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Winter dynamics in an epishelf lake Bonneau, Jérémie 2020

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Winter Dynamics in an Epishelf LakebyJe´re´mie BonneauB.Ing., Universite´ Laval, 2017A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Civil Engineering)The University of British Columbia(Vancouver)August 2020c© Je´re´mie Bonneau, 2020The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Winter Dynamics in an Epishelf Lakesubmitted by Je´re´mie Bonneau in partial fulfillment of the requirements for thedegree of Master of Applied Science in Civil Engineering.Examining Committee:Bernard Laval, Civil Engineering, The University of British ColumbiaCo-supervisorDerek Mueller, Geography and Environmental Studies, Carleton UniversityCo-supervisoriiAbstractThe last intact ice shelf in the Canadian Arctic is located at the mouth of MilneFiord (82.6◦N, 81.0◦W), on Ellesmere Island, Nunavut. During melt season, theice shelf acts as a dam preventing meltwater from flowing freely to the ocean. Thisresults in a permanent layer of freshwater that ”floats” on top of the seawater ofthe fjord. This layer of freshwater is called an epishelf lake. The winter data froma mooring installed in Milne Fiord epishelf lake (2011-2019) is analysed in theframework of a one dimensional model in order to study 1) mixing in the upperwater column and 2) the evolution of a basal channel in the ice shelf. The resultsshow that vertical mixing is surprisingly higher in the epishelf lake than in the sea-water underneath. Estimation of the Richardson number using geostrophic balanceindicates that enhanced mixing in the epishelf lake is associated with horizontaltemperature gradients. Moreover, the analysis suggests that all of the freshwaterreaching the ocean travels through a single basal channel in the ice shelf. Themodel did not detect significant variation in outflow characteristics over the eightsyears of study, implying that the basal channel area is in ice mass balance.iiiLay SummaryAt the mouth of Milne Fiord, in Nunavut, is the last intact ice shelf in Canada. Anice shelf is a thick floating sheet of ice attached to the land. Because Milne Ice Shelfis attached to the land on both sides of the fjord, it acts like a dam preventing freshmeltwater from the watershed to directly reach the ocean. This layer of freshwaterfloating on top of the seawater is called an epishelf lake. This study uses fieldobservations and a numerical model to conclude that there is more mixing in theepishelf lake than in the seawater below. This is surprising because Milne Fiordepishelf lake is ice-covered year round. Moreover, this study suggests that most ofthe water flowing out of the epishelf lake follows a channel under the ice shelf andthat this channel is not evolving rapidly.ivPrefaceThis is a continuation of the work done Andrew Hamilton in Milne Fiord from2009 to 2016. The data analysis and the writing was realized by the author un-der the supervision of Dr. Laval (University of British Columbia) and Dr. Mueller(Carleton University). The data analysed was collected by the Environmental FluidMechanics lab (EFM) from the University of British Columbia (which the authoris part of), the Water and Ice Research Laboratory (WIRL) from Carleton Univer-sity and the Tahoe Environmental Research Center (TERC) from the University ofCalifornia at Davis.A version of chapter 3 of this thesis is being prepared for submission to a peer-reviewed journal as Winter Dynamics in the Last Epishelf Lake in the CanadianArctic, Milne Fiord, Nunavut, Canada by J. Bonneau, B. E. Laval, D. Mueller, A.K. Hamilton, A. M. Friedrichs and A. L. Forrest. For this chapter, the data analysisand the writing was realized by the author under the supervision of Dr. Laval (Uni-versity of British Columbia) and Dr. Mueller (Carleton University). Dr. Hamiltonprovided mooring and CTD data (before 2017) as well as comments and insightson the work. A.M. Friedrichs and Dr. Forrest provided the ADCP data.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Arctic Climate Change and Ice Shelf Loss . . . . . . . . . . . . . 11.2 Milne Fiord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Motivation and Implications . . . . . . . . . . . . . . . . . . . . 51.5 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1 Milne Fiord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.1 Milne Glacier . . . . . . . . . . . . . . . . . . . . . . . . 82.1.2 Milne Ice Shelf . . . . . . . . . . . . . . . . . . . . . . . 102.1.3 Milne Fiord Epishelf Lake . . . . . . . . . . . . . . . . . 10vi2.1.4 Below the Epishelf Lake . . . . . . . . . . . . . . . . . . 112.2 Mixing, Energy, Geostrophy . . . . . . . . . . . . . . . . . . . . 132.2.1 Eddy Viscosity . . . . . . . . . . . . . . . . . . . . . . . 132.2.2 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.3 Energy and Mixing . . . . . . . . . . . . . . . . . . . . . 142.2.4 Geostrophic Scale . . . . . . . . . . . . . . . . . . . . . 162.3 Ice-Covered Lakes . . . . . . . . . . . . . . . . . . . . . . . . . 172.3.1 Seiche . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3.2 Radiative Mixing . . . . . . . . . . . . . . . . . . . . . . 182.3.3 Inflows . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.4 Ice Walls . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.5 Diffusive Convection . . . . . . . . . . . . . . . . . . . . 192.3.6 Earth Rotation . . . . . . . . . . . . . . . . . . . . . . . 202.3.7 Tides . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.4 Arctic Fjords . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.4.1 Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4.2 Meltwater Plumes . . . . . . . . . . . . . . . . . . . . . 212.4.3 Tides . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.4.4 Earth Rotation . . . . . . . . . . . . . . . . . . . . . . . 232.5 Basal Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.5.1 Formation . . . . . . . . . . . . . . . . . . . . . . . . . . 242.5.2 Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . 242.5.3 Melting . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.5.4 Impacts of Basal Channels . . . . . . . . . . . . . . . . . 263 Winter Dynamics in the Last Epishelf Lake in the Canadian Arctic,Milne Fiord, Nunavut, Canada . . . . . . . . . . . . . . . . . . . . . 273.1 Key Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3 Geophysical Setting and Study Area Background . . . . . . . . . 313.3.1 The Fjord . . . . . . . . . . . . . . . . . . . . . . . . . . 313.3.2 The Glacier . . . . . . . . . . . . . . . . . . . . . . . . . 323.3.3 The Ice Shelf . . . . . . . . . . . . . . . . . . . . . . . . 32vii3.3.4 The Epishelf Lake . . . . . . . . . . . . . . . . . . . . . 333.3.5 Offshore Oceanography . . . . . . . . . . . . . . . . . . 333.4 Data and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 343.4.1 Epishelf Lake Mooring . . . . . . . . . . . . . . . . . . . 343.4.2 CTD Casts . . . . . . . . . . . . . . . . . . . . . . . . . 343.4.3 Weather Data . . . . . . . . . . . . . . . . . . . . . . . . 353.4.4 Ice Shelf Channel ADCP . . . . . . . . . . . . . . . . . . 353.4.5 Model Formulation . . . . . . . . . . . . . . . . . . . . . 353.4.6 Model Fitting . . . . . . . . . . . . . . . . . . . . . . . . 393.5 Model Results and Validation . . . . . . . . . . . . . . . . . . . . 413.5.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . 413.5.2 Salinity . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.5.3 Outflow . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.5.4 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.6.1 Numerical Model . . . . . . . . . . . . . . . . . . . . . . 493.6.2 Outflow . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.6.3 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60A Turbulent Lewis Number . . . . . . . . . . . . . . . . . . . . . . . . 72B Ice Circle in Milne Fiord . . . . . . . . . . . . . . . . . . . . . . . . 74C Model Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76D Photo Gallery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78viiiList of TablesTable C.1 Model evaluation statistics . . . . . . . . . . . . . . . . . . . . 77ixList of FiguresFigure 1.1 Schematic of Milne Fiord. The ice shelf acts like a dam pre-venting the freshwater (epishelf lake) to flush in the ocean.In italic are possible processes affecting the ice shelf-epishelflake-glacier system. . . . . . . . . . . . . . . . . . . . . . . . 2Figure 1.2 Geographical location of Milne Fiord. . . . . . . . . . . . . . 3Figure 2.1 Meteorological data from Purple Valley weather station (Fig-ure 2.2). A) Hourly air temperature at 2 m from the ground.Horizontal dashed line is 0◦C. B) Hourly downwelling solarradiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Figure 2.2 Satellite image, bathymetry and ice draft map of Milne Fiord.A) ASTER image of Milne Fiord (July 21st 2009). The glaciergrounding line is in red. MIS: Milne Ice Shelf. MEL: MilneFiord Epishelf Lake. MGT: Milne Glacier Tongue. MLSI:Multi-year land-fast sea ice. The red triangle is MEL mooringand the yellow is the weather station. B) Bathymetry map.Note: shallow section in the red circle is in fact not shal-low, it is ∼300 m. Circles refer to CTD cast locations. Thebathymetry data comes from lead line sounding and CTD casts.C) Ice draft measurements from ice penetrating radar, airborneradar and remote sensing. D) Modeled ice draft with measure-ment from C. This figure comes from Hamilton (2016). . . . 9xFigure 2.3 CTD water profile taken in May 2011 at the location of MELmooring (Figure 2.2). A) Conservative temperature (Θ), withthe different water masses labeled. MEL: Milne epishelf lake,freshwater, 0 to 4◦C. FMW: Fjord modified water, 5 to 30 gkg-1), 0 to -1.5◦C. PW: Polar water, 30 to 34.4 g kg-1, tem-perature lower than 0◦C. AW: Atlantic water, >34.4 g kg-1,∼0◦C. DW: deep water, as AW but generally slightly fresherand colder. B) Salinity profile. C) Stability profile, smoothedwith a 20 point moving average; note the logarithmic transfor-mation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 3.1 A) Location of Milne Fiord (82.6◦N, 81.0◦W). B) Landsat 8image of Milne Fiord taken in September 2018. MEL: MilneEpishelf Lake, MIS: Milne Ice Shelf, MGT: Milne GlacierTongue, MG: Milne Glacier . . . . . . . . . . . . . . . . . . 29Figure 3.2 Schematic of Milne Fiord including Milne Ice Shelf (MIS),Milne Epishelf Lake (MEL) and Milne Glacier Tongue (MGT).A) During the melt season (summer) (∼June 1st to∼September1st), runoff drives the deepening of MEL. B) During the re-mainder of the year, the thickness of MEL decreases slowlytoward the minimum draft of the MIS. . . . . . . . . . . . . . 30Figure 3.3 Schematic of the one-dimensional model. Typical absolutesalinity and stability profiles are on the right. The data fromthe uppermost and the 25 m thermistor are used as boundaryconditions for temperature and the no flux boundary conditionsare used for salinity. Mixing coefficients of the top freshwaterlayer (Ktop) and the bottom seawater layer (Kbot) are param-eters of the model; only molecular mixing is considered forthe halocline layer. The outflow layer is between the minimumdraft of the ice shelf (h0) and the bottom of the halocline layer(z). The top and bottom dashed lines show the top and bottomboundaries of the model. The two middle dashed lines are thetop and bottom of the halocline layer (molecular diffusivity only). 36xiFigure 3.4 Schematic of the outflow of the lake through the basal channelof the ice shelf. A modified weir equation using a two layersimplification (equation 3.3) is used to constrain the numberof parameters related to the outflow. A) Top view. B) Alongfjord section. C) Across fjord section through MIS. Note: notto scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.5 Once the initial conditions (IC) and the boundary conditions(BC) are implemented into the mesh, the model loops throughthe possible outflow coefficients (Ceb and h0) for every winterand through the possible mixing coefficients for every winterdays. (See text for detailed explanation) . . . . . . . . . . . . 42Figure 3.6 Temperature timeseries of the top of the water column in MilneFiord. A) Conservative temperature timeseries of the model re-sults. B) Conservative temperature timeseries from the moor-ing (linearly interpolated). C) Difference between the modeland the mooring data, positive values mean the model tem-perature is higher than the mooring temperature. Trianglesshow the location of the thermistors on the mooring line andthe squares show the location of the conductivity instruments. 44Figure 3.7 Salinity data from the model (solid line) at the depth of theconductivity instruments on the mooring (dashed line). Labelsare the depth of the instruments, in meters. . . . . . . . . . . 45Figure 3.8 A) Depth of MEL (maximum N2 value) given by the modelfor each winter. The staircase effect is due to the vertical dis-cretization of the model (10 cm). Outflow parameters h0 andCeb for each winter are in the legend. B) Outflow through thebasal channel in MIS. Dotted lines are the model estimationusing the rectangular weir equation and an estimated lake areaof 71.2 km2. Solid lines are the ADCP estimation using thechannel morphology data from Rajewicz (2017). . . . . . . . 47xiiFigure 3.9 A) Daily mixing coefficients from the model, for the heat andsalt transport equations for the top and bottom layers (dots).Solid lines are the 30 day averaged quantities for the top (blue)and bottom (red/orange) coefficients of the heat equation. Min-imum possible values of daily mixing coefficients are the molec-ular diffusivities; 1.4x10-7 m2 s-1 for heat and 1.4x10-9 m2 s-1for salt. B) 30 day averaged mixing coefficient of the model(dark blue) and inverse of the Richardson number (light blue)computed according to equation 3.6. N2 (dotted line) com-puted by the model and 30 day maximum density differenceattributed to the temperature oscillations 4ρ30 (dashed line)are used in equation 3.6. Enhanced mixing (dark blue line) islinked to stronger eddy activity (dashed line) hence to a lowerRichardson number (light blue line). . . . . . . . . . . . . . . 48Figure 3.10 30 day averaged mixing coefficient of the model (KTOPΘ ) asfunction of the Richardson number estimated by equation 3.6.Commonly used parameterizations by Peters et al. (1988) (green)and Pacanowski and Philander (1981) (cyan). . . . . . . . . . 54Figure A.1 Parameterization of KSA as function of KΘ . . . . . . . . . . . 73xiiiFigure B.1 RADARSAT-2 Fine Quad image taken on the 27th of April2013 showing a dark disc in the middle of the Milne Fiordepishelf lake (Courtesy of the Canadian Ice Service, Environ-ment and Climate Change Canada). Panels VV, VH and HHare three different polarizations (VV: vertical-vertical, VH: vertical-horizontal and HH: horizontal-horizontal) and the RGB panelis the combined Pauli decomposition (HH: red, VV: green andVH/HV: blue). The disc is visible in all polarizations. Colorand gray scales are qualitative with brighter tones indicatinghigher backscatter. RADARSAT-2 Data and Products c©Mac-DONALD, DETTWILER AND ASSOCIATES LTD. (2013) –All Rights Reserved, RADARSAT is an official mark of theCanadian Space Agency. . . . . . . . . . . . . . . . . . . . . 75Figure D.1 Getting dropped off at Purple Valley campsite by a Kenn BorekTwin Otter. Maximum 2500 pounds, crew included... Photo:Je´re´mie Bonneau . . . . . . . . . . . . . . . . . . . . . . . . 79Figure D.2 Milne Fiord, looking downfjord. The glacier grounding linearea is visible on the right of the icefall and Purple Valley, 75%on the right. The ice-covered ocean on the horizon. Photo:Je´re´mie Bonneau . . . . . . . . . . . . . . . . . . . . . . . . 