulations with both normalizationsfor each canyon. Note that for Monterey and Ascension Canyons, the meanprofiles have similar levels of diffusivity near rim depth (z′rim = 0, dashed blackline) to our locally-enhanced diffusivity runs. We assigned values of e to eachrun based on the variation of Kv above rim depth and found it to be on theorder of 50 m. Data from Monterey and Eel Canyons were kindly provided byG. Carter and A. Waterhouse, respectively. Profiles from Ascension Canyonwere taken directly from Figure 11 in (Gregg et al., 2011) by using an inversealgorithm on the image, so the accuracy of the data is not what is reported onthe original paper. We are using these data to put our experiments into contextand compare it to less idealized mixing profiles. . . . . . . . . . . . . . . . . 133Figure E.1 Initial tracer profiles used to initialize the 10 tracers simulated in the experi-ments come from bottle samples collected during the Pathways Cruise (2013)and cruises to Line C (2013 and 2012). Methane and nitrous-oxide profiles cor-respond to the mean values of profiles taken at stations in Line C, upstream ofBarkley Canyon. All other tracers are mean values of profiles taken along theaxis of Barkely Canyon during the Pathways Cruise. The location of the sta-tions in Line C and Pathways Cruise are shown as orange and red pentagons,respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Figure F.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140Figure F.2 Calibration curves r(r) for the upstream and downstream probes (top row) andthe derivatives of the calibration curves (bottom row). The latter is required tocalculate the uncertainty of the derived density measurement r . . . . . . . . . 141Figure F.3 Probe readings drift over time while they are connected to the circuit. In thisfigure base measurements – readings taken over 7 minutes while the tank rotated– taken in between runs in experiment T02 are shown as a function of time. Thetotal time corresponds to the time it takes to spin up the tank and to run threeexperiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142Figure F.4 The mean drift for each experiment was used as the uncertainty of the probereadings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142xxvFigure F.5 The profiler system is mounted on the aluminium arm that holds the filling hose.The profiler moves the probe vertically completing 2 cycles per minute usingDC motor controlled by an integrated circuit L293D. . . . . . . . . . . . . . . 143Figure F.6 Examples of original and filtered time series for a run in experiments T05 andT08. The original time series are labelled“original”, time series where the iner-tial frequency was removed are labelled“remove freq.” and time series filteredusing the a running mean are labelled “running mean”. . . . . . . . . . . . . . 144Figure G.1 Examples of experiment and recovery conduino time series of two canyon ex-periments. Top and bottom panels corresponds to upstream and downstreamprobes respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Figure G.2 Examples of experiment and recovery conduino time series of two canyon ex-periments. Top and bottom panels corresponds to upstream and downstreamprobes respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Figure G.3 Difference in depth of upwelling between the upstream and downstream canyonsas a function of the Burger number Bu (a) and the Rossby number RW (b) forall two-canyon experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Figure G.4 Five-second mean azimuthal component of velocity in experiment T02 at threedifferent depths. Before the forcing starts (top row), azimuthal velocity is closeto zero. As forcing ramps up the azimuthal velocity increases and it is smallercloser to the shelf break and clockwise (middle rows). After the forcing hasstopped, the flow away of the shelf is still clockwise but smaller than when theforcing was applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149xxviList of Supplementary MaterialI include three animations as supplementary material to Chapters 2 and 3. Captions for each anima-tion are listed below.Animation SI1.mp4 This animation shows the concentration and near-bottom concentration forthe canyon case as the upwelling event evolves. Top left and bottom right panels show alongshelfand cross-shelf sections of tracer concentration normalized by the initial values of concentration ateach cell. This cross-sections are located at the dashed lines in the bottom left panel. The bottomleft panel shows the bottom concentration normalized by the initial concentration at each cell closethe shelf bottom. During the time dependent phase (spin-up of the shelf current) concentration nearthe canyon rim increases quickly. After day 4, concentration near the shelf, away from the canyon,slightly decreases because the canyon suppresses shelf-break upwelling, but the concentration nearthe rim and downstream keeps increasing.Animation SI2.mp4 This animation shows the relative increase in concentration and near-bottom concentration from the no-canyon case as the upwelling event evolves. Top left and bot-tom right panels show alongshelf and cross-shelf sections of tracer concentration anomaly (canyonminus no-canyon case) normalized by the initial values of concentration at each cell. This cross-sections are located at the dashed lines in the bottom left panel. The bottom left panel shows thebottom concentration anomaly normalized by the initial concentration at each cell close the shelfbottom. Compared to the no-canyon case, during the time dependent phase (spin-up of the shelfcurrent) a large blob of water with higher-than-background concentrations upwells onto the shelf.This blob is sustained and fed by the upwelling flux through the canyon and advected along theshelf during the advective phase (days 4-9); it can reach depths of 20 m above the bottom.Animation SI3.mp4 This animation shows the concentration (top panels) and near-bottom con-centration (bottom panel) for the Astoria Canyon run with linear stratification (AST) as the up-welling event evolves. Top left and top right panels show alongshelf and cross-shelf sections oflinear tracer concentration normalized by the initial concentration at shelf break depth. This cross-sections are located at the dashed lines in the bottom left panel. The bottom left panel shows thexxviibottom concentration normalized by the initial concentration at shelf break depth close the shelf bot-tom. During the time dependent phase (spin-up of the shelf current) concentration near the canyonrim increases quickly. After day 4, concentration near the shelf, away from the canyon, slightlydecreases because the canyon suppresses shelf-break upwelling, but the concentration near the rimand downstream keeps increasing.xxviiiList of Symbolsa= NHs= f Rossby radius of deformationAc Vertical viscosity within the canyonAv Vertical viscosityAcan = LWm=2 Area of the canyonApool Area of the pool of upwelled tracer at the bottom of the shelfBu = N0Hs= fWs Burger numberBs = N0Hs= f L Burger numberC¯ Tracer concentration near canyon rimCo Initial tracer concentration at rim depthC Tracer concentrationCs Initial tracer concentration at shelf-break depthCbottom Concentration at the shelf bottomCbg Background distribution of tracer concentration on shelfCpool Mean concentration of the pool of upwelled tracerDh = f L=N0 Depth scaleDe f f = f L=Ne f f Depth scale using stratification Ne f fDm Minimum distance between canyon mouthsDs Distance between canyon headsf Coriolis parameterF = Ro=(0:9+Ro) Tendency of the flow to follow isobathsFW = RW=(0:9+RW ) Tendency of the flow to follow isobathsHd Total depth of the water column in the tankxxixHh Canyon head depthHs Shelf-break depthHr Canyon rim depthH= Lq Vertical scale for BBL on the shelfK = Z2KI=L2KD Isopycnal to diapycnal diffusivity ratioKbg Vertical diffusivity outside the canyon (background)Kcan Vertical diffusivity within the canyonKD Diapycnal diffusivityKI Isopycnal diffusivityKv Vertical diffusivityL Canyon lengthL= fU=(Nq)2 Cross-shelf length scale for BBLManom=Mcan−MncMcan Tracer mass contained in Vcan, åC∆VMnc Tracer mass contained in Vnc, åC∆VM(t) Total tracer mass on shelf for the canyon case at time tMnc(t) Total tracer mass on shelf for the no-canyon case at time tN Buoyancy frequencyN0 Initial buoyancy frequency near canyon rimNe f f Effective buoyancy frequency near canyon rim during advective phasePeh = LU∗=kI Horizontal Pe`clet numberPev = ZΩ∗=kD Vertical Pe`clet numberRL =U= f L Rossby number using L as length scaleR Reading from the conductivity probeRo =U= fR Rossby number usingR as length scaleRW =U= fWs Rossby number using width at shelf-break isobath as length scales Shelf slopeS= N=No Isopycnal stretching or squeezingxxxSupw Isopycnal stretching or squeezingSE = sN= f (Fw=RL)1=2 Scale for horizontal concentration curvaturet Simulation timeU Incoming velocityU∗ Horizontal upwelling velocityVanom=Vcan−VncVcan Volume of water upwelled onto the shelf in the canyon case, å∆VVnc Volume of water upwelled onto the shelf in the no-canyon case, å∆VW Canyon width at mid-length at rim depthWm Canyon width at shelf breakWs Canyon width at mid-length on shelf-break isobathZ Upwelling depthZdi f Length scale for the effect of kcan over iso-concentration linesZ+di f Length scale for the effect of kcan over iso-concentration lines above rimZ−di f Length scale for the effect of kcan over iso-concentration lines below rimG= ZdvC=LdhC Horizontal to vertical concentration gradient ratiodhC Scale for horizontal concentration gradientd 2hC Scale for horizontal concentration curvaturedvC Scale for vertical concentration gradientd 2vC Scale for vertical concentration curvatured 2hC Scale for horizontal concentration curvature∆V Volume of a cell with concentration higher than the initial concentration at shelf break∆r Density change from initial valuee Vertical smoothing distanceq Shelf slope angler Densityr0 Reference density, in lab experiments it is fresh water density.th = Ld 2hC=GdhC Horizontal curvature to gradient ratioxxxitv =−Zd 2vC=dvC Vertical curvature to gradient ratiot = f=Nq Time scale for BBL shut down on shelfF Upwelling flux of waterFTr Upwelling flux of tracerΩ Vertical upwelling velocityw Rotation rate of the tank (rad/s)¶zC Vertical concentration gradient near canyon rim¶zC0 Initial vertical concentration gradient near canyon rim¶zCbg Initial vertical concentration gradient above shelf break depthxxxiiList of AbbreviationsADCP Acoustic Doppler Current ProfilerBBL Bottom Boundary LayerCTD Conductivity-Temperature-PressureCS cross-shelfDIC Dissolved Inorganic CarbonDS Dissolved SiliconMITGCM Massachusetts Institute of Technology general circulation modelMVP Moving Vessel ProfilerPIV Particle Image VelocimetryTTT Total Tracer TransportTWT Total Water TransportVATT Vertical Advective Transport of TracerVTT Vertical Tracer TransportVWT Vertical Water TransportxxxiiiAcknowledgmentsI would like to thank Susan Allen for her trust and support throughout my PhD. I could not haveasked for a better advisor. Her thoughtful feedback, countless hours of meetings and kind advicechanged me and my notion of what being a scientist means. I would also like to thank my super-visory committee, Greg Lawrence and Douw Steyn, and in earlier stages of my PhD, Jody Klymakand Rich Pawlowicz, for their time and feedback.Research is a collaborative endeavour and I would like to thank all the people who helped mein one way or another. Either because I had ruined my repositories, or I needed advice to work outproblems in the lab: Doug Latornell, the MOAD group, Ashutosh Budhia, Charles Krzysik, DavidJones, Joern Unger, Dan Robb, Ted Tedford and Roger Pieters.I had the fortune of navigating my PhD accompanied by a great support system. I am indebted toeveryone in theWaterhole for the warm chats and coffee breaks. To my adopted Vancouverite familyfor making the gloomy winters enjoyable and the sunny summers even more fun. I am grateful forthe visits and calls from my family and friends. I would like to thank my parents, Maru and Javier,and my brother Ivan, because I would not be here today if it wasn’t for their infinite encouragementand love. Finally, to Daniel for helping me in every imaginable way. His love and tireless supportgave me courage in the dark times and the push I needed to keep going. I am thankful for sharingthis journey with him.I received funding from The University of British Columbia through a Four Year Fellowship(2014-2018), from NSERC through a research assistantship, and from Consejo Nacional de Cienciay Tecnologı´a (CONACYT) through a doctoral scholarship (2018-2020).xxxivChapter 1IntroductionOnly the fact that the canyons are deeply hidden in the darkness of the sea preventsthem from being classed with the world’s most spectacular scenery. —Rachel CarsonThe Sea Around Us (1951)The exchange of water and solutes between the deep open ocean and the shallower continentalshelf, denoted cross-shelf exchange, has long been identified as one of the most important prob-lems in coastal oceanography (Brink, 2016; Huthnance, 1995). Cross-shelf exchanges contribute todelivering nutrients to shelf ecosystems, determine shelf residence times, transport planktonic or-ganisms, conduct sediment transport, remove contaminants from the coastal region, and are centralin determining biogeochemical budgets and their response to climate change and human activities(Brink, 2016; Jordi et al., 2008).There is no single answer to the cross-shelf exchange problem and the complexity of the problemhinges on the fact that it involves a large range of processes and phenomena depending on the scaleof interest and location of the shelf (Brink, 2016). In this thesis, I investigate the role that submarinecanyons play in this puzzle. Submarine canyons are topographic features that incise continentalshelves all around the world. They are known to impact the ocean circulation on a regional scale andenhance cross-shelf exchange (e.g., Allen and Hickey, 2010; Connolly and Hickey, 2014; Hickey,1995, 1997; Ka¨mpf, 2010). Canyons also serve the marine ecosystem by enhancing biodiversityand biomass (De Leo and Puig, 2018; Santora et al., 2018), and play an important role in carbonstorage (Masson et al., 2010). However, these biodiversity hotspots also serve as conduits of marinelitter from the coast to the deep ocean and are vulnerable to anthropogenic activities such as fishing,bottom trawling and hydrocarbon exploitation (Puig et al., 2014).The latest survey reports over 9477 submarine canyons worldwide (Harris et al., 2014) of which2076 are shelf-incising canyons and 7401 are blind, which means they are confined to the continentalslope. Shelf incising canyons have, on average, 51% larger areas and 32% longer lengths than blindcanyons (Harris and Whiteway, 2011). In total, canyons constitute 11.2% of the global continental1slope area but fewer than 10% of them have ever been studied. In fact, only 11 canyons in the worldhave been studied in detail (Matos et al., 2018). Moreover, most of the literature has focused onstudying one canyon at a time without investigating the collective, regional impact of these featuresor the interactions and connectivity between them. The large number of canyons and the challengesassociated with studying them observationally require us to develop more general methods and toolsthat can be applied to more than one canyon at a time. Examples of such methods are the use ofidealized models and analytical scaling schemes. In this thesis, I focus on two aspects of canyons:How do they upwell solutes onto the shelf and how do they interact dynamically. To answer thesequestions I use idealized numerical and physical models, and analytical scaling schemes.In the following sections I pose the cross-shelf exchange problem and explain how submarinecanyons fit in this picture dynamically. I expand on the processes, within a shelf-incising canyon,that contribute to the cross-shelf exchange of solutes and tracers such as canyon-induced upwellingand locally-enhanced mixing. Next, I discuss the collective impact of canyons and how can theyinteract dynamically. Later, I explain how physical models have been used in the past to studycanyons. Finally, I pose the research questions that will be addressed in the thesis.1.1 Limits on cross-shelf exchangeConsider a continental shelf in geostrophic balance. That is a balance between the pressure gradientforce and Coriolis forces. Under this assumption the flow varies slowly (steady flow) which meansthe temporal Rossby number Rot = w= f is small, where w is the frequency of variation of the flowand f the Coriolis parameter; mixing and turbulent stresses are not important (adiabatic flow) whichmeans that density variations are governed by the flow field and not by mixing; and finally, the ve-locity of the flow (linear flow) is low so that the Rossby number Ro =U= f L is small, where U isthe characteristic velocity of the flow and L is a characteristic horizontal scale. These three assump-tions (steady, adiabatic and linear flow) lead to the Taylor-Proudman theorem. A consequence ofthis theorem is that the velocity is parallel to isobaths and that steady, slow motions in a rotating,homogeneous, inviscid flow are two dimensional (Cushman-Roisin and Beckers, 2011).Following the derivation by Brink (1998) very closely, but with different notation, the equationsdescribing the flow are the momentum equationsf v=1ro¶P¶x; (1.1)f u=− 1ro¶P¶y; (1.2)0=¶P¶ z+gr ′; (1.3)2the continuity equation¶u¶x+¶v¶y+¶w¶ z= 0 (1.4)and conservation of massu¶r ′¶x+ v¶r ′¶y+w¶r ′¶ z= 0; (1.5)where the velocity vector u⃗ = (u;v;w) has components u;v in the horizontal (x;y) directions andw along the vertical direction z, P(x;y;z) is the pressure and the density has been decomposed asr(x;y;z) = r0+r ′(x;y;z) where r0 >> r ′. Differentiating equations 1.1 and 1.2 with respect to yand x, respectively, and substituting into 1.4¶w¶ z= 0: (1.6)That is, the vertical velocity has to be constant with depth.Additionally, the boundary conditions for the system are no flow through the surfacew= 0 at z= 0; (1.7)and no flow through the bottomw=−u⃗h ·Ñhh at z=−h; (1.8)where u⃗h = (u;v) is the horizontal velocity vector, Ñh = (¶=¶x;¶=¶y) is the horizontal gradientoperator and −h is the bottom depth. Equations 1.6 and 1.7 implyw= 0: (1.9)So, the flow is strictly horizontal. Using 1.9 at the bottom boundary, 1.8 implies− u⃗h ·Ñhh= 0 at z=−h (1.10)which is that the flow at the bottom must be parallel to isobaths.Further, P can be eliminated from 1.1 and 1.2 by differentiating them with respect to z andsubtracting the derivative of 1.3 with respect to x and y, respectively−r fg¶v¶ z=¶r ′¶x; (1.11)r fg¶u¶ z=¶r ′¶y: (1.12)3Finally, substituting 1.11 and 1.12 into 1.5 and using w= 0 yields:−u¶v¶ z+ v¶u¶ z= 0: (1.13)This means that the vertical shear in the flow is always parallel to the velocity. Taken together with1.10, this implies that speed can vary with depth but the direction is set by the bottom slope. Flowsteering due to bottom topography takes place over a depth f L=N above the bottom, where f isthe Coriolis parameter, N2 = −(g=r0)(¶r=¶ z) is the buoyancy frequency and L is a characteristiclength scale of the topography (Hogg, 1973).Although the Taylor-Proudman theorem is valid in a wide range of circumstances, small viola-tions to any of the three initial assumptions lead to cross-shelf, usually second-order, flows. Thereare many ways to break these assumptions and each adds to the myriad of processes that contributeto cross-shelf exchange. The Taylor-Proudman theorem requires the flow to change slowly, for ex-ample slower than an inertial period 2p= f , so the steadiness assumption can be broken by tides andcoastal-trapped waves (Brink, 1998).There are many examples of processes that can break the adiabaticity assumption. For example,turbulent stresses at the ocean-atmosphere interface and ocean bottom are strong enough that theturbulent terms in the momentum equations are comparable to the geostrophic terms. As a conse-quence, an Ekman layer forms both at the surface and at the bottom of the ocean. The bottom layersustains a net water transport to the right of the main flow in the Northern Hemisphere and to theleft of the main flow on the Southern Hemisphere (e.g. Cushman-Roisin and Beckers (2011)). Thebottom Ekman layer is associated with upwelling of deeper water onto the shelf.Finally, the linearity assumption can be broken by inertial effects such as instabilities, mesoscalestructures and topographic effects such as those induced by submarine canyons. A canyon is aregion of higher Rossby number Ro relative to the slope because the relevant length scale is reducedcompared to the length scale on the shelf (e.g. canyon length 10 km vs shelf width 50 km). A higherRossby number implies that inside the canyon advection of momentum is important.1.1.1 Canyon dynamicsAt this point it is useful to define some of the terms and directions used throughout this thesis relativeto the canyon axis and the incidence of the flow in the canyon. The terms upstream and downstreamrefer to the direction of the incident shelf flow (Fig. 1.1). Upstream is the direction opposite tothe incident flow and downstream means along the direction of the incident flow. Also, the canyonhas a head, rim, mouth and axis. The head is the deepest region of the shelf where isobaths are notmodified by the canyon compared to the adjacent shelf; the canyon rim is the contour of maximumcurvature |Ñ2h|, where h is the bottom depth; and the canyon mouth is where the canyon interruptsthe shelf break isobath.4Shelf currents flowing over a submarine canyon, perpendicular to the canyon axis and oppo-site to the propagation of Kelvin waves, can generate upwelling driven by an unbalanced onshorepressure gradient (Freeland and Denman, 1982). Whereas currents in the direction of propagationof Kelvin waves generate an asymmetry on the vertical velocity field, forcing downwelling on theupstream side of the canyon and upwelling on the downstream side (Allen and Durrieu de Madron,2009). In the northern hemisphere upwelling favourable currents are left-bounded by the coast anddownwelling favourable currents are right bounded by the coast, and conversely in the southernhemisphere. Generally, the net vertical flux indicates that downwelling is predominant for right-bounded currents (Spurgin and Allen, 2014).Advection-driven upwelling within a submarine canyonIn the upwelling favourable scenario, the alongshore flow moves against the direction of propaga-tion of Kelvin waves. Upstream of the canyon, the flow is in geostrophic balance. An on-shorepressure gradient is sustained by the tilted ocean surface (lower pressure at the coast). Within thecanyon, the flow is inhibited from moving alongshore because the canyon walls block the flow.Then, the pressure gradient near the rim, sustained by geostrophy, is no longer balanced within thecanyon because the flow has null velocity and the Coriolis contribution decreases or disappears. Theunbalanced pressure gradient initially generates up canyon flow (along the canyon axis) that tilts theisopyncals within the canyon towards the canyon head (Freeland and Denman, 1982). The rising ofisopycnals continues until the generated baroclinic pressure gradient balances the original pressuregradient near the rim. As isopycnals rise, the water column below them is stretched, generating cy-clonic vorticity deeper in the canyon (Hickey, 1997). After this time, advection becomes importantin determining the dynamics in the canyon, although the flow is still dominated by geostrophy. Inthe advective regime, Rossby number (Ro = U= fR) is bounded by Ro > 0:2 (Waterhouse et al.,2009).The tilting of isopyncals allows water deeper within the canyon to upwell onto the shelf. At aparticular depth at the canyon mouth, the pressure is equal to the pressure at the canyon head. Thisdepth is known as the depth of upwelling and it marks the depth of the deepest water that upwellsonto the shelf given that below this depth there is no unbalanced pressure gradient.Over the canyon, the pressure gradient is also modified. From the Taylor-Proudman theoremit follows that the flow will have a tendency to follow isobaths. If the canyon is wide enough, thepressure gradient modifications above the canyon will be such that the flow can turn and follow theisobaths (low Rossby number Ro = U= fR where R is the radius of curvature of the shelf breakisobath on the upstream side of the canyon), but if the canyon is narrow, the flow won’t be able tofollow the bathymetry and it will cross above the canyon turning inshore (Allen and Hickey, 2010).Above rim depth, incoming flow on the upstream rim falls into the canyon. The water column isstretched generating cyclonic vorticity (Hickey, 1997). This deflects the flow towards the canyon5Figure 1.1: Schematics of the advection-driven phase of upwelling in a submarine canyonfollowing Allen and Hickey (2010). The figure represents a canyon where the shelf andslope currents flow equatorwards (left to right) and mixing is locally-enhanced within thecanyon.head. As the water crosses the canyon, the water column shrinks as it encounters the downstreamrim, generating anticyclonic vorticity and turning the flow offshore.An advection driven upwelling event can be divided into three stages: a short, transient stage,an advection dominated stage and a relaxation phase. The first, transient stage, develops within aninertial period; its response is essentially linear and similar for upwelling/downwelling favorableflows (Allen, 1996; Allen and Durrieu de Madron, 2009).The second, advection-driven phase is strongly dependent on the canyon topography and flowstrength. A conceptual model of the upwelling advection-driven phase is illustrated in Figure 1.1.Following Allen et al. (2001), the vertical structure of the flow can be divided into 4 levels. Near thesurface, the flow is weakly affected by the presence of the canyon. Shallower isopycnals are onlyweakly disturbed. Just above the canyon rim depth, water flows over the upstream rim of the canyonand then into the canyon, stretching the water column. This stretching generates cyclonic vorticitythat can be strong enough to generate a closed eddy (Rim Depth Eddy in Figure 1.1). Flow at thisdepth crosses the canyon and leaves the canyon shoreward from its original position. At rim depthand some depth below, water flowing on the slope is advected into the canyon and upwells on thedownstream side of the canyon (Upwelling Current in Figure 1.1). This flow transports the deepestwater advected onto the shelf. Finally, water flowing below the upwelling current does not reachthe shelf. Instead, flow is stretched within the canyon, generating cyclonic vorticity (Deep Flow inFigure 1.1 ). The last phase comes when forcing relaxes (relaxation phase) and it includes strongcyclonic flow within the canyon (Hickey, 1997).The amount of water that upwells through a canyon depends on the dynamical characteristics ofthe flow and the geometrical parameters of the canyon (Allen and Hickey, 2010; Howatt and Allen,62013; Ka¨mpf, 2007; Mirshak and Allen, 2005). Starting from the shallow-water equations for aninviscid, steady, Boussinesq flow Allen and Hickey (2010) and Howatt and Allen (2013) developeda scaling estimate for the upwelling flux. These estimates apply only to flow over a canyon that isuniform over the length of the canyon, and relatively weak; the canyon width should be narrowerthan two Rossby radii with nearly uniform stratification near canyon rim; the canyon must be deepand with steep walls and the continental shelf must be sloped so that the onshore Bottom BoundaryLayer (BBL) flow is shut down. The scaling is general enough that it has been successfully comparedto observations in six canyons, three laboratory models and a recent field study in Whittard Canyon(Porter et al., 2016).Other canyon upwelling mechanismsCanyons can be divided into dynamically wide, intermediate or narrow depending on the ratio be-tween their geometric width and internal radius of deformation am = NHc= f , where Hc is the depthof the canyon at the mouth (Klinck, 1988, 1989). Flows with length scales greater than the defor-mation radius are generally geostrophic. Canyons with widthsW smaller than 2am are considerednarrow (Hyun, 2004; Machuca, 2019).Canyons can also be classified into long and short depending on their shape and how closelythey approach the coast (e.g., Allen, 2000; Waterhouse et al., 2009). Some of the most well-studiedcanyons are long canyons, such as Monterey Canyon off the coast of California and Biobio Canyonoff the coast of southern Chile but short canyons are far more numerous (e.g. Figure 1.2).There are other mechanisms besides advection by which upwelling is generated in canyonsdepending on the Rossby number and whether the canyon is short or long, and narrow or wide. Inthis thesis I study narrow canyons like Barkley Canyon and Nitinat Canyon on the west coast ofVancouver Island, or Astoria Canyon and Quinault Canyon on the Washington shelf (Figure 1.2)that follow the advection-driven upwelling mechanism described above. Long canyons are mostlyaffected by bathymetric effects and are not discussed in this thesis; short canyons are dominantly inthe advection (as above) and time-dependent regimes.An example of a bathymetric effect is isobath convergence. When the flow is forced to followisobaths and these converge, the flow is accelerated and the Rossby number increases thus breakinggeostrophy and allowing the flow to cross isobaths after convergence (Allen, 2000). Under strongisobath convergence, upwelling occurs at quite small initial Rossby numbers. This mechanism isimportant in long canyons because they have more intense convergences. This is why long canyonscan hold upwelling even in steady state experiments (Waterhouse et al., 2009). This mechanismalso exhibits blocking of the flow on the upstream side of the canyon.Another mechanism of upwelling is the time dependent response, when the forcing is starting.Low incident velocity in short canyons show time dependent behaviour (Waterhouse et al., 2009).The condition for time-dependent upwelling to be detectable is that Rot(Lc=Wsb)((W=a)+2)> 0:257Figure 1.2: Bathymetry of a portion of the Pacific Northwest shelf including the southern Van-couver Island and north of Washington State. The approximate shelf break (solid grayline) corresponds to the 200 m depth contour. In this thesis I focus on short, narrowcanyons like all canyons identified in the map except for Juan de Fuca Canyon, which isa long canyon. Note the high density of canyons incising all the continental shelf. Bathy-metric data for this figure was provided by GEBCO Compilation Group (2019) GEBCO2019 Grid (doi:10.5285/836f016a-33be-6ddc-e053-6c86abc0788e).(Boyer et al., 2004), where Rot is the time-dependent Rossby number Rot = 1= f t where t is the timeafter change in forcing L is the length of the canyon, W is the canyon width midway between themouth and head and a is the Rossby radius of deformation. This mechanism is dominant only whenthe advective and isobath convergent criteria are weak (Waterhouse et al., 2009).Downwelling in submarine canyonsDynamics of downwelling canyons have also been studied through observations and numerical mod-els. From these studies, two patterns of circulation can be identified over the canyons (Spurginand Allen, 2014). In the first pattern, flow nearly follows isobaths, leading to cyclonic circulationat shelf-break depth, negative vertical velocities on the upstream side of the canyon and less in-tense positive vertical velocities on the downstream side (Skliris et al. (2002)). The second patternpresents a trapped anticyclonic eddy near the head of the canyon. The dynamics within a specificdownwelling canyon are dependent on the Burger number and secondly on the Rossby number8(Spurgin and Allen, 2014). The former determines the sign of predominant vorticity in the canyon:cyclonic for low Burger numbers and anticyclonic for higher values. The Rossby number influencesthe magnitude of vorticity (Spurgin and Allen, 2014). The combination of a weaker stratificationand a stronger flow lead to a stronger vertical flux.1.1.2 Mixing in submarine canyonsIn addition to enhancing upwelling, submarine canyons can enhance mixing within their walls byfocusing internal waves and tides (Gordon and Marshall, 1976). Enhanced levels of mixing havebeen observed in Monterey Canyon (Carter and Gregg, 2002), Eel Canyon (Waterhouse et al., 2017)and Ascension Canyon (Gregg et al., 2011) on the shelf off California, Gaoping Canyon (Lee et al.,2009) in Taiwan and Barrow Canyon (Shroyer, 2012) in the Arctic Ocean with very different spatialand temporal patterns among them. It is speculated that most canyons have high mixing levelscompared to the adjacent continental shelf and slope (Gregg et al., 2011). Thus, tracer upwellingthrough a canyon will depend on two processes: advection by the upwelling flow, and diffusion andmixing within the canyon.Internal tides can be generated inside submarine canyons through the scattering of barotropictides over the steep shelf break (Wunsch, 1975). These create internal pressure gradients that driveinternal waves that propagate in vertical modes. Enhanced wave to wave and topographic interac-tions cause internal waves to break, dissipating their energy through turbulence (Carter and Gregg,2002). One important factor in internal wave breaking due to topographic interactions is the steep-ness of the topography. Depending of the frequency of the wave and ambient stratification, internalwaves propagate as beams at characteristic angles. The criticality of a surface a is given bya =StopoSwave=¶H=¶x[(w2− f 2)=(N2−w2)]1=2 ; (1.14)where Stopo is the topographic slope, Swave is the wave characteristic slope, x is the cross-slopedirection, H is the total water depth, w is the wave frequency, f the Coriolis parameter and Nthe buoyancy frequency. A slope is supercritical when a > 1 and will reflect the wave towardsdeeper water which can mean towards the canyon floor if the incident wave is perpendicular to thecanyon walls, and down-canyon if the incident wave is perpendicular to the canyon axis. Canyonsare known to focus internal waves towards the canyon floor. Their wedge-shaped topography issupercritical to the most energetic type of internal waves found on the nearby-shelf (Gordon andMarshall, 1976). Subcritical surfaces are those with slope less than the propagation angle. Bothsubcritical and supercritical slopes to local internal tides can occur simultaneously in different partsof a canyon (e.g., Aslam et al., 2017; Hall et al., 2014; Vlasenko et al., 2016).The amount of mixing in canyons due to tidal mixing and internal waves is notoriously large.Extensive measurements of kinetic energy dissipation along Monterey Canyon (California Coast)9in 1997 gave a diapycnal diffusivity of Kp = 2:5×10−2 m2s−1, which is a much larger value thanexpected from fine-scale parametrizations (Carter and Gregg, 2002). Although turbulence has beensampled in only a few canyons, average diapycnal diffusivity in the canyons surveyed is very highcompared to levels outside (e.g. Gregg et al. (2011) in Ascension Canyon kd ≈ 3:9× 10−3 m2s−1and Lee et al. (2009) in Gaoping Canyon kd ≈ 10−2 m2s−1, Shroyer (2012) in Barrow Canyonkd ≈ 3× 10−3− 6× 10−3 m2s−1), so it is reasonable to assume that most canyons induce intensemixing (Gregg et al., 2011).Patterns of enhanced diapycnal mixing within submarine canyons vary spatially and temporally.This variation depends on the nature of the forcing generating turbulence, on the geometry of thecanyon and the temporal cycles of the forcing. It has been observed that mixing is enhanced in anumber of submarine canyons, but the generation of turbulence in each one of them has characteris-tics particular to each canyon. Three examples of observations of mixing in canyons are describedin the following.Ascension Canyon, located off the coast of California, has sides and axis slopes supercritical toM2 internal tides. Maximum dissipation zones in the canyon include near bottom layers associatedwith an internal bore and just below the rim, associated with lee waves and rotors. The averagedissipation rate is larger during spring tides than neap tides (Gregg et al., 2011).Monterey Canyon has subcritical slopes to the M2 internal tide. Intense dissipation was found ina stratified turbulent layer along the axis (bottom 100 to 200 m) with intensity increasing from springto neap tide (Carter and Gregg, 2002). There is a transition from partly standing to progressiveinternal tides when the pycnocline deepens (Hall et al., 2014).Gaoping (formerly Kaoping) Canyon on the south east Taiwan coast is subjected to strongbarotropic and baroclinic (1st mode) tides. It is subcritical and at critical frequencies there is aturbulent overturning due to shear instability and breaking of internal tides and waves. Maximumaverage diapycnal diffusivity (10−2 m2s−1) found within the canyon was 5 times stronger than at themouth with a seasonal variation due to stratification (two times stronger in winter than in summer-fall) (Lee et al., 2009).1.1.3 Cross-shelf exchange of tracersIn this thesis, I refer to all dissolved solutes in the water column, temperature and salinity as tracers.Tracers are active if they influence density, like temperature and salinity, and passive if they do nothave an impact in density. Examples of passive