Landfast Sea Ice Break-Up Processes in Admiralty Inlet, NU by Ada Loewen

Landfast Sea Ice Break-up Processes in Admiralty Inlet, NU by Ada Loewen

A thesis submitted to the Faculty of Graduate and Postdoctoral Aﬀairs in partial fulﬁllment of the requirements for the degree of

Master of Science in Geography

Carleton University Ottawa, Ontario

The timing of spring break-up of landfast sea ice has become less predictable in recent years due to changes in the Arctic climate, which has implications for the traditional lifestyle of Inuit and shipping operations. To study the processes related to landfast ice break-up, meteorological and oceanographic data were collected in Admiralty Inlet, NU in May-June 2019. Numerical experiments using a finite element model (FEM) demonstrated the effects of environmental stresses, ice material properties, and leads on sea ice deformation prior to break-up. Modelled stress magnitudes were well below estimates of tensile yield stress, implying that large-scale ice fracture does not occur under typical conditions. Rather, field data and FEM output suggest the deterioration of ice strength and development of cross-inlet and shore leads preconditioned the ice to allow relatively low wind and current forces to initiate a break-out event in Admiralty Inlet on June 27, 2019.

ii Acknowledgements

Finishing a Master’s during a global pandemic was made much more manageable having such amazing supervisors and friends to support me. I cannot thank my supervisors, Drs. Gregory Crocker and Derek Mueller, enough for their support and sharing their knowledge and enthusiasm for ice with me over the last couple of years. Without your patient guidance, I may have gone down many (more) unnecessary rabbit holes during this project. This project would not have been possible without funding from Crown- Indigenous Relations and Northern Affairs Canada, and support from our project partners at SmartICE and the Canadian Ice Service. Additional financial support came from the Northern Research Training Program, the Ontario Graduate Scholarship, and scholarships from Carleton University. I am exceedingly grateful to have had the chance to go to Arctic Bay to conduct fieldwork and be completely blown away by the beauty of northern Baffin Island. Fieldwork could not have gone as smooth as it did without the expertise of Greg, and the support of Calder Patterson, our local field guides: Nigel Kigutikajuk, Gideon Allurut, and the late Levi Kalluk, and the Arctic Bay Guardians. We could not have conducted our fieldwork without the support of the hamlet of Arctic Bay, and my understanding of sea ice was deeply enriched through conversations with Mishak Allurut and Niore Iqalukjuak. Dr. Richard McKenna developed the model used in this project, and none of the numerical experiments conducted here would have been possible without his patience in helping me troubleshoot the model and thoughtful suggestions for interpreting the output.

iii Acknowledgements

I’m ever thankful for the support of my community of friends and colleagues in the Department of Geography and Environmental Studies, the Water and Ice Laboratory, and beyond, without whom I may have forgotten that there are other joys in life besides studying sea ice. And ﬁnally, to my parents, Mali and Howard, and brothers, Heinrich, Sherwood, and Herbert, thank you for your support and always keeping life interesting. Deo gratias.

iv Table of Contents

Abstract ...... ii

Acknowledgements ...... iii

Table of Contents ...... iv

List of Tables ...... vi

List of Figures ...... vii

1 Introduction ...... 1 1.1 Description of Problem ...... 1 1.2 Research Objectives ...... 3 1.3 Signiﬁcance ...... 4 1.4 Thesis Structure ...... 4

2 Literature Review ...... 6 2.1 Sea Ice Properties ...... 6 2.2 Sea Ice Life Cycle ...... 8 2.3 Landfast Ice ...... 10 2.4 Landfast Ice Break-up ...... 14 2.5 Modelling Sea Ice Dynamics ...... 21 2.6 Sea Ice Rheology ...... 23 2.7 Finite Element Modelling ...... 27

3 Geography of Admiralty Inlet ...... 30 3.1 Admiralty Inlet ...... 30 3.2 Meteorology ...... 32 3.3 Oceanography ...... 33

4 Methods ...... 37

v Table of Contents

4.1 Field Work Overview ...... 37 4.2 Finite Element Modelling ...... 45 4.3 Break-up in 2019 ...... 54

5 Results ...... 57 5.1 Field Work ...... 57 5.2 Finite Element Modelling ...... 68 5.3 Break-up 2019 ...... 86

6 Discussion ...... 93 6.1 Environmental Forcing in Admiralty Inlet ...... 93 6.2 Numerical Experiments ...... 97 6.3 Break-Up 2019 ...... 105 6.4 Sources of Error ...... 110 6.5 Model Limitations ...... 112