80Figure D.3 Northern Ellesmere icefields, looking upfjord from the samelocation as Figure D.2 , ∼ 5000 feet up. Photo: Je´re´mie Bonneau 81Figure D.4 Derek Mueller and Drew Friedrichs looking at Milne Ice Shelf,easily distinguishable by its rolling topography with the throughfilled with melt water. Photo: Je´re´mie Bonneau . . . . . . . . 82Figure D.5 Moving the camp from Purple Valley to the ice shelf. DrewFriedrichs signaling ”upward” to the helicopter pilot. Photo:Je´re´mie Bonneau . . . . . . . . . . . . . . . . . . . . . . . . 83Figure D.6 Drew Friedrichs doing a CTD profile after pulling the epishelflake mooring out. Looking upfjord. Photo: Je´re´mie Bonneau . 84Figure D.7 CTD profile in a crack on the margin of the glacier tongue.Photo: Drew Friedrichs . . . . . . . . . . . . . . . . . . . . . 85xivFigure D.8 Pulling the ice penetrating radar around the grounding line ofthe glacier. Photo: Drew Friedrichs . . . . . . . . . . . . . . 86Figure D.9 Drew Friedrichs ”hole melting” to get the ice shelf channelmooring back. Photo: Je´re´mie Bonneau . . . . . . . . . . . . 87Figure D.10 Picking up a camera from the summit of Mega Nunatak (unof-ficial name). Photo: Derek Mueller . . . . . . . . . . . . . . 88Figure D.11 26-Resolute, 26-Resolute, this is Purple Valley, Purple Valley.Drew Friedrichs and Yulia Antropova broadcasting (blurred).Photo: Je´re´mie Bonneau . . . . . . . . . . . . . . . . . . . . 89Figure D.12 Looking upfjord, with Derek Mueller. Mega Nunatak (unoffi-cial name) on the left of the fjord. Photo: Je´re´mie Bonneau . . 90xvAcknowledgmentsI would like to express my gratitude towards many people and organizations;• The National Sciences and Engineering Research Council of Canada (NSERC),The University of British Columbia (UBC) and the Fond de Recherche duQue´bec Nature et Technologie (FRQNT) for providing the daily bread.• The Northern Scientific Training Program (NSTP), by Polar Knowledge Canada,for fieldwork monetary assistance.• The Polar Continental Shelf Program (PCSP) for providing founding andlogistic assistance necessary for fieldwork...and killer Nanaimo bars.• Dr. Bernard Laval for giving me the opportunity to go check out some of themost remote and beautiful ”corners” of this planet, as well as for the freedomand guidance that led to these pages.• Dr. Derek Mueller for teaching me the fieldwork ropes, improving my rick-ety english writing and keeping calm when I entangled 800 m of CTD lineon my first day.• Drew Friedrichs and Yulia Antropova for help and great company in the field.• Dr. Andrew Hamilton for the amazing work you have done in Milne Fiordand for the feedback and insights. I often feel like I stole your project.• All the people of the EFM lab for the great discussions and the lovely Deekshike; the hut is rusty, but only on the outside.xvi• Mes camarades PERY-BON-Kiens pour le divertissement quotidien, me rap-prochant de la maison.• Mes parents, Annie et Vincent, et toute ma famille pour le soutient in-conditionne´.xviiChapter 1Introduction1.1 Arctic Climate Change and Ice Shelf LossThe area of the planet where climate change is the most pronounced is its northern-most part: the Arctic. Conversely, not many people live there and there is littlenews coverage when a glacier disappears or when an iceberg many times the sizeof Manhattan breaks off in Greenland. Arctic sea ice has shown accelerated loss inextent and thickness from 1990 to 2008 (Lang et al., 2017; Maslowski et al., 2012),which plays a major role in Arctic temperature regulation (Anisimov et al., 2007;Lang et al., 2017). Air temperature near the surface has increased more than twotimes faster than the global average (Screen and Simmonds, 2010). In some areas,air temperature rose by as much as 5◦C in the last century (Anisimov et al., 2007).In the Canadian High Arctic, every major glacier of the Queen Elizabeth Islandsis showing a decrease in surface elevation (Mortimer et al., 2018). Changes areunmistakable on the northern coast of Ellesmere Island, where the ice shelf extenthas been decreasing episodically over the last century (Mueller et al., 2017) Thishas been linked to higher air temperatures (Copland et al., 2007).Ice shelves are floating masses of ice attached to the coast. They are formed bythe extension of glaciers over the ocean, by in situ accumulation of snow and byaggregation of sea ice (Mueller et al., 2017). Ice shelves can be many hundreds ofmeters thick and are much larger in Antarctica than in the Canadian Arctic. On thenorthern coast of Ellesmere Island, there used to be an ice shelf at the mouth of1Figure 1.1: Schematic of Milne Fiord. The ice shelf acts like a dam prevent-ing the freshwater (epishelf lake) to flush in the ocean. In italic arepossible processes affecting the ice shelf-epishelf lake-glacier system.every fjord (Mueller et al., 2017). When an ice shelf is grounded on both sides of afjord and is not connected with the upstream glacier, it creates a dam trapping freshmeltwater from the fjord watershed (Laybourn-Parry and Wadham, 2014). Thislayer of freshwater floating atop the seawater forms what is called an epishelf lake(Figure 1.1). Milne Fiord epishelf lake depends entirely on the ice shelf blockingthe inlet of the fjord; if it fractures completely from north to south, the freshwaterwill simply disperse into the Arctic Ocean. The recent fracture and break up of iceshelves in the Canadian Arctic has left one last intact ice shelf in Milne Fiord andthus, the last remaining epishelf lake of the Canadian Arctic (down from ∼17 in1906 (Laybourn-Parry and Wadham, 2014; Veillette et al., 2008)).1.2 Milne FiordMilne Fiord is located on the northern coast of Ellesmere Island, Canada’s north-ernmost island (Figure 1.2). As depicted in Figure 1.1, the fjord system is com-posed of the glacier, the glacier tongue (floating part of the glacier), the epishelflake and the ice shelf, going downfjord. All of the above are in contact with the2Figure 1.2: Geographical location of Milne Fiord.seawater, emphasizing their interconnection.The most striking feature of the water column in Milne Fiord is the very sharpsalinity gradient at the halocline (∼10 g kg-1 m-1). Hamilton et al. (2017) definedthe bottom of the epishelf lake as the point where the density (salinity) gradientis the highest. The epishelf lake experiences an annual cycle of deepening andshoaling (Hamilton et al., 2017). During the summer, freshwater runoff pushes thehalocline down, increasing the thickness of the lake. Then, when air temperaturedrops below zero, melting stops and the lake thickness decreases until the nextsummer. The lake is approximately 10 m deep and the difference between the startand the end of the melt season is around 2.5 m.Milne Fiord is perennially ice-covered, which prevents the direct impact of wind.Moreover, tides are very limited ( 15 cm amplitude). Current measurements in thetop 100 m of Milne Fiord by Hamilton (2016) have shown horizontal velocitiesaround 1 cm s-1 that only rarely exceed 5 cm s-1. This calm environment with lowtidal amplitudes and no wind implies there is little circulation and mixing in thefjord, especially in winter, when there is no surface runoff and likely no subglacialdischarge.Similar to all major glaciers of the Queen Elizabeth Islands, Milne Ice Shelf isin negative mass balance (i.e. it is thinning) (Mortimer et al., 2012, 2018). Its3thickness varies between ∼8 m and ∼95 m. The thinnest areas are at its marginsand along an east-west depression across the middle of the ice shelf. CTD andice-penetrating radar measurements suggest that this east-west depression is thesurface expression of a basal channel where the epishelf lake water exits the fjord(Hamilton, 2016; Rajewicz, 2017). This basal channel is analogous to those foundunder ice shelves in Greenland and Antarctica and thought to be related to ice shelfstability (Dow et al., 2018; Rignot and Steffen, 2008). Melting rates over 10 m a-1are often observed in Antarctica and Greenland basal channels (Rignot and Steffen,2008; Stanton et al., 2013). This is certainly not the case for the Milne Ice Shelfbasal channel, since at that rate it would have melted through already. However, itis not known if the channel is evolving or if it is stable.1.3 ObjectivesA mooring was deployed in the center of Milne Fiord epishelf lake in May 2011and has been recording continuously until present. The mooring data from 2011 to2014 was used by Hamilton (2016) to study the annual cycle of the epishelf lake,but it has not been analyzed since. The eight years of mooring data available areone of the most extensive oceanographic data sets for an Arctic fjord. The objectiveof this study is to use the mooring data in order to:1. Quantify the mixing occurring in the epishelf lake and associate it with forc-ing mechanisms.2. Confirm that the channel is the main outflow path for the epishelf lake andto get information on the evolution of its morphology.In order to use most of the mooring data in a simple and meaningful way, a one-dimensional model is used. This allows focus on the most important physicalparameters (mixing and outflow through the channel). This study has two mainlimitations, one spatial and one temporal. Because instruments on the mooringline become very sparse below 25 m (3-4 instruments from 30 m to 350 m), thisstudy focuses on the upper water column above 25 m. The second limitation isrelated to the different processes affecting the water column during the melt season(∼mid-June to∼early-August). During that period of the year, surface runoff, solar4radiation and melt water plumes can have a significant impact on the upper watercolumn (Hamilton, 2016; Keys, 1977; Straneo and Cenedese, 2015). Because theseprocesses add extra complexities in the mooring analysis, the melt season period isnot considered in this study.1.4 Motivation and ImplicationsIn addition to other epishelf lakes in Antarctica, Milne Fiord shares physical char-acteristics with ice-covered lakes and fjords. In these isolated water bodies, rela-tively uncommon circulation and mixing mechanisms can have a disproportionateimpact. This is because the ice-cover suppresses the effect of wind and solar ra-diation, when capped with snow (Keys, 1977; Perkin and Lewis, 1978). It thenappears that Milne Fiord (ice-covered all year) is an ideal setting to study thesemore obscure processes. Objectives 1 and 2 are in line with this and it is antici-pated that new knowledge acquired here will improve our understanding of Arcticfjords and ice-covered lakes.As mentioned above, the basal channel in Milne Ice Shelf is very similar to thosefound on glacier tongues and ice shelves of Antarctica and Greenland. Hence,knowledge acquired here can be transferred to these systems. Accordingly, it isanticipated that the third objective will lead to an increased comprehension of therole basal channels play in the stability of ice shelves and in ice-ocean interactions.At a more local scale, due to the strong interconnection between epishelf lakes andtheir environment, they are considered to be ”sentinel ecosystem” (Veillette et al.,2008). For example, the depth of Milne Fiord epishelf lake varies throughout theyear due to runoff from the watershed and outflow under the ice shelf, hence, study-ing the fluctuation of the epishelf lake thickness will also increase the knowledgeof the hydrology and glaciology of Milne Fiord. The realization of each objectivewill lead to a improved map of the interactions between ice and water in MilneFiord.From a biological point of view, Milne Fiord is remarkable because the presence ofthe epishelf lake allows for the presence of freshwater organisms just above marineorganisms (Jungblut et al., 2017; Veillette et al., 2008). Analysis of the microbiotain Milne Fiord (Veillette et al., 2011) showed that the composition of the phy-5toplankton and bacteria communities in the freshwater layer and in the seawaterbelow were absolutely distinct.Even though Milne Fiord epishelf lake will likely disappear in the next decade ortwo, the study of this unique system is important on a local scale, to monitor therapid environmental change in the Canadian High Arctic, and on a global scale, toprovide insights on the evolution of other similar systems in Greenland and Antarc-tica.1.5 Thesis StructureThe core of this thesis is chapter 3, which will be submitted to a peer-reviewedjournal in the near future. Chapter 2 is an overview of the study site and a literaturereview on physical processes in ice-covered lakes and Arctic fjords as well as onbasal channels found under glacier tongues and ice shelves. Appendices A, B andC are supplementary material to chapter 3. Finally, Appendix D is a fieldworkphoto gallery.6Chapter 2Literature ReviewThis literature review is divided in five parts. The first is a overview the studysite and associated literature that points out the main features of Milne Fiord andgives the reader a good understanding of the Milne Fiord system. It is an extendedversion of the geophysical setting and background of study section of Chapter 3.The second part reviews some physical oceanography and limnology concepts thatare relied on in this study. Finally, sections 3-4 are reviews of the relevant physicalprocesses of ice-covered lakes, Arctic fjords and ice basal channels, respectively.2.1 Milne FiordMilne Fiord (82.6◦N, 81.0◦W) is situated on the north coast of Ellesmere Island(Figure 1.2). The closest permanently occupied settlements are Alert, a militarybase 260 km to the east and Eureka, a weather station to the 300 km south. MilneFiord is in the Arctic climate zone (Figure 2.1). Data from a weather station in a bayof Milne Fiord (Figure 2.2, data courtesy: Luke Copland) shows an annual averageair temperature of -18.6◦C with a 10 year maximum of 19◦C and a minimum of-55◦C. Because of its high latitude (82.5◦N), the sun stays below the horizon frommid-October to early March. The melt season is typically from early-June to mid-August, however, freezing temperatures are possible at any time of the year. Thearea experiences between 100 and 300 positive degree days per year (Hamilton,2016).7Figure 2.1: Meteorological data from Purple Valley weather station (Fig-ure 2.2). A) Hourly air temperature at 2 m from the ground. Horizontaldashed line is 0◦C. B) Hourly downwelling solar radiation.The work done by Hamilton (2016) describes the site in detail (Figure 2.2). Thefjord is 44 km long from the outermost extent of the ice shelf to the groundingline of the glacier. From the innermost extent of the ice shelf to the groundingline, its width is approximately 6 km. Alike Greenlandic fjords, there is a sill inMilne Fiord. It is just downfjord of the epishelf lake and its depth is ∼220 m. Themaximum depth below the epishelf lake is ∼400 m. From this point, the seafloorclimbs upfjord to reach ∼150 m at the grounding line (Hamilton, 2016).2.1.1 Milne GlacierMilne Glacier (MG) is over 50 km long and is 4 to 5 km wide. It has a thicknessof approximately 150 m at the grounding line (Hamilton, 2016) but becomes muchthicker upglacier (Narod et al., 1988). From the grounding line, The Milne GlacierTongue (MGT) extends 15 km down the fjord. Its thickness decreases rapidlymoving away from the grounding line and it is less than 10 m on its margins.MGT broke away from the glacier in 2009 but has not moved significantly since.8Figure 2.2: Satellite image, bathymetry and ice draft map of Milne Fiord. A)ASTER image of Milne Fiord (July 21st 2009). The glacier ground-ing line is in red. MIS: Milne Ice Shelf. MEL: Milne Fiord EpishelfLake. MGT: Milne Glacier Tongue. MLSI: Multi-year land-fast seaice. The red triangle is MEL mooring and the yellow is the weatherstation. B) Bathymetry map. Note: shallow section in the red circle isin fact not shallow, it is ∼300 m. Circles refer to CTD cast locations.The bathymetry data