tracers are nutrients (e.g. nitrate, dissolved siliconand phosphate), dissolved gases like oxygen, methane, nitrous-oxide and solutes like inorganic car-bon. Typical vertical profiles of nutrients close to the continental shelf increase with depth, becausethey are mostly used at depths where light is available, in the euphotic zone, while a typical dis-solved oxygen profile decreases with depth because its source is at the atmosphere-ocean interface.The rates at which tracers change with depth depend on the specific solute because they respond to10different physical, chemical and biological processes throughout the water column and location inthe world’s oceans.One of the physical processes that shapes the distribution of tracers is cross-shelf exchange andits contribution is key to understanding global biogeochemical budgets and their response to climatechange and human activities (Jordi et al., 2008). The specific spatial distribution of tracers on theshelf impacts benthic (bottom) and demersal (just above bottom) communities (Keller et al., 2010).Both the distribution and on-shelf inventory of tracers like nutrients and oxygen can have relevantbiological consequences for the shelf system.Upwelling of nutrient rich water can trigger biological productivity. Given that upwelling isoften enhanced in canyons and moreover, that the local flows induced by a canyon can trap organicmatter, submarine canyons are often recognized as biodiversity hotspots (Allen et al., 2001; De Leoet al., 2010; Fernandez-Arcaya et al., 2017). A recent study has identified a vast network of krillhotspots sustained by shelf incising canyons of the US west coast and speculate that this networkmay enhance the latitudinal migration of mammals, seabirds and fish (Santora et al., 2018).Oxygen and carbonHypoxic (low oxygen) events are common on the Washington shelf and advection of oxygen-depleted waters through coastal upwelling is a key mechanism to generate such events (Connollyet al., 2010). A recent numerical study of the coast of Washington State found that changes innear-shelf bottom oxygen concentrations in the presence of three nearby canyons matched levelsof hypoxia in the region (Connolly and Hickey, 2014). These changes were large enough to havean ecological impact if compared to levels of severe hypoxia associated with mortality in marineorganisms. Moreover, it has been reported that on the west coast of the United States small changesin dissolved oxygen concentrations in already hypoxic waters can cause large changes in the totaland species-specific catch of demersal fish (Keller et al., 2017).The combination of canyon induced upwelling and shoaling of oxygen minimum zones (OMZ)could be another contribution to further lowering oxygen concentrations on the shelf. Oxygen min-imum zones are permanently hypoxic regions of the open ocean that extend along the continentalmargins of the eastern Pacific, eastern Atlantic, and Indian oceans [Helly and Levin, 2004]. Fifty-year long time series of oxygen at Ocean Station Papa in the Subarctic Pacific show a persistentshoaling of the upper boundary of the OMZ following climate trends (Whitney et al., 2007).Both, low-oxygen events and local biological consumption of oxygen decrease pH on the shelf.Further, upwelling of hypoxic waters with high CO2 concentrations can displace or kill benthicorganisms (Breitburg et al., 2018). In the past 10 years, corrosive water (undersaturated with respectto aragonite) has been observed covering larger areas of the shelf and reaching shallower depths thannormal on the West Coast of North America (Feely et al., 2008). On the West Coast of VancouverIsland, sediment-associated processes dominate the consumption of oxygen and release of inorganic11carbon to the bottom waters over the shelf (Bianucci et al., 2011).Methane and nitrous-oxideMethane and nitrous-oxide are the most significant greenhouse gases after carbon-dioxide andwater-vapor (IPCC, 2013). On the southern West Coast of Vancouver Island, methane is supplied tothe water column mainly from methane seeps and other sedimentary processes, while nitrous-oxideis supplied from an off-shelf nitrous oxide maximum and from nitrification in the water column(Capelle and Tortell, 2016). The main on-shelf transport mechanism for methane and nitrous oxideis upwelling, but local topography has also been identified to increase the supply of these tracersonto the shelf (Capelle and Tortell, 2016).1.2 Collective effect of submarine canyons on the continental shelfSubmarine canyons are present on shelf breaks all over the world, usually as chains instead ofisolated features (e.g. Figure 1.2). The dynamcial interaction between submarine canyons has notbeen studied previously but there is some evidence of their collective effect on a particular region.For example, in the southeast coast of Spain, the effect of four adjacent canyons on the dominantlysouthwestward downwelling shelf current has been studied using satellite images and CTD casts(Maso´ et al., 1990). The result was a strong coastward deflection of the flow near the surface beforethe upstream wall of the canyons and away from the shelf inside the canyons. At deeper levels, thismay influence the position of the shelf-break depth jet, significantly changing the dynamics insidethe canyons (Alvarez et al., 1996).On theWest Coast of Vancouver Island, winds are predominantly northerly (upwelling-favorable)during summer and southerly during winter. Three canyons cut the southern shelf (Barkley Canyon,Nitinat Canyon and Juan de Fuca Canyon in Figure 1.2) and there is evidence that, in some years,these canyons have produced as much upwelling as the wind (Allen, 2004). A recent numericalstudy of the circulation on the shelf of Washington State indicates that the nitrate contribution ofthree submarine canyons in the region is between 30 to 60% of wind-induced upwelling (Connollyand Hickey, 2014).Another example of the large contribution of canyon systems to coastal upwelling is the caseof the Great Australian Bight, where numerical simulations of the regional summer circulation thatresolve the Murray Canyon Group have a volume flux approximately 3.5 times larger than thesimulations where the canyon group is not resolved (Ka¨mpf, 2010).The influence that one canyon may have on the flow dynamics of an adjacent one is not clear.It might be tempting to assume that the first canyon or upstream canyon leads the dynamics, sincewater will go through it before passing to the downstream canyon. However, the role of the down-stream canyon is not trivial as coastal-trapped waves are moving in the opposite direction to the12shelf current in the case of upwelling canyons. This means that information is also being transmit-ted from the downstream canyon to the upstream one. This type of interaction has been observed inBarkley Canyon where shelf waves propagating northward can have a stronger effect on alongshorecurrents than the local wind (Hickey et al., 1991).Another type of downstream canyon influence could occur in a system with a long canyondownstream of another canyon. Long canyons can reduce flow speed on their upstream side (Wa-terhouse et al., 2009), which would translate to a barrier for the flow on the downstream side of thefirst canyon, causing abnormal deviations of the flow compared to the case with only one canyon.The collective impact that multiple canyons have on the regional circulation on the shelf or theirnutrient input to the shelf has not been investigated, excluding the aforementioned examples. Inparticular, there are neither analytical models nor scaling schemes to parametrize and understandthe interactions between multiple canyons.1.2.1 Rotating tanks and the study of submarine canyon dynamicsSince it is challenging and expensive to conduct oceanographic campaigns to measure real oceansystems, models of these systems have to be developed to study the dynamics of the ocean and in-terpret the observations we have. Also, these models are needed to discover the hidden mechanismsdriving these systems. These models can be analytical, numerical or physical. It is often hard tofind exact solutions to the equations posed for these systems. One option is to integrate them nu-merically and find an approximate solution. Another useful model is a laboratory or physical modelof the system. These are thought to be better analogues to ocean processes than numerical mod-els because there is a larger range of scales active. Oceanic regional systems have scales spanningeight orders of magnitude while laboratory models have scales spanning three orders of magnitude.Numerical models are bounded by their grid length, often spanning two orders of magnitude (Allenet al., 2003). Physical models can also play an important role in improving prognostic numeri-cal models. Physical models can help develop better parametrization schemes of sub-grid scaleprocesses and they can provide high temporal and spatial resolution results to evaluate numericalmodel performance (Boyer and Davies, 2000).Laboratory models of submarine canyons are useful to highlight features of the circulation thatthe accuracy of numerical models fail to reproduce, especially in the case of advection (Allen andDurrieu de Madron, 2009). These models consist of a rotating tank with a shallower step (continen-tal shelf) surrounding the lower inner part of the tank (deep ocean). Currents are forced by changingthe rotation rate of the tank after the water has reached solid body rotation. This causes the flowto accelerate and generate a current travelling opposite to the the direction of propagation of shelfwaves if the rotation rate is increased (upwelling case). Otherwise, the flow is in the direction ofpropagation of shelf waves if the rotation rate is decreased (downwelling case).Physical models have successfully reproduced upwelling events in canyons in a variety of situa-13tions. From these models, calculations of net upwelling flux (Mirshak and Allen, 2005) and testingthe performance of a variety of numerical models (Allen et al., 2003) have been possible. Othermodelled physical situations include oscillatory flows (Perenne et al., 2001), tidal resonance (LeSoue¨f and Allen, 2014) and upwelling in long canyons (Waterhouse et al., 2009).One of the main limitations of rotating tank experiments is that their ocean counterparts areturbulent (high Reynolds number Re =UD=n where U is the velocity scale, D is a characteristicdiameter and n is the viscosity), while the flow in the tank is mostly laminar (Re≤ 103) (Boyer andDavies, 2000). The range of Reynolds number values that can be reproduced is restricted by thesize of the tank. Matching Re between the physical model and the real physical situation is crucialto model turbulent dissipation correctly. However, frictional processes due to turbulent dissipationare more important to oscillatory flows than to the steady upwelling flows that will be studied inthis thesis (Boyer et al., 2004). The second limitation of laboratory models is that the vertical scalehas to be exaggerated to reduce viscous effects, and this can introduce unrealistic non-hydrostaticeffects to the flow (Allen et al., 2003).The role of stratificationStratification plays several roles in determining the dynamics of the flowwithin the canyon. Strongerstratification in the canyon inhibits the stretching of the water columns passing over the rim and thus,inhibits the generation of cyclonic vorticity in the canyon (Waterhouse et al., 2009). Independentof topography, steeply tilted isopycnals along the slope generated by wind-driven upwelling act liketopography to the flow above them (Allen, 2004).When the rotation rate of a rotating tank is changed, the flow will slowly adapt to the newrotation speed. This process is called spin up. During spin up, a bottom Ekman layer is formed. Ina flat bottom with homogeneous fluid, the Ekman layer sucks fluid from above, spinning up rapidlythe whole volume of fluid. Stratification limits the depth of fluid that is sucked into the Ekman layerfrom the whole depth of the column to Ωr=N where Ω is the rate of rotation, r is the radius of thetank. This region is spun up quickly, but the rest of the volume can only be spun up by diffusionof momentum which acts in much longer time scales. In a typical lab experiment (1 m diametertank, 10 cm water column) the homogeneous spin up takes about 17 minutes while the stratifiedcase takes about 2.5 hours (Allen, 2004).Spin up on a slope in a homogeneous fluid is similar to the flat case with a correction in the layerdepth, inversely proportional a1=2 where a is the slope (Pedlosky, 1987), but the stratified case isdramatically different to the flat-bottom stratified situation. The Ekman layer initially generatedover the slope induces an upslope flow that advects denser water upslope. This generates a buoyancyforce parallel to and down slope that, at some point, balances out the background pressure gradient.After this moment, there is no velocity at the bottom and thus no more advection of denser waterupslope. The Ekman layer is shut down after a time scale ts (MacCready and Rhines, 1993) given14byts =1S f cosa(1+S); (1.15)withS=(N sinaf cosa)2: (1.16)Here, N is the buoyancy frequency, a is the slope and f is the rotation rate.Precise estimates of the shut down time of a boundary layer with upslope Ekman transportconsider two regimes depending on the value of the slope Burger number aN= f . The arrestedboundary layer in the weakly sloping case (relatively small aN= f ) is bounded by a very strongdensity gradient separating it from the interior flow (capped boundary layer). In the larger slopingcase the arrested boundary layer is nearly linearly stratified so that it joins smoothly with the interiordensity profile (Brink and Lentz, 2010).1.3 Objectives and StructureI have identified two areas of submarine canyon research to study. There has been extensive researchon the upwelling circulation within submarine canyons (e.g., Allen and Hickey, 2010; Freeland andDenman, 1982; Howatt and Allen, 2013; Ka¨mpf, 2007; Klinck, 1996). However, the canyon contri-bution to biogeochemical budgets and on-shelf distribution of tracers on the shelf is less understood.There is a knowledge gap between the dynamics induced by submarine canyons and their role ashotspots of marine biodiversity and productivity. In particular, we know how much water upwellsthrough a short, narrow canyon but we don’t know how much it contributes to the cross-shelf ex-change of nutrients that make canyons productive regions. On the other hand, we know canyons areimportant to the cross-shelf exchange but we don’t know how or if they interact dynamically witheach other, potentially modifying their impact on cross-shelf exchange.This doctoral project has two main objectives. First, to develop a scaling scheme to estimatethe amount of tracers, such as dissolved oxygen and nutrients, that upwells through a submarinecanyon during an upwelling event taking into account the effect of enhanced mixing within thecanyon and the vertical distribution of the tracer profile. The effect of enhanced mixing in the cross-shelf exchange of tracers is explored in Chapter 2, while the impact of different initial tracer profilesis studied in Chapter 3. Second, to study the dynamical interaction of two submarine canyons underupwelling conditions. Both of these objectives are based on idealized models of the circulationwithin and around a canyon.To fulfill the first objective the research questions tackled in Chapter 2 are:Under upwelling favourable conditions1. How and how much tracer does a submarine canyon transport onto the shelf?152. What is the combined effect of locally-enhanced mixing and advection in the canyon-inducedtransport of tracers onto the shelf?The research questions addressed in Chapter 3 are:Under upwelling favourable conditions1. What is the impact of the initial tracer profile in the canyon-induced transport of tracers ontothe shelf?2. How does the on-shelf distribution of tracers depend on the initial tracer profile tracers?The research questions discussed in chapter 4 concern the second objective: In a system of twoadjacent upwelling submarine canyons1. What is the impact of the upstream canyon on the dynamics of the downstream canyon?2. Which are the relevant physical processes and parameters?3. What are the different regimes of canyon interaction?4. Which of the two canyons is leading and under what conditions?16Chapter 2The Impact of Locally-Enhanced Mixingon Canyon-Induced Tracer Transport2.1 IntroductionThis chapter investigates the impact of locally enhanced mixing within a canyon on the cross-shelfexchange of tracers and water, and develops a scaling estimate for canyon-induced upwelling oftracers, proportional to local concentration, vertical diffusivity, and previously scaled upwellingflux. For that purpose, I performed numerical experiments simulating an upwelling event near anidealized canyon, adding a passive tracer with an initially linear profile. I varied the geographicdistribution of vertical eddy diffusivity and its magnitude, the initial stratification, the Coriolis pa-rameter, and the strength of the incoming flow. Main results of this chapter are that a canyon ofwidth 5% of the along-shelf length of the shelf upwells between 25% and 89% more tracer massonto the shelf than shelf-break upwelling. Locally enhanced vertical diffusivity has a positive effecton the tracer that is advected by the upwelling flow and can increase canyon-upwelled tracer fluxby up to 27%.In the following sections I present the numerical configuration and experiments (Section 2.2);describe the flow dynamics of the base case (Section 2.3.1) and the effect of locally enhanced dif-fusivity on the dynamics of the flow and tracer transport from the canyon to the shelf; we look atthe tracer evolution within the canyon (Section 2.3.2), cross-shelf transports (Sec. 2.3.3) and up-welling through the canyon (Section 2.3.4). In section 2.4 I scale the advection-diffusion equationand provide justification for choosing the parameter space I explored in the numerical experiments.Furthermore, I develop a scaling estimate for the tracer flux onto the shelf as the product of a char-acteristic concentration and the canyon-upwelled water flux derived in previous scaling estimates(Allen and Hickey, 2010; Howatt and Allen, 2013) with a modification to account for the effect ofenhanced mixing. Finally, in section 2.5, I provide a summary and discussion of the results.17This chapter was published as Ramos-Musalem, K. and S.E. Allen, 2019: The Impact of LocallyEnhanced Vertical Diffusivity on the Cross-Shelf Transport of Tracers Induced by a SubmarineCanyon. J. Phys. Oceanogr., 49, 561584, https://doi.org/10.1175/JPO-D-18-0174.1.2.2 MethodsI use the Massachusetts Institute of Technology general circulation model (MITGCM) (Marshallet al., 1997) to simulate a system consisting of a sloping continental shelf cut by a submarine canyon(Figure 2.1), with incoming flow from the west (upwelling favourable), parallel to the shelf. Therange of stratifications, incoming shelf currents and Coriolis parameters selected for all runs repre-sent realistic oceanic conditions over continental shelves around the world and, in this sense, theyconstitute typical dynamical settings for a submarine canyon (Tables 2.1 and 2.2). I explore a widerrange of parameter space for vertical mixing, as we go from low values of vertical diffusivity tothe extreme values observed both in magnitude and vertical distribution. The simulation starts fromrest. A shelf current is spun-up by applying a body force on every cell of the domain directed west-ward, alongshelf with a similar effect as changing the rotation rate of a rotating table (Spurgin andAllen, 2014). The body forcing ramps up linearly during the first simulation day, stays constantfor another day, and ramps down to a minimum, after which it remains constant and just enough toavoid the spin-down of the shelf current. This forcing generates a deeper shelf current, less focusedon the surface, than the coastal jet generated by wind-forced models (Appendix A). The model wasrun for 9 simulation days.The domain is 280 km alongshelf and 90 km across-shelf divided in 616x360 cells horizontally.The cell width increases smoothly alongshelf and cross-shelf (CS), from 115 m over the canyon to437 m at the north boundary, and to 630 m at a distance of 60 km upstream and downstream of thecanyon and then is uniform to the downstream boundary. Vertically, the domain is divided in 90z-levels spanning 1200 m, with grid sizes varying smoothly from 5 m (surface to below shelf) to 20m at depth. The time step used was 40 s, with no distinction between baroclinic and barotropic timesteps. The experiments ran in hydrostatic mode. Some runs were also repeated in non-hydrostaticmode with no significant differences in the results.The canyon was constructed from a hyperbolic tangent function. Geometric parameters of thecanyon (Figure 2.1) are similar to those of Barkley or Quinault Canyons, with geometric and dy-namical non-dimensional groups representative of numerous short canyons, as will be discussed inSection 4e (Allen and Hickey (2010), Allen (2000) for short canyon discussion). The domain hasopen boundaries at the coast (north) and deep ocean (south). Open boundaries use Orlanski radia-tion conditions and no sponge. Bottom boundary conditions are free-slip, and the drag in the bottomboundary layer is parameterized as quadratic with the flow, with a non-dimensional coefficient of0.002 (e.g., Kundu and Cohen, 2004). Vertical walls on the bathymetry steps have a free-slip condi-tion (Deremble et al., 2011). East and west boundaries are periodic. The domain is long enough that1840 60 80C-S distance (km)5004003002001000Depth (m)(a)0.000 0.005 0.010Kv /2s 13002001000mDepth (m)(d)= 5= 10= 25= 50= 1000 20 40 60 80 100 120020406080C-S distance (km)Alongshelf distance (km)280(c)0 6 12T / ∘ C120010008006004002000(e)32 33 34S / g kg 10 25 50Tr /M(f)50 55 60 65 70505254565860C-S (km)Alongshelf distance (km)(b)100120140Figure 2.1: (a) Cross-shelf section through the canyon axis, the dashed line marks the shelfbottom, which can be identified with the canyon rim. The red arrows indicate directionsof transports calculated through CS and LID sections. (b) Top view of the canyon. Theshaded area corresponds to the LID section across which vertical transport was calcu-lated. The solid black line is the shelf-break at 149.5 m. Canyon dimensions: L= 8:3 kmis the length along the axis, Ws = 12:3 km is the width at mid length at the shelf-breakisobath,W = 21:1 km is the width at mid-length at rim depth,Wm = 24:4 km is the widthat the mouth at shelf-break depth, andR= 5:5 km is the radius of curvature of the shelf-break isobath, upstream of the canyon. (c) Top view of the domain. The shelf volumeis bounded by the wall that goes from shelf-break (black contour) to surface in the no-canyon case (sections CS1-CS6), alongshelf wall at northern boundary and cross-shelfwalls at east and west boundaries. (d) Example of initial vertical diffusivity profiles ata station in the canyon with Kcan = 10−2 m2s−1 and different values of e . Note thate = 5 m corresponds to a step profile. The dashed red line indicates the depth of thecanyon rim. Initial profiles of (e) temperature and salinity for the base case, and (f)tracer concentration with maximum and minimum values of 45 and 2 mM, respectively,and shelf-break depth concentration Cs = 7:2 mM. The dashed gray line corresponds tothe shelf-break depth.water does not recirculate through the canyon during the simulation. However, barotropic Kelvinwaves, first and second mode baroclinic Kelvin waves, and long wavelength shelf waves do recir-culate through the domain as in previous studies with similar configurations (e.g. She and Klinck(2000), Dinniman and Klinck (2002)). Subinertial shelf-waves of wavelength likely to be excited19by the canyon (40 km) (Zhang and Lentz, 2017) are too slow to recirculate. The gravest mode hasa wave speed of approximately 0.5 ms−1 against the flow (Calculated using Brink (2006)).The initial fields of temperature and salinity vary linearly in the vertical and are horizontallyhomogeneous (Figure 2.1e). For all runs, temperature decreases and salinity increases with depthbut their maximum and minimum values are changed to generate the different stratifications used inthe simulations. A passive tracer was introduced from the beginning of the simulations with a linearvertical profile that increases with depth, intended to mimic a nutrient such as nitrate (Figure 2.1f).The maximum and minimum values of the profile come from data collected during the PathwaysCruise in summer, 2013 in Barkley Canyon (Klymak et al., 2013).I use the GMREDI package included in MITGCM for diffusing tracers. Since the mesoscale eddyfield is resolved, there is no need to characterize the transport due to these structures. However,it is desirable to numerically handle the effects of tilting isopycnals that are intrinsic to canyonupwelling dynamics (Allen et al., 2001). Mixing and stirring processes are better described withinthe canyon as being along-isopycnal and cross-isopycnal, rather than horizontal and vertical. Insidethe canyon vertical mixing is set to be larger than outside (see below), so diapycnal tracer transportwill be enhanced. Considering this, I use the scheme for isopycnal diffusion (Redi, 1982) but didnot use the skew-flux parametrization (Gent and McWilliams, 1990). In sum, the vertical effectivediffusivity on the tracer is determined by the prescribed vertical eddy diffusivity Kv, the tilting ofisopycnals via the vertical contribution of the Redi scheme and the diffusivity due to the advectionscheme, which is a 3rd order, direct space time, flux-limited scheme that treats space and timediscretizations together and uses non-linear interpolation (Adcroft et al., 2018).Patterns of enhanced diapycnal mixing within submarine canyons vary spatially and temporally.For example, Ascension Canyon, has sides and axis slopes supercritical to M2 internal tides, withmaximum dissipation zones near the bottom, just below the rim, and larger average dissipationrates during spring tides (Gregg et al., 2011). On the other hand, Gaoping Canyon is subject tostrong barotropic and baroclinic (1st mode) tides and, at critical frequencies, there is a turbulentoverturning due to shear instability and breaking of internal tides and waves; diapycnal diffusivityvaries seasonally due to changes in stratification (Lee et al., 2009).Diapycnal diffusivity profiles along Ascension Canyon’s axis show a sharp gradient near rimdepth, close to the head, and the mean profile shows a clear step in diffusivity at rim depth (FigureD.2). There are also sharp, but less intense, variations of diapycnal diffusivity Kr near the rim in themean profile for Eel Canyon (Figure D.2). Monterey Canyon also shows larger levels of diffusivitywithin the canyon, although the increase at the rim is less sharp than in Eel Canyon (Figure D.2,bottom row).Given that there is a wide range of mixing patterns in canyons, I developed a simple representa-tion of enhanced vertical mixing within the canyon by prescribing higher values of Kv and Av to gridpoints within the canyon (Kcan) than background (Kbg) so that the profile of Kv decreases sharply20above the rim at every point along the canyon (Figure 2.1d). I defined cells within the canyon asthe residual grid points from subtracting the bathymetry of a straight shelf from one incised by acanyon. Additionally, I ran experiments with smoother Kv profiles defined by the Heaviside functionwith a smoothing parameter eKv(z) =Kbg if z> Hr+ eKbg+Kcan[0:5+ Hr−z2e +12p sinp(Hr−z)e]if Hr− e < z< Hr+ eKcan+Kbg if z< Hr− e(2.1)where z is depth andHr is the rim depth. I define the rim depth at a point (xc, yc) within the canyon asthe depth of the shelf away from the canyon, at cross-shelf distance yc. Given the vertical resolutionof the model, the smallest effective e is 5 m. The length e defines the smoothing length of the step,so the larger e is, the smoother the profile.Upwelled water on the shelf has been estimated previously by finding water originally belowshelf-break depth based on its salinity (Howatt and Allen, 2013). I take the same approach but usethe tracer concentration at shelf-break depth as the criterion to find water on shelf that was originallybelow shelf-break depth. Enhanced diffusion may cause my algorithm to underestimate the amountof upwelled water on shelf. To minimize this error I added a second tracer with the same linearprofile as the original but with smaller explicit diffusivity. This allows me to find upwelled water onthe shelf without the effects of enhanced diffusivity on concentration, only keeping the dynamicaleffects of enhanced Kv through modifications of density. The constant gradient of the linear profilealso contributes to lower the numerical diffusivity compared to other profiles. The linear advectivetracer is only used to find the upwelled water; all tracer mass integrations are over the original tracerwith the mixing characteristics reported in Table 2.2.I explore the effects of vertical eddy diffusivity Kv and vertical eddy viscosity Av, locally-enhanced vertical diffusivity Kcan and viscosity Ac, stratification N0, Coriolis parameter f , and in-coming velocity U . All reported experiments (Tables 2.1 and 2.2) have Kv = Av since I found thatthe effect of Av is not significant and will not be discussed further. I report the effects of modifyingN0 and f combined as the Burger number Bu =N0Hs( fW )−1, whereW is the width at mid-length atrim depth (Figure 2.1b), and of f and U combined as the Rossby number RW =U( fWs)−1, whereWs is the width at mid-length at the shelf-break isobath (alongshelf direction) (Figure 2.1b).2.3 Results2.3.1 Description of the flowThe body forcing generates an upwelling-favorable shelf current that slightly accelerates after theinitial push (Figure 2.2e). These conditions tilt the sea surface height down towards the coast.21Table 2.1: All runs in the Dynamical Experiment have a corresponding no-canyon run andconstant vertical diffusivity as in the base case in Table 2.2. For all runs, parameters N0, fandU were chosen to represent realistic oceanic conditions for canyons (within values inTable 1 in Allen and Hickey (2010)) while satisfying the dynamical restrictions imposedby Allen and Hickey (2010) and Howatt and Allen (2013). Only values changed from thebase case (bold face entries in first row) are shown.Experiment N0 (s−1) f (s−1) U (ms−1) Bu RL RWbase case 5:5×10−3 9:66×10−5 0.36 0.40 0.45 0.31↑ N0 6:3×10−3 0:38 0:46 0:47 0:32↑↑ N0 7:4×10−3 0:40 0:54 0:49 0:33↓ N0 5:0×10−3 0:35 0:37 0:44 0:30↓↓ N0 4:7×10−3 0:35 0:34 0:43 0:29⇓ N0 4:6×10−3 0:35 0:34 0:43 0:29↑ f 1:00×10−4 0:36 0:39 0:43 0:29↓↓ f 7:68×10−5 0:39 0:51 0:61 0:41↓ f 8:60×10−5 0:38 0:45 0:53 0:36⇓ f 6:40×10−5 0:41 0:61 0:78 0:53↓ U 0:31 0:40 0:39 0:26↓↓ U 0:26 0:40 0:32 0:22⇓ U 0:14 0:40 0:18 0:12⇓ U, ↓↓ N0 4:6×10−3 0:13 0:34 0:17 0:11⇓ U, ↑↑ N0 7:4×10−3 0:15 0:54 0:19 0:13⇓ U, ⇓ f 7:00×10−5 0:15 0:56 0:27 0:18During spin up, simulation days 0-3, the upwelling response is intense on the shelf and through thecanyon. This time-dependent response is linear and thus, directly proportional to the forcing (Allen,1996) and will not be discussed further. I focus on the next stage, after simulation day 4, whenthe current has been established, baroclinic adjustment has occurred, and advection dominates thedynamics in the canyon (advective stage). The highest alongshelf velocities can be found on theslope, at about 200 m (Figure 2.2c), but the scale velocity for canyon upwelling is on the upstream-canyon shelf, between shelf break and canyon head, close to shelf bottom but above the bottomboundary current (Gray box, Figure 2.2c). This constitutes the incoming velocity scale U . In thatarea,U stays between 0.35 ms−1 and 0.37 ms−1 during the advective phase for the base case (Figure2.2e).Circulation over the canyon is cyclonic. An eddy forms near the canyon rim (Figure 2.2f) andincoming flow deviates towards the head on the downstream side of the canyon and offshore onthe downstream shelf. Within the canyon, below shelf-break depth, circulation is also cyclonic.Water comes into the canyon on the downstream side (positive v) and out on the upstream side22Table 2.2: All runs in the Mixing Experiment have the same dynamical parameters as the basecase in Table 2.1. All runs reported have a corresponding no-canyon run. Only valueschanged from the base case (bold face entries in first row) are shown. Values of RL andRW for these runs slightly vary from the base case values with RL between 0.42 and 0.44,and RW between 0.28 and 0.30.Experiment Kbg / m2s−1 Kcan / m2s−1 e / mBase 10−5 10−5 5↑ Kbg 10−4 10−4 5↑↑ Kbg 10−3 10−3 5⇓U ↑↑ Kbg 10−3 10−3 5⇑⇑↑ Kcan 1:2×10−2 5⇑⇑ Kcan 10−2 5⇑⇑ Kcan e10 10−2 10⇑⇑ Kcan e15 10−2 15⇑⇑ Kcan e25 10−2 25⇑⇑ Kcan e50 10−2 50⇑⇑ Kcan e75 10−2 75⇑⇑ Kcan e100 10−2 100⇑↑↑ Kcan 8×10−3 5⇑↑ Kcan 5×10−3 5⇑↑ Kcan e25 5×10−3 25⇑↑ Kcan e100 5×10−3 100⇑ Kcan 2:5×10−3 5↑↑ Kcan 10−3 5↑↑ Kcan e25 10−3 25↑↑ Kcan e100 10−3 100↑ Kcan 5×10−4 5(Figure 2.2d). This circulation pattern is consistent with previous numerical investigations (Daweand Allen, 2010; Howatt and Allen, 2013; Spurgin and Allen, 2014), observations (Allen et al.,2001; Hickey, 1997) and laboratory experiments (Mirshak and Allen, 2005).Upwelling within the canyon is forced by an unbalanced horizontal pressure gradient betweencanyon head and canyon mouth (Freeland and Denman, 1982). In response, a balancing, baroclinicpressure gradient is generated by rising isopycnals towards the canyon head. The effect on the den-sity field drives a similar response on the tracer concentration field (Figure 2.2a). Near the canyonrim, pinching of isopycnals occurs on the upstream side (Figure 2.2b). This region is associated withstronger cyclonic vorticity generated by incoming shelf water falling into the canyon, stretching thewater column (Not shown). This well-known feature has been observed in Astoria Canyon (Hickey,1997) and numerically simulated (e.g., Dawe and Allen, 2010; Howatt and Allen, 2013).2340 50 60 70 80v / cm s 1(d)-25-20-15-10-5051015202540 50 60 70 80C / M(b)20.921.1 21.121.703691215182140 50 60 70 805060CS distance / km50cmsspeed / cm s 1 (f)51015202530354050 60CS distance / km4002000Depth / mu / cm s 1 (c)-50-25025500 2 4 6 80.00.10.20.3U/ ms1(e)50 604002000Depth / mC / M (a)20.921.421.822.303691215182160 80 100 120 140 160 180Al ngshelf distance / km6080CS distance / kmBC / M(h)2.23.24.25.26.27.28.29.210.20 2 4 6 8Days5.06.07.08.0BC / M(g)oFigure 2.2: Main characteristics of the flow during the advective phase. Average days 3-5 con-tours of tracer concentration (color) and sigma-t (solid black lines, units of kgm−3) at analongshelf section close to canyon mouth (b) and along the canyon axis (a). (c) Along-shelf and (d) cross-shelf components of velocity. (e) Evolution of alongshelf componentof incoming velocity U , calculated as the mean in the gray area delimited in (c). Thedashed line marks the beginning of the advective phase. (f) Speed contours and velocityfield at 127.5 m depth with shelf break in white. (g) Evolution of average bottom con-centration on the downstream shelf, bounded by the yellow rectangle in (h). (h) Tracerconcentration on the shelf bottom averaged over days 3-5.Most water upwells onto the shelf over the downstream side of the rim, near the canyon head.This upwelled water has higher tracer concentration than the water originally on shelf since theinitial tracer profile increases with depth (Figure 2.1f). As a result, a ‘pool’ of water with highertracer concentration than background values forms near shelf-bottom (Figure 2.2h). This pool growsrapidly during the time-dependent phase, and more slowly during the advective phase (Animation24SI1, supplementary material). A similar feature was seen in a numerical study of canyon upwellingon the shelf of Washington, USA (Connolly and Hickey, 2014). The average concentration nearshelf bottom increases quickly during days 0 to 3 (by 1.5 mM) and more slowly during the next 6days for the base case (Figure 2.2g).I isolate the canyon effect on the on-shelf tracer distribution by subtracting the correspondingno-canyon run. I look at the near-bottom tracer concentration anomaly (BC anomaly) defined as theconcentration difference near the shelf bottom between the canyon and no-canyon case, normalizedby the initial concentration near the bottom and expressed as a percentage. Contours of BC anomalyfor the base case show a region of positive anomaly or higher tracer concentration relative to theno-canyon case downstream of the canyon (Animation SI2, supplementary material). The verticalextent of the pool can be between 10 m and 30 m above the shelf bottom. The formation dynamics,extension and persistence of the pool will be characterized in the next chapter.2.3.2 Vertical gradient of density and tracerDuring an upwelling event, isopycnals and iso-concentration lines near the canyon rim are squeezedas they tilt up from mouth to head (Figure 2.3a). Close to the canyon head, on the downstream sidewhere most upwelling occurs, stratification N2 increases in time from the initial value N20 , with amaximum increase located close to but above rim depth at 108 m (Figure 2.3h). The maximumstratification increases quickly during the time-dependent phase of upwelling. After day 3, maxi-mum stratification oscillates around