7 Conclusions ...... 114

References ...... 120

Appendices ...... 136 Appendix A: Spatial Resolution Sensitivity ...... 136 Appendix B: Animation of Standard Case Principal Stresses ...... 139 Appendix C: Time Lapse Video : Sujartalik ...... 139 Appendix D: Time Lapse Video : Elwin Inlet ...... 139 Appendix E: Animation of Realistic Case Principal Stresses ...... 140

vi List of Tables

2.1 The albedo of typical sea ice surface types (Perovich and Polashenski, 2012). 16

4.1 Start and end dates for data collection from the 2019 ﬁeld season in Admiralty Inlet...... 39 4.2 Accuracy and resolution of RBR XR620 and Idronaut Ocean Seven 304 CTDs...... 41 4.3 Input ice property model parameters ...... 46 4.4 Ice parameter values in Sinha’s model...... 47 4.5 Material properties for experiments were ice thickness (h), ice tempera-

ture (T8), and Young’s modulus (Y) were changes from the standard case. Model case names are deﬁned by the spatial resolution (’GS_50x50’) and the material property changed (’mpropXX’)...... 50 4.6 Description of idealized simulations. Model case names are deﬁned by the spatial resolution (’GS_50x50’) and main environmental input(s). . . 51

5.1 Mean and standard deviation of maximum principal stress (PS1) within different regions for different model runs at t = 10800 s unless otherwise noted. Tension is positive, compression is negative. Bold values indicate maximum stress for each case...... 71 5.2 Mean and standard deviation of maximum principal stress (PS1) within different regions for different model runs at t = 1800 s...... 81 5.3 Reaction forces per unit length along the east and west shores at t = 10800 s and the percentage of reaction forces at each shore. Arrows show the direction of the reaction force relative to the shore. For example, down (south) arrows indicate the shore is preventing northward movement. . 83

vii List of Figures

1.1 Location of Admiralty Inlet and nearby waterways and communities. . . 3

2.1 Crystal structure of ice Ih (a), view along (b) and normal (c) to c-axis. ¯ ¯ ¯ [1010], [1100], and [1120] are unit vectors that form the basal planes of the crystal structure, and [0001] indicates the c-axis. (from Thomas, 2017). 7 2.2 Measured snow and ice temperature profiles over a full year from fast ice off the northeast coast of Greenland (a), and ocean temperature 2.8 m from the ice surface at deployment and ice temperature 1.8 from the ice surface at the time of deployment (b) (from Wang et al., 2020) ...... 11 2.3 Cross-section of idealized grounded ridge keel (from Jones et al., 2016) . . 13 2.4 Schematic summarizing the main dynamic and thermodynamic processes which may lead to sea ice break-up...... 14 2.5 Normalized borehole strength of sea ice (green) plotted against mean daily air temperatures (red) in Resolute, NU for landfast first-year sea ice during the ice decay season in 2000 (from Timco and Johnston, 2002). . 17 2.6 Break-out processes in Chukchi Sea from Druckenmiller (2011). Drift-out events occur when floating fast ice separates from bottom fast ice, break- out events occur when grounded ice becomes unfastened and drifts away from the shore, and break-away events occur then the floating extension detaches from the grounded ice zone...... 20

viii List of Figures

2.7 Stress and strain relationships with time for Burger’s model. When a

stress () is applied from t0 to t1, the material will experience elastic strain 4 ( ) as soon as the stress is applied, and will continue to deform due to transient creep as the stress is sustained. After the stress is removed at

t1, the elastic strain is immediately relieved, and gradually the delayed 3 E elastic strain ( ) is recovered. Permanent viscous elastic strain ( ) remains in the material (from Xu et al., 2019)...... 25 2.8 Burger’s model of visco-elastic material is composed of an elastic strain 4 E component ( ) represented as a spring, a viscous strain component ( ), which is represented as a dashpot, and a delayed elastic strain component 3 ( ), which is represented as a spring and dashpot in parallel. The three strain components (elastic, viscous, and delayed elastic) are connected in series (from Xu et al., 2019)...... 27

3.1 Topography and bathymetry of Admiralty Inlet and adjacent waterways from Jakobsson et al. (2012). Contour lines indicate 20 m elevation/depth, index contours indicate 100 m elevation/depth. Inset shows location of Admiralty Inlet (black square) within Canada. Locations of ﬁeld sites used in this study are indicated on the map and in the map legend. . . . 31 3.2 Temperature and precipitation climate normal data for 1981-2010 at Nanisivik, NU at 641.9 m elevation. (ECCC) ...... 33