comes from lead line sounding and CTD casts. C)Ice draft measurements from ice penetrating radar, airborne radar andremote sensing. D) Modeled ice draft with measurement from C. Thisfigure comes from Hamilton (2016).9The watershed of MG is 1500 km2 and has a glaciated area of approximately 1100km2 (Hamilton, 2016). It is classified as a possible surge-type glacier (Van Wychenet al., 2016), meaning MG could possibly have fast flowing episodes where it wouldmove faster than its typical flow (∼100 m a -1 from 2000 to 2015 (Van Wychenet al., 2016)). From 1999 to 2016, MG lost up to 10 % of its surface area (Whiteand Copland, 2018).2.1.2 Milne Ice ShelfMilne Ice Shelf (MIS) occupies ∼205 km2 at the mouth of the fjord (Mortimeret al., 2012) and is attached to the land on both sides. The latest estimated meanice thickness is 47 m with a minimum and a maximum around 8 m and 94 m,respectively (Hamilton, 2016). The thinnest area is along a basal channel thatruns westward from the east shore (Hamilton et al., 2017; Mortimer et al., 2012;Rajewicz, 2017) (Figure 2.2). Ice thickness data is from hand and snowmobile-towed ice-penetrating radar (Hamilton, 2016; Mortimer et al., 2012)Figure D.8,aerial radar (Leuschen et al., 2016), and remote sensing surveys from 2008 to 2014(Hamilton, 2016; Mortimer et al., 2012). Therefore, changes certainly occurred,although the ice shelf is still relatively intact relative to other ice shelves in Canada.Mortimer et al. (2012) estimated an average thinning of 8.1 m and a 29% areareduction from 1950 to 2009. Before 1950, MIS and MGT were one single icestructure (Jeffries, 1985) and it is the melting of the area between them that createdthe epishelf lake. (Mortimer et al., 2012)The lake ice can be distinguished from the ice shelf ice and the glacier ice becauseit is absolutely flat (no topography) and displays a light gray tone (Mortimer et al.,2012) on aerial photos. Moreover, in Synthetic Aperture Radar imagery (SAR),the epishelf lake area has a higher backscatter due to the freshwater underneath(Veillette et al., 2008); Hamilton (2016) used a threshold of >-6dB to distinguishthe ice types.2.1.3 Milne Fiord Epishelf LakeIt is estimated that Milne Fiord Epishelf Lake (MEL) surface area was 71.2 km2in 2015 (Hamilton, 2016). Comparison with more recent satellite images does not10show a drastic change in MEL surface area since then. MEL experiences an annualcycle of deepening and shoaling (Hamilton et al., 2017). During the summer, whensnow and ice are melting, water from surface runoff flows into the lake and causesthe halocline to deepen. Meanwhile, lake water deeper than the minimum draft ofthe ice shelf flows out of the fjord to the Arctic Ocean (Figure 1.1). When the meltseason is over, surface runoff stops and the lake slowly shoals until the next meltseason. It is thought that the flow to the ocean occurs within the ice shelf basalchannel and is hydraulically controlled by its dimensions (Hamilton et al., 2017).Hamilton et al. (2017) determined that the annual minimum thickness of MEL hassignificantly decreased since 2004 to reach a minimum of 7.9 m in 2013. The onlydata available before 2004 are water bottle measurements from 1983 that suggeststhe halocline was at 17.7 m depth, if linearly interpolated (Jeffries, 1985). As aresult of short summers and cold long winters, the lake is permanently ice-covered(Hamilton, 2016). The minimum ice thickness observed was 0.65 m in July 2010(Hamilton, 2016) and the maximum was 3.19 m in May 1983 (Jeffries, 1985). Thelatest ice thickness measurement available is 1.7 m, from July 2019. Keys (1977)proposed that formation of frazil ice by heat transfer at the halocline contributessignificantly to the conservation of the ice-cover during summers. As freshwaterloses heat at the interface between the cold ocean and the relatively warm lake,frazil is formed and floats upward to acrete to the ice cover. The water in theepishelf lake is fresh (<0.5 g kg-1) and cold (<4 ◦C) (Figure 2.3). The maximumlake water temperature is normally recorded in late August when ice cover is min-imal and accumulation of heat from solar radiation is maximal. Figure 2.3 shows awater profile taken in May 2011 at the location of MEL mooring (Figure 2.2).2.1.4 Below the Epishelf LakeBelow the epishelf lake freshwater, a layer of fjord modified water (FMW) of ap-proximately 30 m shows intermediate salinity (5 to 30 g kg-1) and temperaturefrom 0◦C to -1.5◦C (Figure 2.3). This layer of relatively fresh water, very closeto the freezing point, is linked to submarine melting from the glacier and ice shelf(Hamilton, 2016). Under the FMW, polar water (PW), of salinity 30 to 34.4 g kg-1and temperature lower than 0◦C spans from ∼50 m to ∼250 m. Below PW is At-11Figure 2.3: CTD water profile taken in May 2011 at the location of MELmooring (Figure 2.2). A) Conservative temperature (Θ), with the dif-ferent water masses labeled. MEL: Milne epishelf lake, freshwater, 0 to4◦C. FMW: Fjord modified water, 5 to 30 g kg-1), 0 to -1.5◦C. PW: Polarwater, 30 to 34.4 g kg-1, temperature lower than 0◦C. AW: Atlantic wa-ter, >34.4 g kg-1, ∼0◦C. DW: deep water, as AW but generally slightlyfresher and colder. B) Salinity profile. C) Stability profile, smoothedwith a 20 point moving average; note the logarithmic transformation.lantic water (AW) of salinity >34.4 g kg-1 and a temperature ∼0◦C. Water deeperthan the depth of the sill (deep water, DW) is slightly colder and fresher insidethe fjord than offshore. Water velocities were measured by Hamilton (2016) withan ADCP from 0 m to 50 m in May 2011 (4 days), from 0 m to 100 m in July2012 (6 days), and in July 2013 (10 days). The results show that the currents werevery weak (<5 cm s-1), especially in the top 25 m of the water column (<2 cms-1). Most of the data acquired was below the instrument accuracy (0.5 cm s-1),which makes it difficult to infer any circulation patterns. Tidal harmonic analysis(Pawlowicz et al., 2002) was carried out using the pressure record from a bottomanchored instrument from September 2016 to July 2017. The results show thattides are semidiurnal and very limited in amplitude. The main components are M2(∼6.1 cm), K1 (∼4.5 cm), S2 (∼2.5 cm) and O1 (∼2.4 cm). Hamilton (2016) alsoreported small baroclinicity linked to the tidal cycle.122.2 Mixing, Energy, GeostrophySome important concepts are introduced here in order to better outline studies ofice-covered lakes and polar fjords related to this thesis. This background is usedto describe earlier studies as well as the methods, results and implication of thisresearch. For further reading, a more thorough treatment of these concepts can befound in Kundu et al. (2012), Cushman-Roisin and Beckers (2011) or Pedlosky(2013).2.2.1 Eddy ViscosityThe most common way to take turbulence into account when investigating geo-physical flow is to use time (t) averaged equations and to account for the effectof small fluctuations (turbulence) by the way of the eddy viscosity approximation(Kundu et al., 2012).∂u∂ t+u∂u∂x+ v∂u∂y+w∂u∂ z− f v =− 1ρ0∂ p∂x− ∂ (u′u′)∂x− ∂ (u′v′)∂y− ∂ (u′w′)∂ z+ν∂ 2u∂x2+ν∂ 2u∂y2+ν∂ 2u∂ z2(2.1)This is the averaged equation for momentum in the x direction (ρu) (Kundu et al.,2012). The overbars denote the time averaging and the primes denote the fluctu-ation quantities. u, v and w are the velocities in the x, y and z directions. f is theCoriolis frequency, ρ0 is a reference density, p is the pressure and ν is the kine-matic viscosity. Using the eddy viscosity approximation, the fluctuation terms arewritten with respect to the averaged velocity and a turbulent mixing coefficient ,Kt[m2 s-1] is introduced, for example:u′v′ =−Kt ∂u∂y ⇒ −∂ (u′v′)∂y= Kt∂ 2u∂y2(2.2)Because the fluctuation terms are now in the same form as the viscosity terms, thesecan be combined and a combined (turbulent and molecular) mixing coefficient cantherefore be used (Kt +ν = K). Moreover, because mixing is normally similar in xand y (Kundu et al., 2012), the same mixing coefficient can be used in the horizontal13directions (KH). Using these simplifications, equation 2.1 becomes (Kundu et al.,2012):∂u∂ t+ u∂u∂x+ v∂u∂y+w∂u∂ z− f v = − 1ρ0∂ p∂x+KH[∂ 2u∂x2+∂ 2u∂y2]+KV∂ 2u∂ z2(2.3)Where the effect of turbulent fluctuations and viscosity is included in KH and KV(i.e. KH = Kt +ν for the x and y directions and KV = Kt +ν in z).2.2.2 StabilityA water column is said to be stable if the water potential density increases from thesurface to the bottom. In that configuration, no vertical movement will arise unlessa force is applied (Kundu et al., 2012). For the same forcing, a water column wherethe density increases slowly with depth will mix more than a water column wheredensity increases rapidly. If, for some reason, a water parcel has higher density thanthe water parcel below it, the water profile is said to be unstable. The water parcelwill sink until it reaches the location where it is less dense than the water below,and denser than the water above; no external forcing is needed for movement in thewater column in that case. The common measure of the water column stability isthe Brunt-Va¨isa¨la¨ frequency, N (Kundu et al., 2012):N2 =− gρ0∂ρ∂ z(2.4)Where g is the gravitational acceleration, ρ is the density and ρ0 is a referencedensity (∼1000 kg m-3). N is the (angular) frequency at which a water parcelwill oscillate if it is displaced upward or downward by a ∂ z distance. Its units areradians per s and are often simplified as s-1. A negative N2 value means the profileis unstable.2.2.3 Energy and MixingRoughly, kinetic energy in a fluid moves from large scales to smaller and smallerscales until it reaches a scale were it is dissipated by viscosity. The large scale canbe seen as the mean flow (u, v, w) and the small scales as the turbulent flow (u′,14v′, w′). It is at the small (turbulent) scale that mixing happens. A simplified steadystate budget for turbulent kinetic energy (TKE) of the following form is typical inoceanography (Osborn, 1980):P = ε−B (2.5)Where P is the TKE production by shear, ε is the TKE dissipation by viscosity andB is the buoyancy term. B is negative when the water profile is stable (N2 > 0)and positive when the water column is unstable (N2 < 0). In other words, if thewater column is stable, a fraction of P will go to potential energy and if the watercolumn is unstable, then this extra potential energy will increase the amount ofTKE dissipated by viscosity (ε). A higher ε means more turbulence. In order tolink turbulence to mixing, Osborn (1980) proposed a semi-empirical relationshipbetween the vertical eddy coefficient (Kt in the z direction), ε and N:Kt ≤ 0.2 εN2 (2.6)A newer version of this relation is found in Shih et al. (2005), but it is quite sim-ilar to equation 2.6. Equation 2.6 shows that even though there is a lot of kineticenergy in a system, if the water column is highly stratified, mixing will be lim-ited. Inversely, if the water column is close to neutral stability (N2=0), then a smallamount of energy injected to the system (potential or kinetic) can lead to a lot ofmixing. This is what happens during lake turnover when the water column is nolonger stratified and wind is able mix the whole water column.A common way of measuring ε is to use microstructure profilers (Osborn, 1974).These instruments are equipped with small shear probes that detect the small veloc-ity fluctuations (u′, v′, w′). Microstrusture instruments can be lowered through thewater column or mounted on gliders (Peterson and Fer, 2014). Many other tech-niques to estimate ε also exists, such as finescale parameterization (Polzin et al.,2014), the structure function method (Wiles et al., 2006) or turbulent instrumentclusters (McPhee, 2008).For context, in the Arctic Ocean, a value of ε below 10-10 W kg-1 is consideredcalm and a value above 10-8 W kg-1 is considered energetic (Chanona et al., 2018).152.2.4 Geostrophic ScaleEquation 2.3 can be scaled by the characteristic dimensions of its terms. Using Uas the scale of horizontal velocities u and v, W for vertical velocity, L and D as thehorizontal and vertical length scales and T for the time scale, 2.3 can be written:UT+UUL+UUL+WUD− fU =− 1ρ04PL+KH[UL2+UL2]+KVUD2(2.7)Length, velocity and time scales are dependent on each other (U = L/T , W =D/T ); the first four terms then become 4U2/L. Dividing all terms by the scale forthe Coriolis term ( fU), equation 2.7 becomes:4Uf L= 1− 1ρ04PfUL+2KHf L2+KVf D2(2.8)The terms in equation 2.8 do not have any dimensions. The term on the left sideis often named the Rossby number (Ro) and the two terms at the far right with themixing coefficients are called Ekman numbers (Ek):4Ro = 1− 1ρ04PfUL+2EkH +EkV (2.9)The Rossby number is commonly seen as the ratio of inertial forces to the Coriolisforce. If Ro 1 then the influence of the Earth’s rotation has to be taken intoaccount. The Ekman number is the ratio of viscous forces to the Coriolis force.Close to boundaries, the mixing coefficient increases and the scale of the flowdecreases; hence Ek 1. If the Coriolis force is much more important than theinertial forces (i.e. Ro 1) and the effect of boundaries can be neglected (i.e.EkH  1, EkV  1), then equation 2.9 collapses to (Kundu et al., 2012):1 =1ρ04PfUL⇒ f v = 1ρ0∂ p∂x(2.10)This balance between the Coriolis force and the horizontal pressure gradient iscalled the geostrophic balance. The equation for u is:f u =− 1ρ0∂ p∂y(2.11)16The solution to equations 2.10 and 2.11 in the Northern Hemisphere is a clock-wise flow around a high pressure center, or an anti-clockwise flow, around a lowpressure center. Horizontal pressure gradients can be set up by external forces thatinduce current (e.g. wind, inflows) or difference in water properties (salinity, tem-perature).Dimensionnal quantities are also related to the Rossby and Ekman numbers. TheRossby radius of deformation (RL = ND/ fpi) is the length scale at which rotationbecomes important for phenomena in a fluid (Cushman-Roisin and Beckers, 2011).For example, using the epishelf lake (82.5◦N) average stratification of ∼10-2 s-1and a ∼10 m vertical scale, the Rossby radius is around 200 m. This means thatphenomena in the epishelf lake that have a horizontal scale at or over 200 m willbe affected by the Earth’s rotation. In the 390 m water column below the epishelflake (similar averaged stratification), the Rossby radius is∼7800 m, which is closeto the width of the fjord. The Rossby radius of deformation (RL) is the horizontalscale at which the Rossby number (Ro) is 1. A phenomenon that has a length scalelonger than RL will be affected by rotation (Ro < 1).A water column in geostrophic balance, away from lateral boundaries is simi-lar to a cylinder of spinning fluid. The only thing that can slow the rotation ofthis fluid is the friction of the fluid column at the top or bottom. The decaytime scale of kinetic energy of this fluid cylinder is the Ekman spin-down time(tE =D/√2KV f )(Pedlosky, 2013). For example, if we consider a geostrophic flowin the epishelf lake (D=10 m) and estimate the mixing coefficient to be ∼10-6 m2s-1 (Chapter 3), this gives a spin-down time of 106 s, or ∼5 days. Hence, if noenergy is added in the system, the water velocities will be significantly reducedafter 5 days because of the friction on the ice (assuming the seawater below doesnot exerts a stress on the freshwater layer).2.3 Ice-Covered LakesLakes at latitude over 40◦ commonly experience ice cover for some time of the year(Kirillin et al., 2012). Therefore, the understanding of mechanisms controlling thephysical regime under ice is essential to predict the future of these lakes. If thebottom boundary is neglected, epishelf lakes and ice-covered lakes are similar in17many ways. Several mechanisms can influence the circulation and mixing in thesewater bodies. The most important are described