the adjusted value; however, it slightly decreases for cases withenhanced Kcan and Kbg because diffusivity weakens the density gradient with time. Maximum strat-ification above rim depth can be more than seven times higher than N20 . The tilting of isopycnals andthus, the increase in stratification near the head, is a baroclinic response to the unbalanced pressuregradient on the shelf. Allen and Hickey (2010) showed that the pressure gradient along the canyonis r0 fUF(Ro), where F(Ro) takes values between 0 and 1, which is consistent with my results: themaximum stratification increase is proportional to U (compare pink to black line, Figure 2.3h) andf (compare purple to black line, Figure 2.3h). They also show that the depth of the deepest isopyc-nal to upwell onto the shelf Z is proportional to N−10 (compare red to black line, Figure 2.3h). Thedeeper Z is, the larger the tilting of isopycnals will be and so the larger the increase in stratification.When diffusivity is locally enhanced, there is an additional effect on stratification. Within thecanyon, enhanced diffusivity Kcan is acting on the density gradient, which was sharpened by thecanyon-induced tilting of isopycnals, more rapidly than it is being diffused above the rim. Sostratification near the rim but within the canyon is lower than it would be if the diffusivity profilewas uniform, and stratification above the rim is higher than for the case with uniform diffusivity.The effect increases with Kcan (blue and solid green lines in Figure2.3a, b and c) and it is maximumwhen the Kv profile is a step (solid green line). Smoother Kv profiles decrease the effect especiallyfor e larger than 25 m (dotted and dashed green lines).2552.5 55.0 57.5CS distance / km−350−300−250−200−150−100−50Depth / mbase case (a)21.021.221.420.720.921.752.5 55.0 57.5CS distance / km↑ ↑Kcan(b)21.021.221.420.720.921.752.5 55.0 57.5CS distance / km⇑ ⇑Kcan(c)21.021.221.420.720.921.752.5 55.0 57.5CS distance / km⇑ ⇑Kcan,ε=50 m(d)C/μμ21.021.221.420.720.921.75 10C / μM(g)Initia  profi e0.0 2.5 5.0 7.5N2/N20 (h)base case↑ ↑  Kbg↑ ↑Kcan⇑ ⇑Kcan⇑ ⇑Kcan, ε15⇑ ⇑Kcan, ε50⇓  N0⇓ f⇓  U46810121416(5 (4 (3 (2log10(Kv / m2s−1)(120(100(80(60(40(200Depth / m(e)0.0 2.5 5.0 7.5∂zC/∂zC0(f)Figure 2.3: Concentration contours averaged over days 4 and 5 are plotted along canyon axisfor the base case (a) and locally enhanced diffusivity cases with Kcan = 10−3 m2s−1 (b),Kcan = 10−2 m2s−1 (c) and Kcan = 10−2 m2s−1, e = 50 m (d). The dotted line indicatesthe location of the shelf downstream (rim depth). (e) Profiles of vertical diffusivity ata station in the canyon indicated by the dashed line in (a-d). (f, g, h) Vertical profilesof vertical tracer gradient divided by initial tracer gradient (¶zC=¶zC0), concentration C,and stratification divided by initial stratification N2=N20 taken on day 5 at same station as(e). Horizontal, dotted, grey lines correspond to the rim depth.Iso-concentration lines mimic isopycnals (Figure 2.3a-d, f). Vertical tracer gradients sharpen atrim depth as upwelling evolves, similar to stratification (Figure 2.3f). Compared to the base case,lower N20 increases the sharpening effect on the tracer gradient (pink line vs. black line).Tracer concentration is relatively higher above rim depth with higher Kcan and lower belowrim depth (all green and blue lines vs. black line above and below rim depth). This increasedconcentration in Figure 2.3g (green and blue lines) is related to the gradient spike above rim depthin Figure 2.3f.262.3.3 Cross-shelf transport of water and tracerTo determine the pathways of water and tracers onto the shelf I calculate their cross-shelf (CS)and vertical transports. I define CS transport of water as the volume of water per unit time thatflows across the vertical planes (CS1-CS6) that extend from the shelf-break in the no-canyon caseto the surface (Figure 2.1a and c); while vertical transports flow across the horizontal plane (LID)delimited by the shelf-break depth in the canyon case and the canyon walls (Figure 2.1a and b). I0 2 4 6 8Days−5.0−2.50.02.55.0(105 μM m3(−1)(a) Tracer )ran(por)0 2 4 6 8Day(−10−505(104 m3(−1)(b) Wa)er )ran(por)LIDCS1CS2CS3CS4CS5CS6To)al−100−50Dep)h / mμM m(−1(c) CS2 CS3 CS440 50 60 70 80Along(helf d ()ance / km−400−2000Dep)h / mμM m(−1(d)55 60 65Along(helf d ()ance / km5254565860C-S / km10−2μM ms−1(e) LID−2 −1 0 1 2−0.48−0.36−0.24−0.120.000.120.240.360.48−1.5−1.0−0.50.00.51.01.52.02.5Figure 2.4: Base case (a) tracer and (b) water cross-shelf and vertical transport anomaliesduring the simulation through cross-sections defined in Figure 2.1. The horizontal, cross-shelf tracer transport anomaly through sections CS2, CS3 and CS4 and averaged overdays 4 to 9 is plotted in (c). A full-depth version is plotted in (d) to include cross-shelftransport anomaly through the canyon. Vertical tracer transport averaged over days 4 to9 is plotted in (e).define the net or Total Water Transport (TWT) and Total Tracer Transport (TTT) onto the shelf as themean during the advective phase of the sum of the water and tracer transports through cross sectionsCS1 to CS6 and LID, and the Vertical Water Transport (VWT) and Vertical Tracer Transport (VTT)onto the shelf as the mean transport through LID during the advective phase (days 4 to 9).Tracer transport is divided into advective and diffusive contributions. The advective part isdefined as Cu⃗ · nˆA, the contribution of the flow, where nˆA is the area vector normal to the cross-section. I compare the advective part to water transport. The flux and transport of tracers come27directly from model diagnostics.The canyon effect on cross-shelf fluxes is the anomaly between canyon and no-canyon cases.Negative transports generally mean that either water or tracer are leaving the shelf; it is only nearthe shelf bottom, where shelf upwelling is onshore, that negative transports mean that transport forthe no-canyon case is larger than in the canyon case.Patterns of cross-shelf transport anomaly of tracer and water are similar. Both, tracer (Figure2.4c) and water (not shown) anomaly flux is onto the shelf through CS3, close to the downstreamside of the canyon mouth and through LID (vertical flux, Figure 2.4e). Tracer and water transportanomalies flux off the shelf, downstream of the canyon, close to canyon mouth (CS4), and bothtransport anomalies are mainly offshore through CS1, CS2, CS5 and CS6. These agree with shelf-break upwelling suppression in the presence of a canyon. Deeper-than-shelf-break-depth watercomes into the canyon through the downstream side and leaves through the upstream side, consistentwith cyclonic circulation (Figure 2.4d).Positive transports through LID and CS3 indicate that tracer and water upwell onto the shelfthroughout the simulation. The vertical upwelling response is maximum at the same time that thebody forcing is maximum and then decreases to a steady value of 20% of the maximum. Cross-shelftransport through CS3 reaches its maximum at day four and then decreases to a steady value of 40%of that maximum (Figure 2.4a, b). In contrast, transport anomaly through CS4, CS1, CS2, CS5 andCS6 is off-shore throughout the nine days. Off-shore transport at CS4 is the main balance to theonshore transports, especially during the time-dependent phase. Its response has similar timing asthat of the vertical transport and it also decreases to a quasi-steady value after reaching its maximumon day 2.5. This off-shore transport is consistent with the off-shore steering of the flow described insection 2.3.1.Overall, total TTT anomaly is onto the shelf (Figure 2.4a) and TWT anomaly is zero (Figure2.4b). During the advective phase there is a constant supply of tracer onto the shelf induced by thecanyon. This result could change if the initial tracer profile was not linear or would reverse if itdecreased with depth.Changing dynamical parameters RW and Bu changes the amount of transport relative to the basecase, but qualitatively follows the same evolution through each section (Not shown). Higher (lower)Bu and lower (higher) RW than in the base case decrease (increase) the amount of tracer transportedonto the shelf during the advective phase (Table 2.3, column TTT). Enhanced Kcan increases themean tracer transport onto the shelf (Table 2.3, column TTT). This increase can be more than doublewhen Kcan is two orders of magnitude larger than in the base case and triple with smoother profiles(e > 25 m).Upwelling through the canyon is well characterized by the vertical transport through LID. VTTis dominated by advection over diffusion. VTT and the advective component Vertical AdvectiveTransport of Tracer (VATT) are equal to 2 significant figures for runs in dynamical experiments (not28Table 2.3: Mean vertical (VTT), advective (VATT) and total (TTT) tracer transport anomaliesthrough cross sections CS1-CS5 and LID as well as vertical water (VWT) and total (TWT)water transport anomalies throughout the advective phase with corresponding standarddeviations calculated as 12 hour variations for selected runs. Results for all runs areavailable in Appendix B.Exp VTT VATT TTT VWT TWT105 mMm3s−1 105 mMm3s−1 104 mMm3s−1 104 m3s−1 102 m3s−1base case 1.6±0.29 1.6±0.29 0.46±0.13 1.9±0.46 -1.6±5.2↑↑ N0 0.73±0.20 0.73±0.20 0.14±0.06 0.91±0.29 -5.5±4.7↓↓ N0 2.2±0.36 2.2±0.36 0.74±0.16 2.5±0.58 -1.4±4.0↑ f 1.7±0.32 1.7±0.32 0.49±0.13 2.0±0.48 -0.57±5.04⇓ f 0.92±0.16 0.92±0.16 0.21±0.09 1.0±0.32 -18.1±6.5⇓ U 0.43±0.05 0.43±0.05 0.12±0.01 0.60±0.09 4.3±2.2⇓ U, ⇓ f 0.26±0.04 0.26±0.04 0.06±0.01 0.37±0.07 0.91±2.2⇑⇑ Kcan, e25 2.5±0.18 2.2±0.18 1.2±0.06 2.4±0.24 4.6±1.1⇑⇑ Kcan, e50 2.8±0.15 2.5±0.16 1.3±0.06 2.8±0.22 3.0±1.3⇑⇑ Kcan, e100 3.0±0.15 2.6±0.16 1.3±0.08 3.0±0.21 1.8±1.3⇑↑↑ Kcan 2.2±0.25 1.9±0.24 1.0±0.10 2.2±0.32 9.5±2.2⇑⇑ Kcan 2.0±0.25 1.8±0.24 0.97±0.11 2.1±0.32 9.6±1.8all shown). Nonetheless, the VATT is modified by enhanced vertical diffusivity through modifica-tions to the density field. Larger diffusivities weaken the density gradients near the rim which allowsmore water to upwell onto the shelf. During the advective phase, VATT tends to increase when dif-fusivity is enhanced and can be as much as 25% larger than in the base case (Table 2.3). VTT can behigher by 25% to 37% for the largest two Kcan used (Table 2.3) and can almost double for smootherKv profiles (e = 100 m). The effect of enhanced Kcan amplifies throughout the simulation dependingon the magnitude of Kcan and the gradient.2.3.4 Upwelling flux and upwelled tracer massUpwelled water on the shelf has been estimated previously by finding water originally below shelf-break depth based on its salinity (Howatt and Allen, 2013). I take the same approach, but use thetracer concentration at shelf-break depth as the criterion to find water on shelf that was originallybelow shelf-break depth. For this I use the low diffusivity tracer described in Section 2.2 .I define the volume of water upwelled onto the shelf through the canyon (Vanom) at day t as thedifference between the volume of upwelled water, that is water with C >Cs = 7:2 mM, where Cs isthe initial concentration at shelf-break depth, on shelf at t = t in the canyon case (Vcan) compared to29the no canyon case (Vnc):Vanom(t) =Vcan−Vnc =åcan∆V −ånc∆V whereC >Cs (2.2)where ∆V is the volume of the cell with concentration higher than that at shelf-break depth (Cs) andthe sum is over all cells on the shelf that satisfy this criterion for the bathymetry with a canyon andwithout a canyon. The shelf volume constitutes all the cells between the shelf break and the coast,and between the shelf bottom and the surface.Similarly, the tracer mass upwelled by the canyon (Manom) is defined as the tracer mass containedwithin the upwelled water VanomManom(t) =Mcan−Mnc =åcanC∆V −åncC∆V whereC >Cs (2.3)where C is the concentration at the cell, ∆V is the volume of the cell and the sum is over all cellswith upwelled water.Water upwells onto the shelf on the downstream side of the canyon rim. The upwelled-watervolume anomaly, Vanom (2.2) alongshelf (integrated in the cross-shore direction) at day 3.5 is con-centrated on the shelf, on the downstream side of the canyon rim (Figure 2.5a). Water continuesupwelling through the canyon and, at the same time, the bulge of upwelled water is advected down-stream. On the upstream shelf, shelf-break upwelling is suppressed as water is redirected to upwellthrough the canyon as indicated by negative values of upwelled water volume anomaly (Figure2.5a). The upwelled tracer mass anomaly, Manom as in (2.3) follows a similar pattern alongshelf(Figure 2.5b). The upwelled water volume (Vcan) through the canyon is larger than that upwelledon a straight shelf and increases throughout the simulation. In the canyon case, water upwelling isdominantly canyon induced; at day 9, it accounts for between 24% to 89% of Vcan throughout theruns and between 25 to 90% of upwelled tracer mass (Mcan) (2.4), except for the lowestU case withenhanced background diffusivity, where canyon-induced upwelling accounts for 0.8%.I calculate the upwelling flux F as the mean of the daily flux of Vcan during the advective phase(between day 4 and 9),F=〈 ¶¶ t(Vcan)〉: (2.4)I considered the full upwelled volume of water for the canyon case following the metric definedby Howatt and Allen (2013) since I will compare my results to their scaling estimate and then usethis estimate for scaling tracer upwelling flux (Sec. 2.4). Consequently, I define the upwelled tracermass flux FTr as the mean daily flux of Mcan between day 4 and 9,FTr =〈 ¶¶ t(Mcan)〉: (2.5)30012345Vcan(c) 1010m3012345Vnc(d) 1010m30 2 4 6 8Days0.00.51.01.52.02.5VcanVnc(e) 1010m3base case  Kcan⥣ ⥣Kcan⥣ ⥣Kcan, 15⥣ ⥣Kcan, 50⥥ N0⥥ f⥥ U01234Mcan(f) 1011Mm301234Mnc(g) 1011Mm30 2 4 6 8Days0.00.51.01.52.0McanMnc(h) 1011Mm30 20 40 60 80 100 120Alongshelf distance / km01Vanom(a) 105 m30 20 40 60 80 100 120Alongshelf distance / km048Manom(b) 108Mm3 TrFigure 2.5: (a-b) Vertically-integrated upwelled water volume and tracer at day 3.5 alongshelf.Dashed lines show the position of the canyon. (c, d, e) Volume of water on the shelf withconcentration values initially below shelf-break depth. (f, g, h) Upwelled tracer mass onshelf. (c) and (f) canyon cases, (d) and (g) no-canyon cases, and (e) and (h) the differencebetween these. The boundaries of the shelf box are the wall that goes from shelf-breakto surface in the no-canyon case, alongshelf wall at northern boundary and cross-shelfwalls at east and west boundaries.The upwelling tracer flux is directly proportional to the water upwelling flux, with small de-viations when the Kv profile is a step (Figure 2.6a). Water and tracer upwelling fluxes (Table 2.4,columns 2 and 3, respectively) are inversely proportional to Bu (for fixed RW ) and directly pro-portional to RW (for fixed Bu). This dependence of the upwelling flux of water on Bu and RW isconsistent with findings by Allen and Hickey (2010) and Howatt and Allen (2013); the same depen-31Table 2.4: Mean water and tracer upwelling fluxes (F (2.4) and FTr (2.5)) for selected runsduring the advective phase, reported with 12 hour standard deviations. All other quanti-ties are evaluated at day 9: Volume of upwelled water (Vcan), upwelled tracer (Mcan) forthe canyon case and fractional canyon contributions to these quantities calculated as thecanyon case minus the no-canyon case divided by the canyon case, and total tracer massanomaly on shelf (M-Mnc (2.6)) in kg of NO−3. Results for all runs are available inAppendix B.Exp F(104m3s−1)FTr(105mMm3s−1)Vcan(1010m3)(Vcan−Vnc) V−1can(%)Mcan(1011mMm3)(Mcan−Mnc) M−1can(%)M−Mnc(106 kgNO−3 )base case 3.85±0.60 2.76± 0.26 2.86 81.61 2.20 82.57 1.96↑↑ N0 1.32±0.55 1.11± 0.44 1.10 77.74 0.82 77.91 0.62↓↓ N0 6.34±0.92 4.84± 0.72 4.35 30.84 3.45 36.36 3.25↑ f 4.03±0.58 2.95± 0.36 2.96 73.08 2.30 74.70 2.06⇓ f 1.83±0.88 1.03± 0.42 1.56 76.77 1.17 77.09 1.03⇓ U 0.14±0.23 0.15± 0.07 0.18 69.05 0.13 69.53 0.31↑ Kbg 3.70±0.73 2.29± 0.24 2.80 87.26 2.05 87.20 2.02⇑⇑ Kcan, e25 4.12±0.71 3.43± 0.50 3.14 83.29 2.52 84.76 4.24⇑⇑ Kcan, e50 4.21±0.71 3.29± 0.55 3.18 83.48 2.46 84.38 4.53⇑⇑ Kcan, e100 4.51±0.64 3.40± 0.46 3.36 84.37 2.52 84.76 4.70⇑↑↑ Kcan 4.08±0.54 3.35± 0.33 3.08 82.94 2.51 84.70 3.48⇑⇑↑ Kcan 4.17±0.65 3.51± 0.39 3.13 83.22 2.55 84.95 3.27⇑⇑ Kcan 4.09±0.58 3.39± 0.37 3.09 83.02 2.53 84.79 3.38dence of the tracer flux on Bu and RW shows that the upwelling of tracers is dominated by advection(Figure 2.6b). Cases with smaller (larger) f and thus, simultaneously higher (lower) Ro and Bu,have smaller (larger) upwelling fluxes. This is consistent with the relatively high values of RW thatwe are exploring. Locally-enhanced diffusivity moderately increases the tracer upwelling flux andthe water upwelling flux which increase by 27% and 19%, respectively compared to the base casefor the highest Kcan. Moreover, high Kcan combined with a smooth Kv profile (e.g. e = 100 m)increases the upwelling flux of water by 26%. The results suggest that larger values of e increasethe water upwelling flux but the average increase is smaller than the standard deviation and so itcannot be confirmed, except by comparing the extreme cases, e = 5 m and e = 100 m. Enhancedbackground diffusivity decreases the tracer mass upwelling flux as much as 61% for the highest Kbgalthough these cases are not physically meaningful.I calculate the total amount of tracer mass on shelf at a given time (M(t)) by integrating thevolume of each cell on the shelf multiplied by its tracer concentration:M(t) = åshel fC∆V; (2.6)where ∆V is the volume of a cell on the shelf and C its concentration. This includes cells from thebottom of the shelf all the way to the surface and from shelf break to the coast. The total volume320 2 4 6 8Upwelling flux / 104 m3s−10123456Tracer flux / 105 μMm3s−1(a)0.0 0.2 0.4 0.6RW0.00.10.20.30.40.50.6BuTracer Flux(b)012345105 μMm3s−1Figure 2.6: (a) Comparison between the mean flux of water and the mean flux of tracer up-welled through the canyon during the advective phase of upwelling for all runs. Errorbars correspond to standard deviations. (b) Upwelled tracer flux increases (darker, largermarkers) with increasing Rossby number RW and decreasing Burger number Bu. The sizeand color of the markers are proportional to the tracer flux, and the red-edged markerscorrespond to runs with locally-enhanced Kcan. Locally-enhanced diffusivity weakensthe stratification below rim depth and allows more tracer to upwell.of the shelf is 6:1× 1011 m3 and the volume of the canyon is approximately 6:8× 109 m3. So,the canyon represents about 1% of the total volume of the shelf. M(t) reflects all processes andexchanges of mass at any depth and from any kind of water; it is the total inventory of tracer onshelf.Given that the tracer we added had an initial linear nitrate profile, the difference in the totalon-shelf nitrate inventoryM as in (2.6) between the canyon case and the straight shelf case can bebetween 0.3-4.7×106 kg NO−3 after 9 days of upwelling (Table 2.4, last column). Considering a twomonth upwelling period, my estimate for one canyon is 0.2-3.1×107 kg NO−3 . Connolly and Hickey(2014) numerically estimated the nitrate input of two canyons in the Washington Shelf during Juneand July to be between 1-2×107 kg NO−3 , which is consistent with my estimate.2.3.5 A note on model resolutionUpwelled flux of water may be underestimated by the model if the resolution is too low for thesolution to converge. Dawe and Allen (2010) found that the canyon upwelling solution is fullyconverged for resolutions higher than 3 mm in the horizontal and 1 mm in the vertical in a numericalmodel of a rotating tank. These restrictions are equivalent to a horizontal resolution within 3% ofthe Rossby radius of deformation, a = N0Hs f−1, and a vertical resolution within 5% of the depthscale Dh = f L=N0. My numerical model has a horizontal resolution of 115 m (1% of a) and avertical resolution of 5 m (3% of Dh) considering the base case (a = 8:5 km and Dh = 146 m).33These resolutions are better than the thresholds found by Dawe and Allen (2010) and thus the fluxof water should be well represented.2.4 Scaling analysisThere are two main processes acting to transport tracer onto the shelf: mixing and advection. Themixing contribution, represented by locally-enhanced diffusivity within the canyon, has been de-scribed in the results and is scaled in this section, while the advective part is driven by the upwellingdynamics described and scaled by Allen and Hickey (2010) and Howatt and Allen (2013). Addi-tionally, I found that enhanced mixing within the canyon can have an effect on advection throughmodifications to the density field near the canyon head and I include a correction for it.The scaling by Allen and Hickey (2010) and Howatt and Allen (2013) starts from the shallow-water equations for an inviscid, steady, Boussinesq flow. They characterize the tendency of theflow to follow the bathymetry to determine the strength of upwelling through the canyon. Then,they calculate the effective, unbalanced pressure gradient within the canyon that is responsible forraising the isopycnals. Next, they calculate the resulting density deformation, from which theyidentify the deepest isopycnal that upwells onto the shelf. The depth of this isopycnal is Hh + Zwhere Hh is the canyon-head depth and Z is called the depth of upwelling:Z =(fULFN20)1=2(2.7)where F = Ro=(0:9+Ro) is the function that characterizes the tendency of the flow to cross thecanyon and Ro =U= fR is a Rossby number that uses the upstream radius of curvatureR as a lengthscale. Other useful estimates from this analysis are the horizontalU∗ and vertical Ω components ofvelocity of the upwelling current, given byU∗ =UF (2.8)Ω=U∗ZL(2.9)I useU∗ and Ω to find the relative importance of the terms in the advection-diffusion equation.Starting from the scales Z, U∗ and Ω, Allen and Hickey (2010) carry on to estimate the upwellingflux F = U∗WmZ by arguing that the flux of upwelling is the flux coming into the canyon at themouth (widthWm), over a depth Z at speed U∗. They use observations and results from numericaland physical models to find the coefficients of the scaled quantities.There were two criteria that guided my choice of the dynamical parameter space: To haverealistic values ofU , N0 and f in the context of shelf regions, and to satisfy the restrictions imposedby Allen and Hickey (2010) and Howatt and Allen (2013). There are 9 restrictions that apply to34the scaling estimates for a canyon (Allen and Hickey, 2010, section 2.5). In summary, the scalingrequires the flow to be uniform over the length of the canyon, L, and relatively weak (FRW < 0:2).The stratification to be nearly uniform near canyon rim. The shelf break to be shallow enough thatisopycnals over the canyon feel the canyon close to the surface, so that the effective depth overthe canyon is the shelf-break depth Hs (Bs < 2 where Bs = NHs= f L). The continental shelf mustbe sloped so that the onshore bottom boundary layer (BBL) flow is shut down. The canyon wallsmust be steep (so that BBL flows are quickly arrested), the canyon much deeper than the depth ofupwelling Z, and the canyon width should be narrower than 2 Rossby radii. The scaling is generalenough that it has been successfully compared to observations in six canyons, three laboratorymodels and a recent field study in Whittard Canyon (Porter et al., 2016).2.4.1 Advection-diffusion equation in natural coordinatesLet (tˆ , hˆ , bˆ) be a flow-following coordinate system that describes the motion of a trihedron alongthe curve given by the upwelling current. The unitary trihedron is defined by tˆ , the vector tangentto the upwelling current; hˆ the normal vector to the tangent in the same vertical plane and pointingupwards, and bˆ= tˆ× hˆ , the vector normal to the plane defined by tˆ and hˆ (Figure 2.7).zsn=bηhorizontal projectionupwelling currentFigure 2.7: The coordinate system (t , h , b) corresponds to the trihedron that moves along theupwelling current (blue line) and (s, z, n) corresponds its horizontal projection (naturalcoordinate system). So s⃗ is the projection of t⃗ in the x− y plane (horizontal) and z isthe usual vertical coordinate (s, z, n). In our derivation, we assume that the coordinatesn and b are the same and moreover, they lie on the isopycnal plane. This means that thedifference between the coordinate systems is a single rotation a around the n=b axis.Let us consider the deepest streamline that upwells within a submarine canyon and assume thatthe isopycnal plane is associated with the t − b plane, since the canyon-induced upwelling flow isfavoured along isopycnals, and the diapycnal direction with hˆ .The equation describing the change in concentration of a passive tracer C, is written in natural35coordinates (s, z, n) (Holton, 1992) as¶C¶ t+u¶C¶ s+w¶C¶ z= Ñ ·KÑC; (2.10)where u is the horizontal velocity, w is the vertical component of velocity, and K is an order 2diffusivity tensor. However, the simplest representation of K is in isopycnal coordinates:K =KI 0 00 KI 00 0 KDwhere KI is the diffusion coefficient along isopycnals and KD is the diffusion coefficient in thediapycnal direction. To use this, we can express the rhs of (2.10) in the coordinates (t , h , b),associated with the isopycnal-diapycnal directions as¶C¶ t+u¶C¶ s+w¶C¶ z= KIÑ2t;bC+KD¶ 2C¶h2: (2.11)Expressing the rhs of (2.11) in terms of (s,z,n) (Appendix C) we arrive at an advection-diffusionequation in terms of isopycnal and diapycnal diffusivities, and the upwelling current velocity com-ponents in natural coordinates:¶C¶ t+u¶C¶ s+w¶C¶ z≈ KI(¶ 2C¶ s2+¶ 2C¶n2+2¶ 2C¶ z¶ s¶ z¶t)+KD(¶ 2C¶ z2+2¶ 2C¶ z¶ s¶ s¶h): (2.12)2.4.2 Relevant parameter spaceThe relevant dynamical variables in (2.12) are the horizontal and vertical velocities u and w, scaledby the horizontal upwelling velocity U∗ and vertical upwelling velocity Ω, respectively; and theisopycnal and diapycnal diffusivity coefficients KI and KD. Additional parameters are the scales forthe horizontal and vertical concentration gradients dhC and dvC; and scales for the horizontal andvertical curvatures of the concentration d 2hC and d2vC, respectively. The curvatures of the concen-tration are the second derivative of the concentration profile with respect to depth (¶ 2C=¶ z2), andwith respect to the cross-shelf direction ¶ 2C=¶ s2, within the canyon. A horizontal length scale isgiven by the canyon length, L and a vertical length scale by the depth of upwelling, Z.In total, there are 10 parameters (U∗, Ω, L, Z, dhC, dvC, d 2hC, d2vC, KI and KD ) with fourdimensions: horizontal length, vertical length, time and concentration. We differentiate betweenhorizontal and vertical lengths because we are assuming that the flow is hydrostatic and thus, vertical36Table 2.5: Non-dimensional groups constructed for the tracer scaling. To calculate thesescales, I took geometric parameters reported by Allen et al. (2001) for Barkley Canyon(L=6400 m, R=5000 m , Wm=13000 m), stratification and incoming velocity values re-ported by Allen and Hickey (2010) (N0 = 10−3 s−1, U = 0:1 ms−1). Although not mea-sured for Barkley Canyon, we used the diapycnal diffusivity (KD = 3:90× 10−3 m2s−1(Gregg et al., 2011) and isopycnal diffusivity KI = 2 m2s−1 (Ledwell et al., 1998).Symbol Definition Description Barkley Canyon estimatePehLU∗KIHorizontal Peclet number 2:1×102PevZΩKDVertical Peclet number 1:2K Z2L2KIKDDiffusivity ratio 5:9×10−3G ZLdvCdhC Gradient ratio Tracer dependentthL2d 2hCZdvC Horizontal curvature to vertical gradient ratio Tracer dependenttv −Zd2vCdvC Vertical curvature to gradient ratio Tracer dependentand horizontal processes are decoupled. According to the Buckingham-P theorem (Kundu andCohen, 2004) there are six non-dimensional groups that dynamically represent the system (Table2.5).In terms of these non-dimensional numbers, the advection-diffusion equation (2.12) for thesteady state can be expressed in non-dimensional form asKPehGu′(¶C¶ s)′+Pevw′(¶C¶ z)′= Kth[(¶ 2C¶ s2)′+2(¶ 2C¶ z¶ s¶ z¶t)′]− tv[(¶ 2C¶ z2)′+2(¶ 2C¶ z¶ s¶ s¶h)′]; (2.13)where the primed variables are non-dimensional, e.g. u′= u(U∗)−1, (¶C=¶ s)′=(¶C=¶ s)(dhC)−1,etc.I estimate the scales U∗, Z and Ω, given by (2.7), (2.8) and (2.9), respectively, using as a test37case Barkley Canyon. The relative importance of each parameter can be drawn from the values ofthese non-dimensional quantities (Table 2.5).Horizontal advection will dominate over isopycnal diffusivity (Peh >> 1) and so we did notinclude it in the parameter space of our experiments. On the other hand, vertical advection and ver-tical diffusivity are both relevant for this flow (Pev ≈O(1)). Finally, the effect of vertical diffusivityis locally larger than that of isopycnal diffusivity (K << 1).Non-dimensional numbers G, th and tv represent the competition between geometric character-istics of the initial vertical and horizontal tracer profiles.2.4.3 Stratification and tracer gradient evolutionIn our system, the evolution of isopycnals during canyon-induced upwelling is very similar to thatof tracer iso-concentration lines, as shown in section 2.3.2; thus, vertical tracer gradient and strati-fication evolve similarly.During the advective phase of upwelling, isopycnals will squeeze near the head of the canyon,increasing the stratification with respect to the initial value (Figure 2.8). Near the downstream sideof the canyon rim the amplification of stratification (the “squeezing”) can be expressed asS=N2N20; (2.14)where S is the squeezing, N2 is the stratification near the rim during the advective phase of upwellingand N20 is the initial stratification at the same location. Let us consider the deepest isopycnal thatupwells onto the shelf r(Z) and a density contour above the canyon rim that is mostly unaffectedby canyon upwelling, r(h) (Figure 2.8). By definition, r(Z) is initially at depth Z+Hh and r(h)is at depth h with h << Hh since the effect of the canyon is felt close to the surface (Shallow shelfassumption in Allen and Hickey (2010)); during the advective phase of upwelling, r(Z) rises toapproximately depth Hh while r(h) stays at h. Given these scales, we can approximate S asS =N2N20≈(∆rHh−h)(∆rHh+Z−h)−1= 1+ZHh−h≈ 1+ ZHh; (2.15)where ∆r = r(Z)− r(h). The last step comes from the fact that h << Hh. Additionally, theenhanced, non-uniform stratification will be diffused as a function of time and the local value of Kv.38LHz=0cross-shorezcanyon axisslopeSqueezinggcankbg> kcanH Hrh(a)Figure 2.8: (a) Isopycnals (gray lines) tilt towards the canyon head during a canyon-inducedupwelling event. This tilt is proportional to the upwelling depth Z, defined as the dis-placement of the deepest isopycnal to upwell onto the shelf (heavy, green line). Locallyenhanced vertical diffusivityKcan compared to the background valueKbg further squeezesisopycnals above rim depth (canyon rim represented by the dashed line) and in turn, fur-ther stretches isopycnals below rim depth. The squeezing effect is proportional to thecharacteristic length Zdi f (2.19). (b) Zoom in of the red square keeping only two isopy-cnals: the heavy, dark green line is the deepest isopycnal that upwells onto the shelf andthe grey one is a reference isopycnal. The light green line represents the deepest isopy-cnal that upwells when diffusivity is homogeneous everywhere (base case). The extradisplacement of this isopycnal when diffusivity is locally-enhanced is the scale Zdi f .For smoother Kv profiles (e > 5 m), Kv is larger than Kbg above the rim and the effect of diffusionover the enhanced stratification will be larger. I find that the effect of S and the local diffusivity KZcan be expressed asSupw =ZHhexp(−KZtZ2); (2.16)39where, KZ is the diffusivity Kv evaluated at a distance Z above or below the canyon rim, dependingon the region of interest.If diffusivity within the canyon is high enough that the time scale on which diffusion acts ison the order of the duration of the upwelling event, enhanced Kcan with respect to the backgroundvalue Kbg will increase the squeezing by further diffusing the density gradient above rim depth andthus decrease it below rim depth (Figure 2.8, lower panel). Consider the case without advection,only diffusion acting on the tracer gradient, and the same linear concentration profile. The top partof the water column, above rim depth, has diffusivity Kbg and the bottom part, below rim depth,has diffusivity Kcan, with Kbg < Kcan. Right at the rim, the change in concentration is driven by thedifference in diffusive fluxes given by Kcan¶r=¶ z−Kbg¶r=¶ z. We know that, initially, the densityderivatives above and below rim depth are the same (¶ri=¶ z), given the initial conditions I imposed,so the flux from below is larger than the flux from above. The flux mismatch increases the densityat the rim. We can estimate the diffusion equation at the rim as¶r¶ t=¶¶ z[(Kcan−Kbg)¶ri¶ z]: (2.17)Assuming that the changes in density in time are of the same order as the density changes aroundthe rim, we can approximate (2.17) by evaluating Kv just above and below the rim∆r∆t≈[Kv(Hr+ dz2)−Kv (Hr− dz2 )]∆z¶ri¶ z; (2.18)whereHr is the rim depth and ∆z>> dz. So, after a time t =∆t and approximating ¶ri=¶ z=∆r=∆za length scale for diffusion Zdi f = ∆z is given byZdi f ≈[{Kv(Hr+dz2)−Kv(Hr− dz2)}t]1=2: (2.19)Physically, Zdi f is the initial depth of the isopycnal that reaches rim depth at time t . Another way tounderstand Zdi f is as the depth that the region with mismatched flux has extended below the rim. Inthe canyon, advection is the main driver of tracer contour upwelling but, if the difference betweenKbg and Kcan is large enough, in just a few days diffusivity can equally contribute to the verticaldisplacement of isopycnals (Zdi f ≈ Z).The extra squeezing and stretching effect of enhanced Kcan is then characterized by the lengthscale Zdi f (Figure 2.8, top panel). Note that if Kcan = Kbg there is no extra diffusion and Zdi f = 0. Iused a 1D model of diffusion (Appendix D) to find the relationship between Zdi f and the stretchingof the tracer gradient below the rim, which is the exponential function (Figure D.1 g):S−di f = exp(−0:15Zdi f∆z); (2.20)40where Zdi f is given by (2.19) with ∆z the vertical resolution of the 1D model (0.25 m).The diffusion-driven squeezing above the rim has a similar functional form as the upwelling-driven squeezing (2.16), in this case using the diffusion distance Zdi f , the depth scale ∆z (5 m forour model) and the length scale e :S+di f =Zdi f∆Zexp(−K+Z te2); (2.21)where K+Z is the local diffusivity above the rim, as defined for (2.16). Taking into considerationboth, the effect of advection (2.16) and diffusion the total density squeezing is scaled asN2maxN20= max(N2N20)≈ A1S+upw+B1S+di f +C1; (2.22)where S+upw is a function of K+Z , A1=7.35, B1=0.21 and C1=0.82 are best-fit parameters to a multi-variable linear regression. Similarly, the total tracer squeezing is scaled as¶zCmax¶zC0= max(¶zC¶zC0)≈ A2S+upw+B2S+di f +C2; (2.23)where A2 = 7:30, B2 = 0:23 andC2 = 0:82.The stretching of isopycnals is scaled asN2minN20= min(N2N20)≈ A3S−upw+B3(1−S−di f )+C3; (2.24)where A3 = 2:72, B3 = 2:19 and C3 = −1:13. The estimates compare well with the maximum andminimum stratification (Figure 2.9 a and b) and tracer gradient near the canyon head (not shown).2.4.4 Average tracer concentrationThe uplift of iso-concentration lines near rim depth provides higher tracer mass on the shelf, es-pecially when kcan is enhanced (Figure 2.3g). Thus, I approximate the relative increase in tracerconcentration in the vicinity of the rim, just above rim depth, as a function similar to the squeezingof tracer contours:C¯C0= A4S+upw+B4S+di f +C4: (2.25)41where C0 is the initial concentration at rim depth, and the coefficients A4 = 0:33 and B4 = 0:06and C4 = 1:00 are proportionality constants. This compares well with the mean concentration nearrim depth between days 4 and 9 (Figure 2.9c). For more realistic initial profiles the constant B4will probably be larger as vertical diffusivity of tracer will have a more prominent role for largergradients and curvatures in the profiles.2 4 6 87.35S+ + 0.21S+dif + 0.822345678max N2/N20Eqn. 22(a)0 1 2 32.72S− + 2.19(1− S−dif)  -1.130123min N2/N20Eqn. 24(b)base case↑  N0↑ ↑  N0⇓  N0↓ ↓N0↓  N0↑ f↓ ↓  f↓ f⇓ f↓  U↓ ↓  U⇓  U⇓  U, ↓ ↓  N0⇓  U, ↑ ↑  N0⇓  U, ⇓  f⇑ ⇑Kcan, ε10⇑ ⇑Kcan, ε25⇑ ⇑Kcan, ε50⇑ ⇑Kcan, ε100⇑ ⇑Kcan, ε15⇑ ⇑Kcan, ε75↑ ↑Kcan↑ ↑Kcan ε25↑ ↑Kcan ε100⇑ ↑Kcan⇑ ↑Kcan ε25⇑ ↑Kcan, ε100⇑ ↑ ↑Kcan⇑ ⇑ ↑Kcan⇑Kcan↑Kcan⇑ ⇑KcanKcan Monterey (bot)Kcan Eel (bot)Kcan MontereyKcan Ascension (bot)1.0 1.2 1.4 1.6̄C /C01.01.11.21.31.41.51.6Crim model /C0Eqn. 25(c)8 10 12 14Neff scaled / 10−̄ s−18101214Neff model / 10−̄ s−1Eqn. 27(d)Figure 2.9: Scaling estimates of maximum stratification Nmax above the canyon (a), minimumstratification below rim depth Nmin (b), tracer concentration just above rim depth Hr (c),and effective stratification Ne f f = 0:75Nmax+ 0:25Nmin (d). Dashed lines correspond to± one mean squared error.2.4.5 Upwelling and tracer fluxesThe scaling estimates by Allen and Hickey (2010) state that the dimensionless upwelling fluxF=(WmUDh) is proportional to F3=2R1=2L . Moreover, Howatt and Allen (2013) corrected this es-timate to account for the impact of a sloping shelf, since, in a stratified water column, the water42upwelled on the continental shelf slope adds pressure that inhibits upwelling, and reduces the up-welling depth and the upwelling flux. Their estimate isFWUDh= 0:9F3=2w R1=2L (1−1:21SE)3+0:07; (2.26)where W is the canyon width at mid-canyon length; the function Fw = RW=(0:9+RW ) is similarto F but uses the Rossby number RW =U= fWs, whereWs is the width at mid-length measured atshelf-break depth. The slope effect is encapsulated in the function SE = sN0= f (Fw=RL)1=2, where sis the shelf slope (s=0.01 for all runs here).I found that locally-enhanced diffusivity has an effect on the upwelling flux: lower stratificationin the canyon allows more water to upwell while high stratification above rim depth acts like a ‘lid’to suppress upwelling. I propose the effective stratification Ne f f as the scale for stratification in(2.26) to account for the effect of enhanced Kcan and e where Ne f f is defined asNe f f = (0:75Nmax+0:25Nmin); (2.27)where Nmax and Nmin are the maximum (2.22) and minimum (2.24) stratification above and belowrim depth, respectively (Figure 2.9d). This givesFWUDe f f= 4:98F3=2w R1=2L (1−0:52SE)3−0:01; (2.28)where De f f = f LN−1e f f and the coefficients were re-fitted to satisfy the equation. Note that Ne f f isonly used to calculate the depth scale De f f . This estimate compares well with the mean upwellingflux calculated from days 4 to 9 (Figure 2.10a and Table B.2). Upwelling flux increases by approx-imately 19% with respect to the base case for the largest Kcan case (Table 2.4, column 2).In section 2.3.4 I found that the tracer flux upwelled onto the shelf by the canyon is directlyproportional the upwelled water flux. Consequently, we approximate the total upwelled tracer fluxas the product of the upwelling flux (2.28) and the average tracer concentration near rim depthwithin the canyon (2.25):FTr = A5C¯F+B5: (2.29)where A5 = 1:00 and B5 = −718:86 mMm3s−1 are best-fit, least-square parameters. This estimatecompares well with the mean upwelled tracer flux calculated from days 4 to 9 shown in column 3of Table B.2 (Figure 2.10b). The relatively larger concentration near the canyon rim characterizesthe increased tracer mass flux when vertical diffusivity is enhanced locally (27% for the largest Kcancase) while the lower Nmin enhances the upwelling flux of water. My scaling estimate successfullyquantifies these effects (2.10b).I included five runs with Kv profiles inspired in observations to provide context to the scaling430 2 4 6Φ / 104 m3s−101234567Upwelling flux / 104 m3s−1Eqn. 28(a)0 1 2 3 4 5ΦTr / 105 μMm3s−1012345Tracer flux / 105 μMm3s−1Eqn. 29(b)Figure 2.10: Scaling estimates of upwelling flux of water (a) and upwelling flux of tracer (b)through a submarine canyon. Dashed lines correspond to ± one mean squared error.Run legend same as for Figure 2.9.