4.1 Main ﬁeld site in Admiralty Inlet after instrument deployment on May 30, 2019. Left to right: ADCP in ABS pipe frozen into ice attached to orange buoy, yellow SAMS data logger, automated weather station with two anemometers at diﬀerent heights, and air temperature and relative humidity sensor...... 38

ix List of Figures

4.2 Mesh outline and locations where the maximum principal stress values were averaged for diﬀerent regions of the grid (grey boxes) in the sensitivity tests (1-4) and idealized cases (1-5). The location of the cross- inlet crack used in GS_50_50_hc is shown in blue. The locations of the ﬁxed shoreline nodes are shown in red. Brown points are node and approximate element locations which are used for plotting in Section 5.2 and are used to show representative output of the model...... 49 4.3 Transformation of stresses in a given coordinate system to principal

stresses (from eFunda, 2020). Left: normal (8) and shear (89) stresses in

given coordinate system. Right: principal stresses (1,2) by transforming

the original coordinate system by the angle (?)...... 54 4.4 Outline of mesh used for the realistic case, locations of ERA5 grid points (green diamonds) for wind, and WebTide markers (blue circles) for current. Pre-existing lead where break-out occurred is shown in red. Sentinel-2 image from June 24, 2019 (left) and MODIS image from June 19, 2019 (right) are shown in the background...... 56

5.1 Time series of air temperatures (a) and wind speeds (b) in Admiralty Inlet from the weather station deployed May 28 - June 23, 2019. Arctic Bay airport data from Environment and Climate Change Canada, and reanalysis data from NCEP and ERA5. Vertical dashed line indicates date after which air temperatures remain consistently above 0 °C. . . . . 58

x List of Figures

5.2 Wind roses from Admiralty Inlet Weather Station (a), Arctic Bay Airport (b), ERA5 (c), NCEP (d). Directions indicate direction wind comes from, and colours indicate wind speed in each direction. Length of bars in each direction indicate the frequency occurrence of wind speed and direction as a percentage in time of the whole time series. Black dashed line indicates approximate orientation of northern part of Admiralty Inlet where the weather station was located...... 59 5.3 Correlation of wind speed (a-c) and direction (d-f) between Admiralty Inlet weather station (Wx Station) and ERA5 (a, d), NCEP (b, e), and Arctic Bay Airport (Env Canada) data (c, f)...... 60 5.4 Temperature (a) and salinity (b) profiles from the Idronaut CTD on May 27 and May 30, 2019 in Admiralty Inlet. Inset zooms in on temperature and salinity profiles from the surface (0 m) to 50 m depth. Dashed line at 25 m on inset indicates depth of surface mixed layer. Only downcasts are plotted here and data were averaged over 35 samples (5 s)...... 61 5.5 Current speeds from the Infinity current meter on May 27 and May 30, 2019...... 62 5.6 Current speeds (a) and single-sided amplitude spectrum (b) for current speeds averaged between 0.4 m and 5.4 m from the ADCP. v (solid) indicates the north-south component and u (dashed) indicates the east- west component...... 63 5.7 Current speed (a) and direction (b) from the ADCP and Webtide from May 30 - June 1, 2019 in UTC...... 64 5.8 Ice temperature (a) and salinity (b) profiles from an ice core taken at the field site in Admiralty Inlet on May 27, 2019. Salinity values were measured using both the Idronaut and YSI Salinometer...... 65

xi List of Figures

5.9 (a) Time series of mean ice temperatures from SAMS thermistor chain, and modelled brine volume from Timco and Weeks (2010). Dashed line

indicates melting point of sea ice. (b) Time series of ice strength (C) from equation 4.3 using salinities from the ice core taken during field work. . 67 5.10 Box plots of maximum principal stresses at each of the four corners of the mesh at 10 x 10 (black), 25 x 25 (red), 50 x 50 (blue), and 75 x 75 (purple) element resolutions. The mean for each location and resolution are shown as blue diamonds...... 69 5.11 Time series of displacement (U), reaction force (F), and maximum principal stress (PS1) for changing temporal resolutions (dt) when wind direction changed abruptly at t = 1800 s. Different line colours indicate the time series at the same node/element for different temporal resolutions. 70 5.12 Time series of (a) displacement (U), (b) reaction force (F), (c) maximum principal stress (PS1), and (d) maximum principal strain (E1) for the standard case at one location (see point a in Figure 4.2). Black vertical dashed line indicates the time when viscous strain begins to dominate over elastic and delayed elastic strain...... 73 5.13 Principal stresses for standard case at t = 21600. Maximum principal stress (PS1) contours shown in the background of the mesh. Compressive (black) and tensile (red) stress tensors of maximum and minimum principal stress superimposed on contours. Arrow shows direction of 5 m/s wind...... 74

xii List of Figures

5.14 Time series of displacement (U) and maximum principal stress (PS) with changing material properties. Diﬀerent line colours indicate the time series at the same node/element for diﬀerent material properties. Displacements and principal stresses are plotted at a node and element at