here, it is however not possible torank them by importance as it can change greatly from a lake to another.2.3.1 SeicheSeiches are standing wave oscillations found in enclosed basins. The oscillationcan be at the surface (surface waves; barotropic) or at density discontinuities inthe water column (internal waves; baroclinic), or both. Strong winds have beenshown to tilt lake ice covers, resulting in significant baroclinic seiches (Bengtsson,1996; Malm et al., 1998). These internal waves create horizontal circulation thatcan lead to shear instabilities and hence mixing. The breaking of these waves onshore slopes can also generate significant mixing (Boegman et al., 2005). Kirillinet al. (2018) measured TKE dissipation rates higher than 2x10-8 W kg-1 under theice during seiching events on Lake Kilpisja¨rvi in Finland. Simpson et al. (2011)even recorded values up to 10-7 W kg-1 on the bottom boundary layer in Lake Balain Wales. This illustrates that seiches can significantly contribute to mixing evenin ice-covered lakes.2.3.2 Radiative MixingWhen the ice cover is free of snow, solar radiation will penetrate into the waterbelow. Because the temperature of maximum density (Tmd) is above the freezingtemperature in water with salinity below 24 g kg-1, heating of water that is belowTmd increases its density. This radiative heating creates convection in the upperwater layer where a heated parcel of water sinks down and is replaced by colder(less dense) water (Bouffard et al., 2019; Farmer, 1975; Forrest et al., 2008). Jonaset al. (2003) and Volkov et al. (2019) reported ε values of∼8x10-10 and∼2.5x10-9W kg-1 during radiative mixing at the daily radiation peak in spring. Radiativemixing can be a very important mechanism for temperate lake as it starts the springmixing before the wind as direct contact with the water (Bouffard et al., 2016).However, as discussed in the Chapter 1, the present study focuses on the winterperiod so radiative mixing will be ignored.182.3.3 InflowsInflows from streams and rivers can drive circulation and mix the water columnof ice-covered lakes. The extent of mixing depends on the characteristics of theinflow (density, velocity and cross sectional area) and on the stratification of thelake (Stigebrandt, 1978). If the conditions at the inlet are subcritical (laminar flow),the inflow will enter the lake without creating much disturbance and spread out atthe depth of neutral buoyancy. If the velocity is high enough, this will produceshear instabilities and there will be mixing at the inflow/lake interface. Mixingand circulation resulting from inflows will be neglected because this is negligibleoutside of the melt season.2.3.4 Ice WallsIf one of the boundaries of the lake is a glacier (e.g. Lake Untarsee, Antarctica(Steel et al., 2015)) melting of the ice at the ice-lake interface produces buoyantfreshwater that induces upward circulation at the glacier boundary. Epishelf lakesare, by definition, in contact with ice walls. Half of the perimeter of Milne Fiordepishelf lake is ice (Figure 2.2) and there are many independent ice pieces of iceshelf and glacier tongue that increase the surface of the ice-water interface.2.3.5 Diffusive ConvectionDouble diffusion is a phenomenon created by the difference in molecular diffu-sivity of heat (∼10-7 m2 s-1) and salt (∼10-9 m2 s-1). One type of double diffu-sion is diffusive convection. Diffusive convection can develop when water withlower temperature is above water with higher salinity and temperature (Ruddickand Gargett, 2003; Schmitt, 1994). In diffusive convection conditions, a relativelycold and fresh water parcel that is displaced downward absorbs heat much fasterthan it looses salt and therefore becomes less dense than it was initially. This is be-cause this water parcel loses density faster due to the increase temperature than itgains density due to salinity increase. This phenomenon creates a growing oscilla-tion that manifests itself by creating vertical convective cells that result in staircasefeatures in the temperature and salinity profiles. This process can significantly in-crease heat and salt fluxes in lakes, as the gradients between the convective cells19can be very sharp (e.g. Lake Vanda, Antarctica (Hoare, 1966; Huppert and Turner,1972)).2.3.6 Earth RotationThe rotation of planet Earth can influence physical processes that have a time scaleof the order of the inertial period (∼12 h) or longer. In geophysical flow, the in-ertial period is the time scale for which the fluid inertia is perfectly balanced bythe Coriolis force. In the Northern Hemisphere, the Earth’s rotation has the ef-fect of ”bending” the flow to the right (Coriolis effect). Away from boundaries,geostrophic flow (balance between Coriolis force and pressure gradient) can de-velop when the Rossby radius is smaller than the horizontal scale. In lakes, thisis often observed as cyclonic or anti-cyclonic gyres (Forrest et al., 2008; Graves,2015; Rizk et al., 2014).2.3.7 TidesEpishelf lakes are hydraulically linked to the ocean, therefore, they experiencetides. The back and forth of water in the conduit between the lakes and the ocean(water jet during flood) is thought to be an important mixing mechanism for someepishelf lake in Antarctica (Galton-Fenzi et al., 2012; Gibson and Andersen, 2002)where tidal amplitude is around 1.3 m. The situation of these epishelf lakes isdifferent than MEL; the connection to the open ocean is more restrained and thetides are stronger. However, as Milne Fiord is a quiet environment, tides do nothave to be huge to have a significant impact.2.4 Arctic FjordsIn recent years, there has been a surge of scientific research on fjords in Greenland.These fjords, where tidewater glaciers terminate, are positioned at the nexus of theGreenland Ice Sheet and the Arctic Ocean (Straneo and Cenedese, 2015). As 50%of the mass loss of the Greenland Ice Sheet is linked to ice discharge (melting andcalving), Greenland fjords are key to understand and predict the effect of climatechange. The fjords that have been studied to date (e.g. Petermann (Johnson et al.,2011), Sermilik (Jackson et al., 2014b), Kangerdlugssaq (Sutherland et al., 2014))20are similar to those of the Canadian High Arctic. It is therefore interesting to lookat the work done in Greenland to get a better understanding of the circulation inMilne Fiord. The main circulation mechanisms in Greenlandic fjords are wind,meltwater plumes, tides and Coriolis force. Fjords in Svalbard are also similar asthey become ice covered in winter.2.4.1 WindAlongshore wind episodes can generate coastal upwelling or downwelling, increas-ing the water exchange between the fjord and the coastal shelf substantially. Up-welling can be observed as a lifting of isotherms, generated as deep denser waterenters the fjord and pushes shallower water out. Conversely, downwelling can beobserved as a deepening of the isotherms as less dense water from the upper wa-ter column enters the fjord and pushes deep water out. This circulation drivenby density differences arising outside the fjord is called intermediary circulation(Sutherland et al., 2014). In Greenland, strong along-shore wind episodes werelinked to rapid water exchange in glacial fjords during both summer (Straneo et al.,2010) and winter (Jackson et al., 2014b). Enhanced water renewal is linked tide-water glacier melt rates. Even though the ocean is ice-covered most of the timeoffshore of Milne Fiord, wind can still generate up- or down-welling (Dmitrenkoet al., 2016; Kirillov et al., 2016; Williams et al., 2006). This is because ice move-ment on the ocean is dictated by the wind so the wind stress can still be transferredto the water through the sea ice.Along-fjord wind can also significantly increase the circulation (Carroll et al.,2017) in fjords. However, because all Milne Fiord ice (ice shelf, glacier tongue,epishelf lake) is effectively immobile (does not move with the wind) year round, itdoes not transfer momentum to the water in the fjord.2.4.2 Meltwater PlumesPlumes of relatively fresh water are released at the base of glaciers via subglacialdischarge or are formed from the melting of the ice in contact with the fjord wa-ter (Figure 1.1). These plumes alter the fjord circulation by moving water upwardclose to the glacier and entraining ambient water until this combined water mass21reaches neutral buoyancy. This leads to a 2-dimensional circulation pattern wherefresher water in the upper water column flows downfjord and more saline wa-ter below this flows upfjord (Carroll et al., 2017; Sciascia et al., 2013; Straneoand Cenedese, 2015; Xu et al., 2012). This circulation driven by density differ-ence arising in the fjord is a form of estuarine circulation (Sutherland et al., 2014).Meltwater plumes from subglacial discharge normally have a bigger impact thanthose from direct melting (Straneo and Cenedese, 2015). Sutherland et al. (2014)estimated that intermediary circulation was an order of magnitude greater than es-tuarine circulation in summer for two Greenland fjords (Sermilik and Kangerd-lugssuaq). On the other hand, Mortensen et al. (2014) showed that estuarine cir-culation can also play an important role in Godtha˚bsfjord (Greenland). It is alsonoteworthy to mention that residual meltwater was observed in Petermann Fjordmonths after the melt season was over (Washam et al., 2019) and subglacial dis-charge was discovered in the middle of the winter under a glacier in the Yukon(Schoof et al., 2014). This implies that meltwater plumes can potentially have animpact on the fjord circulation even after the end of the melt season.2.4.3 TidesThe intensity (currents and amplitude) of the tides and the height of sills determinethe amount of energy available for tidal mixing in fjords. If the tides are weak andthe sill is not very prominent, tides will likely not have a significant effect. As theintensity of the tides and prominence of the sill increases, baroclinic currents willalso increase. If the baroclinic currents are sufficiently strong, shear instabilitiescan develop and lead to turbulent mixing. In cases where the water depth at thesill is very small, the tide can generate a jet (Stoylen and Fer, 2014). In that case,turbulence level can be quite high; Fer and Widell (2007) measured an average εvalue of 1.1x10-7 W kg-1 in ice-covered Van Mijenfjorden (Svalbard).The interaction of the tides with the sill can also generate internal waves of allsorts which can be an important mixing mechanism in Arctic fjords, especiallywhen they are ice-covered and with limited inflow in winter (Perkin and Lewis,1978). As previously mentioned, tidal amplitude and currents are small in MilneFiord. In addition, the sill is not substantially prominent (depth ∼220 m). This22suggests tidal mixing is not important in this context.2.4.4 Earth RotationIn cases where the fjord is wide enough (>Rossby radius), geostrophic flow (thebalance between Coriolis force and pressure gradient) can develop (Inall et al.,2014; Johnson et al., 2011). This can significantly increase exchange with shelfwater and accelerate subglacial melting and freshwater export (Carroll et al., 2017)by increasing the water renewal in the fjord.Despite numerous recent studies on circulation in Greenland fjords, no turbulencedata has been published yet, which leaves a knowledge gap to be filled in the yearsto come. However, turbulent kinetic energy dissipation data from Andvord Bay onthe Antarctic Peninsula shows that polar fjords can be quiet environments, even inthe summer (ε<10 -9 W kg-1 below the surface layer) (Lundesgaard et al., 2020).It is also accepted that the level of turbulence in the Arctic Ocean is quite low(Chanona et al., 2018). There are many explanations for this low turbulent kineticenergy. The first is that the Arctic Ocean is above the turning latitude where lin-ear internal waves generated by semidiurnal tides cannot propagate (Rippeth et al.,2017). The second is that the ice cover reduces the effect of wind and damps inter-nal waves in the upper water column (Guthrie et al., 2013). Taking this into accountand keeping in mind that tides are very small around Milne Fiord, it appears thatthis is a low energy area.2.5 Basal ChannelsIce shelves in Antarctica are very important to the global climate as they act tobuttress terrestrial glaciers. The disintegration of ice shelves therefore causes anacceleration of glacier velocity (Seehaus et al., 2016; Wuite et al., 2015) resultingin an increase of ice flux to the ocean, with its associated consequences (e.g. sealevel rise, sea ice increase (Richardson et al., 2005) and possible global circulationalteration (Park and Latif, 2019)). Channels under ice shelves are a key feature tounderstand in order to predict the stability of these ice structures (e.g. Dow et al.(2018); Drews (2015)). Several studies of these basal channels were carried outin the last 10 years in order to understand the physical processes concerning their23formation, evolution and the consequences of their presence on ice shelves.2.5.1 FormationThe formation of ice shelf basal channels is linked to the path of the meltwaterplumes. Some channels are directly related to subglacial discharge at the groundingline. The discharged water moves upward along the underside of the ice shelfwhere it melts ice above it preferentially as it rises, creating a basal channel (Alleyet al., 2016; Le Brocq et al., 2013). On the other hand, subglacial discharge is notnecessarily needed for these structures to appear. They can spontaneously formalong the bottom of ice shelves, where any kind of irregularity focusses meltwaterflow, melting that area faster and eventually creating a channel (Alley et al., 2016;Sergienko, 2013). Irregularities under ice shelves can be created by the presenceof bathymetric features close to the grounding line (Gladish et al., 2012).The melting potential of seawater depends on its temperature and salinity. Anincrease of temperature or salinity means an increase of melting potential (Jenkinset al., 2010). Therefore, the tidal glaciers in contact with water that has a highermelting potential are more likely to display basal channels. Indeed, Alley et al.