(Figure 2.10 a and b, blue markers). My scaling works well when using less idealized profiles, butit cannot be applied to profiles with Kcan < Kbg because the scale Zdi f is not defined. Nonetheless,these cases demonstrate that our scaling is robust enough to work with non-smooth profiles as theones that could be measured in a canyon. Additional smoothing of measured profiles could be doneto apply the scaling. See Appendix D for the methodology followed to develop these runs.2.5 Discussion and conclusionsAdvection-induced upwelling of water through a canyon is the dominant driver of on-shelf transportof tracer mass from the open ocean, however, the tracer concentration profile and enhanced verticaldiffusivity within the canyon contribute considerably to the amount and spatial distribution of thetracer on shelf. The main characteristics of canyon-induced tracer upwelling are the following(Figure 2.11):1. The upwelling flux carries tracer onto the shelf near the head and the downstream side ofthe canyon rim, to be further spread on the shelf; with decreasing Bu and increasing RW ,the amount transported is larger. Also, for a tracer profile that increases with depth, a largerupwelling depth will bring water with higher concentration onto the shelf; with decreasing Buand increasing RW , the depth of upwelling is larger.442. Locally-enhanced mixing weakens the stratification below rim depth. A smaller stratificationincreases the vertical advective transport of water and thus, of tracers. The mechanism is thatisopycnals close to the head are squeezed due to upwelling, which generates a local increase instratification proportional to the isopycnal tilting generated by upwelling. However, enhanceddiffusivity acts against temperature and salinity gradients, thus reducing this density gradientand locally reducing stratification below the rim. The combined effect of lower N and higherdiffusivity below the rim via a smoother Kv profile (larger e) can increase the water flux byup to 26% for values chosen in this study.3. Enhanced mixing within the canyon increases the tracer concentration near rim depth. Justabove rim depth, where the value of Kcan changes, the tracer gradient increases. This meansthat concentration isolines are higher compared to the situation with uniform diffusivity andin turn, isolines of higher concentrations will be reaching rim depth. This water with highertracer concentration will upwell. Together, this mechanism and 2 above increase the tracerflux onto the shelf. For instance, taken together both contributions can increase tracer up-welling flux by 27% when Kcan is locally enhanced by three orders of magnitude.4. The upwelled water spreads out on the shelf, downstream of the rim and generates a regionof relatively larger tracer concentration near the bottom.For comparison, Messie´ et al. (2009) estimated that the wind-driven nitrate supply for the North-ern Washington Shelf is 6.4 mmol s−1m−1. This corresponds to 153 mol s−1 across a shelf sectionof lengthWm = 24 km, the width of the canyon, while the tracer upwelled through the canyon forthe base case is 160 mol s−1. Considering that the ‘nitrate’ concentration of the upwelled water inthe model is about 4 times smaller than it would be in a coastal environment like the West Coastof Vancouver Island, then the canyon supplies 4 times more nitrate than wind-driven upwelling.For a typical Kcan profile, enhanced diffusivity increases the transport by 25%, thus increasing thetransport by an amount similar to wind-driven upwelling.2.5.1 Implications for internal wavesEnhanced, upwelling-induced stratification near rim depth observed in our numerical results canpotentially alter the propagating characteristics of internal waves in the canyon by two mechanisms.First, canyons are known to focus internal waves towards the canyon floor. Their wedge-shapedtopography is supercritical to the most energetic type of internal waves found on the nearby-shelf(Gordon and Marshall, 1976). Enhanced stratification near rim depth, close to the canyon head,can increase the criticality, a , of the upper canyon walls given that it is dependent on the buoyancyfrequency N.The second mechanism is the transition between a partly standing wave during pre-upwellingconditions to propagating during upwelling conditions. This effect has been observed (Zhao et al.,45Upwelling currentUpwelled tracerEnhanced mixingHigh C poolUpstreamprofileDownstreamprofileFigure 2.11: Schematics of tracer transport through a submarine canyon: 1) The upwellingcurrent (blue arrow) brings tracer-rich water onto the shelf, generating an area of rela-tively higher tracer concentration than the upstream shelf (4). Enhanced vertical diffu-sivity within the canyon (2 and 3) increases the tracer concentration near rim depth andweakens the stratification. These two effects enhance canyon-induced tracer flux ontothe shelf.2012) and modelled (Hall et al., 2014) for the M2, mode 1 internal tide in Monterey Canyon. Dur-ing pre-upwelling conditions, the pycnocline was located below rim depth, which increased thesupercritical reflections (down-canyon) of the up-canyon propagating internal tide. During up-welling conditions, the pycnocline rose above rim depth, decreasing the stratification and with it,the supercriticality of the canyon walls. This decreased stratification decreased the reflection ofthe up-canyon propagating tide. The comparatively large reflection during pre-upwelling condi-tions allowed for a horizontally, partly-standing wave set up, while upwelling conditions caused aprogressive up-canyon wave to dominate.In the model, maximum stratification within the canyon and near the rim is a consequence ofshelf-break and canyon-induced upwelling where isopycnals tilt towards the canyon head, squeezingcloser together around rim depth, not too far above the canyon walls. This enhanced stratification46could push the reflecting characteristics of the canyon walls or bottom towards the supercriticalregime as results from Zhao et al. (2012) and Hall et al. (2014) suggest. Moreover, my resultsshow that having elevated diffusivity within the canyon will erode the increased, canyon-inducedstratification below rim depth and enhance it above rim depth. If we assume that the stratificationthat matters for criticality occurs around rim depth, then the competition between squeezing andstratification erosion will determine the change in criticality. Close above the rim we see stratifica-tion (N2) increasing up to 5 times due to canyon-induced upwelling and up to 7.5 times when Kv islocally-enhanced, which could translate in a change in a from 0.4 to 0.8 - 1.0 (for 5N20 and 7:5N20 ,respectively) alongshelf, and from 1.4 to 3.1-3.9 near the canyon head along the axis. Below rimdepth, enhanced diffusivity can erode the isopycnal squeezing to be 0.3N20 , decreasing the maximumvalue of a alongshelf from supercritical to subcritical (1.4 to 0.8).Upwelling in short canyons is stronger on the downstream half of the canyon and thus, theeroding effect of enhanced diffusivity over increased stratification will also be stronger there dueto the large upwelling-generated gradients. So, the change in criticality will be impacted by thisasymmetry too. A larger shift towards supercriticality is to be expected on the downstream sideof the canyon, close to the head and strongly modulated by the difference in diffusivity below andabove rim depth. This shift will also influence the location of internal wave breaking and, as aconsequence, where vertical diffusivity is enhanced.2.5.2 Extension to other canyonsThe diffusivity-driven weakening of vertical gradients is a function of time. There is a natural timescale in which diffusivity acts on vertical gradients given a characteristic length scale, for example,the upwelling depth. The larger the diffusivity the smaller the time scale given the same lengthscale. We find that diffusivities of around O(10−3 m2s−1) or above are sufficiently high to noticeablyweaken stratification and tracer gradient in the first 4 days. This means that when the flow entersthe advective phase, the effects of high Kcan are already noticeable. Enhanced diffusivity continuesto act on the gradients during the advective phase but the effect weakens as it is proportional to thegradient itself. In canyons such as Monterey, where diffusivities are on the order of 10−2 m2s−1,the weakened gradients would be considerable after only 11 hours, assuming a depth of upwellingof about 20 m.My results and overall scaling scheme are valid only for short canyons, which are canyons forwhich the canyon head occurs well before the coast (Allen, 2000). This criterion removes someof the most iconic canyons, like Monterey and Nazare´ Canyons. For canyons not in the Allen andHickey (2010) scaling, we expect that, provided there is squeezing of isopycnals and a differencein diffusivity above and below the rim, the same effect of non-uniform diffusivity would occur: thelocally-enhanced diffusivity will act to further enhance the stratification above the rim and furtherdecrease it below the rim. The tracer part of the scaling would be similar but an appropriate depth47of upwelling, Z, and fitting parameters would need to be found. For less idealized bathymetries theoverall upwelling pattern is expected to be very similar, provided that the incoming flow is alongthe shelf, perpendicular to the canyon axis, and relatively uniform along the length of the canyon.Scaling of the upwelling flux and depth of upwelling is robust enough that it has been successfullyapplied to real, short canyons like Astoria, Barkley and Quinault Canyons (Allen and Hickey (2010))and in one of the limbs of Whittard Canyon (Porter et al., 2016).Runs with longer canyons (2 times and 1.5 times longer than our original canyon) show that thegeneral circulation pattern and evolution of the upwelling event is similar to the original canyon.Isopycnals and iso-concentration lines tilt towards the canyon head similarly for both canyons, sothat squeezing of isopycnals happens close to the head in both cases. The stratification evolu-tion near canyon head, on the downstream side of the canyon is also similar for longer canyons.Moreover, having locally-enhanced diffusivity within the canyons has the same effect on isopycnalsqueezing near the canyon head as in the original canyon. Locally-enhanced diffusivity increasesthe near-rim depth concentration in all three cases compared to the case with uniform diffusivity andthe concentration is well predicted by Equation 2.25 with root mean square error 0.04 compared to0.03 for the single canyon. These runs show that the effect of diffusivity can be applied to othercanyons, whenever there is isopycnal squeezing and different diffusivities above and below the rim.The tracer mass flux scaling estimated in this work is restricted to flows that follow the sameconditions as Allen and Hickey (2010) and Howatt and Allen (2013) because it depends on theirupwelling flux estimation and as such, it can only perform as good as their estimate. The maincontribution of my scaling scheme is the estimation of tracer concentration and stratification withinthe canyon. My scaling preformed reasonably well when we used it on runs with Kv profiles inspiredby observations.2.5.3 Significance to upwelling nutrientsConnolly and Hickey (2014) estimated that canyon-exported nitrate onto the shelf after two monthsduring an upwelling season can be about 1-2×107 kg NO−3 . I found that after a single upwellingevent (9 days) the canyon can increase the total inventory of tracer mass on the shelf by 0.3-4.7×106kg NO−3 compared to a straight shelf case. If we consider a 60 day upwelling period, then the canyoncontribution to the tracer inventory could be up to 3×107 kg NO−3 . Additionally, after a canyonupwelling event, between 24 and 89% of the upwelled tracer mass on the shelf can be canyonupwelled, given a canyon with a width that represents about 5% of the shelf length and dependingon the dynamical characteristics of the flow.48Chapter 3Cross-Shelf Transport and Distributionof Nutrients and Dissolved GassesInduced by a Submarine Canyon3.1 IntroductionIn chapter 2 I investigated the impact of locally-enhanced mixing in canyon-induced upwelling. Inthis chapter, I investigate the effect of the initial geometry of a tracer profile on the on-shelf distri-bution of that tracer after an upwelling event, and I discuss the impact of the canyon on the oxygenand carbon levels near the adjacent shelf bottom. To that end, I model an upwelling event on ashelf incised by an idealized submarine canyon using realistic initial vertical profiles of 10 differentpassive tracers (nutrients, dissolved gases, carbon, and oxygen), and analyse the canyon-induced up-welling flux, net on-shelf transport, and final on-shelf distribution of these tracers. These numericalsimulations differ from the simulations in Chapter 2 in four aspects: First, I use two different ide-alized bathymetries based on Astoria Canyon and Barkley Canyon’s dimensions; second, for eachbathymetry there is a base case and a realistic case based on hydrographic observations around eachcanyon; third, there are no locally-enhanced diffusivity runs; finally, there are 10 passive tracerswith initial profiles based on nutrients and dissolved gasses measured along Barkley Canyon. Thereis no overlap between the numerical experiments discussed in Chapter 2 and numerical experimentsin this chapter.The structure of this chapter is as follows. The numerical configuration and experiments areexplained in section 3.2; the flow dynamics of the canyon are described in section 3.3.1; the cross-shelf transport, on-shelf distribution and canyon-induced upwelling of tracers are reported in sec-tions 3.3.2, 3.3.3, 3.3.4, respectively; scaling estimates for the amount of tracer upwelled onto theshelf by the canyon and the on-shelf distribution of tracer are derived in section 3.4, and finally,49discussion and summary of this chapter’s findings are presented in 3.5.This chapter was submitted for publication as Ramos-Musalem, K. and S. E. Allen, The impactof initial profile on the exchange and on-shelf distribution of tracers induced by a submarine canyon.3.2 Methods3.2.1 The modelIn this chapter I also use MITGCM (Marshall et al., 1997) with a similar configuration as in Chapter2 but in this chapter I initialize ten different passive tracers instead of one. Model simulations use abathymetry which consists of a sloping continental shelf cut by an idealized submarine canyon andforce shelf currents that flow southward from the northern side of the domain (i.e. in the upwelling-favourable direction), parallel to the shelf (Figure 3.1). The simulations start from rest and havea run duration of 9 simulation days as before. A shelf current is spun-up by applying an along-shelf body force directed southward on every cell of the domain to produce similar effects as thosethat result from changing the rotation rate of a rotating table (Spurgin and Allen, 2014). The bodyforcing ramps up linearly during the first simulation day, remains constant for the second simulationday, and ramps down to a minimum forcing strength on the third day, after which it remains constantto avoid spin-down of the shelf currents. This forcing generates a deeper shelf current, less focusedon the surface, than the coastal jet generated by wind-forced models.The domain is 280 km alongshelf and 110 km across-shelf divided in 616x360 cells horizontally.The cell width increases smoothly alongshelf and cross-shelf, from 115 m over the canyon to 437 mat the west boundary, and to 630 m at a distance of 60 upstream and downstream of the canyonand then is uniform to the downstream boundary. Vertically, the domain is divided into 104 z-levelsspanning a maximum depth of 1200 m, with grid sizes increasing smoothly from 5 m (surface to260 m) to 20 m at depth. The time step used was 40 s, with no distinction between baroclinic andbarotropic time steps. The experiments ran in hydrostatic mode. Some runs were also repeated innon-hydrostatic mode with no significant differences in the results.I ran experiments with two different idealized canyons with geometric parameters (Figure 3.1)similar to those of Barkley Canyon and Astoria Canyon, respectively. The bathymetries were con-structed from a hyperbolic tangent function.The domain has open boundaries at the coast (east) and deep ocean (west). Open boundariesuse Orlanski radiation conditions without a sponge layer. At the bottom, boundary conditions arefree-slip using a quadratic bottom drag with coefficient 0.002. At the vertical walls of the modelbathymetry steps, boundary conditions are free-slip. North and south boundaries are periodic. Thealongshelf width of the model domain is sufficiently large to avoid the recirculation of water throughthe canyon. However, barotropic Kelvin waves, first and second mode baroclinic Kelvin waves,and long wavelength shelf waves do recirculate through the domain as in previous studies with505 10 15T / C(d)ARGOBARPATH32 34S / g kg 110008006004002000AST(e)30 40 50 60 70 80C-S distance / km5004003002001000Depth / m(a)0 50 100 150Alongshelf distance / km020406080100C-S distance / km(c)28050 55 60 65 70Alongshelf distance / km506070C-S / km(b)0100200300400500600700Depth / mIncoming flowCS1 CS2CS3CS4 CS5 CS6LIDCS3AstoriaLIDLIDCS3Barkley LWsWWmRN SWEFigure 3.1: (a) Cross-shelf section showing depth profiles of the shelf (dashed) and canyonaxis (solid) for Astoria-like (black) and Barkley-like (orange) bathymetries. Gray andpeach lines correspond to the location of cross-sections CS3 and LID for Astoria-likeand Barkley-like bathymetries, respectively. (b) Top view of Astoria-like (colormap) andBakley-like (orange contours) bathymetries with shelf break isobaths in black. Dimen-sions of Astoria-like bathymetry in purple correspond to the cross-shelf length of thecanyon from head to mouth L=21.8 km; Ws=8.0 km and Wm=15.7 km the alongshelfwidths at mid-length at shelf break depth and mouth, respectively; and R=4.5 km, theupstream radius of curvature. Barkley Canyon dimensions are L=6.4 km, Ws=8.3 km,Wm=13.0 km and R=5.0 km. (c) Top view of the Astoria-like domain with depth con-tours 20, 100, 200, 400, 600, 800, 1000, 1200 m. The solid black line corresponds tothe shelf break isobath along which I defined the cross-sections CS1-CS6 to calculatecross-shelf transport. The horizontal section LID was used to calculate vertical transportthrough the canyon. (e, f) Temperature and salinity profiles for all runs. Gray and blackdotted lines indicate the shelf break depth for Barkley-like and Astoria-like bathymetries,respectively.51Table 3.1: All experiments were initialized with 10 passive tracers (Table 3.2). Active tracerprofiles, temperature and salinity, vary between runs. Stratification for ARGO and PATHexperiments corresponds to the mean stratification through the upwelling depth (about100 m below head depth) following Allen and Hickey (2010). For every run there is acorresponding no-canyon case.Experiment Bathymetry Active tracers N0 (10−3 s−1) f (10−4 s−1) U (ms−1)AST Astoria linear 5.5 1.00 0.30BAR Barkley linear 5.5 1.00 0.30ARGO Astoria ARGO float 9.9 1.05 0.33PATH Barkley Pathways 3.8 1.08 0.29similar configurations (e.g., Dinniman and Klinck, 2002; Ramos-Musalem and Allen, 2019; She andKlinck, 2000). Subinertial shelf-waves of wavelength likely to be excited by the canyon (l ≈ 2Wm)Zhang and Lentz (2017) are too slow to recirculate with speeds AST 0.07 ms−1, BAR 0.04 ms−1,ARGO -0.04 ms−1 and PATH 0.02 ms−1 against the mean incoming flow (Calculated using Brink,2006).Four types of experiments were conducted (Table 3.1) using either Astoria-like or Barkley-likebathymetry and either idealized or realistic profiles of temperature and salinity. None of the runsreported in Table 3.1 overlap with runs analysed in Chapter 2 (Tables 3.1 and 2.2). Control runsfor Astoria-like and Barkley-like bathymetry (AST and BAR in Table 3.1) use initial fields of tem-perature and salinity that vary linearly in the vertical (Figure 3.1 d,e). To compare the effect of thecanyon on tracers in a more realistic scenario, I did two runs using temperature and salinity profilesfrom observations (ARGO and PATH runs in Table 3.1). For ARGO (Astoria-like bathymetry) Iused temperature and salinity profiles from ARGO platform 5903601 (cast 94, 2014-05-31) at themouth of Astoria Canyon. These data were collected and made freely available by the InternationalArgo Program and the Coriolis project (http://www.argo.ucsd.edu, https://www.coriolis.eu.org). ForPATH (Barkley-like bathymetry) I used temperature and salinity profiles from the Pathways Cruise(Klymak et al., 2013) (see section 3.2.2) averaged along canyon axis stations. The circulation aroundboth canyons using realistic stratification is similar to that around the corresponding counterpartswith linear stratification, except near the surface where the effect of the canyon topography on theflow is less pronounced. In all runs temperature and salinity are initially horizontally homogeneous.Notably, for all aforementioned runs (hereafter referred to as canyon cases), I conducted corre-sponding runs with identical conditions except that the bathymetry includes only a shelf and slopewhich are not incised by a canyon (hereafter referred to as no-canyon cases).520 25−1200−1000−800−600−400−2000Depth / m(a)Linear32 34(b)Salinty (g/kg)0 250(c)Oxygen0 20 40(d)Nitrate50 100(e)DS20.0 22.5 25.0σθ / kg m−3(f)Densit.0.0 2.5C / μM/1200/1000/800/600/400/2000Depth / m(g)Phosphate0.010.020.03C /μM(h)Nitrous O−ide0.02 0.04C /μM(i)Methane0 250C­C0 / μM(j)DICμs A μs B 0 200C­C0 / μM(k)Alkalinit.0 25N / 10−3s−1(l)ASTARGOBARPATHFigure 3.2: (a-e, g-k) Initial tracer profiles for all tracers used in the simulations. Dotted anddashed gray lines correspond to the shelf-break depth for the Astoria Canyon and BarkleyCanyon bathymetries, respectively. (f) Initial density sq and (l) buoyancy frequency Nprofiles for the four runs analysed in this chapter.3.2.2 TracersIn this chapter I explore the impact of realistic tracer profiles with different geometric features froma linear tracer on the canyon-induced exchange of tracers (Figure 3.2 and Table 3.2). To do this,ten passive tracers were introduced from the beginning of the simulations with vertical profiles ofsalinity, nitrate, Dissolved Silicon (DS), phosphate, dissolved oxygen, Dissolved Inorganic Carbon(DIC) and total alkalinity collected during the Pathways Cruise in summer, 2013 in Barkley Canyon(Klymak et al., 2013); with vertical profiles of methane and nitrous oxide sampled along Line C,upstream of Barkley Canyon (Figure E.1) in May and September from 2012 and 2013 (Capelle andTortell, 2016) as well as a linear tracer.The Pathways campaign took place from August 18th to September 18th, 2013 on board of53Table 3.2: Initial concentration (Cs) and vertical gradient at shelf break depth (¶zC) for alltracers initialized in the four runs analysed in this chapter.Astoria-like Bathymetry Barkley-like BathymetryTracer Cs(mM)¶zC(mMm−1)Cs(mM)¶zC(mMm−1)Linear 7.2 3:6×10−2 9.0 3:6×10−2Oxygen 1:1×102 −2:9×10−1 86.6 -0.36Nitrate 32.6 3:8×10−2 34.9 4:4×10−2DS 47.6 8:5×10−2 52.5 0.11Phosphate 2.2 2:2×10−3 2.4 2:9×10−3DIC 2:3×103 0.67 2:3×103 0.25Alkalinity 2:3×103 0.17 2:3×103 0.17Nitrous-oxide 2:8×10−2 4:7×10−5 2:8×10−2 6:4×10−6Methane 1:8×10−2 2:4×10−4 3:6×10−2 2:3×10−4the R/V Falkor. The aim of the cruise was to study low-oxygen, acidic waters that form natu-rally in the deep sea off Vancouver Island. The western continental shelf of the Vancouver Islandwas extensively sampled during the Pathways Cruise. Data from a Moving Vessel Profiler (MVP),Acoustic Doppler Current Profiler (ADCP), Conductivity-Temperature-Pressure (CTD) sensors andbottle samples for nitrate, phosphate, oxygen, DS DIC and total alkalinity were collected for theWestVancouver Island Shelf. The campaign included 7 CTD stations along the axis of Barkley Canyon.Four of these stations also had bottle samples at various depths (Figure E.1). The vertical profilesmeasured at each station were interpolated and averaged to find a mean profile for the canyon region(Figure 3.2).3.2.3 Transport sectionsTo determine the pathways of water and tracers onto the shelf, I calculate their cross-shelf (CS) andvertical transports. I define CS transport of water as the volume of water per unit time that flowsacross the vertical planes (CS1-CS6) that extend from the shelf break in the no-canyon case to thesurface (Figure 3.1 a, c), while vertical transports flow across the horizontal plane (LID) delimitedby the shelf break depth in the canyon case and the canyon walls (Figure 3.1 a, c). I define the netor total water and tracer transport onto the shelf as the temporal mean during the advective phase,from days 4 to 9, of the sum of the water and tracer transports through cross sections CS1-CS6 andLID. I define the vertical water transport and tracer transport onto the shelf as the mean transportthrough LID during the advective phase. The flux and transport of tracers are derived as modeldiagnostics. The effect of the canyon on cross-shelf fluxes is defined as the flux anomaly betweencanyon and no-canyon cases (canyon contribution). Negative transports generally mean that either54water or tracer is leaving the shelf; it is only near the shelf bottom, where shelf upwelling is onshore,that negative transports mean that transport for the no-canyon case is larger than in the canyon case.3.2.4 Upwelling quantificationUpwelled water on the shelf has been estimated previously by finding water originally below shelf-break depth based on its salinity or concentration of a linear tracer (Howatt and Allen, 2013; Ramos-Musalem and Allen, 2019). I take a different approach, similarly as in Chapter 2, to calculate theupwelling flux of water F(t) by calculating the cross-shelf transport of water through cells alongthe shelf-break wall (CS2-CS5) and LID section (Figure 3.1a, 3.1c), with concentration of the lineartracer C larger or equal than the initial concentration at shelf break depth Cs. This algorithm onlyconsiders cross-shelf exchange of water that was originally below shelf-break depth by selectingcells with a concentration of linear tracer higher or equal than Cs:F(t) =åivi(t)ai whereCi(t)>Cs+åjw j(t)a j whereC j(t)>Cs; (3.1)where the first sum is over cells on sections (CS2-CS5) and the second sum over cells in the hori-zontal section LID, vi is the cross-shelf velocity at the i-th cell on the shelf wall (CS2-CS5), ai itsarea and Ci its concentration of linear tracer, wi is the vertical velocity of the i-th cell on sectionLID, a j its area and C j its concentration of linear tracer.Once the cells with upwelled water on the cross-shelf sections CS2-CS5 and LID have beenidentified, I calculate the flux of all 10 tracers through those selected cells. For any tracer withconcentration C , the upwelling tracer flux FTr is given byFTr(t) =åivi(t)Ci(t)ai where Ci(t)>Cs+åjw j(t)C j(t)a j whereC j(t)>Cs; (3.2)where vi, w j are the cross-shelf and vertical velocities at the i-th and j-th cells on the shelf wall(CS2-CS5) and LID sections, respectively; ai and a j their areas; Ci, C j their concentration of lineartracer; and Ci, C j their tracer concentration, respectively.I calculate the total amount of tracer mass for any given tracer on shelf at a given time ,M(t),by integrating the volume of each cell on the shelf multiplied by its tracer concentrationC(t):M(t) = åshel fC(t)∆V; (3.3)where ∆V is the volume of a cell on the shelf and C its concentration. This includes cells from thebottom of the shelf all the way to the surface and from the shelf break to the coast. M(t) reflects allprocesses and exchanges of mass at any depth and from any kind of water; it is the total inventoryof tracer on shelf.553.3 Results3.3.1 Canyon upwelling and circulationThe model starts from rest. During the first day, body forcing ramps up linearly; it is kept constantfor a day and ramps down to a lower value, just enough to prevent the generated slope current fromspinning down for the rest of the simulation. For the first four days the circulation within the canyonis strongly time-dependent (time dependent phase) and its response is linear (Allen, 1996) with theforcing. After day 4, the circulation is dominated by advection (advective phase). A rim deptheddy forms, circulation is cyclonic within the canyon and water upwells close to the canyon head,on the downstream side. The circulation and upwelling response to the forcing is similar for bothbathymetries, Astoria Canyon and Barkley Canyon and both idealized and realistic temperature andsalinity profiles. These results follow previous descriptions of upwelling in short canyons (e.g.,Allen et al., 2001; Howatt and Allen, 2013; Ramos-Musalem and Allen, 2019; Waterhouse et al.,2009). The main characteristics of canyon upwelling and circulation are more intense for AstoriaCanyon than for Barkley Canyon. Compared to Astoria Canyon runs, Barkley Canyon runs includenot only a shorter, narrower canyon, but also a deeper shelf break, both which reduce near-surfaceeffects in Barkley Canyon runs. The mean velocities of the coastal jet and slope current are higher inAstoria Canyon than in Barkley Canyon (Figure 3.3 c, g) but the magnitude of the incoming velocityU (i.e. the flow that encounters the canyon on its upstream rim) is the same, by construction, forboth canyons (Figure 3.3i). The incoming velocity U is the alongshore velocity upstream of thecanyon, above the bottom boundary layer, which has been identified as the relevant velocity scalefor canyon-induced upwelling (Allen and Hickey, 2010). The incoming shelf flow veers towardsthe canyon head when crossing over the canyon and slightly offshore on the downstream side ofthe canyon. This effect is more intense for Astoria Canyon runs than for Barkley Canyon runs(Figure 3.3 a, e).Upwelling within the canyon is forced by an unbalanced horizontal pressure gradient betweencanyon head and canyon mouth (Freeland and Denman, 1982). In response, a balancing, baroclinicpressure gradient is generated by rising isopycnals toward the canyon head (Figure 3.3 d and h).The advection of the tracer field is similar to the density (Figure3.3 d and h). Near the canyon rim,pinching of isopycnals occurs on the upstream side (Figure 3.3 b and f). This well-known featurehas been observed in Astoria Canyon (Hickey, 1997) and numerically simulated [e.g., Howatt andAllen (2013); Dawe and Allen (2010)].In the no-canyon case, shelf-break upwelling caused by on-shelf transport in the bottom Ekmanlayer brings water onto the shelf through a thin band along the shelf bottom (not shown). Elsewhere,above that band, water transport is off-shore. In the presence of a submarine canyon, water isalso upwelled through the canyon, mostly on the downstream side of the canyon, as seen fromvertical velocities and vertical transport through horizontal cross-section LID (Figure 3.3 a, e, j,56Figure 3.3: Advective phase (days 4-9) averages of (a, e) vertical velocity in color and hori-zontal velocity vectors at rim depth (mid-length depth), every 6th quiver is shown; (b, f)cross-shelf velocity in color (positive onto the shelf) and sq contours every 0.1 kg m−3at the canyon mouth; (c, g) alongshelf velocity at the canyon axis with positive velocitiesin the upwelling-favourable direction and (d, h) linear tracer concentration (color) andsq contours every 0.1 kg m−3 along the canyon axis. Top and middle rows correspondto AST and BAR runs, respectively. (i) Along shelf velocity averaged over the yellowrectangles in c and g. (j, k) Water transport across sections CS1-CS6 and net CS wa-ter transport for Astoria Canyon (j) and Barkley Canyon (k) runs, note the difference inscale.57k). Water is pushed onto the shelf, above the canyon more strongly closer to the shelf break depthand within the canyon, while shelf upwelling is suppressed just upstream of the canyon becausewater is redirected to upwell through the canyon (Figure 3.3 j, k). Cross-shelf transport of wateris on-shelf through the canyon lid (LID) and above the canyon (CS3), and balanced by the rest ofthe shelf (CS1,CS2,CS4,CS5,CS6) by mostly off-shelf transport. Small variations in net cross-shelfwater transport can be explained by variations in sea surface height. Vertical water transport andCS3 on-shelf transport peak around day 3, when maximum forcing has been reached, and decreaseslowly during the advective phase. This pattern is mimicked by off-shelf transport downstream ofthe canyon with a lag of half day. Water transports are higher through all cross-sections for AstoriaCanyon than for Barkley Canyon. The realistic run for Astoria Canyon (ARGO) has weaker watertransports than AST and there is little difference between Barkley Canyon (BAR) and its realisticrun, PATH, although the former tends to be slightly stronger.3.3.2 Cross-shelf transportIn this section I describe the pathways followed by the tracers as they are upwelled onto the shelfduring an upwelling event. Tracer transport is on-shelf and strong near shelf bottom and off-shelfand weak above the upwelling band. For tracers that increase with depth this means that highertracer concentrations are being transported onto the shelf while lower concentrations are exportedoff the shelf.Tracer transport onto the shelf occurs mostly above the canyon and through the canyon lidand right above the shelf break due to shelf-break upwelling (Figure 3.4 a1-e1). Off-shelf tracertransport occurs downstream of the canyon and above the shelf-break upwelling band both upstreamand downstream of the canyon (Figure 3.4 a1-e1).The main on-shore tracer transport patch and off-shore structure of tracer transport are similar towater transport (Figure 3.3j, k) but the vertical extent and finer structure depend on the initial tracerprofile (Differences in panels a− e Figure 3.4 1 and 2). The downstream offshore transport is asso-ciated with a stationary topographic Rossby wave, and as such, is very dependent on stratification.We see a different pattern in ARGO (not shown) but the mean flow is still off-shore downstream ofthe canyon. Due to the downstream vertical structure observed for water and thus, tracer transport,I ran AST in non-hydrostatic mode. For all tracers, net cross-shelf transport is slightly larger in thenon-hydrostatic case (not shown) but for each tracer the maximum difference is less than 0.3% ofthe mean transport.Considering the linear profile, tracer transport is onto the shelf through sections CS3 and LIDand mostly offshore upstream and downstream of the canyon (sections CS1, CS2, CS4, CS5, CS6)(Figure 3.4f1-f6) for all runs. The strong initial on-shore transport induced by the canyon throughLID and CS3 is mostly balanced by off-shore transport through CS4 but not completely. Upstreamof the canyon there is not much transport either onshore or offshore but downstream through CS6580 25 50 75 100 12515010050Depth/ m105M m3s 1Linear a155 60 65505560C-S distance / kma20.60.30.00.30.60.91.21.53.62.41.20.01.22.43.64.86.00 25 50 75 100 12515010050Depth/ m105mol kg 1 m3s 