the northeast section of the mesh (see point b in Figure 4.2 for location). T8

indicates ice temperature, h8 indicated ice thickness, Y indicates Young’s modulus...... 75 5.15 Time series of displacement (U) and maximum principal stress (PS1) with increasing wind speed. Displacements and principal stresses are plotted at a node and element at the northeast section of the mesh (see point b in Figure 4.2 for location)...... 77 5.16 Maximum principal stress (PS1) at the element with the maximum stress in the mesh (a) and wind speed (b) for GS_50x50_sinwind. Dashed line in (a) indicates the assumed ice strength...... 79 5.17 Maximum principal stress magnitudes and tensors for standard case (a), NE wind (b), NW wind (c), SE wind (d) at time step 10800. Arrows show the direction of wind at 5 m/s for each case. Tensile stresses are positive (red), compressive stresses are negative (blue). Distribution and locations of maximum tensile and compressive stresses changes depends on the direction of wind...... 80 5.18 Maximum principal stress magnitudes and tensors for standard case (a), cross-inlet lead (b) at t = 1800 s. Tensile stresses are positive (red), compressive stresses are negative (blue). Magnitudes and distribution of stresses change when the mesh extent changes...... 82

xiii List of Figures

5.19 Close-up of maximum principal stresses (PS1) and reaction forces along eastern shore with irregular shoreline at time step 10800 s for the standard case. Large black arrow indicates wind direction. Arrows along shoreline indicate reaction force magnitude and direction. Red (positive) contours indicate tensile stresses, blue (negative) contours indicate compressive stresses...... 85 5.20 Time series of wind speed (a) and direction (b) from 12 ERA5 grid points in Admiralty Inlet from 5.5 hours before break-up to half an hour after. Time of break-up indicated by the vertical black dashed line...... 86 5.21 Time series of current speed (a) and direction (b) from 6 WebTide markers in Admiralty Inlet from 5.5 hours before break-up to half an hour after. Time of break-up indicated by black dashed line...... 87 5.22 Left: Sentinel 2 image on June 29, 2019 with locations of cameras and approximate camera ﬁeld of view. #1 indicates the camera at Sujartalik, and #2 indicates the camera at Elwin Inlet. Top-right: photo from time lapse camera at Elwin Inlet at 19:00 EDT on June 7, 2019. Bottom-right: photo from time lapse camera at Elwin Inlet at 19:00 EDT on June 30, 2019. Note substantial expansion of the shore lead in the bottom image. 89 5.23 Maximum principal stress for the realistic case at time step 19800 (02:30 on June 28, 2019 UTC). Tensile stresses are positive (red), compressive stresses are negative (blue). Black arrows wind direction at 02:30 June 28, 2019 UTC from ERA5...... 91

xiv List of Figures

5.24 Total and sum of wind (F0) and current (FF) force magnitudes in the realistic case throughout the whole mesh (a) and normalized mean directions (colours correspond to legend entries in a) (b), and reaction forces along each coast (E = east coast; W = west coast) (c), and normalized net direction of reaction force along each coast (colours correspond to legend in c) (d) from 21:00 June 27, 2019 to 03:00 June 28, 2019 UTC. Black dashed line indicates the time of break-up...... 92

6.1 Summary of the factors affecting break-up which were investigated in the numerical modelling experiments. Current/wind speed/direction discussed in Section 6.2.2. Thermodynamics affects all the factors under ’Ice Properties/Configuration’, and is discussed in Sections 6.2.1, 6.2.3, and 6.2.4. Leads discussed in Sections 6.2.3 and 6.2.4. Ice temperature, ice thickness, and Young’s Modulus are discussed in Section 6.2.1. Items in the third level of the hierarchy with the same colour are considered to be in the same subcategory within the level...... 98

A.1 Displacement magnitudes and vectors for 10 x 10 element (a), 25 x 25 element (b), 50 x 50 element (c), 75 x 75 element (d) resolutions at time step 10800. Note the displacement vector arrows are scaled diﬀerently for each spatial resolution. Arrows beside each mesh show the direction of wind at 5 m/s for each case...... 136 A.2 Maximum principal stress magnitudes and tensors for 10 x 10 element (a), 25 x 25 element (b), 50 x 50 element (c), 75 x 75 element (d) resolutions at time step 10800. Arrows beside each mesh show the direction of wind at 5 m/s for each case. Tensile strains are positive (red), compressive strains are negative (blue)...... 137

xv List of Figures

A.3 Maximum principal total strain magnitudes and tensors for 10 x 10 element (a), 25 x 25 element (b), 50 x 50 element (c), 75 x 75 element (d) resolutions at time step 10800. Arrows beside each mesh show the direction of wind at 5 m/s for each case. Tensile strains are positive (red), compressive strains are negative (blue)...... 138