(2016) showed that the area where the density of basal channels is the highest inAntarctica is where the water reaching the grounding line has the highest meltingpotential. In Antarctica, the circumpolar deep water (CDW) is of special interestas it has a high melting potential Alley et al. (2016). The Arctic counterpart of theCDW is Atlantic water (Straneo et al., 2012).2.5.2 EvolutionNumerical studies (Gladish et al., 2012; Millgate et al., 2013) and observations(Alley et al., 2016; Dutrieux et al., 2013) showed that melting in basal channelsis higher close to the grounding line and diminishes in the seaward direction. Aswater moves toward the ocean in the channels, the freshwater content increases andits melting potential decreases (Gladish et al., 2012; Millgate et al., 2013). This iswhy channels are normally narrow and deep close to the grounding line but becomeflatter and wider as the distance from the grounding line increases. One exceptionto this is the Dotson Ice Shelf, where it appears that melting is sustained from the24grounding line to the calving front, likely because of the presence of warm waterrelatively high in the water column (Gourmelen et al., 2017).Ice shelves and glacier tongues are normally in hydrostatic equilibrium (Alleyet al., 2016; Vaughan et al., 2012). The consequence of this is that the relief un-derneath the ice is reproduced at the surface and this allows for the use of remotesensing to study the basal channels. In Milne Fiord, Rajewicz (2017) used ice pen-etrating radar and water measurements (CTD and current meter) to describe thechannel and path of the epishelf lake water under MIS. In summer, the depressionsat the surface above basal channels can fill with meltwater and form streams andrivers (Dow et al., 2018; Rajewicz, 2017).2.5.3 MeltingNumerical modeling (Gladish et al., 2012; Millgate et al., 2013) and observations(Dutrieux et al., 2013; Malm et al., 1998) also confirm that melting is much higherinside the basal channels than outside. Melting is also much higher in summer thanin the winter. For example, Washam et al. (2019) found basal channel vertical meltrates of 80 m a-1 and 2 m a-1 in summer and winter, respectively, 16 km from thegrounding line of Petermann Glacier, Greenland. In Antarctica, summer meltingrates of∼22 m a-1 where observed in channels under the Pine Island (Stanton et al.,2013) and Ross (Marsh et al., 2016) ice shelves. This is higher than the annualaverage basal melt rate for Ross (∼5 m a-1 (Marsh et al., 2016)) Filchner-Ronne(∼5 m a-1, (Le Brocq et al., 2013)) and Getz (8.8-14.7 m a-1,(Alley et al., 2016))ice shelves. Hamilton (2016) calculated that melt rates were only significant atthe very top of MIS channel because the epishelf lake water has a higher meltingpotential. However, if the melt rates are estimated using the offshore water profile,there is no melting happening in the MIS channel. The reality must be in between,where melt rates at the apex of MIS channel can be significant in the upfjord partof the channel, but decreases as the epishelf lake water loses heat by melting theice.252.5.4 Impacts of Basal ChannelsEven though the presence of basal channels reduces the overall amount of melting(Gladish et al., 2012), it is thought that these area of reduced ice thickness jeopar-dize the mechanical stability of ice shelves and glaciers and therefore can increasethe ice flux to the oceans (Alley et al., 2016; Rignot and Steffen, 2008). Vaughanet al. (2012) showed that on Pine Island Glacier Ice Shelf, hydrostatic readjustmentof the ice in response to channelized melting has formed longitudinal crevasses atthe apex of the basal channels (under the ice) and between the channels (at the sur-face). In addition to parallel crevasses, Dow et al. (2018) showed that high meltingin basal channels can also cause transverse fractures, increasing vulnerability tocalving.The main difference between the channel in MIS and others found in Greenlandand Antarctica is that the water flowing through MIS channel is much fresher atthe top of the channel (as it comes from the epishelf lake). Indeed, the water foundin channels outside of Milne Fiord is seawater that is slightly fresher than the am-bient water offshore. Other than this peculiarity associated with the epishelf lake,comparison of MIS channel and other basal channels is straightforward, reinforc-ing the relevance of this study.26Chapter 3Winter Dynamics in the LastEpishelf Lake in the CanadianArctic, Milne Fiord, Nunavut,CanadaA version of this chapter is being prepared for submission to a peer-reviewed jour-nal as Winter Dynamics in the Last Epishelf Lake in the Canadian Arctic, MilneFiord, Nunavut, Canada by J. Bonneau, B. E. Laval, D. Mueller, A. K. Hamilton,A. M. Friedrichs and A. L. Forrest.3.1 Key Points• One-dimensional model to analyse eight years of winter mooring data of theupper water column in an perennially ice-covered fjord.• Mixing is more pronounced in the isolated freshwater layer (epishelf lake)than in the seawater below.• The morphology of the basal channel under the ice shelf is apparently stable.273.2 IntroductionGlobal climate change effects are the most pronounced in the Arctic (IPCC, 2013).In the Canadian High Arctic, all major glaciers of the Queen Elizabeth Islands areshowing a decrease in surface elevation (Mortimer et al., 2018). Climate-relatedchanges are unmistakable on the northern coast of Ellesmere Island where the iceshelf extent has decreased over the last century (Mueller et al., 2017). In this re-gion, where historically there was an ice shelf at the mouth of every fjord (Vincentet al., 2001), the continuous fracture and break up of ice shelves has left only onerelatively intact, in Milne Fiord. This platform of ice is grounded on both sides ofthe fjord and acts like a dam, preventing summer freshwater runoff from dispersingfreely into the ocean. This perennial layer of freshwater overlaying to Arctic sea-water behind the ice shelf is called an epishelf lake. Since Milne Ice Shelf (MIS)is the only ice shelf in Canada that has not recently calved, Milne Fiord epishelflake (MEL) is the last epishelf lake along its coast. Figure 3.1 is a satellite imageof Milne Fiord showing the downstream part of Milne Glacier (MG), the glaciertongue (MGT), the epishelf lake (MEL) and the ice shelf (MIS). MG, MGT, MELand MIS form a strongly interconnected system not yet fully understood (Hamiltonet al., 2017). Studying one of the pieces of this puzzle also improves knowledgeof the other parts. Moreover, even though MEL is the last epishelf lake in Canada,several can be found in Antarctica (Gibson and Andersen, 2002; Laybourn-Parryand Wadham, 2014) and one in Greenland (Bennike and Weidick, 2001). Hence,knowledge acquired in the study of Milne Fiord can be transferred to the other sitesin the Polar Regions.It is known that MEL experiences annual cycles of deepening due to meltwaterrunoff in summer and shoaling due to outflow below MIS (Hamilton et al., 2017)(Figure 3.2). It is thought that epishelf lake outflow is through a basal channel un-der the ice shelf, analogous to those found beneath Petermann Glacier in Greenland(Rignot and Steffen, 2008) or Pine Island Glacier Ice Shelf (Dutrieux et al., 2013;Stanton et al., 2013) in Antarctica. Basal channels have attracted attention in recentyears as meltwater concentrates in these structures (Millgate et al., 2013) (Gladishet al., 2012) and increases melt rates (Alley et al., 2016; Dutrieux et al., 2013;Stanton et al., 2013). Even though they reduce the overall melting of ice shelves28Figure 3.1: A) Location of Milne Fiord (82.6◦N, 81.0◦W). B) Landsat 8 im-age of Milne Fiord taken in September 2018. MEL: Milne EpishelfLake, MIS: Milne Ice Shelf, MGT: Milne Glacier Tongue, MG: MilneGlacier29Figure 3.2: Schematic of Milne Fiord including Milne Ice Shelf (MIS), MilneEpishelf Lake (MEL) and Milne Glacier Tongue (MGT). A) During themelt season (summer) (∼June 1st to ∼September 1st), runoff drives thedeepening of MEL. B) During the remainder of the year, the thicknessof MEL decreases slowly toward the minimum draft of the MIS.(Gladish et al., 2012; Millgate et al., 2013), it is thought that the localized strongmelting within channels will lead to faster breakup (Dow et al., 2018; Gourmelenet al., 2017; Rignot and Steffen, 2008).From an oceanographic perspective, the physical structure of the water column inMilne Fiord is well known during summer (Hamilton et al., 2017), but less duringwinter. Because the fjord is ice-covered all year long, no wind-induced circulationor mixing occurs. Moreover, the tidal amplitudes are very small (∼ 10 cm). Windand tides are the two main forcing mechanisms in an Arctic fjord (Keys, 1977).Nonetheless, other mechanisms of lower importance can modify the water columnof ice-covered fjords. Sciascia et al. (2013) found that even during the winter,meltwater plumes influenced the circulation in Sermilik Fjord, Greenland. Also inSermilik, Jackson et al. (2014b) and Straneo et al. (2010) showed that water prop-erties changed in response to along-shore wind episodes creating downwelling. InCambridge Bay, Canada, Perkin and Lewis (1978) concluded that during winter,breaking of internal waves on the shore was the main mixing mechanism. TheEarth’s rotation can also alter the circulation when the fjord is sufficiently wide(Straneo and Cenedese, 2015). Due to the presence of the ice shelf, the upperwater column in Milne Fiord has similarities with ice-covered lakes where the in-fluence of the Earth’s rotation has also been reported (Bengtsson, 1996; Forrest30et al., 2013; Huttula et al., 2010; Rizk et al., 2014; Steel et al., 2015). Regardingmixing mechanisms, it is noteworthy to mention that solar radiation does not playimportant role outside of the melt season as the ice is quickly covered by snow.Circulation and mixing processes have implications for the location of the halo-cline; important to understand the outflow in the channel and the amount of surfacerunoff. Furthermore, a better understanding of mixing processes in the fjord wouldimprove insight on the fate of the ice shelf and the glacier. Finally, in additionto other epishelf lakes in Antarctica, physical processes in MEL can be similar tothose in ice-covered lakes, where external forcing is limited, especially when snowcover significantly reduces solar radiation reaching the water. With that perspec-tive, MEL is a great laboratory to study these lakes since it is ice-covered all yearlong.Extensive (relative to Arctic research) field work has been carried out in MilneFiord over the last 15 years and a mooring deployed in the lake in May 2011 hasbeen recording continuously to present. This study has two main objectives. Thefirst is to quantify the mixing occurring in the epishelf lake and associate it to forc-ing mechanism(s). The second is to confirm that the channel is the main outflowpath for the epishelf lake and to get information on the evolution of its morphology.In order to do this, a one-dimensional model was calibrated with the mooring data(July 2011 to July 2019) in order to estimate the mixing in the top of the watercolumn and the discharge through the channel from the end of one melting seasonto the start of the next one.The next section (2) describes the important geophysical features of Milne Fiord.It is followed by the description of the field data and the numerical model (section3). Section 4 goes over model validation and results. Section 5 is the discussion ofthe main results and their implications. Finally, section 6 is the conclusion.3.3 Geophysical Setting and Study Area Background3.3.1 The FjordMilne Fiord (82.6◦N, 81.0◦W) (Figure 3.1) is 40 km long from the glacier ground-ing line to the outer edge of the ice shelf. Its width is 6 km from the glacier ground-31ing line to the epishelf lake and then becomes wider downfjord. The bathymetryof the fjord, inferred from CTD casts and depth soundings (Hamilton et al., 2017)exhibits a U-shape profile with a maximal depth of 436 m. A sill with a maxi-mum depth of 220 m is present 22 km upfjord from the tip of the ice shelf, justdownfjord of the epishelf lake. The maximum fjord depth below the epishelf lakeis approximately 400 m and the depth near the grounding line of Milne Glacier is150 m Figure 2.2. Tides in Milne Fiord are semidiurnal with an amplitude around10 cm. Tidal baroclinicity was found from current measurements but was too lowto produce shear mixing (Hamilton et al., 2017). The average annual air tempera-ture at sea level is -19◦C, with the number of positive degree days between 100 and300 from June 1st to September 1st (Hamilton, 2016). At this high latitude, thereis no direct solar radiation from mid-October to the beginning of March.3.3.2 The GlacierMG is over 50 km long, 4 to 5 km wide, has a thickness of approximately 150m at the terminus (Hamilton, 2016) and becomes thicker going upglacier. Thewatershed of this tidewater glacier is 1500 km2 and has a glaciated area of approx-imately 1100 km2 (Hamilton, 2016). MG is classified as a possible surge glacier(Van Wychen et al., 2016), meaning MG could possibly have fast flowing episodeswhere it would move at velocities many times the normal 100 m/year observedlately (Van Wychen et al., 2016). Downfjord from the grounding line, MGT ex-tends 15 km. The thickness of the MGT decreases rapidly and the ice thickness isless than 10 m at its margins. It broke away from the glacier in 2009 but did notmove significantly since.3.3.3 The Ice ShelfMIS occupies 200 km2 at the mouth of Milne Fiord and is attached to land on bothsides (Figure D.4). The estimated mean ice thickness is 47 m with a maximum anda minimum around 94 m and 8 m, respectively (Hamilton, 2016). The thinnest areais along a basal channel that runs westward from the east shore (Hamilton et al.,2017; Mortimer et al., 2012; Rajewicz, 2017) (Figure 3.1).323.3.4 The Epishelf LakeFrom a physical perspective, the most striking feature in MEL is the extremelysharp salinity interface between the freshwater and the ocean below (Figure 3.3).The salinity gradient, over 6 g kg-1 m-1, is well above what is typically found year-round in an Arctic fjord. The depth of the halocline, taken as the depth of maximumstratification, is used to mark the depth of the epishelf lake (Hamilton et al., 2017).MEL experiences an annual cycle of deepening and shoaling. During the sum-mer, when snow and ice are melting, water from surface runoff flows into the lakedeepening the freshwater layer (Figure 3.2A). Meanwhile, water deeper than theminimum draft of the ice shelf flows to the ocean. When the melting season is over,surface runoff stops and the lake slowly shoals until summer (Figure 3.2B). It isthought that the flow to the ocean is exclusively along the ice shelf basal channeland is hydraulically controlled by its dimensions; this study tests this hypothesis bymodeling the outflow during the winter period. Hamilton et al. (2017) showed thatthe annual minimum thickness of the epishelf lake significantly decreased from2004 to reach a minimum of 7.9 m in 2013. The only data available before 2004are water bottle measurements from 1983 that, if linearly interpolated, suggests thehalocline was at 17.7 m (Jeffries, 1985). Using satellite imagery and aerial photos,it is estimated that the MEL surface area went from 13.5 km2 in 1959 to 71.2 km2in 2015 (Hamilton, 2016). Comparison with more recent satellite images does notshow a drastic change in MEL surface area since 2015 so 71.2 km2 will later beused for hydrological analysis. As a result of short summers, cold long winters anda freshwater cap, the lake is permanently ice-covered. The minimum ice thicknessobserved was 0.65 m in July 2010 (Hamilton, 2016) and a maximum of 3.19 m wasobserved in May 1983 (Jeffries, 1985).3.3.5 Offshore OceanographyOceanographic measurements offshore from Ellesmere Island are sparse. Jacksonet al. (2014a) used mooring, CTD data and numerical modeling to state that cur-rents are weak (less than 10 cm s-1) and directed westwards on the North Ellesmerecontinental shelf. This is in agreement with other numerical experiments (Aksenovet al., 2011) and iceberg drift paths (Copland et al., 2007; Garbo). CTD profiles33offshore of Milne Fiord every year since 2011 show a mixed layer of 30 to 60 mon top of water gradually transitioning from -1.6◦C and 31 g kg-1 at the base of themixed layer to 0.3◦C and 35 g kg-1 at 250 m. Water properties lower than 250 mdo not change greatly.3.4 Data and Methods3.4.1 Epishelf Lake MooringAn ice tethered mooring was deployed in the center of MEL in May 2011 andhas been recording since then (Figure D.6). To the authors knowledge, this is thelongest deployment of a mooring in a Canadian High Arctic fjord or lake. The datafrom the original deployment to July 2019 are analyzed here. The only time gapsare during fieldwork when the mooring was serviced. Over the years, the mooringconfiguration changed substantially and different types of instrument were used.The mooring line configuration for each deployment is included in Figure 3.6.Since the focus here is on annual and interannual variations, data from all the moor-ing instruments were averaged daily for the following analysis. When pressure datawas available (6 out of 8 years), instrument depth was corrected for shifts in ele-vation due to ice formation. All temperature and salinity data in this study wereconverted to the TEOS-10 standard as conservative