1Oxygen b155 60 65505560C-S distance / kmb21284048121620644832160163248640 25 50 75 100 12515010050Depth/ m105M m3s 1Nitrate c155 60 65505560C-S distance / kmc23.62.41.20.01.22.43.64.86.02015105051015200 25 50 75 100 12515010050Depth/ m105 nM m3s 1Methane d155 60 65505560C-S distance / kmd22101234512840481216200 25 50 75 100 125Alongshelf distance / km15010050Dept / m105mol kg 1 m3s 1DIC e155 60 65Alongs elf dist. / km505560C-S distance / kme2240160800801602403204001200900600300030060090012000246a37550250b30510c30102030d30 2 4 6 8Days0100200e30 3 6 9Days10010Transport / M m3s1f10 3 6 9Daysf20 3 6 9Daysf30 3 6 9Daysf40 3 6 9Daysf50 3 6 9Daysf6AstoriaARGOBarkleyPat waysCS1+CS2 CS3 CS6CS4+CS5CS1 NetFigure 3.4: Mean cross-shelf (a1-e1) and vertical (a2-e2) transport of linear tracer, oxygen,nitrate, methane and DIC (top to bottom) during the advective phase. (a3-e3) Canyoneffect on the net cross-shelf transport of tracer during the simulation for all runs with thesame units as given in left panel of each row. (f1-f6) Linear tracer transport through cross-sections CS1+CS2, CS3,CS4,CS5+CS6, LID, and net transport for all runs. Tracer trans-port onto the shelf occurs mostly above the canyon and through the canyon lid (canyoninduced) and right above the shelf break (shelf-break upwelling).59the sign of the transport depends on the run we look at.The net transport of linear tracer is onto the shelf and higher for Astoria Canyon runs than forBarkley Canyon runs and highest for Astoria Canyon with linear stratification (AST). It is maximumat day 3, when maximum forcing is reached, and then it decreases to be nearly constant after day 4during the advective phase (Figure 3.4 f6).This tracer transport pattern is similar for profiles of tracers that increase with depth such asmethane and nitrate (also for DS, phosphate and nitrous-oxide, not shown), with varying magnitudes.For DIC, the net transport is mostly balanced but strictly on-shelf (also for alkalinity and salinity,not shown). Given that oxygen has a decreasing profile, tracer transport is different from the othertracers. Although transport through CS3 and LID is onshore as for the other tracers, there is a largeroff-shore contribution from CS4 and CS6 for all runs so net oxygen transport is off-shore throughoutthe upwelling event. The maximum off-shore transport occurs at day 3 and after day 4 it is mostlyconstant. (Not shown).I calculate the canyon contribution to net cross-shelf tracer transport by subtracting the nettracer transport calculated for corresponding runs with no-canyon bathymetry (Figure 3.4 a3-e3).The residual from this anomaly is the canyon contribution. I look at the mean net CS transportduring the advective phase (Table 3.3 Mean NT) and the canyon contribution during that period oftime (shown as a percentage in table 3.3, Canyon Contribution). Additionally, I compare the meannet tracer transport in a run to the corresponding mean net tracer transport for the Astoria run (AST)(Table 3.3, Mean NT relative to AST).Net tracer transport is largest in AST followed by ARGO (70-80% of AST). Runs with BarkleyCanyon bathymetry have lower net transports for most tracers (BAR 34-71%, PATH 35-78%) exceptfor methane, which is very similar for ARGO, BAR and PATH. This general trend can be explainedby the vertical transport and cross-shelf transport of water through CS3 for each run, which arelargest for AST, followed by ARGO, PATH and BAR, and carry water with higher tracer concen-tration than the water that is leaving the shelf. Deviations in the net tracer transport from AST areexplained by the initial shape of the tracer profile. Net transport will be closer to zero, as for water,the more uniform the tracer profile is, but if the gradient close to the shelf break is large then thetransport will be larger. This impact is most evident for methane.Considering the impact of a canyon on total transport Astoria Canyon’s contribution to tracertransport is also larger than Barkley Canyon’s (Table 3.3). This can be explained by canyon up-welling scaling and seen in water transport anomaly. An example of this is that, even thoughmethane transport is similar for all runs, the contribution of Astoria Canyon is 42-58% but BarkleyCanyon’s is only 4-6%, showing that shelf break upwelling of methane is more important forBarkley Canyon and canyon upwelling of methane is more relevant for Astoria Canyon runs. Thelargest difference in net transport compared to AST is for DIC (Barkley is 55% of AST).As stated earlier in this section, the maximum net cross-shelf tracer transport occurs when the60Table 3.3: In columns 2-4: Mean net transport (NT), Mean NT relative to AST transport andcanyon contribution to Mean NT for selected tracers; in columns 5-7: Same as 2-4 butfor Maximum net transport (Max NT). Tracer transport units (TU) are mMm3s−1, mmolkg−1m3s−1, mMm3s−1, nMm3s−1, mmol kg−1m3s−1, where M=mol/L.Exp Mean NT(104 TU)Mean NTrelative toAST (%)Canyoncontribution%Max NT(104 TU)Max NTrelative toAST (%)Canyoncontribution%AST Lin 50.6 ± 3.4 100.0 52.6 83.2 100.0 80.2ARGO Lin 37.7 ± 2.0 74.4 37.2 57.7 69.4 65.0BAR Lin 28.1 ± 1.0 55.5 6.8 33.7 40.5 18.7PATH Lin 33.0 ± 1.5 65.2 12.0 40.5 48.7 24.3AST Oxy -644.9 ± 26.0 100.0 31.7 -60.6 100.0 36.4ARGO Oxy -515.1 ± 16.4 79.9 15.8 -59.7 98.3 32.6BAR Oxy -380.7 ± 14.0 59.0 1.9 -35.4 58.3 8.4PATH Oxy -429.6 ± 22.6 66.6 5.6 -38.8 63.8 9.3AST Nit 114.0 ± 5.0 100.0 42.9 168.3 100.0 76.9ARGO Nit 89.5 ± 4.3 78.5 29.5 127.8 75.9 57.2BAR Nit 56.5 ± 2.0 49.6 6.4 67.5 40.1 17.7PATH Nit 62.6 ± 3.3 54.9 8.4 78.4 46.6 18.8AST Met 0.19 ± 0.02 100.0 58.5 0.4 100.0 87.4ARGO Met 0.14 ± 0.01 71.7 42.2 0.3 66.6 80.9BAR Met 0.14 ± 0.01 71.3 4.6 0.2 46.9 17.5PATH Met 0.15 ± 0.01 78.0 6.8 0.2 52.4 20.4AST DIC 1928.1 ± 123.6 100.0 67.9 2377.0 100.0 85.8ARGO DIC 1433.1 ± 128.1 74.3 61.2 1856.9 78.1 63.6BAR DIC 664.4 ± 31.0 34.5 20.8 906.7 38.14 34.4PATH DIC 686.5 ± 36.1 35.6 19.3 981.7 41.30 32.8maximum body forcing is reached around day 3, during the time dependent phase of canyon-inducedupwelling. I look at this maximum (or minimum for oxygen) in tracer transport because it will beimportant to explain the near bottom tracer distribution later. As with the mean net transport, Ireport the maximum transport, the canyon contribution and the relative value with respect to AST(Table 3.3 columns 6 to 8 ). As with the mean net transport, the highest maximum occurs for AST,followed by ARGO, PATH and BAR but the canyon contribution is larger than for the mean, whichis consistent with the fact that the transport peak is induced by the canyon. The maximum followssimilar patterns to the mean except for methane which shows more discrepancy between ARGO,BAR and PATH.3.3.3 On-shelf tracer distributionIn the previous chapter, I described the distribution of tracer caused by canyon-induced upwellingfor a linear profile. I found that tracer is upwelled up onto the shelf by canyon-induced upwelling61of water and through vertical mixing. Water upwells on the downstream side of the canyon, nearthe head and close to the shelf bottom carrying deeper tracer with it. The upwelled water, havinghigher density, spills onto the downstream shelf forming a pool of water. In this chapter we see thatthe pool forms a dense, nutrient-rich, oxygen-depleted region on the downstream shelf. Above thislayer, tracer is being exported on-shelf near the canyon by the flow that veers towards the canyonhead and off-shelf by off-shelf water transport balancing shelf-break and canyon-induced upwelling.Bottom effectThe signature of the upwelled water is found close to shelf bottom, around the canyon rim and alongthe shelf break and is characterized by higher concentrations than background values (AnimationSI3, supplementary material and Figure 3.5 a, b). Tracer that is upwelled onto the shelf throughthe canyon forms a ‘pool’ near shelf bottom, downstream of the canyon. I define this pool as thecells, at shelf bottom, where tracer concentration is larger or equal to that initially at shelf breakdepth (C≥Cs). The horizontal extent of the pool at shelf bottom (bounded byC=Cs) is larger for allAstoria Canyon tracers than for Barkley Canyon tracers, because the amount of water upwelled islarger for Astoria Canyon and so more tracer is advected onto the shelf. The ARGO run has smallerpools than AST for the same reason.At the peak of the time dependent phase, on day 3, the pool builds up around the canyon rim,mostly on the downstream side and head of the canyon, with the highest concentration close to thehead (Animation SI3 supplementary material and, Figure 3.5 a, b). As with water, this pool growsfaster during the time-dependent phase and slower during the advective phase of upwelling (Figure3.6 a, c). Even though the pool is formed during the time-dependent phase, it is maintained duringthe advective phase and generally continues to grow. The pool is a feature of all tracers and itshorizontal extension strongly depends on the initial tracer profile and canyon bathymetry. Methaneon Astoria Canyon’s shelf has the largest pool, spanning an area 47 times the canyon area. Nitrate,oxygen and linear tracer profiles have similarly large pools spanning about 37 times the area ofAstoria Canyon while DIC has a smaller pool of 16 times Astoria Canyon’s area. For oxygen, thepool constitutes a low oxygen region. Maximum pool area and pool area at day 9 are reported inTable 3.4 columns 1 and 2.The vertical extent of the pool, delimited by the contour of value 1 (C=Cs = 1) consideringthe concentration normalized by the initial tracer concentration at shelf break depth, is between 10m and 40 m above the shelf bottom. For the linear tracer over Astoria Canyon, deviations fromthe initial tracer profile are identified up to 40 m above shelf bottom near the canyon head (virtualstation S1, Fig 3.5 c). Stations farther away from the head (S2, S3) show deviations up to 25m above shelf bottom. In BAR, deviations reach up to 20 m (Figure 3.5 d). This suggests thatthere is a stronger bulging of the pool near the canyon head for Astoria Canyon than for BarkleyCanyon. All tracers follow a similar pattern and although the pool’s vertical extension does not6260 80 100 120 140 160 180 200Alongshelf distance / km6080100Cross-shelf distance / kmASTORIA CANYON0.51.01.00.5 1.0 1.5C/Cs020406080100120140Height above bottom / mS10.5 1.0 1.5C/CsS20 d2 d4 d6 d8 d0.5 1.0 1.5C/CsS30.5 1.0 1.5C/CsS460 80 100 120 140 160 180 200Alongshelf distance / kmBARKLEY CANYON0.51.0 1.00.5 1.0C/Cs0306090120150180S10.5 1.0C/CsS20.5 1.0C/CsS30.5 1.0C/CsS460 80 100 120 140 160 180 200Alongshelf distance / km6080100Cross-shelf distance / kmS1S2S3S40.5 0.0C/Cs20406080100120140Height above bottom / mOxygen0.0 0.2C/CsNitrate0 1C/CsMethane0.000 0.025C/CsDIC60 80 100 120 140 160 180 200Alongshelf distance / mLinearOxygenNitrateMethaneDIC0.25 0.00C/Cs306090120150180Oxygen0.00 0.05C/CsNitrate0.00 0.25C/CsMethaneS1S2S3S40.00 0.01C/CsDIC0.20.40.60.81.01.21.41.61.8a bc1 c2 c3 c4 d1 d2 d3 d4feg1 g2 g3 g4 h1 h2 h3 h4Figure 3.5: (a,b) The pool of upwelled linear tracer (contour value 1) shown as the mean bot-tom concentration of linear tracer during advective phase,Cbottom, normalized by the ini-tial concentration at shelf breakCs. (c1-4, d1-4) Linear tracer profiles at days 0 through 8at virtual stations S1-S4 (black triangles) show the near-bottom impact of the pool. (e, f)The pool boundaries for 5 different tracers (contour 1 Cbottom=Cs) show the dependenceon the initial tracer profile. (g1-4, h1-4) Mean profiles showing changes from initial con-centration (∆C(z) =C(z)−C0(z)) at virtual stations S1-S4 during the advective phase.63Table 3.4: Pool area normalized by canyon area at day 9, maximum pool area, mean and max-imum pool concentration, and maximum change in concentration (%) from initial con-centration for selected tracers. Concentration units are mM, mmol/kg, mM, nM, mmol/kg.Results for other tracers are available in Table E.2.Tracer Apool=Acan atday 9Max(Apool=Acan)Mean Cpoolat day 9maxCpool max ∆Cpool(%)AST Lin 38.9 38.9 8.3 9.2 28.1ARGO Lin 22.8 22.8 8.3 8.7 20.7BAR Lin 6.6 11.2 9.8 9.9 10.3PATH Lin 23.5 23.5 10.1 10.4 15.4AST Oxy 35.3 35.3 96.2 86.7 -16.7ARGO Oxy 20.4 20.4 95.5 90.8 -12.7BAR Oxy 1.9 6.5 79.4 79.4 -6.4PATH Oxy 5.7 11.0 75.7 75.7 -10.7AST Nit 37.0 37.0 33.7 34.9 6.9ARGO Nit 21.9 21.9 33.8 34.3 5.2BAR Nit 3.1 7.7 35.7 35.8 2.4PATH Nit 9.2 14.6 36.1 36.1 3.5AST Met 47.3 47.3 25.6 32.4 85.4ARGO Met 32.9 32.9 24.9 29.6 69.2BAR Met 0.6 5.0 38.6 38.9 7.1PATH Met 1.2 7.5 38.4 39.2 8.1AST DIC 16.8 21.8 2233.4 2242.6 1.0ARGO DIC 10.2 11.6 2234.7 2238.3 0.8BAR DIC 2.7 9.4 2249.3 2249.5 0.3PATH DIC 7.8 15.8 2253.2 2253.3 0.4reach the euphotic zone, which is particularly important if the tracer is nitrate. The pool is relevantto the overall tracer inventory on the shelf and the demersal and benthic ecosystems. The pool’smean concentration peaks around day 2.5, when the maximum forcing is being applied and fromthere, the pool’s mean concentration decreases throughout the rest of the simulation (Figure 3.6 b,d). Maximum changes in concentration occur for methane over Astoria Canyon with a 70-85%increase from the initial concentration at shelf break (Table 3.4 max∆Cpool , Figure 3.6) and smallestchanges are for DIC with less than 1%. Concentration of the oxygen pool decreases by 13-17%from the initial concentration at shelf-break in Astoria Canyon runs and between 6-11% for BarkleyCanyon runs.64010203040Apool/AcanAstoria Canyona0.81.01.21.41.61.8Cpool/CsbbLin ASTLin ARGOOxy ASTOxy ARGONit ASTNit ARGOMet ASTMet ARGODIC ASTDIC ARGO05101520Apool/AcanBarkley Canyonc0.91.01.1Cpool/CsbdLin BARLin PATHOxy BAROxy PATHNit BARNit PATHMet BARMet PATHDIC BARDIC PATHFigure 3.6: (a and c) Pool area normalized by canyon area increases faster during the timedependent phase (days 0-4) and is larger for AST and ARGO runs. (b and d) The meanpool concentration normalized by initial concentration at shelf-break depth Cs is max-imum (minimum for oxygen) around day 2.5 but stays higher than Cs through out thesimulation.Near-surface effect on oxygen and nitrateCanyon-induced upwelling has a near surface signature. Profiles of oxygen and nitrate near theshelf break and downstream of the canyon (station S4 in Figure 3.5) show a negative (oxygen) andpositive (nitrate) anomaly near the surface with respect to their initial concentration profiles. Thisanomaly is larger than the bottom anomaly in the ‘pool’ at that station for both, Astoria Canyon andBarkley Canyon runs (Figure 3.5 g1, g2, h1, h2). This anomaly is also present in profiles at stationsS1-S3 for Barkley Canyon and less so for Astoria Canyon.3.3.4 Canyon-induced tracer upwellingI identify water upwelled through the canyon by its concentration of linear tracer. Water that wasoriginally below shelf break depth has a linear tracer concentration larger than the shelf break value(see section 3.2). I find there is a larger upwelling flux F (Equation 3.1) of water onto the shelf forAstoria Canyon runs than for Barkley Canyon runs (Figure3.7a) and that the canyon effect is largertoo (Figure 3.7c). For Astoria Canyon runs the water upwelling flux during the advective phase Fis 8:36×104 m3s−1 for AST and 4:77×104 m3s−1 for ARGO, while the water upwelling flux forBarkley Canyon runs is 1:43× 104 m3s−1 for BAR and 2:18× 104 m3s−1 for PATH. The scaling650.00.51.01.5U.welling flux /105 m3s−1can5on(a)ASTARGOBARPATH0.00.51.01.5T/ u.welling flux /109 μmol s−1linea/ 1/ace/(b)ASTARGOBARPATH0 2 4 6 8day0.00.51.01.5can5on­no­can5on(c)0 2 4 6 8da50.00.51.01.5linear­1racer(d)1051071091011ΦCsb­model­/ μmol s−11051071091011ΦTr model / μmol 0−1(e)Linea/Salin15Ox5genNi1/a1eDSPho0pha1eNi1/ou0 OxideMe1haneDICAlkalini150.00 0.05 0.10 0.15ΔZΔ∂zC/Csb)−40−2002040Err−r (%)(f)ASTARGOBARPATHFigure 3.7: Flux of water (a) and flux of linear tracer (b) upwelled onto the shelf. The cor-responding canyon contribution is calculated as the difference between canyon and no-canyon runs in (c) and (d). The dotted line marks the beginning of the advective phase ofupwelling. (e) Upwelling flux of tracer from model output compared to the modelled wa-ter upwelling flux multiplied by the initial tracer concentration at shelf break depth FCs.Note that the marker for DIC is behind the marker for alkalinity. (f) Percentile error be-tween quantities in (e) calculated as (FTr−FCs)=FTr is a function of the tracer gradientnear shelf break (local average 10 m) normalized by the averaging length ∆Z =10 m overCs.estimate developed by Howatt and Allen (2013), predicts these values within 20%. Similarly, theupwelled tracer flux FTr (Equation 3.2) is quantified by summing the tracer flux through cells iden-tified in the previous step (see section 3.2). Consistent with results for the water upwelling flux,tracer upwelling flux is larger for Astoria Canyon runs than for Barkley Canyon runs (Figure 3.7b).Tracer upwelling flux spans several orders of magnitude due to the very different concentrationsof each tracer but for all tracers, FTr is largest for AST followed in descending order by ARGO,PATH, and BAR (Table 3.5, Ftr).I compare FTr during the advective phase to the upwelled water flux from the model F multi-66Table 3.5: In column 2: Mean tracer upwelling flux [FTr in 3.2] for selected tracers duringthe advective phase (days 4-9), reported with 12-h standard deviations. In columns 3 and4: Tracer inventory or anomaly of total tracer mass on shelf [see (3.3)] and percentagerelative to no-canyon case. Results for other tracers are available in Table E.3.Tracer FTr/109 mmol s−1 (M−Mnc)/ 1012 mmol (M−Mnc)/(Mnc−Mnc0)(%)AST Lin 0.81±0.08 212.7 145.5ARGO Lin 0.47±0.05 107.0 72.6BAR Lin 0.15±0.04 16.0 9.8PATH Lin 0.24±0.04 32.0 17.6AST Oxy 7.06±0.54 -2564.6 96.2ARGO Oxy 3.97±0.62 -1298.7 47.9BAR Oxy 1.13±0.33 -161.2 6.8PATH Oxy 1.63±0.33 -282.4 10.9AST Nit 2.94±0.27 355.2 88.2ARGO Nit 1.69±0.20 177.2 43.0BAR Nit 0.51±0.14 22.4 6.8PATH Nit 0.79±0.14 38.3 10.5AST Met 2.79×10−3±0.31×10−3 1.0 203.5ARGO Met 1.64×10−3±0.16×10−3 0.5 109.4BAR Met 0.53×10−3±0.15×10−3 0.1 7.8PATH Met 0.81×10−3±0.15×10−3 0.1 11.5AST DIC 187.55±16.44 3493.1 89.0ARGO DIC 107.20±13.74 1756.1 44.0BAR DIC 32.26±8.98 208.6 6.4PATH DIC 49.17±8.97 360.5 10.1plied by the initial concentration at shelf break depthCs (Figure 3.7e). The quantityFCs reproducesthe tracer flux within 20% for all tracers except methane, oxygen and linear tracer (Figure 3.7f).The relative error between FTr and FCs increases as a function of the initial tracer gradient (Figure3.7e), normalized by a characteristic length scale ∆Z and the concentration at shelf break depth Cs.This dependence will be explained in section 3.4.1.The on-shelf tracer inventory or the total amount of tracer mass on the shelf (3.3) increases asthe canyon upwells water and tracers onto the shelf, except for oxygen. Since oxygen concentra-tion decreases with depth, the water upwelled by the canyon has lower oxygen concentrations thanthe water exported off-shelf at shallower depths. I compare the effect of the canyon in upwellingeach tracer by looking at the difference and fractional contribution of the canyon at the end of thesimulation compared to the runs having a straight shelf break, i.e. runs with no-canyon bathymetry(columns M-Mnc and M-Mnc/Mnc-Mnc0, Table 3.5). For all tracers, the tracer inventory in-67creases more for Astoria Canyon runs than for Barkley Canyon runs. The relative contribution ofthe canyon is largest in the AST run for all tracers (204-88%) followed by ARGO run (109-43%),PATH run (18-10%) and BAR (10-6%).3.4 Scaling considerationsThere are two main processes acting to transport tracer onto the shelf: mixing and advection. Sub-marine canyons are considered regions of enhanced mixing because their steep walls and axis fa-cilitate the breaking of internal tides and waves (e.g., Carter and Gregg, 2002; Gregg et al., 2011;Lee et al., 2009; Waterhouse et al., 2017). In Chapter 2 I provided numerical evidence that locally-enhanced mixing within a canyon can increase the tracer transport by up to 25% (Ramos-Musalemand Allen, 2019). On the other hand, the upwelling flux that advects the tracer onto the shelf hasbeen scaled by Allen and Hickey (2010) and Howatt and Allen (2013). In the following sections Iquantify the tracer mass content that is advected by the upwelling flow and the extension of the poolformed by the advected tracer on the shelf.3.4.1 Scaling tracer upwelling fluxIn section 3.3.4 I found that the upwelling flux FTr is proportional to the product between the waterfluxF and the initial concentration at shelf-break depth,Cs, with an error proportional to the verticalgradient of the tracer concentration evaluated at shelf break depth (Figure 3.7f). The rationale forapproximating FTr ≈ FCs is that if the tracer concentration is uniform, then the flux of tracer ontothe shelf FTr is the flux of water upwelled onto the shelf F multiplied by the concentration ofthe water. Since the initial concentration is not uniform, the upwelling flux carries water withconcentrations up to C(Hh + Z), that is up to the concentration of the deepest water that upwells(Figure 3.8a). Allen and Hickey (2010) and Howatt and Allen (2013) identify the deepest isopycnalthat upwells onto the shelf (Figure 3.8a). The depth of this isopycnal is Hh+Z, where Hh is thecanyon-head depth, and Z is called the depth of upwelling, given by (Howatt and Allen, 2013)ZDh= 1:8(FWRL)1=2(1−0:42SE))+0:05; (3.4)where Dh = f L=N is a depth scale, the function Fw = RW=(0:9+RW ) is the tendency of the flow tofollow isobaths and RW =U= fWs is a Rossby number that uses the width at at mid-length measuredat shelf-break depth Ws as a length scale. The slope effect is encapsulated in the function SE =sN0= f (Fw=RL)1=2, where s is the shelf slope (s=2:30×10−3 for the Astoria-like bathymetry, 4:54×10−3 for the Barkley-like bathymetry).Then, the concentration that multiplies the water flux can be written as the concentration at shelfbreak depth Cs plus the concentration ∆C between Hh and Hh+Z. This correction will be larger ifthe gradient within the canyon is larger because the difference in concentrations at depths Hh+Z68LHhz=0cross-shelfzcanyon axisslopeHstracer fluxiso-concentration line(a)(b)LFigure 3.8: (a) The cross-shelf section at the canyon axis shows the tilting of isopycnals (graysolid lines) and iso-concentration lines (lines in shades of green) towards the canyon headduring the upwelling event. Tracer upwelled by the upwelling flux (tracer flux) comesfrom depths between Hh and Hh+Z and has a concentration betweenC(Hh) andC(Hh+Z). (b) Length scales used to scale the pool area are shown in a cross-shelf section of theshelf downstream of the canyon. The background pool, shown in tracer contours (shadesof green, increasing with depth), has a cross-shelf length L and associated vertical scaleH. The shelf slope is given by q << 1.691.0 1.5 2.00.57(Z∂zC/Csb)+0.980.751.001.251.501.752.00ΦTr model/ΦCsb model(a)ASTARGOBARPATH0 5 105.4Π2Acan­0.32 /109 m20246810Apool model / 109 m2(b)LinearSalinit/O./genNitrateDSPho+phateNitrou+ O.ideMethaneDICAlkalinit/Figure 3.9: Scaling estimates for (a) tracer upwelling flux and (b) maximum pool area, equa-tions (3.8) and (3.13), respectively. Tracer upwelling flux is proportional to upwellingflux and the initial tracer distribution within the canyon. The maximum pool area is afunction of P, a non-dimensional number given by the ratio between on-shelf canyon-induced tracer flux and the initial background tracer distribution on shelf .and Hh will be larger. If the initial tracer concentration decreases with depth then the concentrationCs will overestimate the mean concentration of the water that is being upwelled and the correction∆C then decreases the concentration of the upwelled water. I propose the scaling for FTr to be:FTr µ F(Cs+∆C): (3.5)The correction ∆C can be written in terms of its derivative with respect to depth z:∆C =∫ HhHh+Z¶C¶ zdz (3.6)≈ Z¶zC; (3.7)where ¶zC is the mean vertical gradient over Hh to Hh+Z. Substituting (3.7) in (3.5)FTrFCs= a1+b1ZCs¶zC (3.8)where a1 = 0:98 and b1 = 0:57 are found as the best-fit, least squares parameters with a standarderror of 0.025 from the model results (Figure 3.9a).3.4.2 Scaling the pool areaThe formation of the pool of upwelled tracer described in section 3.3.3 depends on the flux of tracersonto the shelf described above. Once on the shelf, the alongshelf current will help spread the poolfurther downstream.70Detection of the pool relies on the tracer concentration of the upwelled water and the tracerconcentration of the water on the shelf being different. So, the size of the pool as defined in section3.3.3 depends on how much tracer is upwelled onto the shelf through the canyon as well as on thebackground tracer distribution on the shelf. I will find a scale for the pool area by comparing thedistribution of the tracer upwelled by the canyon compared to the background distribution of thetracer on the shelf. The size of the pool will then depend on the same parameters as the upwellingflux of tracer, Z and ¶zC, and analogous parameters characterizing the background tracer distributionon the shelf (Figure 3.8b).Allen and Hickey (2010) scale the upwelling flux by UFWmZ, where F is similar to FW butuses the Rossby number Ro =U= fR where R is the radius of curvature of the shelf break isobathupstream of the canyon andWm is the width of the canyon at the mouth. In addition, we know thechange in concentration is proportional to Z¶zC from section 3.4.1. So the tracer flux into the poolfrom canyon upwelling is scaled by UFWmZ2¶zC. The rate of change of the depth averaged traceranomaly in the pool is that flux over Apool , the area of the pool.If there was no canyon-induced upwelling, the distribution of tracer on the shelf, close to thebottom, would only depend on bottom friction generating an upslope Ekman transport through abottom boundary layer (BBL). Thermal wind balance would eventually bring the along-isobathflow to rest at the bottom, shutting down the BBL. This is known as the buoyancy arrest of abottom Ekman layer (Brink and Lentz, 2010). A cross-shelf length scale for the BBL is given byL= fU=(Nq)2, where q << 1 is the slope angle (MacCready and Rhines, 1993). A correspondingvertical scale is given byH= Lq . So, the depth of the BBL can be estimated asH.A timescale for the shutdown time is given by t0 = f=(Nq)2 (MacCready and Rhines, 1993)(More precise estimates for the buoyancy arrest time of an upwelling BBL are derived in Brinkand Lentz, 2010). So the depth integrated rate of change of the background concentration can beestimated asFbg ≈ Ht0 (Hs−Hh)¶zCbg; (3.9)where (Hs−Hh)¶zCbg is analogous to ∆C and represents the background concentration on the shelfwithin the shelf pool. We can distinguish the pool where the pool anomaly is greater than thebackground anomaly so approximating them as equalApool µUFWmZ2¶zCt0H(Hs−Hh)¶zCbg : (3.10)Further, the slope s = (Hs−Hh)=L and angle q are related as q ∼ s, and we can approximatethe area of the canyon, Acan, as the area of a triangle of baseWm and height L. Substituting s, Acan,and the expressions forH and t0 in (3.10)Apool µ 2AcanP: (3.11)71whereP=FZ2¶zC(Hs−Hh)2¶zCbg : (3.12)The pool area is a function of the canyon area and the non-dimensional numberP that represents thecompetition between the tracer that is upwelled onto the shelf through the canyon, which dependson the initial gradient of the tracer below the shelf, and the background tracer distribution on theshelf.The relationship between the maximum area of the pool during the simulation, Apool , (Table3.4) and P (Figure 3.9b) as follows:Apool = a2(2AcanP)+b2 (3.13)where a2 = 5:4, b2 =−3:2×108 m2 are found as best-fit, least squares parameters with a standarderror of 0.3 from the model results (Figure 3.9b).3.5 DiscussionTracer is upwelled onto the shelf through advection and mixing. Canyon induced tracer upwelling isdominated by advection-induced upwelling of water through the canyon. In Chapter 2 it was shownthat locally-enhanced vertical diffusivity within the canyon can increase canyon-induced water andtracer upwelling of a linear tracer by more than 25%. In this chapter, I show that variations inthe vertical gradient of the initial tracer profile can have an impact on the amount of tracer that isupwelled onto the shelf through the canyon, as well as on the final distribution of the tracer on theshelf.Tracer upwelled onto the shelf through the canyon forms a pool on the downstream side of thecanyon rim that extends along the shelf downstream and shoreward. The horizontal extent of thispool is different for each tracer and it increases inversely with the relative magnitude of the initialgradient of the profile above shelf break depth compared to the mean gradient below shelf breakdepth. Larger gradients bring up water with higher concentration than can then be mixed up on theshelf which takes longer to dilute to a value below the initial concentration at shelf break depth Cswhile being advected downstream. Given that the pool is bounded, by definition, by the contourC =Cs, having larger concentrations upwelled onto the shelf allows for a larger pool. The area ofthe pool relative to the area of the canyon can be characterized by the non-dimensional number P(3.12) that represents the ratio between the tracer that is upwelled onto the shelf through the canyonand the initial distribution of the tracer on the shelf.Upwelled tracer flux is scaled as the product of the upwelling flux F and the concentrationCs+∆C. The effect of the geometry of the tracer profile is to increase the amount of tracer upwelledonto the shelf compared to a uniform profile. The quantity ∆C is proportional to the mean gradient7248.348.448.5Lat(a)Bottom 20 m-1000-750-500-300-200-150 -100(b)-1000-750-500-300-200-150 -100-126.2 -126.0 -125.8Lon48.348.448.5LatPSU(c)Top 10 m-1000-750-500-300-200-150 -100-126.2 -126.0 -125.8Lon C(d)-1000-750-500-300-200-150 -10030 32 34PSU / m(e)8 12 16T / C1251007550250Depth / m(f)up str.down str.33.733.833.933.934.05.96.36.77.07.430.730.830.931.031.113.313.914.515.215.8Figure 3.10: Mean bottom 20 m (a, b) and top 10 m (c, d) salinity and temperature values atCTD stations sampled around Barkley Canyon during 1997 cruise. Salinity (e) and po-tential temperature (f) profiles at stations upstream and downstream of Barkley Canyonmarked by pink and purple circles in maps, respectively. Bottom data shows a patch ofhigher salinity and lower temperature at stations on the downstream side of the canyonrelative to stations on the upstream side of the canyon head. Surface data shows canyoninfluence more strongly above the canyon head.at the depth of upwelling. For a profile that increases with depth, a larger depth of upwelling allowswater with higher concentration to be upwelled onto the shelf. Thus, the mass of tracer upwelledis larger. For profiles that have sharp changes or large gradients within the depth of upwelling, theconcentrations that are upwelled will also be larger.3.5.1 Canyon-induced tracer distribution on the shelfAllen et al. (2001) sampled Barkley Canyon during an upwelling event in July, 1997. Their resultsshow that the pycnocline is shallower above Barkley Canyon and that a deeper isopycnal is alsoshallower at the downstream side of the canyon head compared to its location in the open ocean.These results show evidence for the near surface effect of canyon upwelling and isopycnal tiltingtowards the canyon head, respectively.I use the data collected by Allen et al. (2001) to find salinity and temperature concentrationsnear the bottom of the Barkley Canyon shelf. Averaging the bottom 20 m of all stations, the datareveals a patch of higher salinity and lower temperature at stations on the downstream side of thecanyon relative to stations with the same maximum depth on the upstream side of the canyon head(Figure 3.10 a, b). This patch forms closer to the coast than our model predicts likely because theaxis of Barkley Canyon is tilted with respect to the shelf break isobath. Near the surface, the top10 m mean of all the stations shows higher salinity and lower temperature values than in nearby73stations around the canyon head (Figure 3.10 c, d). Comparing temperature and salinity profilesof a station near the canyon head to a station of similar maximum depth upstream of the canyon,profiles differ starting above 25 m. In agreement, my simulations show that nitrate and DIC havelarger values, while oxygen has lower values, than the initial profile in the top 20 m on all virtualstations above the pool, but more strongly at the station close to the canyon head S4 (Figure 3.5).In a numerical study of the regional effect that three submarine canyons have on the circulationand upwelling on the Washington Shelf, Connolly and Hickey (2014) identified a similar feature tothe pool. They found that upwelling near canyons has a more direct influence on near-bottom waterover the shelf when compared to runs with uniform bathymetry (without the canyons).Another example of the near shelf bottom influence of submarine canyons is the contributionof the Murray Canyon Group to the formation of a cold and nutrient-rich water pool on the shelfof the eastern Great Australian Bight. Using numerical simulations, (Ka¨mpf, 2007) showed a linkbetween the formation of the pool and upwelling in the canyons, and estimated that the canyonscontribute 72% of the volume and 81% of the nitrate in the pool. My simulations show that duringthe advective phase of one upwelling event, Astoria Canyon contributes 30% of the nitrate, 42% ofthe methane and 61% of the DIC transported onto the shelf, while Barkley Canyon contributes withabout 8% nitrate, 7% of the methane and 19% of the DIC, both when using realistic stratification(Table 3.5).3.5.2 Significance to the near-bottom carbon systemThe presence of corrosive, oxygen-depleted waters near the shelf bottom is common in upwellingsystems. However, in the past 10 years this water has been reaching shallower depths and coveringlarger areas than normal on the West Coast of North America (Feely et al., 2008). Under a changingclimate, the occurrence of these waters can be more frequent and in larger volumes than before. Inmy model, the canyons contribute between 19-68% of all the DIC that is transported onto the shelfduring the advective phase of upwelling. By the end of the simulation, the DIC inventory on theAstoria Canyon shelf had increased between 1.7-3.5×109 mmol relative to the no canyon case whileBarkley Canyon upwelled 0.2-0.4×109 mmol DIC when using linear and realistic stratifications,respectively. Considering the realistic stratification cases, the increase in DIC and total alkalinityrelative to the no-canyon cases in the pool of upwelled water corresponds to a decrease in pH of0.1 for Astoria canyon close to the canyon head and 0.04 for Barkley Canyon (station S1 in Figure3.5e). Downstream of the canyon (S2 and S3) these changes are 0.03-0.06 for Astoria Canyon and0.02-0.03 for Barkley Canyon. Closer to the shelf break (S4), the decrease in pH is 0.02 and 0.01 forAstoria Canyon and Barkley Canyon, respectively. To calculate the equivalent pH of the system Iused MOCSY 2.0, which is open source collection of Fortran 95 routines to model ocean carbonatesystem thermodynamics (Orr and Epitalon, 2015).743.5.3 Significance to nutrient upwellingAlthough the near-bottom pool does not reach the euphotic zone, which is particularly important ifthe tracer is nitrate, the pool is relevant to the overall tracer inventory on the shelf and the demersaland benthic ecosystems. Additionally, it has been shown that the presence of instabilities on the shelfand slope interacting with submarine canyons can transport water closer to the surface (Saldı´as andAllen, 2019).Connolly and Hickey (2014) estimated that canyon-exported nitrate onto the shelf after 2 monthsduring an upwelling season can be about 1.0-2.3×107 kg NO−3 . I found that after a single, albeitstrong, upwelling event, Astoria Canyon can increase the total inventory of nitrate mass on the shelfby 1.1 to 2.2×107 kg NO−3 and Barkley Canyon by 1.4 to 2.4×106 kg NO−3 compared to a straightshelf case. If we consider a 60-day upwelling period, then the canyon contribution to the tracerinventory could be up to 1.5×108 kg NO−3 for Astoria canyon and up to 1:6× 107 kg NO−3 forBarkley Canyon. Using the linear tracer, which was used to do the same calculation in Chapter2, the nitrate inventory contribution for Astoria Canyon is 0.7-1.3 ×107 and for Barkley Canyon1.0-2.0×106 kg NO−3 . So, using the realistic initial profile of nitrate represents an increase of 40%and 17-28%, respectively over using the linear tracer.75Chapter 4Dynamical Interaction BetweenSubmarine Canyons4.1 IntroductionSubmarine canyons are present along shelf breaks all over the world, usually as systems of canyonsinstead of isolated features. The dynamical interaction between adjacent submarine canyons hasnot been studied previously but there is some evidence of their collective effect on a particularregion. It might be tempting to assume that the first canyon or upstream canyon leads the dynamics,since water will go through it before passing to the downstream canyon. However, the role of thedownstream canyon is not trivial as coastal-trapped waves move in the opposite direction to the shelfcurrent in the case of upwelling canyons. This means that information is also being transmitted, viawaves, from the downstream canyon to the upstream one.In this chapter I present preliminary results of a physical model of a continental shelf incisedby two adjacent