xvi 1 Introduction

1.1 Description of Problem

The presence or absence of sea ice has important implications for the global climate, polar ecosystems, marine navigation, and Northern communities. Decreases in summer sea ice area extent and the length of the ice-covered season have been observed (Stroeve et al., 2014), which are related to changes in the global climate system. Landfast ice is sea ice that is attached to a coastline and may extend up to hundreds of kilometres from the coast depending on the nearshore bathymetry and ice dynamics (Eicken et al., 2005). At its annual maximum extent, landfast ice covers 1.8 × 106 km2 in the Northern Hemisphere (Li et al., 2020). Fall freeze-up and spring break-up are transitional seasons for landfast ice, where ice conditions may change rapidly and pose a risk to ship navigation and travel over sea ice. Changes in landfast ice freeze-up and break-up timing have been observed in certain regions in the Arctic in recent years (Tivy et al., 2011; Galley et al., 2012). The timing of sea ice break-up has been suggested to have a signiﬁcant inﬂuence on the growth of sea ice the following winter (Massonnet et al., 2018). Landfast ice break-up may be caused by thermal and/or mechanical processes. Thermal break-up is characterized by thinning and structural deterioration of the ice and can be forecast using air temperatures and incoming shortwave radiation (Bitz and Lipscomb, 1999; Petrich et al., 2012). Mechanical break-up may be induced when stresses acting on the ice due to adjacent ice, wind, ocean currents, or waves exceed the strength of the ice. Due to the complexity of conditions which may lead to mechanical failure, few models of the mechanical break-up of sea ice exist (Crocker

1 1. Introduction and Wadhams, 1989; Jones et al., 2016). This project uses observations of landfast ice and environmental conditions associated with the break-up of landfast ice in Admiralty Inlet, Nunavut, along with a Finite Element Model (FEM) of the forces, stresses, and strains that occur during break-up, to gain a better understanding of the critical processes controlling break-up. Admiralty Inlet extends south from Lancaster Sound along the northern coast of Baffin Island and is an important region culturally and economically for Inuit in Ikpiarjuk (Arctic Bay), NU (Figure 1.1). Changes in the Arctic climate have made environmental indicators for break-up harder to interpret using traditional knowledge (Ford et al., 2010), and there is a growing need for people in the North to adapt to changes in their environment (Laidler et al., 2009). Interest has increased in studying changes in sea ice extent and variability on both local and regional scales due to the economic, cultural, and political impacts of these changes. The predictive capacity of the mechanical break-up of sea ice in this region may be improved using environmental observations throughout the break-up season to evaluate the effectiveness of break-up models and guide further model development. The topic for this thesis came from the development of a larger project (Landfast Sea Ice Break-up Prediction in a Changing Climate, hereafter called the Landfast Ice Break-up Prediction project), a collaboration between Carleton University, SmartICE, the Canadian Ice Service (CIS), and the community of Ikpiarjuk (Arctic Bay). SmartICE is a social enterprise that combines Inuit knowledge with environmental monitoring technology to aid Northern communities in adapting to climate change (https://www.smartice.org/). The CIS is a government agency which provides information about ice in Canada’s navigable waters. The overall goal of this project is to augment Inuit knowledge of landfast ice conditions and break-up with a scientific understanding of the physical processes related to sea ice break-up to develop short-term statistical and physics-based break-up models of landfast sea ice in Admiralty Inlet that can be used by the community of Ikpiarjuk. This thesis will

2 1. Introduction

95°W 90°W 85°W 80°W 75°W

Baffin Bay 75°N

Barrow Strait Lancaster Sound

74°N

Admiralty Inlet

73°N Prince Regant Inlet

72°N

Figure 1.1: Location of Admiralty Inlet and nearby waterways and communities. begin the investigation of mechanical landfast sea ice break-up processes through ﬁeld observations and the application and evaluation of a FEM of break-up in Admiralty Inlet.

1.2 Research Objectives

This study used a break-up event of landfast ice in Admiralty Inlet, NU in June 2019 as a case study of the mechanisms of landfast ice break-up and to determine what factors are most important for predicting break-out events in Admiralty Inlet. The objectives of this research were to:

1. Identify the processes that may contribute to mechanical sea ice break-up in Admiralty Inlet using ﬁeld observations and a FEM.

3 1. Introduction

2. Determine the relative importance of these processes using numerical experiments in a FEM.

3. Demonstrate the eﬀectiveness of a FEM for modelling a break-up event in June 2019 in Admiralty Inlet.

1.3 Signiﬁcance

This research is needed based on: (1) expressed support and desire by the Ikpiarjuk community for a landfast ice break-up model, (2) the lack of effective predictive models of sea ice break-up that can be used for this purpose, and (3) the need to investigate the processes relating to mechanical sea ice break-up before an operational predictive model can be developed. While models of varying complexity exist for the prediction of mechanical sea ice break-up (Petrich et al., 2012; Lemieux et al., 2016a; Olason, 2016), they either operate on larger spatial and/or temporal scales to be relevant for sea ice users to evaluate hazards, or have not been evaluated for effectiveness in this region. The unique configuration of geography, oceanography, and meteorology can significantly affect the dominant factors affecting sea ice break-up in different regions (Goldstein et al., 2004; Mahoney et al., 2007a; Olason, 2016), and a model developed for one region must be evaluated and potentially modified before being applied to another region. This research will provide the framework for further development of a predictive model for landfast ice break-up in Admiralty Inlet by deepening our understanding of the processes that control break-up in this region.