temperature, Θ [◦C] and abso-lute salinity, SA [g kg-1] using the GSW oceanographic toolbox (McDougall andBarker, 2011).3.4.2 CTD CastsWater profiles have been taken annually in MEL since 2009. Instruments used forprofiling are an Idronaut Ocean304plus (2015-2016) and a RBR XR-620 (2009-2014, 2017-2019). The 2010 CTD profile is from NEIGE (2017). The profiles weretaken in natural holes made with a power auger or hand tools. Profiles were takenat recovery and deployment of the mooring to crosscheck the mooring instrumentsand get a full vertical resolution.343.4.3 Weather DataA weather station installed next to a small bay in Purple Valley (Figure 3.1) hasbeen recording hourly data continuously since 2009 (data courtesy: Luke Cop-land). A weather station was also installed on the ice shelf from July 2016 to July2018. Even though the Purple Valley station is much more sheltered than the iceshelf station, decomposed N-E-S-W wind at ∼2 m show similar trends. Wind datacan be compared to the model to investigate forcing mechanisms.3.4.4 Ice Shelf Channel ADCPAn ADCP moored at the top of the ice shelf basal channel (green circle in Fig-ure 3.1) recorded from July 2017 to July 2019. Using the July 2016 channel mor-phology data from Rajewicz (2017) and the approximated 71.2 km2 lake area, thedata from the ADCP and the model can be compared in order to evaluate the modeloutflow over the 2016-2017 and 2017-2018 deployments.3.4.5 Model FormulationA one-dimensional model was used to analyze the mooring data outside of themelting season (i.e. winter). It is emphasized here that the model was used as adiagnostic tool to examine mixing and the outflow, not a prognostic one. It wasdesigned to relate all the available winter data from the mooring together and an-alyze these data in a simplified context with a small number of free parameters.The model works to estimate the vertical mixing in the upper water column andthe outflow through the basal channel. In order to do this, the mooring data wasemployed to determine the parameters of the model using an iterative method.To model the transport of heat and salt, the Reynolds-averaged transport equationfor scalar properties was used (Kundu et al., 2012):∂ϕ∂ t+u j∂ϕ∂x j+∂ (u′jϕ ′)∂x j= Km∂ 2ϕ∂x2j(3.1)Where ϕ is a Reynolds-averaged scalar (e.g. conservative temperature or absolutesalinity) , u j is the Reynolds-averaged velocity vector and Km is the moleculardiffusivity. t is the time and x is the dimension ([x1 x2 x3] = [x y z], x3 (z) being in35Figure 3.3: Schematic of the one-dimensional model. Typical absolute salin-ity and stability profiles are on the right. The data from the uppermostand the 25 m thermistor are used as boundary conditions for temperatureand the no flux boundary conditions are used for salinity. Mixing coef-ficients of the top freshwater layer (Ktop) and the bottom seawater layer(Kbot) are parameters of the model; only molecular mixing is consid-ered for the halocline layer. The outflow layer is between the minimumdraft of the ice shelf (h0) and the bottom of the halocline layer (z). Thetop and bottom dashed lines show the top and bottom boundaries ofthe model. The two middle dashed lines are the top and bottom of thehalocline layer (molecular diffusivity only).the vertical direction). The following simplifying assumptions were made:• The average vertical velocity u3 is nil (u3 = 0)• The horizontal gradients are negligible (u1 ∂ϕx1 ≈ u2∂ϕx2≈ ∂ 2ϕ∂x21 ≈∂ 2ϕ∂x22≈ ∂ 2u′1ϕ∂x21 ≈∂ 2u′2ϕ∂x22≈ 0)• Eddy diffusivity can be used to estimate turbulence (u′3ϕ ′ ≈−Kt ∂ϕ′∂x3 )36This leads to :∂ϕ∂ t= K∂ 2ϕ∂x23(3.2)where K is the combined (Kt +Km) mixing coefficient.In order to take into account the outflow of the epishelf lake (Figure 3.3), the basalchannel was simplified as a rectangular weir (Figure 3.4), which allowed the out-flow to be described with two annual parameters (Ceb, h0, see below). The modelworks to estimate four different parameters: two mixing coefficients (Ktop, Kbot , asin section 3.2, see below) for every day and two annual outflow parameters (Ceb,h0, see below). To find the value of these parameters, these quantities were con-strained to a number of possible values and then the best fit was found using thedaily averaged mooring data as the evaluation data set.Equation 3.2 was solved on a 10 cm by 30 minute grid using a Crank-Nicolsonfinite difference scheme. Grid space and time independence was verified usinghigher and lower order of magnitude meshes.Boundary conditionsFor temperature, the daily averaged data from the uppermost unfrozen thermistorand the thermistor at 25 m depth were used as Dirichlet boundary conditions atthe top and bottom nodes. For salinity, a no flux (∂SA/∂ z = 0) Neumann boundarycondition was used. Since mixing is very limited (demonstrated below), a null saltflux at 25 m is a reasonable assumption even though gradients exist at that depth.Initial conditionsFor temperature, initial conditions were given by a linear interpolation betweenthe mooring instruments. Initial salinity conditions were obtained by using the lastCTD cast taken during fieldwork and fitting this profile to the mooring salinity databy shifting it vertically to get the best fit (minimum RMSE).MixingIn order to account for mixing, the water column was divided into three layers(freshwater, halocline and seawater, Figure 3.3), each with different mixing coeffi-37cients. The layer boundaries were defined as the points where the squared Brunt-Va¨isa¨la¨ frequency equals 10-2 s-2. This demarcation is supported by the minimumRichardson number (Ri = N2/( ∂u∂ z )2) found in the water profile. An observed ve-locity gradient around 0.01 s-1 from Hamilton (2016) and induction current metermeasurements (not shown) in combination with perpetual high stratification (>10-2s-2) made it possible to rule-out turbulent mixing in the halocline. However, withinthe top freshwater and bottom seawater layers, CTD measurements indicate strat-ification is not strong enough to preclude turbulent mixing. The threshold of 10-2s-2 was arbitrarily chosen as it delineates the region of high salinity gradient withgood precision in all CTD profiles (Figure 3.3). To summarize:• The top layer, from the top boundary to N2 =10-2 s-2 had mixing coefficientsfor heat (KtopΘ ) and salt (KtopSA ).• The halocline layer, where N2 >10-2 s-2, only had molecular diffusion.• The bottom layer, from N2 =10-2 s-2 to the bottom boundary, had mixingcoefficients for heat (KbotΘ ) and salt (KbotSA ).Values of 1.4x10-7 m2 s-1 and 1.4x10-9 m2 s-1 were employed for molecular diffu-sivities of heat and salt, respectively (Jackson and Rehmann, 2014). Possible KΘcoefficients were: [1.4, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]x10-7 m2 s-1. Thepower of two increment was chosen to reasonably cover orders of magnitude from10-7 to 10-4 for KΘ while keeping the required computational power reasonablylow (normal laptop). The upper limit of 1024x10-7 m2 s-1 was chosen as KΘ onlyvery rarely reaches this value (as will be shown later).As first pointed out by Turner (1968), when turbulence is weak, the mixing ofheat and salt is not the same (i.e. the turbulent Lewis number (Le = Kt,ΘKt,SA ) is notone). Differential diffusion (Le 6=1) has been observed in oceanic measurementsand demonstrated in laboratory and numerical experiments (Gargett, 2003). Be-cause Milne Fiord is a quiet environment, it is important to take into account dif-ferential diffusion in order to model the water column properly. To account forthis phenomenon, the parameterization of Jackson and Rehmann (2014) was ap-plied to link KtopΘ to KtopSA and KbotΘ to KbotSA . This related the mixing parameters inthe top and bottom layers, thereby reducing the number of unknowns. Using the38ratio determined by Jackson and Rehmann (2014), possible KSA coefficients were:[0.0014, 0.002, 0.004, 1.5, 4.3, 12, 33, 81, 191, 425, 915]x10-7 m2 s-1.OutflowAssuming most of the water outflow is through the basal channel in the ice shelfand that it can be simplified as a rectangular channel (Hamilton et al., 2017), theoutflow was modelled based on an inverse rectangular weir equation (Kindsvaterand Carter, 1959) (Figure 3.4):d(z−h0)dt=23Alake√2g′Ceb(z−h0)2/3 (3.3)Where h0 is the depth of the minimum draft of the ice shelf, Ce is a friction coeffi-cient, b is the width of the rectangular channel, z is the depth at the bottom of theoutflow layer and Alake is the area of the lake (∼ 71.2x103 m2). g′ is the reducedgravity ( g4ρ0ρ ≈ 0.25 m s-2), where g is the gravitational acceleration, 4ρ is thedensity difference between the freshwater and the seawater (25 kg m-3) and ρ isa reference density (1000 kg m-3). Ceb and h0 are two unknown parameters thatwere assumed constant outside of the melt season. d(z−h0)dt was computed every dayand the amount of water flowing out to the ocean was modeled by shrinking theoutflow layer (i.e. z− h0 was reduced). This assumes that the outflow velocity isthe same everywhere in the outflow layer. The above simplifications were derivedfrom current measurements and ice penetrating radar measurements over the chan-nel (Rajewicz, 2017). In order to compensate for the outflow, water was added atthe bottom of the model using the properties of the bottom node. Using equation3.3, possible values for h0 ranged from 3 to 10 m. The possible values for Cebranged from 2 to 10 m, which gives a minimum channel width from 2.5 to 18 musing common rectangular weir coefficients (0.55 to 0.8) (Hamilton et al., 2017).3.4.6 Model FittingIn order to find the optimal model parameters, an iterative scheme was employedusing a custom coefficient of agreement (Ca). All mooring instruments in the top25 m were used for the calibration. For the temperature calibration, the model39Figure 3.4: Schematic of the outflow of the lake through the basal channel ofthe ice shelf. A modified weir equation using a two layer simplification(equation 3.3) is used to constrain the number of parameters related tothe outflow. A) Top view. B) Along fjord section. C) Across fjordsection through MIS. Note: not to scaleoutput was compared to the linearly interpolated data at every grid node and theroot mean squared error (RMSEΘ,model) was computed and then normalized bythe standard deviation of daily averaged and linearly interpolated mooring data(ST DΘ,mooring). For the salinity data, the model output was linearly interpolatedto the precise depth of each salinity instrument, then the root mean squared error(RMSESA,model) was computed and normalized by the standard deviation of thesalinity data (ST DSA,mooring). The temperature score(RMSEΘ,modelST DΘ,mooring)and the salinityscore(RMSESA,modelST DSA,mooring)were weighted to take into account the number of temperaturemeasurements (nT ) and conductivity measurements (nC). For example, if therewere 10 temperature data points and four conductivity data points on the mooringline, the temperature score was weighted by 10/(10+4) and the salinity score wasweighted by 4/(10+4). To summarize, the Ca was computed with the following40equation:Ca =(nTnT +nc(RMSEΘ,modelST DΘ,mooring)+ncnT +nc(RMSESA,modelST DSA,mooring))−1(3.4)The normalization by the standard deviation of the mooring data allowed combi-nation of temperature and salinity data by placing them on a similar scale. Theweights allowed combination of these evaluation scores by adjusting their impor-tance according the respective number of measurements. The −1 exponent wasused to yield a positive relationship between Ca and the model skill (i.e. a high Cameans a good agreement). A value around 1 would mean that the model did poorly,since the RMSE would have the same magnitude as the ST D (basically random).On the other hand, a value of 10 would mean the model performed well since theRMSE would be 10 times smaller than the ST D.Figure 3.5 is a schematic of the model iterative calibration workflow. The first stepwas to write the boundary and initial conditions into the model mesh (1). Then, apair of outflow coefficients (Ceb and h0) was selected in order to calculate the dailyoutflow throughout the deployment (2). Next, the mixing coefficients returning thehighest Ca were found for day 1 (3-6). Steps 4-6 were repeated for every consecu-tive day. Once the daily mixing coefficients were determined, the Ca for the wholedeployment was computed (7) and steps 2-7 were repeated, narrowing down on theoptimal Ceb / h0 pair. Finally, the pair of outflow coefficient returning the high-est Ca for the whole deployment was selected as the best fitting parameters. Thisprocedure was repeated for the eight winters of mooring data (2011-2019). Themodel version with the best fitting parameters was used to generate the output inthe Results section.3.5 Model Results and Validation3.5.1 TemperatureTemperature output from the model (Figure 3.6A) agrees well with the tempera-ture data from the mooring (Figure 3.6B). The average RMSE for the whole time-series is 0.19◦C, the standard deviation is 0.17◦C, the R2 is 0.97 and the bias is41Figure 3.5: Once the initial conditions (IC) and the boundary conditions (BC)are implemented into the mesh, the model loops through the possibleoutflow coefficients (Ceb and h0) for every winter and through the pos-sible mixing coefficients for every winter days. (See text for detailedexplanation)0.067◦C. The Ca is 5.6 for the 8 years. Figure 3.6C shows the difference betweenthe model and the linearly interpolated mooring data. The model output appearsas a smoothed version of the mooring data, which signifies that the main seasonalphysical characteristics are reproduced. Three main differences can be observedbetween the model and the mooring data. First, the temperature oscillations abovethe halocline present in the mooring data are not reproduced in the model. Sincethere is no significant addition of heat during the winter, these oscillations must42be the result of horizontal advection, which are not considered in the model. Thesecond major disparity is found near the halocline where slight deviations in themodeled halocline depth result in substantial temperature errors because of thesharp gradient at this location. The blue line at 7.5 m in fall 2014 (Figure 3.6C) isthe best example of this. This type of error is due to the simplified considerationof the outflow in the model, which is held constant for the whole winter. The lastmajor difference is the inflow of cold water between 15 m and 22 m in the mooringdata of 2015-2016 and 2016-2017 (Figure 3.6B). This increased the error for thebottom part of the water column for many months. These main differences be-tween the model and the mooring data are the result of the simplifications made inthe model (one-dimension, no advection, rectangular weir outflow). However, con-sidering the visual and statistical agreement, the model is considered appropriatefor the study of the full winter timeseries.43Figure 3.6: Temperature timeseries of the top of the water column in Milne Fiord. A) Conservative temperature time-series of the model results. B) Conservative temperature timeseries from the mooring (linearly interpolated). C)Difference between the model and the mooring data, positive values mean the model temperature is higher thanthe mooring temperature. Triangles show the location of the thermistors on the mooring line and the squares showthe location of the conductivity instruments.44Figure 3.7: Salinity data from the model (solid line) at the depth of the con-ductivity instruments on the mooring (dashed line). Labels are the depthof the instruments, in meters.3.5.2 SalinityThe agreement between the model and the mooring salinity data is inferior to thatfor temperature but the model still fits the main characteristics of the salinity profilein the fjord (Figure 3.7). The average RMSE is 2.0 g kg-1, the standard deviationis 1.7 