submarine canyons under upwelling conditions. Two techniques of visualizationof the flow were used: dye and Particle Image Velocimetry (PIV), and quantitative measurements ofthe horizontal velocity field in and around the canyons and the densities at the canyons heads weretaken. The configuration of the experiment is explained in Section 4.2. Results for experimentsusing one and two canyons are presented in Section 4.3 and discussed in Section 4.4.4.2 Methods4.2.1 Experimental designThe physical model simulates a system of two identical submarine canyons that incise a continentalshelf under upwelling conditions. The model bathymetry consists of a plexiglass tank mounted on76Table 4.1: Geometrical parameters of the tank canyons and Astoria Canyon and BarkleyCanyon for comparison.Description Parameter Lab Canyons Astoria Canyon Barkley CanyonCanyon length L 12.0 cm 21.8 km 6.4 kmWidth at half-length Ws 5.0 cm 8.9 km 8.3 kmWidth at shelf break Wm 8.0 cm 15.7 km 13.0 kmShelf break depth Hs 2.9 cm 150 m 0.200 mHead depth Hh 1.5 110 m 170 mTotal depth Hd 9.5 cmDistance between heads Dh 15.0 cmDistance between mouths Dm 5.0 cmRossby number RW =U= fWs 0.06-0.13 0.21 0.11Burger number Bu= NHs= fWs 1.0-1.8 1.2 1.0-1.1Radius of deformation a= NHs= f 5.1-9.0 10.7 km 8.3-9.3 kma rotating table. A plexiglass sloping step around the wall of the tank represents the continentalshelf, and the two adjacent canyons cut through the plexiglass step (Fig. 4.1). The tank is filledprogressively with fresher water to stratify the water column. An upwelling favourable currentaround the tank is generated by varying the rotation rate of the table. Conductivity probes fixed atthe canyons’ heads measure the change in density through the upwelling event while another con-ductivity probe measuring density profiles allows us to track the original depth of the water passingthrough the canyons’ heads. Simultaneously, I use a PIV system to measure the horizontal velocityfield around the canyons at a specific depth in the water column. Through similarity theory (e.g.,Kundu and Cohen, 2004) I can link my observations of the physical model to the real continentalshelf. Experiments with only one canyon were also run as a base line for circulation and dynamicsin a canyon.Bathymetry, stratification and forcingThe continental shelf in the tank, represented by a plexiglass step, has a steep slope and a gentlesloping shelf (See contours in Figure 4.1b). The canyons were 3D printed in PLA material atEngineering Services, UBC Department of Electrical and Computer Engineering (Appendix F). Thecanyon bathymetries and aspect ratio are based on the dimensions of Astoria Canyon and BarkleyCanyon and their dimensions are shown in Table 4.1.77Rotating tableShelf Canyon axisCameraLaserSide viewLaser sheetconductivityprobesmirrorTop viewFlowupstream canyondownstream canyonDepth / cmWsb=8.0 cmWmid=5.0 cmWhead=3.0 cmL=12.0 cmDheads=15 cmrsh=21.5 cmrtank=49.5 cmrdeep=21.2 cm0−2−4−6−8Figure 4.1: Top row: Side and top views of the experimental set up. Bottom row: Top view ofa tank bathymetry slice showing the two canyons annotated with geometric dimensions.78Table 4.2: List of laboratory experiments. Names starting with T correspond to experiments with two canyons, names starting with Sto experiments with a single canyon and DYE to experiments with dye visualizations. Most two-canyon experiments have replicateruns. For those experiments the buoyancy frequency N is the mean of the replicates and the error corresponds to the standarddeviation (Same for Burger number Bu and radius of deformation a.)Experiment Canyons # Replicates # N (s−1) f0 (s−1) maxU (cm s−1) RW Bu a (cm)T01 2 3 1.46±0.06 0.5 0.5 0.20 1.69±0.07 8.47±0.35T02 2 3 1.02±0.01 0.5 0.5 0.20 1.18±0.01 5.91±0.06T03 2 3 1.23±0.02 0.5 0.5 0.20 1.40±0.02 6.99±0.10T04 2 4 1.41±0.10 0.5 0.5 0.20 1.64±0.12 8.18±0.61T05 2 2 1.45±0.01 0.5 0.5 0.20 1.68±0.01 8.40±0.05T06 2 2 1.74±0.09 0.8 0.5 0.12 1.24±0.07 6.20±0.34T07 2 3 1.49±0.05 0.8 0.5 0.12 1.08±0.04 5.41±0.19T08 2 3 1.82±0.12 0.8 0.5 0.12 1.32±0.09 6.61±0.44T09 2 3 1.55±0.10 0.5 0.2 0.10 1.80±0.12 8.98±0.60T10 2 1 1.90 0.7 0.38 0.11 1.60 8.01T11 2 1 1.59 0.7 0.50 0.14 1.34 6.71T12 2 1 1.60 0.7 0.62 0.18 1.34 6.72DYE01 2 1 1.20 0.7 0.38 0.11 0.99 4.94DYE02 2 1 1.19 0.7 0.62 0.18 0.99 4.94S01 1 1 1.83 0.7 0.36 0.10 1.52 7.59S02 1 1 1.60 0.7 0.50 0.14 1.33 6.63S03 1 1 1.47 0.7 0.62 0.18 1.21 6.07S04 1 1 1.48 0.8 0.50 0.12 1.08 5.38S05 1 1 1.40 0.8 0.50 0.12 1.01 5.06S06 1 1 1.39 0.8 0.50 0.12 1.01 5.03S07 1 1 1.24 0.5 0.25 0.10 1.44 7.21S08 1 1 1.29 0.5 0.38 0.15 1.50 7.50S09 1 1 1.18 0.5 0.50 0.20 1.37 6.86S10 1 1 1.77 0.7 0.38 0.11 1.46 7.32S11 1 1 1.67 0.7 0.50 0.14 1.38 6.91S12 1 1 1.43 0.7 0.62 0.18 1.18 5.91791.01 1.02Density / gcm 30246810Depth / cmDYE01DYE02Shelf­break  depthFigure 4.2: Example of density profiles from water samples taken before experiments DYE01and DYE02 at 7 different depths marked on the tank’s sloping bottom. Both experimentruns happened on the same day, one after the other. Note the the linearity of the densityprofile, especially above shelf break depth.The tank is stratified using the two-bucket method (Oster, 1965) which consists of two buckets,one with salty water (bucket 1) and one with fresh water (bucket 2), connected by a hose at thebottom. Bucket 1 is also connected to a pump which draws water from bucket 1 into the tank. As thewater level in bucket 1 decreases, water from bucket 2 flows into bucket 1 driven by the hydrostaticpressure difference between the water level in the buckets. A mixer in bucket 1 guarantees thatthe water is well-mixed before it is pumped into the tank. The final stratification achieved withthis method is close to linear, with a gentle pycnocline close to the surface (Figure 4.2). Differentstratifications were achieved by adding 400 g, 800 g and 1200 g of non-iodized salt to between 16 L-18 L of water in bucket 1 with buoyancy frequencies N at shelf break ranging between 1 s−1 and2 s−1 (Table 4.2). Initial stratifications were inferred from density measurements of water samplesusing an Anton Paar densitometer at the shelf break and surface taken before each run. Assumingthat the density profile is linear, as figure 4.2 suggests, the stratification above the shelf break iscalculated asN2 ≈ gr0∆r∆z; (4.1)where N is the buoyancy frequency, r0 is a reference density that I took to be the density of fresh-water measured from bucket B2, ∆r is the density difference between surface and shelf break depthwater samples and ∆z is the depth change between surface and shelf-break depth. For some runs,initial density profiles were measured using a profiler device consisting in a wooden, two-part, mo-80bile arm, attached to a DC motor (12 V, 2 rpm). The motor moved one segment of the arm incircles, and the circular motion was translated into vertical, linear motion by a clamp between thefirst and second segments (See appendix F). A conductivity probe attached to the second segment ofthe device was then lowered and raised through the water column 2 times per minute. Conductivityreadings were then converted into densities, as the water column is salt stratified. Calibration of thisdevice was challenging and thus I am not using these profiles to calculate the stratification in thetank. In the future, this profiler will determine the stratification and improve the precision of ourstratification values. See Appendix F for details of the workings of the profiler.Water in the tank takes between 2.5 to 3 hours after filling to reach solid body rotation (the tankis filled while rotating over 1.5 hours). An upwelling favourable current in the tank is generatedby changing the rotation rate of the table w . Accelerating the table generates upwelling favourablecurrents (left-bounded) and decelerating the table generates downwelling favourable currents (right-bounded). The linear acceleration a = du=dt at a distance r from the tank center is given by a =rdw=dt. If the tank is ramped up linearly from w0 to w1 in a time T , the linear velocity at a radiusr after a time T will be u1 = r(w1−w0) = r∆w since the water was in solid body rotation (u0 = 0).In terms of the Coriolis parameter f = 2w this isu= r∆ f2(4.2)where u is the alongshelf velocity of the current at a distance r from the center after the ramp uptime T . In our experiments, f varied between 0.5 to 0.8 s−1 and alongshelf velocities u at shelfbreak depth (r=25 cm) varied between 0.250 cm s−1 to 0.625 cm s−1 according to this estimation(Table 4.2). Our ramp-up time T spanned several inertial periods (21 s) and was the same for allruns.Density measurements at canyon headsA customized (5 cm long) conductivity probe is located at the head of each canyon (Fig. 4.1). Theprobes are installed below the bathymetry insert and only the electrodes at the tip of the probe stickout 4 mm above the bathymetry insert. The probes at the canyon heads, as well as the probe onthe profiler system, are part of the open-platform system Conduino, developed by Marco Carminati(Politecnico di Milano) and Paolo Luzzatto-Fegiz (FESlab, University of California Santa Barbara)(Carminati and Luzzatto-Fegiz, 2017). See Appendix F for a detailed explanation of the workingsof the system and customization of the probes for this experiment.Using the Conduino system, continuous measurements of density at the head of the canyons areobtained for the duration of the experiments. The density of the upwelled water passing over thecanyon head can then be mapped back to its original depth using the initial density profiles. Thisgives an estimate of the depth of upwelling in each canyon.81Dye visualization of the flowTo visualize streak lines in the experiment I added red and blue food colouring to the tank. Twosyringes were prepared taking 5 ml of water from the bottom of the canyons along the axis, at amark previously put at half-length. The water in each syringe was mixed with 3 drops of red dye.The same was done for syringes containing water at about shelf break depth and mixed with bluedye. The origin of the blue water is less precise and harder to reproduce than the red-dyed water.Before accelerating the tank, water from each syringe was carefully added into the canyons, at thesame location from where the water was originally taken. Then, the forcing profile of the tank wasstarted and the evolution of the dye was recorded from a video camera mounted at the top of thetable’s frame, looking down.Particle image velocimetryHorizontal velocity fields at different depths of the water column were inferred from Particle ImageVelocimetry (PIV) measurements. Our system consists of a camera (Sony Handy Cam recording at30 fps) located at the top of the tank’s frame looking down at the tank (Fig. 4.1); a laser locatednext to the camera (Z-laser, 532 nm, 40 mW) with optics to beam a laser sheet down onto a mirrorat the bottom of the tank; and reflective particles (TIO2 and wax) seeded through the water columnto reflect the light from the laser. The mirror is positioned below the laser sheet at an angle suchthat the reflected laser sheet is parallel to the tank bottom. The depth of the laser sheet in the watercolumn can be adjusted by moving the mirror horizontally.Every PIV system has 5 main components: seeding, illumination, recording, calibration, eval-uation and post-processing (Raffael et al., 2018). These are the details for each component in theexperiment:Seeding Seeding particles consisted of a mixture of titanium dioxide TiO2 (r=4000 kgm−3) andhigh temperature wax (CALWAX220, congealing point 104 ◦C, r <1000 kgm−3), groundinto particles of diameter between 0.33 and 0.50 mm. To make the particles I followed thesame procedure as Le Soue¨f and Allen (2014) and Reuten (2006). These particles cover awide range of densities depending on the ratio between wax and TiO2; they can withstandheat, and they are white colour, which is important for visibility.Illumination Tracer particles have to be illuminated in the plane of the flow at least twice withina short and known time interval. To generate a light plane or a light sheet, I mounted a laser(Z-lasers, Germany) with the appropriate factory configuration to generate a light sheet. Thelaser sheet has 40 mW of power, 532 nm wavelength, 4 mm thickness and a fan angle of 20◦.The laser sheet reflected off an angled mirror at the bottom of the tank to generate a horizontalplane that cuts through the two canyons at specific depths, such that only particles moving atthat depth are illuminated and thus captured by the camera.82Recording The light scattered by the tracer particles has to be recorded as a sequence of frames ofa camera. A Sony Handycam was mounted next to the laser, at the top of the tank’s frame torecord the particles moving in the laser sheet plane. The camera focus was set to manual (5.6m), white balance set to automatic, low lux option on. The frame speed was 30 fps.Calibration In order to determine the relation between the particle image displacement in the im-age plane and the tracer particle displacement in the flow, a calibration is required. For thatpurpose I took a short video of the canyons without water and added a ruler and with the samesettings as the video (same focal distance and zoom) so that the ruler could provide a pixel todistance conversion factor.Evaluation The displacement of the particle images between the light pulses has to be determinedthrough evaluation of the PIV recordings. I evaluated the quality of the video by eye, con-sidering the density of particles and distribution in the field of view. This process eliminatedmore than half of the experiment runs for further PIV analysis. An automated and objectivecriteria is desirable for future experiments.Post-Processing In order to detect and remove invalid measurements and to extract complex flowquantities of interest, sophisticated post-processing is required. Before the velocity field wasextracted, images were filtered to enhance contrast and to remove the background sunkenparticles using a high pass filter (kernel 3 pix) and a Wiener de-noise filter with window size3 pixels. To obtain a velocity field from the images, correlation functions of the frames werecalculated using an interrogation window of 128 pixels in the first pass, 64 pixels in the secondpass and 32 pixels in the third pass with an overlap of 50% in all passes.Calibration, evaluation and post-processing of the images was done using the Matlab toolboxPIVlab which is a GUI based tool that allows you to analyse, validate, post-process and visualizePIV data (Thielicke and Stamhuis, 2014).4.2.2 Similarity theory and non-dimensional regimeThe dynamical parameters that describe the system are the Coriolis parameter f = 2w where wis the rotation rate of the tank, the stratification N, kinematic viscosity n and a velocity scale U .Geometric parameters that describe the bathymetry are the length of the canyons L, the width ofthe canyons at mid-length W , the distance between canyon mouths Dm and the shelf break depthHs. There are 8 quantities with 2 dimensions (time and length). According to the BuckinghamPi theorem (Buckingham, 1914) there are 6 non-dimensional groups that completely describe thedynamics of the flow. I chose the groups as the Rossby numbers RW =U= fWs and RL =U= f L, aBurger number Bu = NHs= fWs, an Ekman number Ek = n= fW 2s , and the aspect ratios Dm=Ws andL=Ws. It is difficult to match the Ekman number between ocean flows and the lab.83In these experiments, all geometric parameters were kept constant, so choosing the right lengthscales is complicated because I cannot account for their effect on the flow. However, it is useful tokeep the scale Dm to guide future experiments.To chose the parameters for the experiments I used typical values of Astoria Canyon and BarkleyCanyon under upwelling conditions as a guide. According to Allen and Hickey (2010), AstoriaCanyon has a Rossby number RW = 0:12 if using the width of the canyon Ws and RW = 0:21 ifusing W, and a Burger number Bu= 1:2, which gives a Rossby radius of 10.7 km. Barkley Canyonhas RW = 0:07, RW = 0:11 and Bu= 1:1−1:0 for a Rossby radius of 8.3-9.3 km.4.2.3 Depth of upwellingI calculate the depth of upwelling as the change in depth associated with the maximum change indensity recorded at the canyon head, assuming that the initial density profile is linear. Close to shelfbreak depth this is a reasonable assumption considering the profile in figure 4.2. I approximatestratification as being linear:N2 ≈− gr0∆r∆z(4.3)where N is the buoyancy frequency, g the gravitational acceleration, r0 a reference density, and∆r the change in density over a depth ∆z measured at the canyon head. I associate the change indensity at the head of the canyons ∆r with the upwelling of isopycnals caused by canyon inducedupwelling and the distance those isopycnals rose ∆z with the depth of upwelling Z. Thus, the depthof upwelling derived from density (conductivity) measurements Zlab is given byZlab =gr0∆rN2: (4.4)4.2.4 Sources of error and measurement uncertaintyNear-inertial oscillationsThere is a strong presence of near-inertial oscillations in all conductivity readings using the probes.Oscillations are also recognizable in the velocity field. It was not possible to filter the exact in-ertial frequency. Oscillations are there before the experiment starts (base measurements) but theysometimes intensify during or after the experiment. To reduce their impact on the conductivitytime series I filtered every time series using running mean with a window of the same length as theinertial period. This worked better than filtering the exact inertial frequency (Figure F.6).84Error associated to density time seriesDensity time series derived from the measurements of the conductivity probes installed at the headof the canyons have several sources of error. A detailed section of the error estimations is providedin Appendix F. Here I provide a summary of the errors calculated for density measurements.First, there is an error associated with the calibration curve to go from probe readings to den-sity values. To calibrate the probes I prepared 10-15 saline solutions with different densities andcompared the probe reading while immersed in the solution to the density measurement from anAnton Paar densitometer (Appendix F). Moreover, since the calibration curves are not linear, theerror from associating a density value to a conductivity reading is larger for higher readings.Second, probe readings drift over time. In every experiment I monitored this drift from the timethe tank was filled until the last run was done. The drift in the density time series is not negligiblein the course of 7 min, which is the full length of the Conduino time series. The two forcing phasesof the tank take 71 s but I recorded 7 min of conductivity measurements. To account for the driftthat may occur during the experiment I calculated the mean drift of the probe reading R during basemeasurements of one experiment (3 runs, approx 7 hrs) dR and calculated the uncertainty dr asdr =¶r¶RdR: (4.5)4.3 ResultsThere are conductivity probes at the head of each canyon from which I can infer density changes(Figure 4.1). Using PIV I can reconstruct the velocity field around the canyons at a particular depth.Using dye (food colouring) I can visualize streaklines from water that was initially in the canyon.Experiments with only one canyon incising the shelf were run to compare to the results of two-canyon experiments. In this section I report the results obtained using three tools to understand theflow (dye, conductivity derived density measurements and PIV) in experiments with one and twocanyons incising the shelf.4.3.1 Qualitative description of upwelling in two canyons from dye experimentsThe experiment starts from rest. The forcing ramps up linearly until the tank reaches the maximumvelocity over a period of 21 s after which the tank keeps accelerating to avoid the spin down of thecurrent for another 50 s. After that, the tank’s rotation rate is kept constant. The surface of the wateris parabolic due to the centrifugal force caused by rotation. The difference in surface height betweenthe center of the tank and the tank walls is between 0.08 and 0.2 cm depending on the rotation ratefor a homogeneous water column (Appendix F). These values are an upper bound for a stratifiedfluid. The first accelerating period spins up an upwelling favourable current (travelling with the tank85wall on the left); the objective of the second accelerating period is to prevent the shelf current fromspinning down due to friction. The shelf current accelerates everywhere around the tank, includingwithin the canyons.Dye mixed with water from within the canyons was added before starting the tank accelerationprofile. This allows us to visualize the flow within the canyons under two different forcings (experi-ments DYE01 and DYE02 in Table 4.2): high and low incoming velocities (Fig. 4.3). In both cases,the first thing to note when the dye has been added is that there are oscillations along the canyon axisand the dye moves up and down canyon in both canyons, similar to tides. Then the forcing startsand most of the dye starts moving towards the canyon head. A portion of the dye moves past thecanyon head and onto the shelf where it is further advected downstream (after 30 s). This ‘plume’or ‘pool’ of canyon water is larger for the case with higher forcing. The plume from the upstreamcanyon eventually reaches the downstream canyon’s head (DYE02, 50-80 s).At the same time, a filament of dye moves along the upstream wall of both canyons, towardsthe shelf break, where it encounters the slope current (50 sec). The filament tries to move upstreamagainst the slope current; a portion of the filament is advected downstream by the slope current andre-enters the canyon closer to the downstream wall through an eddy that forms on the downstreamside of the canyon, close to the mouth (80 s). A last portion of the original filament keeps movingdownstream (120 s).4.3.2 Depth of upwelling from conductivity measurementsOne-canyon experimentsThere are 9 experiments with the downstream canyon covered and 3 experiments with the upstreamcanyon covered (Table 4.1). I expect the upwelling dynamics in both canyons to be the same andthat for any two runs with the same parameters differences in the density change at the head of thecanyon are due differences in the location of the probes relative to the canyon head, the shape of theelectrodes after bending or even rust formation on the electrodes.The change in density of the probe on the shelf (where the canyon is covered) increases duringthe forcing time and it reaches its maximum value around the time when the forcing stops. Afterthat time, density change slowly decreases (Figure 4.4 blue lines in a-h). Conduino time series are7 minutes long. During that time, density at the shelf does not return to its initial value because thetank is rotating faster than before the experiment started. I conducted measurements during the spindown of the tank (returning the tank to its initial rotation rate) and then the density returns to itsinitial value (Figures G.1 and G.2).The electrode on the shelf is recording the shelf break upwelling caused by the on-shelf transportthough the bottom boundary layer on the slope and shelf. Note that, for most experiments, thedensity change signal at the electrode does not increase until the second phase of forcing starts86Figure 4.3: Dye visualizations of the flow during two upwelling experiments DYE01 (firstand third rows) and DYE02 (second and fourth rows). Strong oscillations along thecanyon axis. Red dye, originally in the canyon is upwelled onto the shelf and advecteddownstream of the canyons. These plumes are larger and spread faster for larger forcing(DYE02). Eventually, the upstream canyon plume reaches the head of the downstreamcanyon. An eddy trapped within the canyon can be seen at around 80 s close to down-stream side of the canyons for DYE02. Blue dyed water in DYE01 frames is lighter(shallower) than the red dyed water.870.0000.005 / gcm3 S01  RW=0.10  Bu=1.52aS02  RW=0.14  Bu=1.33b0.0000.005 / gcm3 S03  RW=0.18  Bu=1.21cS04  RW=0.12  Bu=1.08d0.0000.005 / gcm3 S05  RW=0.12  Bu=1.01eS06  RW=0.12  Bu=1.01f0.0000.005 / gcm3 S07  RW=0.10  Bu=1.44gS08  RW=0.15  Bu=1.50h0.0000.005 / gcm3 S09  RW=0.20  Bu=1.37i0 100 200 300 400time / sS10  RW=0.11  Bu=1.46j0 100 200 300 400time / s0.0000.005 / gcm3 S11  RW=0.14  Bu=1.38kUpstream canyonDownstream canyonUpstream - DownstreamFigure 4.4: Density change from initial value at the upstream (orange) and downstream (blue)probes. The grey line corresponds to the difference between upstream and downstreamprobes. Most experiments were performed covering the downstream canyon, so only theupstream canyon is active (a-i), and three experiments were performed with the oppositeconfiguration (j-l), upstream covered and downstream uncovered. Note how the canyonprobe has a larger response to the forcing and reaches its maximum faster than the shelfprobe.88(Figure 4.4). There is a larger density change in the shelf upstream of a canyon than downstream ofa canyon (Figure 4.4 blue lines in panels a-h vs. orange lines in panels i-k). This is an unexpectedbehaviour but I consider it to be a real effect because the signal in the canyon is consistent whenusing either of the canyons and will be explored further in future experiments. It is unexpectedbecause it contradicts numerical results, where we see shelf break upwelling inhibited upstream ofthe canyon. Moreover, the electrode on the shelf is “far away” from the shelf break where no sucha large effect is expected.The probe at the canyon head has a different response. The response at the canyon head is muchfaster and higher than on the downstream shelf (Figure 4.4 orange lines in panels a-h, blue lines inpanels i-k). Density increases quickly during the first phase of forcing and reaches its maximumvalue at the beginning of the second phase of forcing. After this, density change decreases slowlytowards a plateau, at a larger value than the shelf probe. During the tank spin down, density at thecanyon head also decreases to its original value (Figures G.1 and G.2).The electrode at the canyon head is recording canyon-induced upwelling. In particular, the risingof isopycnals that is sustained by an unbalanced baroclinic pressure gradient within the canyon(Freeland and Denman, 1982). The large peak generated during the first forcing phase is known asthe time-dependent phase. This concept has been described as linear or proportional to incomingvelocity (Allen, 1996). This is in agreement with the measurements in Figure 4.4, the peak growslinearly while the current increases linearly, except for some variation due to the inertial oscillations.After that stage the advective phase of canyon induced upwelling starts. In this phase the peakdecreases slowly but it is generally maintained.The depth of upwelling Zlab in the canyon is derived from density measurements (Section 4.2.3).The change in density used to calculate the depth of upwelling is the maximum of the density timeseries. Howatt and Allen (2013) derived a scaling estimate for Z given byZDh= 1:8(FwRL)1=2(1−0:42SE)+0:05; (4.6)whereDh= f L=N is a depth scale,FW =Rw=(0:9+RW ) is a function that characterizes the tendencyof the flow to cross the canyon, RL = U= f L is a Rossby number using the canyon length as alength scale, and SE = sN= f (FW=RL)1=2 encapsulates the effect of the sloping shelf since, in astratified water column, the water upwelled on the continental shelf slope adds pressure that inhibitsupwelling, and reduces the upwelling depth. Our derived measurement Zlab agrees with the scalingestimate Z with a root mean squared error of 0.27 cm (Figure 4.5) and rmse normalized by the meandepth of upwelling of 27%. Note that runs with the upstream canyon tend to have larger or equaldepths of upwelling than the scaling estimate and runs with the downstream canyon tend to havelower depths of upwelling than the scaling estimate predicts. This may suggest there is a bias in thederived upwelling depth depending on which canyon is considered. The bias from the 1-1 line was890.0 0.5 1.0 1.5 2.0Z / cm0.00.51.01.52.0Zlab / cmdownstream uncoveredupstream uncovered± rmseupstream biasdownstream biasFigure 4.5: Comparsion between the depth of upwelling derived from density measurementsand the scaling estimate proposed by Howatt and Allen (2013). There is good agreementbetween both quantities with a root mean squared error of 0.27 cm. Depth of upwellingmeasured in the downstream canyon (blue dots) tends to be lower than the scaling esti-mate while depth of upwelling in the upstream canyon (orange dots) tends to be larger.found by finding the y-intercept that minimized the sum of the residuals for each canyon, keepingthe 1-1 slope fixed. The bias for the upstream canyon is 0.24 cm and for the downstream canyon is-0.30 cm. This bias calculation is only valid for the maximum Zlab.Two-canyon experimentsIn general, the density change at the head of the canyons when two canyons are present is similarto the one canyon case. Density change occurs fast during the initial stage and slower during thesecond forcing stage, after which it slowly plateaus to a lower constant value (Figure 4.6), but thereare significant differences between the response in the canyons. For most experiments, the densitychange from the initial state is larger or equal in the upstream canyon than in the downstreamcanyon at all times. There are some cases in which the maximum change in density is larger in thedownstream canyon and cases in which the downstream canyon reaches its maximum value afterthe upstream canyon does.From Figure 4.6 I see two types of behaviour in the downstream canyon. If the two canyonsare independent, the change in density at the canyon heads mimic each other and ideally, have thesame magnitude. If they interact, the downstream canyon’s response is delayed with respect to theupstream response: the maximum occurs later and the curve is smoother. The pool of upwelledwater from the upstream canyon may eventually reach the downstream probe. This also appearsas a change in density in the downstream canyon. Based on the dye experiment observations, Ihypothesize that the smoother peak appearance of the downstream density change curve is due to900.02.5 / 103 gcm3 T02  RW=0.20  Bu=1.18a T03  RW=0.20  Bu=1.39b0.02.5 / 103 gcm3 T04  RW=0.20  Bu=1.67c T05  RW=0.20  Bu=1.68d0.02.5 / 103 gcm3 T01  RW=0.20  Bu=1.69e DYE02  RW=0.18  Bu=0.99f0.02.5 / 103 gcm3 T12  RW=0.18  Bu=1.34g T11  RW=0.14  Bu=1.34h0.02.5 / 103 gcm3 T07  RW=0.12  Bu=1.07i T06  RW=0.12  Bu=1.24j0.02.5 / 103 gcm3 T08  RW=0.12  Bu=1.35k0 100 200 300 400time / sT10  RW=0.11  Bu=1.60l0 100 200 300 400time / s0.02.5 / 103 gcm3 T09  RW=0.10  Bu=1.80mUpstream canyonDownstream canyonUpstream-DownstreamFigure 4.6: Density change from initial value at the upstream canyon (orange) and downstreamcanyon (blue) head probes. The grey line corresponds to the difference between upstreamand downstream probes. Each line is the mean time series of 3 repeats per experiment(except f, g,h, l that don’t have repeats).The shaded areas around the lines correspond tothe largest between the standard deviation and the uncertainty, calculated as in Section4.2.4.91the passing of the upstream pool on the downstream probe. An example of this can be seen in figure4.6 panels a, b, f, i and k. In all of these cases, the time of the passing of the pool water wouldbe around 50 s. This is consistent with the dye observations, where the ink from the upstreamcanyons can be seen reaching the downstream probe after 50 s for a maximum forcing velocityof 0.625 cms−1 (Figure 4.3, higher forcing panels). In other cases, it may be possible that theupstream pool does not reach the downstream probe because it deflected offshore before reachingthe downstream canyon head and I measure a smaller density change in the downstream probe thanin the upstream canyon.To simplify the dependence on Bu and RW , I look at the depth of upwelling time series of Zlabnormalized by the estimated depth of upwelling from the scaling estimate by Howatt and Allen(2013) Z (Figure 4.7). In this way, I can compare the experiments to each other and avoid the largedependence on Bu and RW from the one-canyon dynamics. From here I identify three ways in whichthe upstream and downstream canyons can be different. First, which one has a larger depth of up-welling over all? Second, when does the peak happen, that is, is there a lag between maximums?Finally, how much do the peaks lag and how different are they? First, I compare the maximumdepth of upwelling in each canyon max(Zlab) to the scaling estimate Z (Figure 4.8). Both canyonsare in good agreement with the scaling but the upstream canyon has a better agreement (root-meansquare error 0.14, normalized rmse 12%) than the downstream canyon (root-mean squared error0.23, normalized rmse 20%). Figure 4.9 suggests that the difference between depth of upwellingin the canyons is proportional to both the Burger number and the Rossby number but the linearfits shows that the difference in depth of upwelling is positively correlated RW (correlation coeffi-cient 0.52) and not significantly correlated with Bu (p-value is 0.2). The depth of upwelling in thedownstream canyon will be larger than in the upstream canyon for a combination of large Bu andRW .Now, consider the difference between the depth of upwelling in the upstream and downstreamcanyons through time (Figure 4.7, gray line). The difference between the maximum and minimumof the curve within the forcing time is a measure of the lag between the maximum depths of up-welling in each canyon and how different they are. It is a measure of the interaction between thecanyons. This metric is inversely proportional to Bu with a correlation coefficient of -0.83 and it isnot significantly correlated with RW .4.3.3 Particle image velocimetry and the velocity fieldHorizontal velocities on a plane at a specific depth were obtained after processing PIV videos. Giventhe cylindrical shape of the tank and canyon inserts it is more natural to decompose the horizontalvelocity vectors into its radial and azimuthal components. Using cylindrical coordinates with depthz fixed at the laser sheet depth, the velocity components correspond to the cross-shelf (radial) andalong shelf (azimuthal) components of the velocity flow.9201Z lab/ZT02  RW=0.20  Bu=1.18a T03  RW=0.20  Bu=1.40b01Z lab/ZT04  RW=0.20  Bu=1.64c T05  RW=0.20  Bu=1.68d01Z lab/ZT01  RW=0.20  Bu=1.69e DYE02  RW=0.18  Bu=0.99f01Z lab/ZT12  RW=0.18  Bu=1.34g T11  RW=0.14  Bu=1.34h01Z lab/ZT07  RW=0.12  Bu=1.08i T06  RW=0.12  Bu=1.24j01Z lab/ZT08  RW=0.12  Bu=1.32k0 100 200 300 400time / sT10  RW=0.11  Bu=1.60l0 100 200 300 400time / s01Z lab/ZT09  RW=0.10  Bu=1.80mUpstream canyonDownstream canyonUpstream-DownstreamFigure 4.7: Depth of upwelling derived from density change at the upstream canyon (orange)and downstream canyon (blue) head probes. The grey line is the difference betweenupstream and downstream probes. Each line is the mean time series of 3 repeats perexperiment (except f, g, h, l that don’t have repeats). The shaded areas correspond to themaximum of the standard deviation and the uncertainty. The depth of upwelling evolvessimilarly in both canyons, but Zlab=Z is larger in the upstream canyon and there is a lagbetween the maximums in general.930.0 0.5 1.0 1.5 2.0Z / cm0.00.51.01.52.0max Zlab / cm0.0 0.5 1.0 1.5 2.0Z / cmdownstream canyon upstream canyon± rmseFigure 4.8: Comparsion between the depth of upwelling derived from density measurementsand the scaling estimate proposed by Howatt and Allen (2013). Both canyons followthe scaling estimate well but the depth of upwelling measured in the upstream canyon(orange dots) has a better fit with a root mean square error (rmse) of 0.14 cm while thedownstream canyon has a rmse of 0.23 cm (blue dots). Error bars correspond to themaximum of the standard deviation and the uncertainty.1.0 1.5Bu0.60.40.20.00.20.4ZupslabZdnslab / Z(a)0.10 0.15 0.20Rw(b)linear fit  r=0.521.00 1.25 1.50 1.75Bu0.0750.1000.1250.1500.1750.2000.2250.250Rw(c)0.40.30.20.10.00.10.20.30.4ZupslabZdnslab / ZFigure 4.9: The difference in depth of upwelling between the upstream and downstreamcanyons is not significantly correlated to the Burger number Bu (a) and it is proportionalto the Rossby number as 2:2RW − 0:28 with correlation coefficient of r=0.52 (b) for alltwo-canyon experiments. Error bars correspond to the maximum of the standard devia-tion and the uncertainty. Panel (c) shows the difference in upwelling depth as a functionof both RW and Bu. The colours of the markers are proportional to Zupslab −Zdnslab and theirsizes are proportional to the magnitude of Zupslab −Zdnslab . The dependence of Zupslab −Zdnslabon Bu and RW defines two regimes: upstream depth of upwelling larger or lower thandownstream.941.0 1.5 2.0Bu0.20.40.60.81.0max(Zanomlab)min(Zanomlab) / cm (a)linear fit  r=­0.830.10 0.15 0.20Rw(b)1.0 1.5Bu0.080.100.120.140.160.180.200.22Rw(c)0.20.30.40.50.60.7max(Zanom)min(Zanom) / cmFigure 4.10: Difference between the maximum and minimum of the depth of upwellinganomaly (upstream-downstream) max(Zanomlab )−min(Zanomlab ) is inversely proportional tothe Burger number Bu as −0:54Bu+ 1:18 with a correlation coefficient of -0.83 (a)while the Rossby number RW is not significantly correlated (b) for all two-canyon ex-periments. Panel (c) shows max(Zanomlab )−min(Zanomlab ) as a function of both Bu and RWwith marker colours and sizes