1.4 Thesis Structure

A traditional thesis format will be followed. Chapter 2 describes the break-up processes in Admiralty Inlet and provides background information on the break-

4 1. Introduction up processes and FEM that will be used in this thesis. Chapter 3 describes the meteorology and oceanography of Admiralty Inlet. Chapter 4 describes the field observations and methods used to analyze break-up in Admiralty Inlet. Chapter 5 shows the data collected from the field work, and the FEM results. Chapter 6 puts the results of the field observations and model output into the context of break-up. Chapter 7 summarizes the results and discussion of this work.

5 2 Literature Review

2.1 Sea Ice Properties

At the most basic level, sea ice is composed of molecules of H2O arranged in a crystal lattice which may contain salt impurities. The small-scale physical characteristics of sea ice are mainly determined by its crystal structure. H2O has several different crystal forms depending on the temperature and pressure conditions of its environment (Thomas, 2017). The only ice phase seen naturally on the surface of the Earth is ice Ih, which has a hexagonal crystal symmetry where water molecules are arranged tetrahedrally with six-fold symmetry around each other (Figure 2.1). The plane these molecules create is called the basal plane, and perpendicular to this plane is the principal crystallographic axis (c-axis), which is the axis of maximum symmetry of the crystal. Ice breaks and grows preferentially ¯ ¯ along the basal plane. In Figure 2.1, [1120] and [1010] indicate the unit vectors that form a plane which lies parallel to the basal plane, and [0001] indicates the c-axis (Weeks, 2010). The left panel shows the crystal structure of ice Ih and some of the axes which form it, the middle panel shows a view along the c-axis, and the right panel shows a view normal to the c-axis. The crystal structure of ice does not easily permit the inclusion of impurities, leading to pockets of brine (solutions of highly concentrated salty water) and gas becoming trapped in between ice crystals. Young ice generally contains a higher percentage of inclusions than old ice, as these inclusions are depleted over time through various brine rejection processes (Vancoppenolle et al., 2010). Different salinity profiles are characteristic for different types of ice in the different regions in

6 2. Literature Review

Figure 2.1: Crystal structure of ice Ih (a), view along (b) and normal (c) to c-axis. ¯ ¯ ¯ [1010], [1100], and [1120] are unit vectors that form the basal planes of the crystal structure, and [0001] indicates the c-axis. (from Thomas, 2017). the world. In the Arctic, the ‘C’-shaped salinity profile is prominent, but the salinity profile may change depending on the ice thickness and temperature regime (Weeks, 2010). After the initial entrainment of salt, there are several mechanisms which result in the rejection of salts (Weeks, 2010). Gravity drainage is the main driver in salinity profiles in ice, where the gravitational force preferentially pulls brine, which is heavier than seawater, through tubes and pockets within the ice and out to the underlying seawater. Brine pocket migration, where the gradient between the cold ice surface and the warm ice bottom drives diffusion of salts from the top of the ice to the bottom, is a mainly temperature gradient-driven process, which makes it very slow. Brine expulsion occurs when the pressure due to the liquid in a brine pocket builds up and causes cracks in the ice, allowing brine to escape through the pockets, migrating towards the warm side of the ice. During the melt season, brine

7 2. Literature Review pockets may expand and drain, reducing the salinity and strength of the ice (Shokr and Sinha, 2015). Over the course of its lifetime, sea ice will deform due to various external forces acting on it, and the mode of deformation will depend on the mechanical properties of the ice. Young’s modulus is a measure of the relationship between stress and strain of an elastic material (Mellor, 1983). Sea ice can be considered an elastic material (Girard et al., 2009), and Young’s modulus for sea ice depends on temperature, the volume fraction of brines, and the porosity of the material (Timco and Weeks, 2010; Girard et al., 2011). Young’s modulus can range from 7 and 10 GPa (Timco and Weeks, 2010), where lower values correspond to ice more susceptible to deformation.