g kg-1 and the bias is 1.1 g kg-1. The main discrepancies are found in the topof the water column where the model tends to diffuse more salt into the freshwaterthan the mooring instruments indicate. This is likely because the simulated halo-cline is compressed in the outflow process, increasing the salinity gradient to valueshigher than observed in the field. Since the salt flux is proportional to the gradient,more salt makes its way to the top layer as a result of this artifact. Nonetheless, themodel shows the main features of the epishelf lake which are a freshwater layeratop a sharp halocline that moves upwards during the winter.3.5.3 OutflowThe depth of the halocline (bottom of the epishelf lake) returned by the model isshown is Figure 3.8A, as well as the outflow parameters for each year (legend).The trajectory of the halocline from 2014 to 2019 are closely grouped but the first45two years of the record (2011-2012 and 2012-2013) exhibit a more pronouncedshoaling. The minimum draft of the ice shelf (h0) returned by the model is similarfor every year (between 6.7 and 7.9 m) except for the 2015-2016 year (5.3 m). Theoutflow friction-width coefficient (Ceb) varies more but stays within the range ofrealistic values. There is no perceptible trends in either Ceb or h0.Figure 3.8B shows the approximated flow rate through the channel according tothe model (dashed lines) and the moored ADCP (solid lines). The total dischargeof 2.0x108 (2017-2018) and 2.3x108 m3 (2018-2019) for the model and 1.4x108(2017-2018) and 0.9x108 m3 (2018-2019) for the ADCP are similar.3.5.4 MixingThe daily mixing coefficients returned by the model are shown by the dots in Fig-ure 3.9. The solid lines represent a 30 day moving average of apparent thermal dif-fusivity. The top layer of freshwater above the halocline experiences more mixingthan the seawater below except during the first months (September and October)after the melt season. The total amount of mixing in the top of the water columndiffers greatly from year to year, with a minimum winter average of 2.5x10-7 m2 s-1in 2015-2016 and maximum 1.2x10-5 m2 s-1 in 2018-2019. The mixing below thehalocline is more uniform, spanning from 1.8x10-7 m2 s-1 in 2015-2016 to 2.3x10-6m2 s-1 in 2013-2014.If the model would be over mixing, the heat content of the freshwater layer wouldbe lower in the model than in the mooring data, as a higher KtopΘ means a higherheat flux out of the top layer. Analysis of the heat content in the top freshwaterlayer shows that the model does not over- or under-mix, increasing the confidencein the results.46Figure 3.8: A) Depth of MEL (maximum N2 value) given by the model foreach winter. The staircase effect is due to the vertical discretization ofthe model (10 cm). Outflow parameters h0 and Ceb for each winter arein the legend. B) Outflow through the basal channel in MIS. Dottedlines are the model estimation using the rectangular weir equation andan estimated lake area of 71.2 km2. Solid lines are the ADCP estimationusing the channel morphology data from Rajewicz (2017).47Figure 3.9: A) Daily mixing coefficients from the model, for the heat and salt transport equations for the top andbottom layers (dots). Solid lines are the 30 day averaged quantities for the top (blue) and bottom (red/orange)coefficients of the heat equation. Minimum possible values of daily mixing coefficients are the molecular diffu-sivities; 1.4x10-7 m2 s-1 for heat and 1.4x10-9 m2 s-1 for salt. B) 30 day averaged mixing coefficient of the model(dark blue) and inverse of the Richardson number (light blue) computed according to equation 3.6. N2 (dottedline) computed by the model and 30 day maximum density difference attributed to the temperature oscillations4ρ30 (dashed line) are used in equation 3.6. Enhanced mixing (dark blue line) is linked to stronger eddy activity(dashed line) hence to a lower Richardson number (light blue line).483.6 Discussion3.6.1 Numerical ModelThe one dimensional model employed in this study was shown to compared fairlywell with the winter mooring data in Milne Fiord. It enables the description of themain physical mechanisms using only four different parameters. Consequently,these parameters can be examined in order to get a better understanding of MilneFiord system.3.6.2 OutflowConsidering the simplifications (rectangular weir equation with h0 and Ceb con-stant throughout the winter) and estimations (channel cross section, lake area), it isreasonable to state that the basal channel is the main outflow path for the epishelflake water. Moreover, since ice penetrating radar measurements did not detect an-other probable path for outflow, the basal channel taken into account in this studyis most likely the only outflow for the epishelf lake water.There are yet some differences in trends between the model output and the ADCPdata. For example, the flow rate increase at the end of December 2018. Possible ex-planations are 1) an abrupt (7 day) change in the channel morphology at the ADCPlocation and 2) a mixing event disrupting the halocline. No mixing was inferredby the model in November 2017 which indicates the first process is more likely.On the other hand, h0 and Ceb are very similar from July 2016 to 2019 which sug-gests channel thinning may have occurred in the area of the ADCP mooring butnot in the area of the principal channel constriction (where weir equation param-eters come from). In other words, if the cross sectional area decreases (increases)at the ADCP location, the outflow rate inferred will be higher (lower) than realitybecause the velocity recorded by the ADCP would be greater (smaller). Moreover,the model Ca is no worse for 2017-2019 than for the other years, suggesting theoutflow increase, as estimated by the ADCP, is not directly linked to the epishelflake and that the constant outflow parameter assumption holds.Channels under ice shelves and glacier tongues have attracted attention in recentyears (e.g. Alley et al. (2016); Dow et al. (2018); Le Brocq et al. (2013)). Buoy-49ant water from subglacial melt and discharge converge in these longitudinal icedepressions, concentrating the melting in the channel apex (Millgate et al., 2013;Rignot and Steffen, 2008). Many recent studies estimated basal channel melt rates(Alley et al., 2016; Dutrieux et al., 2013; Gourmelen et al., 2017; Stanton et al.,2013), all agreeing that these locations experience enhanced melt (negative icemass balance). For the present study, the outflow parameters of the model leadto the conclusion that the minimum draft of the ice shelf has not experienced amajor change since September 2011. Indeed, if the melting was continuous in thechannel, there would be a trend in the outflow coefficients, but this is not the case.The fact that h0 went from 7.0 m (2014-2015) to 5.2 m (2015-2016) then up to7.9 m (2016-2017) implies that the apex of the channel at the main constriction isin neutral mass balance over a multi-year time scale. Likewise, the fact that Cebdoes not show any trend and experiences only small variations (±50%) also pointstowards a multi-year equilibrium in ice mass along the channel. This agrees withthe insignificant melting rate obtained by Hamilton (2016) in the Milne channelarea and the evidence past ice accretion under Ward Hunt Ice Shelf (100 km to theeast) (Jeffries, 1985). Moreover, CTD casts in the channel (not shown here) alsosupport this hypothesis, showing that the water flowing in the channel at the ADCPmooring location is generally within 0.02◦C of its freezing temperature during thesummer. This result shows that the MIS basal channel is not necessarily an area ofconcentrated melt, even in the summer. This is in marked contrast to what is foundin the literature at other locations (Alley et al., 2016; Dutrieux et al., 2013; Rignotand Steffen, 2008; Stanton et al., 2013).The present study can only make a statement on the channel area of the ice shelfand it is important to keep in mind that the ice shelf in general has a negative massbalance (Hamilton, 2016; Mortimer et al., 2012). Moreover, even though the chan-nel area is in mass balance, ∼8 m of ice is not a lot and a sudden break up canhappen any time, has it happened for Ward Hunt Ice Shelf, which had a minimumice thickness of 30 m (Mueller et al., 2003). This is in line with studies forecastingenhanced fracture and break up of ice shelves in Antarctica because of channeling(Dow et al., 2018; Gourmelen et al., 2017; Rignot and Steffen, 2008).503.6.3 MixingThe most surprising result of this study is that mixing is higher in the epishelflake than below the halocline. MEL is constantly covered with ice which limitswind mixing and radiative convection (as soon as snow covers the ice). This sug-gests the epishelf lake should be mixing less, being isolated from the seawater bya sharp halocline.Mixing during the first part of the winter (September-November) occurs both aboveand below the halocline which suggests this is linked to coastal upwelling (c.f.Jackson et al. (2014b)). Wind data from the Purple Valley weather station (2011 topresent) and from a weather station on the ice shelf (2016-2018) shows that along-coast (NE) winds are low during the whole year except from July to September. If ashore lead is present or if the wind stress drives sea ice movement (Williams et al.,2006), coastal upwelling is expected to happen during these NE wind episodes.Examination of the 50, 150 and 300 m temperatures shows an upward deflectionof isotherms during these periods (not shown). Another possible mechanism in-fluencing summer circulation is subglacial discharge. Recent studies identifiedsubglacial discharge as an important circulation driver in Greenland fjords (Carrollet al., 2015; Mortensen et al., 2014; Sciascia et al., 2013; Straneo and Cenedese,2015; Xu et al., 2012). We then suggest that mixing occurring just after the endof the melt season is linked to coastal upwelling and possible residual subglacialmelting and discharge; these two processes generating mixing by increasing the cir-culation (energy) in the fjord. It is noteworthy to mention that residual meltwaterwas observed in Petermann Fjord months after the melt season was over (Washamet al., 2019) and subglacial discharge was discovered in the middle of the winterunder a glacier in Yukon (Schoof et al., 2014).Aside from a peak in January 2012 and April 2019, mixing below the haloclineis at molecular levels (KΘ = 1.4x10−7m2 s-1) for the entire time after the residualsummer mixing vanishes. Without wind or solar radiation, with minimal tides anda solid sea ice cover, the processes leading to enhanced mixing above the haloclinein winter are very limited. Analysis of available meteorological data found no cor-relation with mixing. However, examination of the water temperature timeseriessuggests that enhanced mixing is linked to the presence of 7 to 30 day oscillations51in the temperature signal (Figure 3.6B). Because there is no addition of heat tothe lake during winter, these temperature oscillations can only be due to advectionof horizontal temperature gradients in MEL. Considering that forcing mechanismsare weak and the mooring is in the middle of the lake (i.e. away from lateral bound-aries), geostrophic equilibrium can be assumed. Horizontal eddies, created by thebalance between the Coriolis force and horizontal pressure gradients are relativelycommon in ice-covered lakes (Forrest et al., 2013; Rizk et al., 2014) and oceans(Hunkins, 1974; Timmermans et al., 2008). These coherent rotary structures haverecently been observed in Lake Baikal as they create circles of thinner ice that ap-pear darker from above (Kouraev et al., 2016). An image from Milne Fiord takenin 2013 shows a black disc similar to those in Lake Baikal, which may indicate thepresence of eddies that year (see Appendix B).In order to link the temperature oscillations seen by the mooring and the possiblepresence of horizontal eddies, the thermal wind equation is used to calculate thevertical shear from the horizontal density gradient (Kundu et al., 2012) :∂u1∂x3=gρ0 f∂ρ∂x2(3.5)Where f is the Coriolis frequency (1.45x10-4 s-1 at 82.6◦N). The thermal windequation is employed to scale the Richardson number:Ri =N2(∂u1∂x3)2 ≈ N2( gρ0 f∂ρ∂x2)2 ≈ N2( gρ0 f4ρ30RL)2 = ( N2ρ0Hg4ρ30pi)2(3.6)Where the Rossby radius of deformation (RL = NH/ fpi) is used to scale the hori-zontal span of the eddies. 4ρ30 is the 30 day maximum density variation related tothe temperature oscillations. It is calculated using the mooring temperature data,assuming that the mooring captures both the center and the periphery of the tem-perature anomalies (eddies) during a 30 day interval. The temperature oscillations(period of 7 to 30 days) from the mooring data have a greater amplitude than the 30day temperature difference given by the model (i.e. 4T mooring30 >4T model30 ) whichgives confidence that4ρ30 is attributable to horizontal movements (eddies movingaround). Moreover, it is acknowledged that the model has higher mixing coeffi-52cients when it encounters temperature oscillations because of the fitting methodemployed. However, consistently high mixing coefficients (30 day average) areundeniably related to increased vertical mixing. N2 is computed with the modelresults and the vertical height scale is taken as the distance between the bottom ofthe ice cover and the point where N2 becomes larger than 0.01 s-2, which is largerthan the top layer of the model because its top boundary is at the first unfrozenthermistor. The ice thickness is approximated to increase linearly from 0.5 m atthe end of the melt season to 1.5 m at the beginning of the next one. This roughapproximation is derived from the small number of data available (14 data pointsin 8 years from direct measurement and moored thermistor freezing). Figure 3.9Bshows the average Richardson number in the epishelf lake as well as vertically av-eraged quantities used for its calculation (N2 and 4ρ30) and the 30 day averagedmixing coefficient for heat in the top layer returned by the model (KtopΘ ). Peaks inthe Richardson number (and 4ρ30) are definitely correlated with increased mix-ing. This supports the hypothesis that vertical mixing in MEL during the winteris linked to one or more geostrophic wave-like structures. Comparing results withcommon K ∝ Ri parameterizations (Figure 3.10) (Pacanowski and Philander, 1981;Peters et al., 1988), the mixing in the epishelf lake is lower than what would be ex-pected for a traditional shear flow with a similar Richardson number. Consideringthat the top of the water column in Milne Fiord is very calm (maximum 30 dayaveraged mixing is 3.6x10-5 m2 s-1) in comparison with the studies parameterizingmixing in the ocean (Pacanowski and Philander, 1981; Peters et al., 1988), this isnot surprising. Moreover, also taking into account our hypothesis that the mixingis linked to the temperature oscillations with long periods, we do not expect smallRichardson numbers (large shear values) but rather a laminar environment with en-hanced molecular diffusion modulated by the strength of the eddies.Equation 3.6 can also be used to estimate horizontal velocities. Using average val-ues of ≈10-4 s-2 for N2, ≈102 for Ri and ≈8 m for the vertical scale, a horizontalvelocity of ≈ 1 cm s-1 is obtained. This is similar to that reported in ice-coveredlakes (Bengtsson, 1996; Forrest et al., 2013; Huttula et al., 2010) and what ADCPmeasured in MEL (Hamilton, 2016).As previously mentioned, sources of energy in the epishelf lake are very limitedduring winter. Because mixing does not show any tendency to decrease after the53Figure 3.10: 30 day averaged mixing coefficient of the model (KTOPΘ ) as func-tion of the Richardson number estimated by equation 3.6. Commonlyused parameterizations by Peters et al. (1988) (green) and Pacanowskiand Philander (1981) (cyan).end of the melt season, something has to be energizing the lake motion throughoutthe winter. Estimation of the Ekman spin down time tE = D/(√2K f ) (Pedlosky,2013) with the height of the eddies D ≈ 8 m and the eddy viscosity K ≈ 10-6 m2s-1, gives a time scale around 5 days. This is obviously too short to attribute theexistence of the eddies to residual energy from summer processes. Even usingonly molecular diffusivity, the spin down time is too small (50 days). Numericalmodeling of Lake Untersee (Antarctica) has shown that the presence of an ice wallcreated a gyre in winter due to the change of water properties following ice-waterinteractions Steel et al. (2015). Since the main body of MEL is bordered by iceupfjord and downfjord (Figure 3.1), cooling of epishelf lake water due to ice melt-54ing could possibly create a clockwise gyre. This could explain the presence of theeddies (and enhanced mixing) throughout winter.3.7 ConclusionHere we have used a one-dimensional model to analyze the winter mooring data ofthe top water column in Milne Fiord from 2011 to 2019. Three major results standout from the analysis.1. The model outflow rates, compared with two years of ADCP data, show thatthe main outflow path for the epishelf lake water is likely through a basalchannel under the ice shelf. This can be exploited in hydrological studies ofMilne Fiord watershed.2. The model outflow coefficients indicate that the channel area is in ice massequilibrium over a multi-year time scale. This implies that Milne Ice Shelfhas been stable in the last 8 years but could suddenly break at any time,similar to the Ward Hunt Ice Shelf in 2001/2002.3. The model mixing coefficients reveal that mixing is greater in the epishelflake than in the seawater below the halocline. Moreover, estimation of theRichardson number shows that enhanced mixing in the epishelf lake is linkedto one or more geostrophic wave-like structures (eddies). This demonstratesthat even though a body of water is ice- and snow-covered, it is not necessar-ily quiescent and processes of lower importance can play a significant role.As the climate continues to change, a better knowledge of ice-covered waterbodies is important to predict their evolution.55Chapter 4Conclusion4.1 SummaryThe goal of this study was to further the work done in Milne Epishelf Lake (Hamil-ton, 2016) and analyze the mooring data more in depth. Eight years of mooringdata outside of the melt season (∼September to ∼May) were used, together with aone-dimensional model, to study the mixing in the upper water column and the hy-draulic characteristics of the ice shelf basal channel. The mooring data and modelwere used in an inverse fashion in order to find four key parameters: 1) the dailymixing coefficient in the freshwater above the halocline (∼3 to∼10 m), 2) the dailymixing coefficient in the seawater below the halocline (∼14 to 25 m), 3) the an-nual minimum ice shelf draft in the ice shelf basal channel and 4) a width-frictioncoefficient for the flow in the channel. An iterative calibration procedure was usedto find the best fitting mixing coefficients that matched the mooring data. As themodel validation indicates, these four parameters are sufficient to describe the mainphysical processes in the upper water column of Milne Fiord during winter.The results show the upper water column of the fjord is very calm, which isexpected, but, surprisingly, mixing is more pronounced in the freshwater layer(mean KΘ=2.5x10-6 m2 s-1) above the halocline than in the seawater below (meanKΘ=1.0x10-6 m2 s-1). This is the first quantitative estimation of mixing in anepishelf lake. Using geostrophic balance to scale the Richardson number, it ap-pears that high mixing episodes from November to May are related to horizontal56density gradients caused by temperature anomalies. It is suggested that these gradi-ents are associated with horizontal eddies similar to those observed in Lake Baikal(Kouraev et al., 2016). These findings have implications for ice-covered lakes,epishelf lakes and polar fjords where the dynamics of these systems are poorly un-derstood. They demonstrate that even though a water body seems fairly isolated, itsphysical structure can be dynamic. Understanding the underlying physics in theseremote and vulnerable systems is key to predict the future of these water bodies inregards to climate change.ADCP measurements in the Milne Ice Shelf channel from July 2017 to July 2019show an outflow of the same order of magnitude as calculated by the model. This,combined with ice penetrating radar measurements on the ice shelf, implies thatthis channel is likely the only outflow pathway for the epishelf lake water. Theweir equation parameters of the model (minimum draft of the ice shelf, h0, andwidth-friction parameter, Ceb) do not exhibit any trend over the eight years of thestudy. If melt was occurring at a similar rate to what is reported for many channelsunder Antarctic ice shelves (e.g. Alley et al. (2016); Dutrieux et al. (2013); Rignotand Steffen (2008); Stanton et al. (2013)), there would be a consistent decrease inthe minimum draft and an increase in the channel width. Since the model indi-cates these parameters do not change appreciably, it is then suggested that MilneIce Shelf basal channel is in ice mass balance on a multi year time scale. This isin marked contrast to what is found in the literature at other locations (e.g. Al-ley et al. (2016); Dutrieux et al. (2013); Rignot and Steffen (2008); Stanton et al.(2013)). This implies melting and refreezing can have similar magnitudes even inbasal channels. However, this does not preclude a catastrophic failure as the icethickness along the channel is relatively thin. Therefore, a break up like the oneon the Ward Hunt Ice Shelf in 2002 (Mueller et al., 2003), could happen at any time.4.2 Future WorkEven though this study helps understanding Milne Fiord system a little better, italso leaves many possible research topics that would be interesting to elucidate be-fore the ice shelf breaks up.57A natural continuation of this study would be to confirm the presence of eddies inMilne Fiord epishelf lake by direct measurement and explain how they form. Inorder to do this, better horizontal coverage is needed during the winter period. Thiscould be achieved in different ways. Adding several shallow moorings or carryingout an intensive CTD profiling campaign would clarify this topic. The problemwith adding supplemental moorings is that the actual extent and structure of theeddies is unknown and could be missed or the acquired information maybe insuffi-cient. A CTD campaign would be more flexible in that it can be adjusted as the dataare acquired, but the temporal resolution would be limited and it would present alogistical challenge to sample closely and rapidly over kilometers. The best methodto improve horizontal coverage would be to use an autonomous underwater vehicle(AUV). This would give the best data but would also entail a substantial risk dueto the inferior reliability of AUVs, especially under ice (Kaminski et al., 2010).Indeed, the deployment of an AUV under ice involves additional risks since the ve-hicle cannot surface if a problem arises. In addition to the increased risks, an AUVsurvey is a high cost operation with complex logistics. However, at the presenttime, no AUV has been deployed in a Canadian or Greenlandic fjord (for sciencepurposes), which would definitely make the experience more rewarding.The further constraint of the basal channel dimensions would definitely help im-prove the usefulness of the ice shelf mooring data. This could be achieved by de-ploying a remotely operated vehicle (ROV) in the channel, with mapping a sonar.This would enable a more precise calculation of the freshwater outflow and a betterestimation of the heat and mass fluxes in the channel, the latter achieved by com-paring the data from the epishelf lake and the ice shelf moorings. This would givegreat insights on processes happening in other channels in Antarctica and Green-land (e.g. (Washam et al., 2019)).The present study used the first 25 m of the available mooring data, but other in-struments also recorded temperature a lower depths (50 m, 150 m, 315 m andsometimes 260 m). Although most likely not enough on its own, this data couldbe combined with the bank of over 100 summer CTD profiles or more extensivewinter data to make a macroscopic heat, salt and freshwater budget, as it is donefor Greenlandic fjords (Jackson and Straneo, 2016). This would allow a quantifica-tion of the circulation mechanisms in the fjord and a further constraint of the melt58estimates by Hamilton (2016).Milne Fiord epishelf lake is the last remnant of what used to be a common hy-drographic system on the northern coast of Ellesmere Island. Yet, it is realistic tosay that it will drastically change in the next decade or two, when Milne Ice Shelfcollapses and the epishelf disappears. The study of this unique site is ideal to un-derstand the effect of climate change in the Canadian High Arctic and advance theknowledge on ice-covered lakes, glacial fjords and ice shelves.59BibliographyY. Aksenov, V. V. Ivanov, A. G. Nurser, S. Bacon, I. V. Polyakov, A. C. Coward,A. C. 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Annals of Glaciology, 53(60):229–234, 2012. → pages 22, 5171Appendix ATurbulent Lewis NumberIn order to reduce the number of unknown parameters of the model, the mixingcoefficients for heat and salt in the top layer (epishelf lake) are linked togetherand the mixing coefficients for heat and salt in the bottom layer are also linkedtogether (section 3.5.4). This reduces the number of daily mixing parameters fromfour to two. In order to link together heat and salt mixing coefficients, the param-eterization by Jackson and Rehmann (2014) based on laboratory experiments isemployed. This is done in two steps. The first is to estimate the ε/νN2, where ν isthe kinematic viscosity, ε is the rate of dissipation of turbulent kinetic energy andN is the buoyancy frequency. This is done using the following equation (see table2 of Jackson and Rehmann (2014)):KCTν = 0.31(ε/νN20.36)0.16f or ε/νN2 < 0.36 (A.1)KCTν = 0.31(ε/νN20.36)1.06f or ε/νN2 > 0.36 (A.2)Once ε/νN2 is found, KSA is computed with the following equation:KCTKSA=1+R2+(1−R2)∗ tanh(0.92[log10( ενN2)−0.6])(A.3)Where R is the ratio of molecular diffusivity for salt over molecular diffusivity forheat.72Figure A.1: Parameterization of KSA as function of KΘEquation A.1 and A.2 introduce a steep jump around the critical value ε/νN2 =0.36,which is the cause of the greater discrepancy between KSA and KΘ when KΘ <5.4x10−7. From a physical point of view, it means that when KΘ < 5.4x10−7, heatdiffuses much more rapidly than salt. From KΘ = 5.4x10−7 upward, the differ-ence between KSA and KΘ becomes smaller as turbulent mixing dominates. Thisparameterization discrepancy definitely has an impact on daily values, but it is notsignificant here as 30 day average values are used for the analysis.73Appendix BIce Circle in Milne FiordGiant ice rings have been observed in Lake Baikal and Lake Hovsgol (Mongolia)from 1974 to 2014 (Kouraev et al., 2016). Using optical imagery, Kouraev et al.(2016) identified 45 dark rings created by circles (not discs) of thinner ice. Thediameter of these rings ranged from 2.2 to 8.2 km and had a dimension similar tothe Rossby radius (RL = ND/ fpi). The formation of these ice rings is attributed tothe presence of anti-cyclonic eddies. These rotary structures are thought to increasethe heat exchange between the water and the ice, resulting in a thinner ice at theperiphery of eddies.A RADARSAT-2 image from Milne Fiord in April 2013 (Courtesy of the CanadianIce Service, Environment and Climate Change Canada) shows a similar feature inMilne Fiord epishelf lake with diameter around 3000 m (Figure B.1). However,Figure B.1 is a radar image (not optical) and ice cores suggest that the disc-shapedreduction of backscatter in the epishelf lake is due to a decrease of the amount ofbubbles in the ice (McCallum, 2015). Clear ice has a lower microwave backscatterthan ice with bubbles, which results in a darker tone in Figure B.1. Thinner icewould also decrease the amount of backscatter, but there is no evidence that the icewas thinner under the dark disc. What caused the ice to have less bubbles might belinked to snow melt, which in turn could be linked to water properties.74Figure B.1: RADARSAT-2 Fine Quad image taken on the 27th of April2013 showing a dark disc in the middle of the Milne Fiord epishelflake (Courtesy of the Canadian Ice Service, Environment and Cli-mate Change Canada). Panels VV, VH and HH are three differentpolarizations (VV: vertical-vertical, VH: vertical-horizontal and HH:horizontal-horizontal) and the RGB panel is the combined Pauli decom-position (HH: red, VV: green and VH/HV: blue). The disc is visible inall polarizations. Color and gray scales are qualitative with brightertones indicating higher backscatter. RADARSAT-2 Data and Productsc© MacDONALD, DETTWILER AND ASSOCIATES LTD. (2013) –All Rights Reserved, RADARSAT is an official mark of the CanadianSpace Agency.75Appendix CModel EvaluationThis is a more extensive explanation of the evaluation of the model. The root meansquare error (RMSE), the standard deviation (ST D) are calculated for conservativetemperature (CT) and Salinity (SA). The coefficient of determination (R2) and thebias are also shown for conservative temperature. In addition, the custom coeffi-cient of agreement (Ca, see equation 3.4) is presented.76Table C.1: Model evaluation statisticsYear /Simula-tionCTRMSECTST DCT R2 CT bias SARMSESAST DCa2011-2012 0.21 0.21 0.96 -0.008 3.7 3.3 4.22012-2013 0.19 0.19 0.98 0.050 1.9 0.7 6.02013-2014 0.13 0.12 0.98 0.048 0.3 0.2 8.72014-2015 0.23 0.22 0.96 0.08 0.2 0.18 5.02015-2016 0.19 0.15 0.98 0.11 1.2 0.94 6.62016-2017 0.29 0.22 0.94 0.19 2.6 2.3 3.72017-2018 0.16 0.15 0.97 0.055 2.8 2.2 4.92018-2019 0.13 0.13 0.98 0.004 3.2 2.4 6.2Average 0.19 0.17 0.97 0.067 2.0 1.7 5.677Appendix DPhoto Gallery78Figure D.1: Getting dropped off at Purple Valley campsite by a Kenn Borek Twin Otter. Maximum 2500 pounds, crewincluded... Photo: Je´re´mie Bonneau79Figure D.2: Milne Fiord, looking downfjord. The glacier grounding line area is visible on the right of the icefall andPurple Valley, 75% on the right. The ice-covered ocean on the horizon. Photo: Je´re´mie Bonneau80Figure D.3: Northern Ellesmere icefields, looking upfjord from the same location as Figure D.2 , ∼ 5000 feet up.Photo: Je´re´mie Bonneau81Figure D.4: Derek Mueller and Drew Friedrichs looking at Milne Ice Shelf,easily distinguishable by its rolling topography with the through filledwith melt water. Photo: Je´re´mie Bonneau82Figure D.5: Moving the camp from Purple Valley to the ice shelf. DrewFriedrichs signaling ”upward” to the helicopter pilot. Photo: Je´re´mieBonneau83Figure D.6: Drew Friedrichs doing a CTD profile after pulling the epishelf lake mooring out. Looking upfjord. Photo:Je´re´mie Bonneau84Figure D.7: CTD profile in a crack on the margin of the glacier tongue. Photo: Drew Friedrichs85Figure D.8: Pulling the ice penetrating radar around the grounding line of the glacier. Photo: Drew Friedrichs86Figure D.9: Drew Friedrichs ”hole melting” to get the ice shelf channel mooring back. Photo: Je´re´mie Bonneau87Figure D.10: Picking up a camera from the summit of Mega Nunatak (unofficial name). Photo: Derek Mueller88Figure D.11: 26-Resolute, 26-Resolute, this is Purple Valley, Purple Valley. Drew Friedrichs and Yulia Antropovabroadcasting (blurred). Photo: Je´re´mie Bonneau89Figure D.12: Looking upfjord, with Derek Mueller. Mega Nunatak (unofficial name) on the left of the fjord. Photo:Je´re´mie Bonneau90

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