proportional to max(Zanomlab )−min(Zanomlab ).The flow around the canyons during an experiment can be divided into three stages. The first oneis dominated by the impulsive start of the forcing and ramping up of the alongshelf current (timedependent); the second one is driven by advection, when the current is steady and the last stageis dominated by the near-inertial oscillations that have been identified in the dye experiments anddepth of upwelling time series. As an example, take experiment T02 (Figures 4.11 and 4.12), whichhave RW = 0:2 and Bu= 1:18 (Table 4.1), although the flow structure is similar for all two-canyoncases (Figure 4.13).During the first stage, the tank’s rotation rate is ramped up to the maximum forcing in 21 s. Atshelf break depth, the flow within the canyons is up-canyon (towards the canyon head) along thecanyon axis and intensifies over the first 20 seconds. Deeper in the canyon, the flow is slower thanat shelf-break depth but in the same direction. Both canyons seem to have the same response to theforcing in this stage.After 20 seconds, a cyclonic eddy starts developing on the upstream side of the canyons. Theeddy can be identified earlier in the downstream canyon than in the upstream canyon. Cycloniccirculation is also present deeper in the canyons, 1 cm below shelf break depth and much weaker2 cm below. During this time, the intensity of up and down canyon flows vary but the main cycloniccirculation persists. Up-canyon flows on the downstream side of the canyons reach their maximumvelocity between 20-25 s after the forcing starts and during the advective phase they decrease andbecome of similar magnitude as the down-canyon flows on the upstream side of the canyons (40-45 s). This is also the case deeper in the canyon, 1 cm below shelf break depth.950°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 2.8 cmMean field between 5.0-10.0 s0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 3.8 cm0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 4.8 cm0.00.10.2Radial velocity / cms10°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 2.8 cmMean field between 20.0-25.0 s0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 3.8 cm0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 4.8 cm-0.10.00.10.20.30.40.5Radial velocity / cms10°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 2.8 cmMean field between 25.0-30.0 s0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 3.8 cm0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 4.8 cm-0.10.00.10.20.30.40.5Radial velocity / cms10°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 2.8 cmMean field between 40.0-45.0 s0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 3.8 cm0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 4.8 cm-0.2-0.10.00.10.20.30.4Radial velocity / cms1Figure 4.11: Mean 5 second velocity direction field (arrows) and radial speed (color map) forthe first 45 seconds of experiment T02 (RW = 0.2, Bu= 1:18) at three different depths:shelf break depth at 2.8 cm, 3.8 cm and 4.8 cm. The velocity vectors are normalizedto show only the direction of the flow and only every second arrow is plotted. Radialor cross-shelf velocities are green when going up-canyon or on-shelf and red whengoing down-canyon or off-shelf. Flow is up-canyon during time dependent phase andcirculation is cyclonic during advective phase. Flow is stronger at shelf break depththan deeper.960°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 2.8 cmMean field between 70.0-75.0 s0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 3.8 cm0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 4.8 cm-0.2-0.10.00.10.20.3Radial velocity / cms10°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 2.8 cmMean field between 85.0-90.0 s0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 3.8 cm0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 4.8 cm-0.3-0.2-0.10.00.10.2Radial velocity / cms10°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 2.8 cmMean field between 100.0-105.0 s0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 3.8 cm0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 4.8 cm-0.10.00.1Radial velocity / cms10°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 2.8 cmMean field between 115.0-120.0 s0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 3.8 cm0°10°20°30°40°50°cm10 15 20 25 30T02 Depth = 4.8 cm0.00.1Radial velocity / cms1Figure 4.12: Mean 5 second velocity direction field (arrows) and radial speed (color map) forthe last 50 seconds of experiment T02 (RW = 0.2, Bu = 1:18) at three different depths:shelf break depth at 2.8 cm, 3.8 cm and 4.8 cm. The velocity vectors are normalized toshow only the direction of the flow and only every second arrow is plotted. Radial orcross-shelf velocities are green when going up-canyon or on-shelf and red when goingdown-canyon or off-shelf. After the advective phase, the up-canyon flow relaxes and anoscillating flow up and down canyon takes over the circulation in the canyons.97After 75 seconds, when all forcing has stopped, near-inertial oscillations within the canyon takeover the circulation with an alternating pattern of flow down-canyon followed by up-canyon flow(Figure 4.12). At this time the cyclonic circulation is still present but the effect of the internal oscil-lations is more obvious. The oscillation dominated motion is more evident below shelf break depth(1 and 2 cm below) although the magnitude of the cross-shelf velocity is smaller. The oscillatingflows in the two canyons are not in phase.Azimuthal velocities are very weak within the canyon (Figure G.4) compared to outside. Theyhave little variation and are mainly constant following the bathymetry (along lines of constant ra-dius).Comparing the initial 5 second mean of all two-canyon experiments at shelf-break depth withPIV measurements I see the presence of oscillatory flows before the experiment starts (Figure 4.13,first row). The oscillations are not in phase within the two canyons for any experiment. Even if theflow has the same direction in both canyons (Eg. T04), the radial velocity magnitude is larger inone of them.As the forcing ramps up, most experiments have the same response as T02 (Figure 4.13, secondrow). The flow is dominantly up-canyon but the magnitude of the radial component is different.There is also a region downstream of each canyon where off-shelf flow occurs. The magnitude ofthe off-shelf velocity is proportional to the strength of the up-canyon flow. Runs with larger forcingdevelop larger up-canyon velocities (T12 has maximum U = 0.63 cms−1, RW = 0.18) but also runswith smaller stratification develop larger up-canyon flows. Run T07 has a forcing of U = 0.50 cms−1but the smallest stratification of all runs. In terms of non-dimensional parameters experiment T07has RW = 0.12 which is the smallest among all experiments and Bu = 1.07, the smallest of all Bu.Experiment T04 has larger RW than T12 but the flow is slower because Bu = 1.67 is larger than inT12. In summary, it is a combination of high RW and low Bu number that increases the up-canyonflow.During the advective phase, at 30 s, runs with lower Bu have a larger up-canyon flow on thedownstream side of the canyons and this flow is slightly stronger in the downstream canyons ofall experiments (Figure 4.13, third row). The lowest Bu case has almost no down-canyon flow.Circulation in both canyons is cyclonic for all experiments.Jumping ahead in the experiments to 85 s, after the forcing has stopped (Figure 4.14, first row)oscillatory flows take over the circulation in the canyons. An eddy can still be identified in thecanyons but almost disappears at times of maximum up or down-canyon flow. This oscillatory flowis not in phase between the two canyons. The period of oscillation is larger for experiments withlower Coriolis parameter (longer inertial period) like T04 (f = 0.5 s−1) if we compare the 5 secondmeans from 85-95 s in figure 4.14.980°20°40°cm10 15 20 25 30T04Mean field between 0.0-5.0 s at shelf-break depth0°20°40°cm10 15 20 25 30T120°20°40°cm10 15 20 25 30T110°20°40°cm10 15 20 25 30T070.0Radial velocity anomaly / cms10°20°40°cm10 15 20 25 30T04Mean field between 15.0-20.0 s at shelf-break depth0°20°40°cm10 15 20 25 30T120°20°40°cm10 15 20 25 30T110°20°40°cm10 15 20 25 30T07-0.4-0.3-0.2-0.10.00.10.20.30.4Radial velocity anomaly / cms10°20°40°cm10 15 20 25 30T04Mean field between 30.0-35.0 s at shelf-break depth0°20°40°cm10 15 20 25 30T120°20°40°cm10 15 20 25 30T110°20°40°cm10 15 20 25 30T07-0.3-0.2-0.10.00.10.20.30.40.5Radial velocity anomaly / cms1Figure 4.13: Mean 5 second velocity direction field (arrows) and radial speed (color map) for the first 35 seconds of experiment T04,T12, T11 and T07 (RW = 0.20, 0.18, 0.14, 0.12 and Bu =1.67, 1.34, 1.34, 1.07, respectively) at shelf break depth. The velocityvectors are normalized to show only the direction of the flow and only every second arrow is plotted. Up-canyon velocities aregreen and down-canyon velocities are red. Radial velocities are larger for lower Bu and larger RW and up-canyon flow is strongerin the downstream canyon for all runs.990°20°40°cm10 15 20 25 30T04Mean field between 85.0-90.0 s at shelf-break depth0°20°40°cm10 15 20 25 30T120°20°40°cm10 15 20 25 30T110°20°40°cm10 15 20 25 30T07-0.10.00.10.20.3Radial velocity anomaly / cms10°20°40°cm10 15 20 25 30T04Mean field between 90.0-95.0 s at shelf-break depth0°20°40°cm10 15 20 25 30T120°20°40°cm10 15 20 25 30T110°20°40°cm10 15 20 25 30T07-0.3-0.2-0.10.00.10.2Radial velocity anomaly / cms10°20°40°cm10 15 20 25 30T04Mean field between 95.0-100.0 s at shelf-break depth0°20°40°cm10 15 20 25 30T120°20°40°cm10 15 20 25 30T110°20°40°cm10 15 20 25 30T07-0.4-0.3-0.2-0.10.00.10.20.3Radial velocity anomaly / cms1Figure 4.14: Mean 5 second velocity direction field (arrows) and radial speed (color map) for the last 15 seconds of experiment T04,T12, T11 and T07 (RW = 0.20, 0.18, 0.14, 0.12 and Bu = 1.67, 1.34, 1.34, 1.07, respectively) at shelf break depth. The velocityvectors are normalized to show only the direction of the flow and only every second arrow is plotted. Cross-shelf velocities aregreen when going up-canyon and red when going down-canyon. For all runs, oscillations of period similar to the inertial periodtake over the circulation. Oscillations are not in phase between upstream and downstream canyons.100Experiments with only the upstream canyon covered and only the downstream canyon coveredwere run to compare the response of both canyons and the circulation around a single canyon. Thestructure of the flow around a single canyon is consistent with the structure of the flow aroundeither of the two canyons described above. Five-second averages of radial velocity for runs S03 andS12 at shelf break depth (Figures 4.15 and 4.16) show a similar response in magnitude and directionbetween the flow around both canyons. Runs S03 and S12 have similar non-dimensional parametersbut each one has a different canyon covered (RW = 0.18, Bu = 1.21 and 1.18, respectively). The two-canyon experiment with most similar non-dimensional parameters to S03 and S12 is T02 (RW = 0.2,Bu =1.18). Maximum up-canyon velocities are larger in T02 because it has a larger Rossby number,but the overall structure of the flow is the same as in S03 and S12.4.4 DiscussionCirculation around two submarine canyonsGathering the results from dye experiments, conductivity measurements at the canyon heads andvelocity fields derived from PIV analysis, the circulation around two adjacent submarine canyonsunder upwelling conditions evolves as follows (Figure 4.17):1. In both canyons, during the initial ramp up of the shelf current, the flow is up-canyon (towardsthe canyon head) everywhere in the canyons and it increases in magnitude in time. The flowis stronger near shelf break depth and weaker deeper in the canyon. A pool of water originallywithin the canyon upwells onto the shelf and it is advected downstream on the shelf.2. After the ramp up time, cyclonic circulation develops within the canyons. An eddy startsforming in the upstream side of the canyons which then moves to the downstream side, closeto the canyons’ mouths. The eddy develops earlier in the downstream canyon. Up-canyonflow on the downstream side of the canyons is stronger with increasing Bu and stronger inthe downstream canyons. During this phase the upwelled pool of water keeps growing andreaching farther downstream on the shelf. If the forcing and initial conditions are right (RWand Bu combination), the upstream pool reaches the downstream canyon’s head.3. After the forcing has stopped, the advection dominated flow within the canyons starts to relaxand near-inertial oscillations, that had been present throughout the experiment, take over thecirculation. The oscillatory flow up and down canyon is not in phase between the upstreamand downstream canyons. Deeper than shelf break depth, the dominance of the oscillationsappears earlier than at shelf break depth.1010°10°20°30°40°50°cm10 15 20 25 30S03Mean field between 15.0-20.0 s at shelf-break depth0°10°20°30°40°50°cm10 15 20 25 30S12-0.10.00.10.2Radial velocity anomaly / cms10°10°20°30°40°50°cm10 15 20 25 30S03Mean field between 30.0-35.0 s at shelf-break depth0°10°20°30°40°50°cm10 15 20 25 30S12-0.3-0.2-0.10.00.10.20.30.40.5Radial velocity anomaly / cms10°10°20°30°40°50°cm10 15 20 25 30S03Mean field between 5.0-10.0 s at shelf-break depth0°10°20°30°40°50°cm10 15 20 25 30S120.00.10.2Radial velocity anomaly / cms10°10°20°30°40°50°cm10 15 20 25 30S03Mean field between 45.0-50.0 s at shelf-break depth0°10°20°30°40°50°cm10 15 20 25 30S12-0.2-0.10.00.10.20.3Radial velocity anomaly / cms1Figure 4.15: Mean 5 second velocity direction field (arrows) and radial speed (color map)for the first 50 seconds of experiments S03 and S12 (RW = 0.18, Bu = 1.21, 1.18) atshelf break depth (2.8-3 cm). The velocity vectors are normalized to show only thedirection of the flow and only every second arrow is plotted. Cross-shelf velocities aregreen when going up-canyon and red when going down-canyon. Both canyons respondconsistently to the same forcing and their circulation is similar to the circulation withtwo canyons (Figure 4.11).1020°10°20°30°40°50°cm10 15 20 25 30S03Mean field between 95.0-100.0 s at shelf-break depth0°10°20°30°40°50°cm10 15 20 25 30S12-0.10.00.1Radial velocity anomaly / cms10°10°20°30°40°50°cm10 15 20 25 30S03Mean field between 90.0-95.0 s at shelf-break depth0°10°20°30°40°50°cm10 15 20 25 30S12-0.10.00.10.2Radial velocity anomaly / cms10°10°20°30°40°50°cm10 15 20 25 30S03Mean field between 100.0-105.0 s at shelf-break depth0°10°20°30°40°50°cm10 15 20 25 30S12-0.10.00.1Radial velocity anomaly / cms10°10°20°30°40°50°cm10 15 20 25 30S03Mean field between 105.0-110.0 s at shelf-break depth0°10°20°30°40°50°cm10 15 20 25 30S120.00.1Radial velocity anomaly / cms1Figure 4.16: Mean 5 second velocity direction field (arrows) and radial speed (color map)for the last 20 seconds of experiments S03 and S12 (RW = 0.18, Bu = 1.21, 1.18) atshelf break depth (2.8-3 cm). The velocity vectors are normalized to show only thedirection of the flow and only every second arrow is plotted. Cross-shelf velocities aregreen when going up-canyon and red when going down-canyon. In both canyons anoscillatory flow takes over in the same way as in the two-canyon experiments (Figure4.12).103Figure 4.17: The three stages of the flow around two submarine canyons during an upwellingevent are illustrated in four panels where the stream plots show the direction of the flowand the color map shows the cross-shelf component of velocity for 15 second meansof experiment T02 at shelf break depth. From top left to bottom right: During thetime dependent phase the flow is up-canyon and increases from rest. Then, cycloniccirculation develops in both canyons that lasts while the current is steady (panels in topright and bottom left). After the forcing stops, the cyclonic circulation is weaker andthe flow within the canyons is dominated by up and down canyon oscillations.1044.4.1 Differences between upstream and downstream canyon responsesIn general, for the non-dimensional parameter space covered in the experiments, the circulationin two-canyon experiments is similar to the one-canyon cases, however there are some importantdifferences between the response in the two canyons.The depth of upwelling after the time dependent phase was consistently larger or equal in theupstream canyon than in the downstream canyon for a combination of large RW and large Bu. Thedifference between depths of upwelling is proportional to RW (correlation coefficient of 0.52) butthe correlation to Bu is not significant (correlation coefficient is 0.37 but p value is 0.2) and themaximum depth of upwelling difference between the two canyons is 30%. Compared to the onecanyon experiments, upstream canyon depth of upwelling fitted the scaling estimate derived byHowatt and Allen (2013) within 12% and the downstream canyon within 20% (Root-mean squareerror normalized by mean derived depth of upwelling), while one-canyon runs fitted the scalingestimate within 27%.The maximum density change at the downstream canyon’s head generally occurs after the maxi-mum in the upstream canyon, suggesting that the water upwelled upstream reaches the downstreamcanyon’s head and, since it comes from deeper (larger depth of upwelling), further increases thedensity change. However, during the advective phase at shelf-break depth, the up-canyon flow onthe downstream side of the canyons is stronger for the downstream canyon. If we associate largerup-canyon velocities with larger upwelling velocities, the difference between upstream and down-stream up-canyon flow could indicate that the delayed peak is due to increased upwelling withinthe downstream canyon. The largest source of interaction that I measure in this work comes fromthe arrival of the pool of upwelled water form the upstream canyon to the head of the downstreamcanyon. A metric designed to measure this interaction is inversely proportional to Bu (correlationcoefficient -0.8).It was not possible to directly compare the velocity field of two-canyon and one-canyon runswith the same non-dimensional parameters. Nonetheless, the experiments that are most similar toeach other show a consistent pattern and magnitude of radial velocities throughout an upwellingevent.When deriving the non-dimensional groups that explain the dynamics of the flow, the groupD=Ws emerged. That aspect ratio was not changed in the experiments. A more suitable numberto determine a dynamical distance between the canyons is D=a where D could be the distancebetween the head of the canyons, Dh, or the distance from downstream rim in the upstream canyonto upstream rim in the downstream canyon at the shelf break, Dm and a is the Rossby radius (Table4.1). Choosing Dm as the length scale for the distance between canyons our experiments span fromDm=a= 0:55 to 1. For these values ofDm=a, the canyons act primarily as independent canyons. Thismeans that using one-canyon models is a good approximation for a two-canyon system, providedthey are within the parameter space investigated in this work.1054.4.2 LimitationsThe results presented in this chapter are a first attempt to tackle the complex system that arises fromthe dynamical interaction between two canyons. Although there has been an effort in quantifying thedepth of upwelling and velocity fields, there are still questions about the uncertainty and precisionof the measurements to give compelling confidence ranges to our results. Sources of error thatshould be taken into account are the uncertainty of the PIV algorithms, the error associated withthe assumption of a linear density profile and the estimation of the incoming velocity of the shelfcurrent.The linear density profile assumption will be avoided once the calibration of the profiler devicedescribed in the Methods section is complete. The error associated with the incoming velocity canbe derived by comparing the velocity at a known radius from PIV measurements and compared tothe estimate I would get using the analysis in Methods.Another challenge that remains is a better characterization of the conductivity probes to beable to compare with more confidence the density measurements and decide which one is larger.For example, estimating the uncertainty of the density measurements using the drift of the probesoverestimates the error because the drift after 1 minute is smaller than the drift after 7 minutes.Comparing the circulation between upstream and downstream canyons requires more quantita-tive metrics and analysis of the velocity fields. This is will allow for a more definitive answer tohow different is the circulation within the canyons.4.5 Conclusions• Two canyons separated by a non-dimensional distance 0:6 < Dm=a < 1:0, where Dm is thedistance between canyons at the shelf break and a is the Rossby radius, primarily act asindependent canyons. The depth of upwelling in the canyons is correctly estimated by the-ory developed for a single canyon within 12% and 20% for the upstream and downstreamcanyons, respectively.• The upstream canyon induces deeper upwelling during the time dependent phase with a max-imum depth of upwelling difference of 30%.• The downstream canyon induces stronger up-canyon velocities during the advection phase.106Chapter 5ConclusionIn this thesis, two aspects of canyon-induced cross shelf exchange were addressed. The first one wasthe contribution of a submarine canyon under upwelling conditions to biogeochemical budgets andon-shelf distribution of tracers on the shelf. The second one was the collective effect of submarinecanyons to cross-shelf exchange. In this chapter I summarize the contributions of this thesis.5.1 Research questionsThere was a gap between our knowledge of upwelling dynamics in a canyon and how much itcontributes to the cross-shelf exchange of nutrients that make submarine canyons such productiveregions. To address this gap I posed four research questions that were answered in chapters 2 and3. The overall objective of these research questions was to develop a scaling scheme to estimate theamount of tracer, such as dissolved oxygen and nutrients, that upwell through a submarine canyonduring an upwelling event taking into account the effect of enhanced mixing within the canyon andthe vertical distribution of the tracer profile. Considering chapters 2 and 3, concrete answers to theresearch questions posed in the introduction are:1. Under upwelling favourable conditions how and how much tracer does a submarine canyontransport onto the shelf?Advection-induced upwelling of water through a canyon is the dominant driver of on-shelftransport of tracer mass from the open ocean, however, enhanced vertical diffusivity withinthe canyon and the initial tracer concentration profile contribute considerably to the amountand spatial distribution of tracer on shelf.The upwelling flux of water carries tracer onto the shelf near the head and the downstreamside of the canyon rim, to be further spread on the shelf, forming a pool of upwelled waterand tracer on the shelf downstream of the canyon. The amount of water, and thus tracer,transported onto the shelf is larger with decreasing Burger number and increasing Rossby107number. For a tracer profile that increases with depth, a larger upwelling depth will bringwater with higher concentration onto the shelf.The question of how much tracer is upwelled through a canyon is answered via scaling es-timates. In chapter 2, a scaling estimate of tracer flux as a function of the upwelling flux ofwater and the vertical diffusivity profile was proposed (Equation 2.29). In Chapter 3, a scalingestimate of tracer flux was proposed as a function of the upwelling flux and the gradient ofthe tracer profile (Equation 3.8). The area covered by the pool of upwelled tracer was alsoestimated as a function of the initial tracer profile gradient near shelf break depth, the amountof water upwelled and the initial background tracer distribution on shelf (Equation 3.13).2. What is the combined effect of locally-enhanced mixing and advection in the canyon-inducedtransport of tracers onto the shelf?Locally-enhanced mixing impacts the transport of tracers in two ways. First, it weakensthe stratification below rim depth. A smaller stratification increases the vertical advectivetransport of water and thus, of tracers. The mechanism is that isopycnals close to the headare squeezed due to upwelling, which generates a local increase in stratification proportionalto the isopycnal tilting generated by upwelling. However, enhanced diffusivity acts againsttemperature and salinity gradients, thus reducing this density gradient and locally reducingstratification below the rim. The combined effect of lower buoyancy frequency and higherdiffusivity below the rim via a smoother vertical eddy diffusivity profile can increase thewater flux by up to 26% for values chosen in Chapter 2.The second mechanism is that enhanced mixing increases the tracer concentration near rimdepth. Just above rim depth, where the value of canyon eddy diffusivity Kcan changes, thetracer gradient increases. This means that concentration isolines are elevated higher comparedto the situation with uniform diffusivity and in turn, isolines of higher concentrations willbe reaching rim depth. This water with higher tracer concentration will upwell. Together,both mechanisms increase the tracer flux onto the shelf. For instance, taken together bothcontributions can increase tracer upwelling flux by 27% when Kcan is locally enhanced bythree orders of magnitude. In this case the the flux of water was enhanced by 19%.3. What is the impact of the initial tracer profile in the canyon-induced transport of tracers ontothe shelfTracer upwelling induced by a submarine canyon depends on the vertical gradient of theinitial tracer profile near shelf break depth and through the depth of upwelling. The errorfrom approximating the canyon-induced tracer flux as the upwelling flux of water multipliedby the initial concentration of the tracer at shelf break depth as has been done previously, canbe as large as 40%.1084. How does the on-shelf distribution of tracers depend on the initial tracer profile tracers?The canyon modifies the distribution of tracers on the shelf. During a canyon-induced up-welling event, a pool of dense water with low oxygen, high DIC and nutrients is formed onthe shelf downstream of the canyon, near the bottom. This pool can be as large as 40 timesthe canyon area for Astoria Canyon and 15 times the canyon area for Barkley Canyon. Theconcentration of tracer within the pool can be up to 1.5 times that initially at shelf break depth,but the maximum value depends on the specific tracer. Pool area is a function of the on-shelfcanyon-induced tracer flux and the background tracer distribution on the shelf.The second area of research concerned the collective effect of submarine canyons and how theycontribute to cross-shelf exchange. For this thesis I narrowed down this broad topic into a systemof two adjacent submarine canyons under upwelling conditions. The following research questionswere answered in chapter 3.1. What is the impact of the upstream canyon on the dynamics of the downstream canyon?The dynamics of the downstream canyon are mainly independent of the upstream canyon forthe parameter space investigated in this thesis (0:55<Dm=a< 1:0), whereDm is the minimumdistance between canyon mouths and a is the Rossby radius. The flow in both canyons ismostly the same as it would be in a single canyon with two differences. Upwelling depthtends to be larger in the upstream canyon (up to 30%) and up-canyon velocities developedduring the advective phase tend to be larger in the downstream canyon.2. Which are the relevant physical processes and parameters?Canyons interact through the pool of upwelled water. The upwelled water from the upstreamcanyon was observed near the head of the downstream canyon during some experiments,further increasing the density in that region for longer periods of time. Results from chapter3 suggest that the pool will reach the downstream canyon if the canyons are close enough andif the off-shore deviation of the pool is small (dye experiments).The combination of stratification and Coriolis parameter is encapsulated in the Rossby radiusa. Our experiments consider values of a non-dimensional distance 0:55 < Dm=a < 1, whereDm is the separation between canyons. For this range of values the impact of coastal trappedwaves does not seem to have any effect in the circulation around the canyons.3. Which of the two canyons is leading and under what conditions?Given that the canyons act independently there is no leading canyon. Considering the answersabove, the upstream canyon could be considered as somewhat leading given that its pool ofupwelled water can arrive to the head of the downstream canyon and modify the distributionand maximum value of density and potentially any other property of the water there. The109Figure 5.1: Schematic of tracer transport through two submarine canyons. (1) The upwellingcurrent, which is similar for both canyons (blue arrow), brings tracer-rich water onto theshelf, generating an area of relatively higher tracer concentration than the upstream shelf(4). Enhanced vertical diffusivity within the canyons increases the tracer concentrationnear rim depth and weakens the stratification (2). These two effects enhance canyon-induced tracer flux onto the shelf. Initial tracer gradient at shelf-break depth determinesthe upwelling flux of tracer (3) and the size of the pool (4). Canyons may interact via theupstream pool (5).upstream canyon also tends to have a larger depth of upwelling, but the downstream canyonhas larger on-shelf velocities.5.2 Contributions to the fieldAnswering the research questions has narrowed the existing gap between the previously studieddynamics of canyons and the observations of canyons as productive areas and regions of enhancedbiodiversity. Following the results from this thesis we can now arrive at the following schematic ofcross-shelf transport of tracers through two adjacent submarine canyons under upwelling conditions,allowing us to expand previous schematics (e.g., Allen and Hickey, 2010; Allen et al., 2001) toinclude tracers and multiple canyons:1. The upwelling flux carries tracer onto the shelf near the head and the downstream side of thecanyon rim, to be further spread on the shelf; with decreasing Burger number and increasingRossby number, the amount transported is larger. The two canyons act mostly as independentcanyons as long as 0:55< Dm=a< 1 although up-canyon flow in the downstream side of thecanyons can be larger in the downstream canyon and the depth of upwelling is usually larger110in the upstream canyon (by up to 30%).2. Enhanced mixing within the canyons can impact the flow in two ways: first, it increases theupwelling flow by weakening the stratification below rim depth due to isopycnal stretching;second, it increases the tracer concentration near rim depth, upwelling water with higherconcentration than in the case with uniform diffusivity. These combined effects can increasethe tracer upwelling flux by 27% in a submarine canyon with enhanced diffusivity 3 orders ofmagnitude larger than background (along adjacent shelves) values.3. Tracer flux is proportional to the tracer gradient near the shelf break. The error from approxi-mating the canyon-induced tracer flux as the upwelling flux of water multiplied by the initialconcentration of the tracer at shelf break depth as has been done previously, can be as largeas 40%. For a tracer profile that increases with depth, a larger upwelling depth will bring wa-ter with higher concentration onto the shelf; with decreasing Burger number and increasingRossby number, the depth of upwelling is larger.4. The upwelled water spreads out on the shelf, downstream of the rim and generates a regionof relatively larger tracer concentration near the bottom. During a canyon-induced upwellingevent, a pool of dense water with low oxygen, high DIC and nutrients is formed on the shelfdownstream of the canyon, near the bottom.5. Canyons can interact when the pool of the upstream canyon reaches the downstream canyon’shead.Additionally, within the schematic picture of the tracer and water transport there are quantitativemodels to estimate the canyons’ contribution to on-shelf tracer budgets taking into account locally-enhanced mixing and the geometry of the initial tracer profile.5.3 Research implications and limitations5.3.1 Scaling schemesCanyons are numerous but highly understudied oceanic regions. So much so that only 11 out of2076 shelf incising canyons have been studied in detail (Matos et al., 2018). The large numberof canyons and the challenges associated with studying them observationally require us to developmore general methods and tools that can be applied to more than one canyon at a time. In thiscontext, scaling estimates are a valuable tool. They allow us to parametrize and infer things aboutcanyons that have not been studied yet.Considering that canyons don’t interact much, our current upwelling estimates are a good ap-proximation to several canyons. In particular, the fact that canyons are independent means that111adding their individual cross-shelf transport estimates is a good approximation to account for theircollective contribution to the on-shelf budget of tracers. The scaling estimates derived in this thesiscould be easily applied to a specific canyon after an observational campaign or used to parametrizethe contribution of a number of canyons to the cross-shelf exchange of nutrients and solutes inmodels with coarse resolution.The results and overall scaling scheme presented in Chapters 2 and 3 are valid only for shortcanyons. This criterion removes some of the most iconic canyons, like Monterey and Nazare´Canyons. For other canyons, we expect that, provided there is squeezing of isopycnals and a differ-ence in diffusivity above and below the rim, the same effect of non-uniform diffusivity would occur:the differentiated diffusivity will act to further enhance the stratification above the rim and furtherdecrease it below the rim. The tracer part of the scaling would be similar but an appropriate depthof upwelling, Z, and fitting parameters would need to be found. For less idealized bathymetries theoverall upwelling pattern is expected to be very similar, provided that the incoming flow is alongthe shelf, perpendicular to the canyon axis, and relatively uniform along the length of the canyon.Scaling of the upwelling flux and depth of upwelling is robust enough that it has been successfullyapplied to real, short canyons like Astoria, Barkley and Quinault Canyons (Allen and Hickey, 2010)and in one of the limbs of Whittard Canyon (depth of upwelling in Porter et al. (2016)).5.3.2 Mixing effectsThe effects that enhanced mixing within the canyon have on the stratification can potentially alterthe propagating characteristics of internal waves in the canyon. Enhanced, upwelling-induced strat-ification near rim depth, close to the canyon head (upper canyon), can increase the criticality, a ,of the upper canyon walls, changing the direction from up-canyon to down-canyon or vice versa.It can also affect the transition between a partly standing wave during pre-upwelling conditions topropagating during upwelling conditions. Moreover, my results show that having elevated diffusiv-ity within the canyon will erode the increased, canyon-induced stratification below rim depth andenhance it above rim depth. If we assume that the stratification that matters for criticality occursaround rim depth, then the competition between squeezing and stratification erosion will determinethe change in criticality.5.3.3 Impact of the initial tracer profileThe impact of tracer cross-shelf transport is different depending on the depth of interest in the watercolumn and the tracer that is considered. For example, nutrient upwelling through the canyon isrelevant to the overall tracer inventory on the shelf (nutrients in general) even if it does not reachthe euphotic zone. Reaching the euphotic zone is particularly important if the nutrient is nitrate.If the tracer is oxygen, DIC or alkalinity then the largest impact will be on demersal and benthicecosystems given that the pool of upwelled tracer sits at the bottom of the shelf.112The presence of corrosive, oxygen-depleted waters near the shelf bottom is common in up-welling systems. However, in the past 10 years this water has been reaching shallower depths andcovering larger areas than normal on the West Coast of North America (Feely et al., 2008). Undera changing climate, the occurrence of these waters can be more frequent and in larger volumes thanbefore. In the numerical experiments in Chapter 3, in cases with realistic stratification, the increasein DIC and total alkalinity relative to the no-canyon cases in the pool of upwelled water correspondsto a decrease in pH of 0.1-0.04 for the canyons studied.5.3.4 Laboratory modelsAs our numerical models improve and our computing capability increases, there is less interest insetting up physical models of the systems we study. A reason for this may be that laboratory modelsgive a lot less information, in terms of data resolution, about the system than a numerical model,but that is not necessarily a disadvantage. My short experience has been that you can easily get lostin the huge amount of data that you get from the numerical model. Setting up a physical modelrequires you to think about what you really want and need to know about the system. Moreover, itdevelops your intuition of the system and allows you to define what is needed from the numericaloutput. The most advantageous strategy is to let the information from the physical model guide theexploration of the output from the numerical model. Not all problems are suitable for this kind ofresearch but if they are, using a physical model can enrich and focus the analysis of the numericaloutput, in addition to providing data to evaluate the numerical model.5.4 Future research directionsFurther research is needed to determine the interaction between two upwelling canyons. In thisdissertation, experiments with non-dimensional distance Dm=a between 0.55 and 1 were studied,but in all of them the quantity that changed was the Rossby radius a and not the distance betweencanyons Dm. In fact, no geometrical parameters were changed in any of the experiments. In turn,the selection of length scales to generate non-dimensional groups was somewhat arbitrary. In futureruns, geometric parameters of the canyons have to be changed to be able to determine which are therelevant length scales of the flow.Two canyons with exactly the same geometry are a good first attempt to study canyon interac-tion, but it is not a very realistic configuration. Although short canyons are more numerous than longcanyons, they differ in shape and size. Experiments with canyons of different shapes and lengths,in particular the interaction of a long canyon and a short canyon, would be a natural next step forthese tank experiments.Submarine canyons are well known hot spots of biodiversity and highly productive regions.Certainly, upwelling of nutrient rich water can trigger biological productivity, but near the shelf113bottom canyons may have another important impact on biological systems. A recurring topic inChapters 2, 3 and 4 is the presence and extension of a pool of upwelled water and tracer that mayreach adjacent canyons. More work and attention is needed to address the link between these poolsand the effect they may have on benthic and demersal communities on adjacent shelves and nearbycanyons. 