2.2 Sea Ice Life Cycle

Falling air temperatures and reduced incoming solar radiation signal the beginning of freeze-up in polar regions. The direction of heat fluxes between the ocean and atmosphere switch from heat flow directed to the ocean in the summer, to heat flow directed to the atmosphere in the winter as air temperature falls below water temperature. In most oceanic regions, some preconditioning of the ocean surface must take place before sea ice can form. Freshwater has a maximum density at 4°C, whereas saltwater continues to increase in density as it approaches its freezing point. As surface water loses heat to the atmosphere, it becomes more dense and sink, and be replaced with warmer water from below. Before freezing can occur, the entire surface layer must be cooled to the freezing point (Thomas, 2017). Once preconditioning of the surface layer has finished, ice growth begins with the formation of separate disk-like crystals suspended within the water which is called frazil ice or grease ice (Thomas, 2017). The next stages in ice growth depend on the dynamic conditions of the environment.

8 2. Literature Review

In calm conditions, frazil ice will continue to grow and eventually form a continuous sheet of grease ice or nilas. From here, the ice growth process modifies, and congelation growth, were water molecules freeze on to the bottom of the existing ice sheet occurs. The ice that grows during this stage is of a different structure than the initial frazil ice crystals, and contain larger elongated crystals and a horizontal c-axis (Thomas, 2017). Congelation growth occurs for the rest of the growth season, at the end producing first-year ice. Calm conditions allowing for this kind of growth mainly occur in the Arctic, where the many islands prevent large surface areas for wind fetch to produce large waves. In rough waters, more common in the Antarctic, frazil ice does not consolidate into nilas ice, but instead a dense suspension of frazil ice forms within the wave field. The waves compress the frazil crystals, which may then freeze together and form pancake ice (Wadhams et al., 2002). These pancakes grow in diameter and thickness and may freeze together, covering the water surface in consolidated pancake ice. As pancakes consolidate, they may raft over each other, and form a very rough underside and upper surface. Initial ice growth occurs quickly due to a strong thermal gradient between the ice-ocean boundary and the atmosphere, causing heat to be transferred from the bottom of the ice, through the ice layer, to the atmosphere. Ice grows in the direction of greatest heat transfer, which in this case is in the vertical, explaining the horizontal c-axis (Thomas, 2017). The direction of the c-axis may depend on the growth environment; if ocean currents are present and variable in direction, crystals may grow without any preferential direction. In the presence of ocean currents c-axes have a tendency to be aligned in the direction of the current flow (Wadhams, 2000). Several factors play a role in modulating the thermodynamics of sea ice. The salinity and temperature of ice affect its thermal properties, such as thermal conductivity, specific heat and latent heat of fusion (Petrich and Eicken, 2009). Snow

9 2. Literature Review creates an insulating layer on the top of the sea ice due to its lower thermal conductivity than sea ice, which reduces heat transfer and slowing ice growth. The albedo of the upper surface of ice or snow also plays an important role during the melt of ice in determining how much incoming solar radiation is absorbed or reflected at the surface (Perovich and Polashenski, 2012). Currents carrying heat may reduce or reverse heat fluxes at the bottom surface of ice, reducing growth or inducing melting (Kirillov et al., 2015). A representative thermodynamic cycle of multiyear landfast ice in the Arctic is shown in Figure 2.2. Near the surface of the snow or ice, temperatures are highly variable due to fluctuations in air temperatures. Closer to the ice-ocean interface, temperatures are less variable and closer to the freezing point. When snow is present, only the snow temperatures vary with changes in air temperature, but ice temperatures are relatively constant. During the summer, temperatures throughout the ice are approximately isothermal, and significant melt at the upper ice surface can be seen from June - August. The end of the ice growth season occurs once air temperatures start to rise consistently above zero, and incoming solar radiation increases.

2.3 Landfast Ice

Landfast ice makes up a significant portion of the ice in the Canadian Arctic Archipelago (CAA) and in contrast to pack ice, which is mobile, landfast ice is immobile and attached to the shore or between shoals or grounded icebergs (Galley et al., 2012). Pack ice is more likely to survive the summer melt, and become multiyear ice, particularly in the Beaufort Gyre (Belchansky et al., 2005), while landfast ice generally follows a seasonal cycle: formation and growth in the fall/winter, and melt and decay in the spring/summer (Galley et al., 2012). This leads to differences in the physical characteristics between pack ice and first year ice, as first year ice

10 2. Literature Review

Figure 2.2: Measured snow and ice temperature profiles over a full year from fast ice off the northeast coast of Greenland (a), and ocean temperature 2.8 m from the ice surface at deployment and ice temperature 1.8 from the ice surface at the time of deployment (b) (from Wang et al., 2020) . is thinner, saltier, and weaker than pack ice (Johnston, 2017). The relative ratio of multiyear pack ice to first year ice in the Arctic is reducing (Tivy et al., 2011), and the onset dates of freeze-up and melt of landfast ice have also changed in recent years (Galley et al., 2012). Understanding the underlying causes of these changes is important to help sea ice users to adapt to current and future changes in sea ice presence in the Arctic. The extent and appearance of landfast ice varies regionally within the Arctic based on the different processes which dominate the formation and deformation of the ice in each region. At the Siberian coast, Kara, and Beaufort seas, the seaward landfast ice edge (SLIE) approximately follows the 10 - 30 m bathymetry line, while near Severnaya Zemlya (Russian high Arctic) and off the eastern coast of Baffin Island, landfast ice can be found in water depths up to 180 m (Mahoney et al., 2014). Narrow passages between islands or pieces of grounded ice can facilitate the