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Persistently declining oxygen levels in theinterior waters of the eastern subarctic pacific. Prog. Oceanogr., 75(2):179 – 199. Time Seriesof the Northeast Pacific. → pages 11Wunsch, C. (1975). Internal tides in the ocean. Rev. Geophys., 13:167–182. → pages 9Zhang, W. G. and Lentz, S. J. (2017). Wind-driven circulation in a shelf valley. Part I: Mechanismof the asymmetrical response to along-shelf winds in opposite directions. J. Phys. Oceanogr.,47:2927–2947. → pages 20, 52Zhao, Z., Alford, M. H., Lien, R.-C., Gregg, M. C., and Carter, G. (2012). Internal Tides andMixing in a Submarine Canyon with Time-Varying Stratification. J. Phys. Oceanogr.,42(12):2121–2142. → pages 45, 47121Appendix ANotes on Body ForcingIn the numerical model used in chapters 2 and 3 The flow is started from rest by applying a bodyforce on every cell of the domain directed alongshore. This forcing has a similar effect as changingthe rotation rate of a rotating table. The body forcing ramps up linearly during the first day ofsimulation, stays constant for another day and ramps down to a minimum during day 3, after whichthe forcing remains constant and just enough to avoid the spin down of the shelf current (Fig. A.1).The maximum forcing applied is equivalent to a velocityUmax= 0:315ms−1 that gives a maximumacceleration of gU =Umax=(FT+ST=2)where FT is the time during which the maximum forcingis applied (86400 s or 1 day) and ST is the ramping time (86400 s). The force ramps up over theshort time (ST) setting, Umax is applied over the forcing time (FT). The body forcing is added tothe along shore velocity (u) tendency for each point (xi,yi,zi) as gU(i; j;k)=gU(i; j;k) + b f . Thebody forcing b f is defined for each cell in the domain at time t and alongshore distance y asat yDcoast−DSB t < STa(ST ) yDcoast−DSB ST < t < FT +STa(FT +2ST − t) yDcoast−DSB FT +ST < t < FT +(2− sr)STa(sr)ST yDcoast−DSB FT +(2− sr)ST < twhere122Figure A.1: The left panel shows the body forcing (units ms−2) applied to the alongshorevelocity tendency at 5 different cross-shore locations (indicated in the right panel) at alldepths.Setting Value DescriptionFT 86400 s Time Umax is appliedST 86400 s Short time, ramp up timeUmax 0.315 ms−1 Max. velocity alongshoregUmax Umax/(FT+ST/2) Max forcing at coast (ms−2)a gUmax/ST Slope of forcingDcoast 90000 m Cross-shore distance to coastDSB 35000 m Cross-shore distance to shelf break from coastsr 0.15 Final, steady forcing ratioThis forcing generates a deeper shelf current, less focused on the surface, than the coastal jetgenerated by wind-forced models. This is a desirable feature since this kind of flow is observed, forexample, on the western shelf and slope Vancouver Island. Besides, when comparing wind-forcedand body forced models of downwelling in canyons, Spurgin and Allen (2014) see no real differencein terms of the canyon response.Previous studies (Allen and Hickey (2010), Ka¨mpf (2007)) show that canyon upwelling scaleswith U , the magnitude of the alongshore velocity upstream of the canyon (The correct relation isthat it goes asU3 from Allen and Hickey (2010)). How this velocity is achieved is unimportant forthe canyon dynamics. One way to get an upwelling-favourable incoming flow is to have a coastaljet set up via wind-stress, but this is not the only way. For example, Sobarzo et al. (2016) reportseveral occurrences of upwelling of cold, nutrient-rich, oxygen depleted waters through the Biobio123Canyon in Chile related to the passage of coastal trapped waves and not driven by the wind.The reason to simulate a 9 day upwelling event comes from observations on the the West Coastof Vancouver Island; from ADCP data at the slope of the west coast of Vancouver Island we canfind characteristic time scales of upwelling-favourable currents near Barkley Canyon. Alongshoreand cross-shore velocities were provided by the Neptune Observatory operated by Ocean NetworksCanada at Pod 2, on the upper slope station of the Barkley Canyon network (map on figure A.2).The instrument I used was the 75kHz ADCP located at 400 m depth, located upstream of BarkleyCanyon during upwelling-favourable conditions. Tides were removed after applying a Doodsonfilter (39 days).Although summer 2014 was not particularly upwelling favourable, we can see two longer events,one from May 29th to June 17th and the second one from July 29th to August 15th (Fig. A.2). Eachone lasts no more than 20 days including spin up to the maximum magnitude of the incoming flowand spin down into slower or positive flow. This is consitent with evidence reported by Mirshak andAllen (2005) and Hickey (1997). The flow is nearly-uniform in the vertical between 50-250 m depthduring the two periods of canyon-driven upwelling favourable flow, consistent with the circulationgenerated by our body forcing.124128 127 126 125 124 12347.548.048.549.049.5Lat126.6 126.2 125.8Lon48.148.248.348.448.548.6Lat-1500-1000-800-500-350-350-20050100150200250300350Depth (m)(a)15/May 15/Jun 15/Jul 15/Aug 15/Sep0.10.00.10.20.3Alongshelf speed (ms−1) (b)ms−1-0.60-0.45-0.30-0.150.000.150.300.450.60Figure A.2: The main reason to choose simulations no longer than 9 days is that the time scaleof upwelling events near the short canyons on the west coast of Vancouver Island, BCare on this order. To illustrate this, we show ADCP data at the slope on the west coastof Vancouver Island near Barkley Canyon. Alongshelf and cross-shore velocities wereprovided by the Neptune Observatory operated by Ocean Networks Canada at Pod 2 ofthe upper slope station of the Barkley Canyon network, taken from the 75kHz ADCPlocated at 400 m depth, upstream of Barkley Canyon, during upwelling conditions. Thealongshore velocity was filtered using a Doodson filter (39 hours) to remove the tides.Although summer 2014 was not particularly upwelling favourable, we see two longerevents, one from May 29th to June 17th and the second one from July 29th to August15th (b). Each one lasts no more than 20 days each. This is consistent with evidencereported by Mirshak and Allen (2005) and Hickey (1997). Also note that the flow isnearly-uniform in the vertical between 50-250 m depth during the two periods of canyon-driven upwelling favourable flow, supporting the use of body forcing to generate a deepershelf current than wind stress would (a). Negative (upwelling-favourable) flows aredirected southwards.125Appendix BSupplementary Results for Chapter 2126Table B.1: Mean vertical (VTT), advective (VATT) and total (TTT) tracer transport anomaliesthrough cross sections CS1-CS5 and LID as well as vertical water (VWT) and total (TWT)water transport anomalies throughout the advective phase with corresponding standarddeviations calculated as 12 hour variations for all runs.Exp VTT VATT TTT VWT TWT105 mMm3s−1 105 mMm3s−1 104 mMm3s−1 104 m3s−1 102 m3s−1base case 1.6±0.29 1.6±0.29 0.46±0.13 1.9±0.46 -1.6±5.2↑ N0 1.1±0.24 1.1±0.24 0.29±0.09 1.4±0.36 -2.4±6.0↑↑ N0 0.73±0.20 0.73±0.20 0.14±0.06 0.91±0.29 -5.5±4.7⇓ N0 2.3±0.40 2.3±0.40 0.79±0.18 2.5±0.61 -1.4±3.3↓↓ N0 2.2±0.36 2.2±0.36 0.74±0.16 2.5±0.58 -1.4±4.0↑ f 1.7±0.32 1.7±0.32 0.49±0.13 2.0±0.48 -0.57±5.04↓↓ f 1.1±0.17 1.1±0.17 0.30±0.10 1.3±0.33 -11.4±6.2↓ f 1.3±0.22 1.3±0.22 0.37±0.11 1.6±0.39 -6.1±5.7⇓ f 0.92±0.16 0.92±0.16 0.21±0.09 1.0±0.32 -18.1±6.5↓ U 1.4±0.29 1.4±0.29 0.38±0.09 1.7±0.48 0.61±6.8↓↓ U 1.1±0.26 1.1±0.26 0.27±0.06 1.4±0.39 -0.55±5.8⇓ U 0.43±0.05 0.43±0.05 0.12±0.01 0.60±0.09 4.3±2.2⇓ U, ↓↓ N0 0.72±0.04 0.72±0.04 0.21±0.01 0.94±0.08 5.9±2.1⇓ U, ↑↑ N0 0.21±0.04 0.21±0.04 0.06±0.01 0.32±0.06 3.4±1.2⇓ U, ⇓ f 0.26±0.04 0.26±0.04 0.06±0.01 0.37±0.07 0.91±2.2⇑⇑ Kcan, e10 2.2±0.21 1.9±0.21 1.1±0.09 2.2±0.28 8.5±1.3⇑⇑ Kcan, e25 2.5±0.18 2.2±0.18 1.2±0.06 2.4±0.24 4.6±1.1⇑⇑ Kcan, e50 2.8±0.15 2.5±0.16 1.3±0.06 2.8±0.22 3.0±1.3⇑⇑ Kcan, e100 3.0±0.15 2.6±0.16 1.3±0.08 3.0±0.21 1.8±1.3⇑⇑ Kcan, e15 2.4±0.20 2.0±0.20 1.2±0.08 2.3±0.27 7.5±1.05⇑⇑ Kcan, e75 2.9±0.14 2.5±0.16 1.3±0.07 2.9±0.21 2.2±1.3↑↑ Kcan 1.9±0.25 1.8±0.25 0.74±0.10 2.1±0.39 0.64±3.7⇑↑ Kcan 2.2±0.22 2.0±0.22 1.0±0.09 2.4±0.32 7.7±2.5↑↑ Kcan e25 1.9±0.25 1.8±0.26 0.71±0.10 2.1±0.40 -0.70±4.2↑↑ Kcan e100 1.9±0.25 1.8±0.25 0.69±0.10 2.1±0.40 -1.6±3.8⇑↑ Kcan e25 2.4±0.20 2.1±0.20 1.1±0.07 2.4±0.31 2.14±2.01⇑↑ Kcan, e100 2.5±0.18 2.3±0.19 1.1±0.07 2.7±0.29 0.36±1.9⇑↑↑ Kcan 2.2±0.25 1.9±0.24 1.0±0.10 2.2±0.32 9.5±2.2⇑⇑↑ Kcan 1.9±0.25 1.7±0.23 0.94±0.11 1.9±0.30 9.7±1.5⇑ Kcan 2.1±0.22 2.0±0.23 0.91±0.08 2.3±0.34 4.2±2.9↑ Kcan 1.8±0.26 1.7±0.26 0.65±0.11 2.0±0.42 -0.55±4.4⇑⇑ Kcan 2.0±0.25 1.8±0.24 0.97±0.11 2.1±0.32 9.6±1.8127Table B.2: Mean water and tracer upwelling fluxes (F (4) and FTr (5)) for all runs during theadvective phase, reported with 12 hour standard deviations. All other quantities are eval-uated at day 9: Volume of upwelled water (Vcan), upwelled tracer (Mcan) for the canyoncase and fractional canyon contributions to these quantities calculated as the canyon caseminus the no-canyon case divided by the canyon case, and total tracer mass anomaly onshelf (M-Mnc (6)) in kg of NO−3.Exp F(104m3s−1)FTr(105mMm3s−1)Vcan(1010m3)(Vcan−Vnc) V−1can(%)Mcan(1011mMm3)(Mcan−Mnc) M−1can(%)M−Mnc(106 kgNO−3 )base case 3.85±0.60 2.76± 0.26 2.86 81.61 2.20 82.57 1.96↑ Kbg 3.70±0.73 2.29± 0.24 2.80 87.26 2.05 87.20 2.02↑↑ Kbg 3.72±1.58 0.96± 0.40 3.12 63.77 1.79 58.68 2.35↑ N0 2.86±0.44 1.99± 0.19 2.08 88.29 1.57 88.52 1.21↑↑ N0 1.32±0.55 1.11± 0.44 1.10 77.74 0.82 77.91 0.62⇓ N0 6.78±0.94 5.21± 0.82 4.63 29.03 3.69 34.85 3.48↓↓ N0 6.34±0.92 4.84± 0.72 4.35 30.84 3.45 36.36 3.25↓ N0 5.15±0.95 3.86± 0.74 3.69 35.50 2.90 40.33 2.73↑ f 4.03±0.58 2.95± 0.36 2.96 73.08 2.30 74.70 2.06↓↓ f 2.95±0.72 1.96± 0.33 2.18 85.80 1.65 86.09 1.38↓ f 3.42±0.73 2.28± 0.14 2.51 88.28 1.92 88.62 1.64⇓ f 1.83±0.88 1.03± 0.42 1.56 76.77 1.17 77.09 1.03↓ U 3.02±0.39 2.27± 0.27 2.18 86.87 1.66 87.30 1.48↓↓ U 1.92±0.39 1.50± 0.26 1.41 82.16 1.06 82.63 1.03⇓ U 0.14±0.23 0.15± 0.07 0.18 69.05 0.13 69.53 0.31⇓ U, ↓↓ N0 0.61±0.27 0.40± 0.12 0.49 66.83 0.37 67.73 0.59⇓ U, ↑↑ N0 0.01±0.07 -0.02± 0.02 0.03 40.56 0.02 41.18 0.13⇓ U, ⇓ f 0.11±0.35 -0.02± 0.04 0.10 17.99 0.08 18.79 0.18⇓ U, ↑↑ Kcan 1.23±0.46 0.74± 0.09 0.88 0.78 0.65 1.26 0.25Kcan Monterey (bot) 4.97±0.48 3.77± 0.31 3.62 85.48 2.71 85.81 4.57Kcan Eel (bot) 3.86±0.59 2.74± 0.20 2.89 81.81 2.22 82.69 2.81Kcan Monterey 3.87±0.53 2.80± 0.16 2.87 81.69 2.25 82.94 2.85Kcan Ascension (bot) 4.18±0.60 3.01± 0.24 3.07 82.91 2.37 83.82 3.29⇑⇑ Kcan, e10 4.07±0.55 3.42± 0.34 3.10 83.05 2.53 84.83 3.71⇑⇑ Kcan, e25 4.12±0.71 3.43± 0.50 3.14 83.29 2.52 84.76 4.24⇑⇑ Kcan, e50 4.21±0.71 3.29± 0.55 3.18 83.48 2.46 84.38 4.53⇑⇑ Kcan, e100 4.51±0.64 3.40± 0.46 3.36 84.37 2.52 84.76 4.70⇑⇑ Kcan, e15 4.08±0.65 3.47± 0.41 3.12 83.17 2.54 84.89 3.94⇑⇑ Kcan, e75 4.39±0.67 3.36± 0.50 3.28 84.01 2.49 84.57 4.63⇑⇑ Kcan, e150 4.70±0.61 3.50± 0.40 3.45 84.80 2.56 85.00 4.71↑↑ Kcan 3.77±0.62 2.71± 0.13 2.84 81.53 2.24 82.83 2.77⇑↑ Kcan 4.05±0.50 3.21± 0.29 3.03 82.65 2.46 84.35 3.50↑↑ Kcan e25 3.73±0.63 2.65± 0.13 2.82 81.41 2.21 82.60 2.70↑↑ Kcan e100 3.70±0.67 2.57± 0.17 2.81 81.34 2.17 82.31 2.66⇑↑ Kcan e25 3.98±0.53 3.09± 0.30 3.00 82.47 2.39 83.91 3.73⇑↑ Kcan, e100 4.14±0.56 3.04± 0.27 3.07 82.92 2.35 83.63 3.86⇑↑↑ Kcan 4.08±0.54 3.35± 0.33 3.08 82.94 2.51 84.70 3.48⇑⇑↑ Kcan 4.17±0.65 3.51± 0.39 3.13 83.22 2.55 84.95 3.27⇑ Kcan 3.91±0.56 2.93± 0.16 2.92 82.03 2.34 83.57 3.23↑ Kcan 3.65±0.67 2.57± 0.13 2.78 81.14 2.17 82.33 2.50⇑⇑ Kcan 4.09±0.58 3.39± 0.37 3.09 83.02 2.53 84.79 3.38128Appendix CAdvection-Diffusion Equation inNatural CoordinatesWe need to express the rhs of (2.11) in terms of (s,z,n) to compare the relative size of each term. Todo that we calculate the first and second spatial derivatives of the concentration:¶C¶h=¶C¶ s¶ s¶h+¶C¶n¶n¶h+¶C¶ z¶ z¶h: (C.1)Note that,¶n¶h=¶n¶t= 0; (C.2)¶ z¶ s=¶n¶ s= 0; (C.3)and¶n¶b= 1; (C.4)since n= b. Further,¶ z¶h≈ ¶ s¶t≈ cosa; (C.5)¶ s¶h≈ ¶ z¶t≈ sina; (C.6)so that for small angles,129cosa ≈ 1; (C.7)sina ≪ 1: (C.8)The second derivative with respect to h , after eliminating terms and approximating the trigono-metric functions of small angles is¶¶h(¶C¶h)=¶¶h(¶C¶ s¶ s¶h)+¶¶h(¶C¶ z¶ z¶h): (C.9)Expanding and eliminating terms according to (C.3) and (C.4) gives¶ 2C¶h2≈ 2 ¶2C¶ z¶ s¶ s¶h¶ z¶h+¶ 2C¶ z2(¶ z¶h)2: (C.10)The second derivative with respect to t is approximated as¶ 2C¶t2≈ 2 ¶2C¶ z¶ s¶ s¶t¶ z¶t+¶ 2C¶ s2(¶ s¶t)2: (C.11)Finally, the second derivative with respect to b is¶ 2C¶b2=¶ 2C¶n2: (C.12)The final approximation of (2.10) is¶C¶ t+u¶C¶ s+w¶C¶ z≈ KI(¶ 2C¶ s2+¶ 2C¶n2+2¶ 2C¶ z¶ s¶ z¶t)+KD(¶ 2C¶ z2+2¶ 2C¶ z¶ s¶ s¶h): (C.13)130Appendix DEffect of Diffusivity DistributionI use a 1D model of diffusion through two layers of water with different diffusivities to illustratethe effect of a sharp diffusivity profile and progressively smoother versions of that step describedby the smooth Heaviside function (2.1). Increasing e increases the depth where the concentration ischanging due to a mismatch in the flux (Fig. D.1, panels a-c), and at the interface (z= Hr) we see asmaller increase in concentration relative to the step profile.1310.00 0.05 0.10 0.15C-Co−300−250−200−150−100−500depth / m(a)τ=6 d, ε=30 m0.00 0.02 0.04C-Co(b)Kcan=10−3 m2s−1, ε=30 m1 days2 days4 days6 days8 days10 days12 days0.00 0.02 0.04 0.06C-Co(c) τ=6 d, Kcan=10−3 m2s−11 m5 m10 m20 m30 m40 m50 m60 m0 5 10∂zC/∂zC0−300−250−200−150−100−500depth / m(d)10−5m2s−15×10−4m2s−110−3m2s−15×10−3m2s−18×10−3m2s−110−2m2s−11.2×10−3m2s−10.5 1.0 1.5 2.0 2.5∂zC/∂zC0(e)0 2 4 6 8∂zC/∂zC0(f)0 5 10 15 20 25 30 35Zdif/Δz0.00.20.40.60.81.0min (∂zC/∂zC0)(g)ε runsKcan runsτ runsexpΔ−0.15Zdif/Δz)Figure D.1: (a-c) Tracer concentration difference from the initial profile for runs from the 1Ddiffusion model varying (a) Kcan, (b) t and (c) e . (d-f) Corresponding tracer profilegradients. (g) Minimum tracer gradient for 1D model runs covering the parameter spacee = 1 to 50 m (e runs), Kcan = 10−5 to 1:2× 10−2 (Kcan runs) and t = 1 to 12 days (truns). The orange line corresponds to the fitted decreasing exponential function relatingthe stretching and Zdi f =∆z.132Ascension0.00.20.40.60.81.0z7.55.02.5log10(K/ m2s 1)0.250.000.250.500.751.00z rim0.00.20.40.60.81.0z7.55.02.5log10(K/ m2s 1)0.250.000.250.500.751.00z rimEelMonterey0.00.20.40.60.81.0z7.55.02.5log10(K/ m2s 1)0.50.00.51.0z rimFigure D.2: Diffusivity profiles from observations in Monterey (Carter and Gregg, 2002) , Eel(Waterhouse et al., 2017) and Ascension (Gregg et al., 2011) Canyons. Green lines cor-respond to individual profiles along the canyon axis and black lines correspond to themean profile. For comparison, the vertical coordinate is normalized in two differentways: by bottom depth, z′ = z=zbottom where zbottom is the depth of the canyon at eachparticular station; or using the rim depth, z′rim = (z− zrim)=(zbottom− zrim). We run simu-lations with both normalizations for each canyon. Note that for Monterey and AscensionCanyons, the mean profiles have similar levels of diffusivity near rim depth (z′rim = 0,dashed black line) to our locally-enhanced diffusivity runs. We assigned values of e toeach run based on the variation of Kv above rim depth and found it to be on the orderof 50 m. Data from Monterey and Eel Canyons were kindly provided by G. Carter andA. Waterhouse, respectively. Profiles from Ascension Canyon were taken directly fromFigure 11 in (Gregg et al., 2011) by using an inverse algorithm on the image, so theaccuracy of the data is not what is reported on the original paper. We are using thesedata to put our experiments into context and compare it to less idealized mixing profiles.133Appendix ESupplementary Results for Chapter 3Supplementary to the methods section I include a figure showing the location of the stations wheremeasurements of nutrients, dissolved oxygen, dissolved inorganic carbon, methane and nitrous-oxide, used to generate the initial profiles of the simulations, were taken. These stations correspondto stations visited during research cruises on the West Coast of Vancouver Island: the PathwaysCruise 2013 Klymak et al. (2013) and Line C cruises in May 2012, May 2013. Methane and nitrous-oxide profiles from Line C were provided by Dr. David Capelle and published in Capelle and Tortell(2016).Initial tracer profiles used to initialize the 10 tracers simulated in the experiments come frombottle samples collected during the Pathways Cruise (2013) and cruises to Line C (2013 and 2012).Methane and nitrous-oxide profiles correspond to the mean values of profiles taken at stations inLine C, upstream of Barkley Canyon. All other tracers are mean values of profiles taken along theaxis of Barkely Canyon during the Pathways Cruise.134126.6 126.4 126.2 126.0 125.8Longitude48.148.248.348.448.548.6LatitudePathwaysLine C 1500 1000 800 600 400 300 200  100128 127 126 125 124 123Longitude47.548.048.549.049.5Latitudem2400180012006000600120018002400Figure E.1: Initial tracer profiles used to initialize the 10 tracers simulated in the experimentscome from bottle samples collected during the Pathways Cruise (2013) and cruises toLine C (2013 and 2012). Methane and nitrous-oxide profiles correspond to the meanvalues of profiles taken at stations in Line C, upstream of Barkley Canyon. All othertracers are mean values of profiles taken along the axis of Barkely Canyon during thePathways Cruise. The location of the stations in Line C and Pathways Cruise are shownas orange and red pentagons, respectively.Supplementary to the results section I include the same tables as in Chapter 3 but for tracers notreported in Chapter 3: salt, DS, phosphate, nitrous-oxide, and total alkalinity.135Table E.1: Tracer transport units (TU) for each tracer are mMm3s−1, mMm3s−1, nMm3s−1and kg−1m3s−1, respectivelyExp Mean NT (104TU)Mean NTrelative toAST (%)Canyoncontribution%Max NT(104 TU)Max NTrelative toAST (%)Canyoncontribution%AST Sal 21.38 ± 1.38 100.00 77.60 24.90 100.00 82.06ARGO Sal 15.65 ± 1.65 73.22 75.38 20.03 80.43 74.54BAR Sal 5.36 ± 0.28 25.05 35.87 8.31 33.37 47.43PATH Sal 5.05 ± 0.28 23.63 31.50 8.59 34.49 43.87AST DS 201.53 ± 10.64 100.00 47.22 309.21 100.00 78.80ARGO DS 154.76 ± 7.54 76.79 33.05 227.39 73.54 60.38BAR DS 103.80 ± 3.94 51.50 6.71 124.82 40.37 18.37PATH DS 118.83 ± 5.88 58.96 10.59 147.42 47.68 21.45AST Pho 8.27 ± 0.33 100.00 40.76 12.15 100.00 75.62ARGO Pho 6.56 ± 0.30 79.28 27.29 9.34 76.87 55.32BAR Pho 4.08 ± 0.15 49.30 5.92 4.87 40.12 17.00PATH Pho 4.52 ± 0.24 54.60 7.99 5.69 46.83 17.31AST NiO 0.09 ± 0.00 100.00 37.26 0.13 100.00 72.24ARGO NiO 0.07 ± 0.00 80.72 24.08 0.10 78.36 53.64BAR NiO 0.04 ± 0.00 47.40 5.54 0.05 36.60 16.34PATH NiO 0.04 ± 0.00 50.61 6.36 0.05 40.85 16.40AST Alk 1453.89 ± 98.06 100.00 79.03 1709.11 100.00 84.45ARGO Alk 1054.76 ± 110.26 72.55 77.15 1352.24 79.12 76.07BAR Alk 374.98 ± 20.13 25.79 35.18 576.91 33.76 47.25PATH Alk 365.87 ± 19.21 25.16 31.50 604.85 35.39 45.33136Table E.2: Pool area normalized by canyon area at day 9, maximum pool area, mean andmaximum pool concentrations and maximum change in concentration from initial con-centration. Concentration units are: PSU, mM, mM, nM, mmol/kg.Tracer Apool=Acanat day 9max(Apool=Acan)C at day9maxC max ∆C(%)AST Sal 3.8 10.7 33.9 33.9 0.1ARGO Sal 2.7 7.1 33.9 33.9 0.1BAR Sal 3.4 7.8 33.9 34.0 0.0PATH Sal 7.9 15.0 34.0 34.0 0.1AST DS 35.3 35.3 50.2 52.9 11.1ARGO DS 19.8 19.8 50.4 51.5 8.1BAR DS 4.4 8.8 54.7 54.9 4.6PATH DS 17.0 18.0 55.6 56.2 6.9AST Pho 35.9 35.9 2.3 2.4 6.2ARGO Pho 20.5 20.5 2.3 2.3 4.6BAR Pho 2.4 6.9 2.4 2.4 2.0PATH Pho 8.4 12.6 2.5 2.5 3.2AST NiO 1.5 6.5 28.1 28.1 1.6ARGO NiO 1.2 4.4 28.2 28.2 1.8BAR NiO 5.3 10.4 28.1 28.2 0.6PATH NiO 9.5 19.0 28.2 28.2 0.8AST Alk 9.0 16.7 2264.3 2265.3 0.3ARGO Alk 6.0 8.2 2264.4 2264.4 0.3BAR Alk 7.1 11.4 2267.0 2267.5 0.2PATH Alk 27.1 27.1 2267.6 2269.5 0.3137Table E.3: Column 2: Mean tracer upwelling flux for selected tracers during the advectivephase (days 4-9), reported with 12-h standard deviations. Columns 3 and 4: Tracer in-ventory or anomaly of total tracer mass on shelf and percentage relative to no-canyoncase.Run and tracer FTr/109 mmol s−1 (M−Mnc)/1012 mmol(M−Mnc)/(Mnc−Mnc0) (%)AST Sal 2.84±0.25 19.77 64.96ARGO Sal 1.62±0.21 9.77 31.57BAR Sal 0.49±0.14 0.99 4.86PATH Sal 0.74±0.14 1.49 6.69AST DS 4.51±0.42 717.68 109.96ARGO DS 2.59±0.30 360.42 54.28BAR DS 0.80±0.21 49.61 8.18PATH DS 1.26±0.22 95.35 14.16AST Pho 0.20±0.02 24.85 79.03ARGO Pho 0.12±0.01 12.32 38.52BAR Pho 0.04±0.01 1.52 6.68PATH Pho 0.05±0.01 2.61 10.38AST NiO 0.00±0.00 0.25 72.27ARGO NiO 0.00±0.00 0.12 35.48BAR NiO 0.00±0.00 0.01 5.01PATH NiO 0.00±0.00 0.02 7.20AST Alk 189.44±16.53 1636.70 85.54ARGO Alk 108.22±13.93 821.13 42.73BAR Alk 32.52±9.06 101.28 6.88PATH Alk 49.52±9.04 177.60 10.96138Appendix FNotes on Laboratory MethodsF.1 Density measurementsI derived density values at the head of the canyons and density profiles from conductivity measure-ments. To measure conductivity I used the open-platform system Conduino, developed by MarcoCarminati (Politecnico di Milano) and Paolo Luzzatto-Fegiz (FESlab, University of California SantaBarbara) (Carminati and Luzzatto-Fegiz, 2017). The Conduino system has two parts: a set of up to4 four two-electrode conductivity probes and a circuit that electrically stimulates the impedance ofthe probes, and senses and processes their response. The circuit sends an electrical impulse to theprobes and depending on the conductivity of the solution the impedance of the probes will change.Following the instructions provided by FESlab (https://github.com/feslab/conduino/wiki/Preparing-a-Conduino-probe) we customized the probes for our experimental design. The two probes at thehead of the canyons (A1, A2) were built on 5 cm braided stainless steel shaft to be screwed into themodel bathymetry (Fig. F.1a) while the profiler probe was built on a 21 cm long stainless steel shaft(Fig.F.1b). Al probes use micro-usb cables from the brand ANKER. The total length of probes A1,A2 and probe P21 is 1 m.F.1.1 Probe calibrationConductivity depends on salinity and temperature. The water column is stratified using salt, and thelaboratory is temperature controlled. I am ignoring the dependence on temperature so we calibratethe probes relating probe readings with density measurements from an Anton Paar densitometer.Calibration of the probes is made in-situ and simultaneously for all probes. I see interference be-tween probes (difference in readings depending on how many probes are connected) so I calibratedusing the same probe configuration we use in the experiments.I calibrated the probes directly using density. The caveat is that I am assuming that the tempera-ture of the water in every experiment is the same; that there are no temperature gradients within the139(a) Profiler system (b) Profiler circuitFigure F.1tank. Under that assumption, the density of the water is proportional to the conductivity measuredby the conduino. I relate conduino readings (proportional to conductivity) to density measurementsfrom an Anton par densitometer and find a calibration curve that fits the data (Figure F.2). To do this,between 10 and 15 water samples spanning the densities covered in the experiments are preparedby adding different amounts of salt. I build clay walls around the canyon probes to hold the watersamples, and place a container to submerge the profiler probe in the salty water. With all the probesconnected at the same time (profiler probe and canyon probes) I read a 500 sample conduino timeseries. The average of the time series and the density of the sample measured with the densitometercorrespond to one point in the calibration curve. I suck the salty water out of the canyon probe poolsand empty the container below the profiler probe, rinse the probes with fresh water, and repeat withthe next sample. I always start with the freshest sample and work towards the saltiest sample. Thelaboratory facilities are located in the basement of a temperature controlled building. Water usedfor calibration and experiments is left to sit overnight to make sure it is at room temperature whenused.Probe readings drift overtime as shown in base readings in experiment T02 (Figure F.3). Basereadings consist in conduino measurements taken for 7 minutes in between experiments, when thereis no activity in the canyons.I define the uncertainty associated to the readings as the mean drift of all base readings. That is,for a given base reading r(t) file, the drift is abs(r(t = 0min)r(t = 7min)). The mean drift is then themean of the drifts of all base reading files for one experiment. The mean drift for each experimentis shown in figure F.4.Let r ± dr be the density derived from the conduino reading r± d r where dr and d r are theuncertainties associated to r and r, respectively. I obtain the derived density from the calibration1401.001.021.041.06ρ / g cm3Aug 17th: ρups = 0.997004+0.008108r+­0.002737r2+0.000769r3Aug 17th: ρdns = 0.996888+0.009153r+­0.004260r2+0.001388r3Aug 09th: ρups = 0.997724+0.003955r+0.000772r2+0.000136r3Aug 09th: ρdns = 0.997546+0.005198r+­0.000409r2+0.000470r3Upstream probe Downstream probeFit Aug. 17thFit Aug. 9thSamplesSamples0 2 4Reading r / AU0.010.020.030.040.050.06dρ/dr0 2 4Reading r / AUAug. 17thAug. 9thFigure F.2: Calibration curves r(r) for the upstream and downstream probes (top row) and thederivatives of the calibration curves (bottom row). The latter is required to calculate theuncertainty of the derived density measurement r .curve r(r) (Figure F.2) and the uncertainty dr as:dr = (¶r¶ rd r)1=2: (F.1)Given that the probe readings drift overtime, I assigned the mean drift to the uncertainty dR.The uncertainty associated to derived quantities such as the depth of upwelling Z were calculatedaccording to the uncertainty propagation rules.F.1.2 Density profilesSome density profiles were measured using a conductivity probe mounted on a profiling device.The profiling device consists of a wood structure mounted on the filling aluminium arm on the tankwith a two-part wooden arm controlled by a DC motor (Fig. F.5). The wooden arm transforms thecircular motion of the DC motor to linear vertical motion so that the probe can move from surface tobottom to surface again of the water column. The motor can move clockwise or counter clockwise14140 60 80 100 1201.92.02.12.2ReadingBase measurements T02downstream canyonupstream canyon280 300 320 340 360 380Minutes1.952.002.052.102.15ReadingFigure F.3: Probe readings drift over time while they are connected to the circuit. In thisfigure base measurements – readings taken over 7 minutes while the tank rotated – takenin between runs in experiment T02 are shown as a function of time. The total timecorresponds to the time it takes to spin up the tank and to run three experiments.T01T02T03T04T05T06T07T08T09T10T11T12DYE02S01S02S03S04S05S06S07S08S09S10S11S120.000.010.020.030.04Mean Drift in Readingsdownstream canyonupstream canyonFigure F.4: The mean drift for each experiment was used as the uncertainty of the probe read-ings.with variable speed. The circuit that controls the motor is based on Project 10 (ZOETROPE) of theArduino Starter Kit (https://store.arduino.cc/usa/arduino-starter-kit) with minor modifications. Thecircuit uses a 12 V DC motor, geared down to 2 rpm with a 12 V power supply to feed the motor.An integrated circuit allows the motor to move forward or in reverse and a potentiometer modulatesthe voltage that is fed into the motor and thus the speed of the motor. One push button starts the142motor.Figure F.5: The profiler system is mounted on the aluminium arm that holds the filling hose.The profiler moves the probe vertically completing 2 cycles per minute using DC motorcontrolled by an integrated circuit L293D.Ideally, the profiler describes a sinusoidal motion but due to friction and gravity, the motionis not perfectly sinusoidal and approximating the motion as such leads to large errors in convertingtime between density measurements to depth. To correct the conversion from time to depth I trackedthe motion of the profiler using the free software Tracker Video Analysis and Modelling Tool. Oncehaving position and time of the profiler probe I calculated the velocity at every time and found aninterpolation function to apply to the time measured by the probe while profiling. Integrating theinterpolated velocity, I obtained the depth travelled by the probe for every density measurement.Unfortunately, the probe readings and profiler motion have proved hard to reconcile. Fixing thismismatch is a priority for future work.F.2 Near-inertial oscillationsNear-inertial oscillations can be observed in dye visualizations, density time series and PIV velocityfields. The origin of these oscillations is not clear but it could be associated to a slight misalignmentof the table. Density timeseries were filtered to remove the oscillation signal because it was not thefocus of the work in chapter 3. Two methods of filtering were tested to remove the signal: removingthe inertial frequency from the time series and a running mean filter with a window length of thesame size as the inertial period. The fist method minimally changed the original data (Figure F.6),so the second filter was chosen for all conduino timeseries.1430 25 50 75 100 125 150 175 200time / s0.0000.0010.0020.003 / g cm3T05remove freq. T05running mean T05T08remove freq. T08running mean T08Figure F.6: Examples of original and filtered time series for a run in experiments T05 and T08.The original time series are labelled“original”, time series where the inertial frequencywas removed are labelled“remove freq.” and time series filtered using the a running meanare labelled “running mean”.F.3 Canyon insertsCanyon inserts were 3D printed at Engineering Services, UBC Department of Electrical and Com-puter Engineering. The material used for printing was polylactide filament (PLA) which is apolyester derived from fermented plant starch. The canyon insert bathymetry was designed inpython and saved as a text file containing triads (x, y, z). To print the inserts, the text file wasread into the software Paraview where a Delauny triangulation was applied to prepare the insert forprinting (stl file).F.4 Surface deformationWater in the tank has a free surface boundary condition. When solid body rotation is reached, thefree surface has a parabolic shape because the magnitude of the centrifugal force grows with theradius. So a parcel of water closer to the centre of rotation is being pushed by a smaller centrifugalforce than a parcel close to the tank wall. The pressure acting on a cubic parcel of water of facearea dA and radial width dr at a distance r from the tank centre is p at the face closer to the centreof rotation and p+¶ p=¶ rdr at the face farther from the centre. The centripetal acceleration is rw2.Then, applying the second law of motion on the parcel of water gives:(p+¶ p¶ rdr− p)dA= rdAdrrw2; (F.2)144wherew is the rotation rate. The right hand side corresponds to the sum of forces acting on the parceland the left hand side to the mass times the acceleration of the parcel. Assuming that pressure is afunction of depth z and radius, in the radial direction the equation above is¶ p¶ r= rrw2: (F.3)Note that the gauge pressure is zero at all points on the interface. Then the pressure difference abetween centre and wall is ∫ pwallp=0dp= rw2∫ R0rdr; (F.4)pR =12rw2R2; (F.5)where R is the radius of the tank and pR is the pressure at the tank wall. At the wall, and assumingthe fluid is homogeneous, we know that the hydrostatic pressure is rgz. Solving for z gives us thedepth of the water column at the wall above the surface at the centre:z=12gw2R2: (F.6)For a rotation rate of 0.25 rad/s ( f=0.5 rad/s), the surface at the wall is 0.08 cm higher than at thecentre; for a rotation rate of 0.4 rad/s, the surface at the wall is 0.2 cm higher than at the centre.145Appendix GAdditional Laboratory ResultsG.1 Recovery stage of upwelling experimentsThe initial rotation rate of the tank Ω0 is increased to Ω1 to generate an upwelling favourable cur-rent and then to Ω2 to avoid the current from spinning down. The forcing time from Ω0 to Ω2 is71 seconds. The tank rotates at Ω2 for 7 minutes, the total time of the experiment. In selectedexperiments, I recorded the density at the probes for 7 minutes while the tank’s rotation rate wasbrought back to Ω0 in preparation for the next experiment (Figures G.1 and G.2). The reduction ofthe rotation rate was done linearly in 15 min and the tank was left to reach solid body rotation foran hour after reaching Ω0.G.2 Lag between upwelling depth maximaThe difference in depth of upwelling between the upstream and downstream canyons as a functionof the Burger number Bu (a) and the Rossby number RW (b) for all two-canyon experiments isshown in figure G.3.G.3 Azimuthal velocity from PIVThe azimuthal component of the velocity fields is two orders of magnitude smaller than the radialcomponent within the canyons (Figure G.4). Most of the flow outside the canyon is along isobathsand the azimuthal velocity is larger closer to the centre of the tank.1460.0010.0000.0010.0020.003 / g cm3ANK1 ­ upstream probeT08T08­recoveryT09T09­recoveryT08­1T08­1­recoveryT08­2T08­2­recovery0 5 10 15 20Time / minutes0.0010.0000.0010.0020.0030.004 / g cm3ANK2 ­ downstream probeT08T08­recoveryT09T09­recoveryT08­1T08­1­recoveryT08­2T08­2­recoveryFigure G.1: Examples of experiment and recovery conduino time series of two canyon ex-periments. Top and bottom panels corresponds to upstream and downstream probesrespectively.0.0010.0000.0010.0020.0030.004 / g cm3ANK1 ­ upstream probeS07S07­recoveryS08S08­recoveryS01S01­recoveryS02S02­recovery0 5 10 15 20time / s0.0010.0000.0010.0020.003 / g cm3ANK2 ­ downstream probeS07S07­recoveryS08S08­recoveryS01S01­recoveryS02S02­recoveryFigure G.2: Examples of experiment and recovery conduino time series of two canyon ex-periments. Top and bottom panels corresponds to upstream and downstream probesrespectively.1471.00 1.25 1.50 1.75Bu2002040lag between max dns and max ups / s(a)0.100 0.125 0.150 0.175 0.200Rw(b)Figure G.3: Difference in depth of upwelling between the upstream and downstream canyonsas a function of the Burger number Bu (a) and the Rossby number RW (b) for all two-canyon experiments.1480°20°40°cm10 15 20 25 30T02 Depth = 2.8 cmMean field between 5.0-10.0 s0°20°40°cm10 15 20 25 30T02 Depth = 3.8 cm0°20°40°cm10 15 20 25 30T02 Depth = 4.8 cm-0.010.00Azimuthal velocity / cms10°20°40°cm10 15 20 25 30T02 Depth = 2.8 cmMean field between 25.0-30.0 s0°20°40°cm10 15 20 25 30T02 Depth = 3.8 cm0°20°40°cm10 15 20 25 30T02 Depth = 4.8 cm-0.04-0.03-0.02-0.010.00Azimuthal velocity / cms10°20°40°cm10 15 20 25 30T02 Depth = 2.8 cmMean field between 45.0-50.0 s0°20°40°cm10 15 20 25 30T02 Depth = 3.8 cm0°20°40°cm10 15 20 25 30T02 Depth = 4.8 cm-0.04-0.03-0.02-0.010.00Azimuthal velocity / cms10°20°40°cm10 15 20 25 30T02 Depth = 2.8 cmMean field between 115.0-120.0 s0°20°40°cm10 15 20 25 30T02 Depth = 3.8 cm0°20°40°cm10 15 20 25 30T02 Depth = 4.8 cm-0.04-0.03-0.02-0.010.00Azimuthal velocity / cms1Figure G.4: Five-second mean azimuthal component of velocity in experiment T02 at threedifferent depths. Before the forcing starts (top row), azimuthal velocity is close to zero.As forcing ramps up the azimuthal velocity increases and it is smaller closer to the shelfbreak and clockwise (middle rows). After the forcing has stopped, the flow away of theshelf is still clockwise but smaller than when the forcing was applied.149

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