11 2. Literature Review formation of landfast ice or the jamming of ice floes in the passageways, which can form ice bridges and prevent the circulation of ice downstream of the ice bridge (Plante et al., 2020). Thermodynamics play an important role in the formation of landfast ice and the onset of melt (Johnson et al., 2012), and dynamic forces such as wind and current stresses can play a role in the deformation of landfast ice (Mahoney et al., 2007a). Landfast ice forms in the fall as air temperatures fall, and ice growth usually starts in shallow waters which can reach the freezing point faster than deeper waters where the entire surface layer must reach the freezing point before freeze-up can occur. Depending on the region, waves and tides can cause rafting of the ice along the shore during freeze-up, creating grounded ridges (Barry et al., 1979). The landfast ice extent and thickness grow throughout the fall and winter. Snow cover is a major controlling factor for the thickness of the ice by the end of the season (Sato and Inoue, 2018). The two main forces that are thought to anchor landfast ice include bottomfast ice and grounded ice (Mahoney et al., 2007a). Bottomfast ice is sea ice that that freezes to the bottom of the seabed, while grounded ice usually refers to ridges of deformed ice that have become grounded at the seafloor, but may also include ice islands that have become incorporated into landfast ice (Mahoney et al., 2007a). Tidal cracks separating bottomfast ice from floating landfast ice may reduce the attachment of the floating landfast ice to the shore. Implicit and explicit parametrizations of the anchoring force due to grounded ridges have been incorporated into numerical sea ice models to improve simulations of landfast ice (König Beatty and Holland, 2010; Lemieux et al., 2016a; Olason, 2016). The frictional coupling of grounded ridges with the sea floor (B1) can be estimated using (Jones et al., 2016):

¯ 2 5 =6F 66 B1 = (2.1) C0= :

12 2. Literature Review

Figure 2.3: Cross-section of idealized grounded ridge keel (from Jones et al., 2016)

where 2 5 is the coeﬃcient of static friction with the sea ﬂoor, =6 is the number of ¯ grounded ridges, F is the density of sea water, g is gravitational acceleration, is ¯ the degree of grounding, and : is the angle of the ridge keel. is given as

=6 ¯ 1 Õ 2 = (: − F6) (2.2) =6 8=1 where F6 is the water depth and : is the depth of a ridge keel. Figure 2.3 shows an idealized grounded ridge keel cross-section from Jones et al. (2016). Admiralty Inlet is very deep so grounded or bottomfast ice can only occur within a narrow region along the eastern and western shores. The extent and seasonal duration of landfast ice in the Arctic has been changing in recent years (Mahoney et al., 2014; Galley et al., 2012). Freeze-up of landfast ice generally occurs between September and January, and break-up occurs between May and August, depending on the location (Galley et al., 2012). Trends towards later freeze-up, and earlier break-up dates have been aﬀecting Northern communities

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(Ford et al., 2019; Eicken et al., 2018).

2.4 Landfast Ice Break-up

Landfast ice break-up can be caused by a variety of mechanisms. The two main categories of break-up processes are thermal (thermodynamic) and mechanical (dynamic), which can be further subdivided into diﬀerent driving mechanisms. These processes will be explained in further detail in the next few subsections, and a summary of the processes associated with break-up is shown in Figure 2.4.

Thermal Processes Mechanical Processes

Ocean heat Solar Increasing air Current Wind Wave Sea surface fluxes radiation temperature stress stress stress slope

Thinning / Internal Decay / Shore Leads Drag / Flexure / Body Force

Break-up

Figure 2.4: Schematic summarizing the main dynamic and thermodynamic processes which may lead to sea ice break-up.

These processes are not isolated, but often occur in conjunction with each other. Thermodynamically-driven sea ice break-up occurs when the ice decays in-situ with signiﬁcant surface and sub-surface melting (thinning and internal decay) due to heat input from the atmosphere or ocean (Petrich et al., 2012). Enhanced melt along the shore due to increased oceanic heat ﬂuxes in shallow water and increased absorption of solar radiation results in the formation of shore leads, which act to free the ice from the grounding points. In addition, the mechanical strength of the ice diminishes with warming and decay (Timco and Weeks, 2010), making it more

14 2. Literature Review susceptible to break-up due to mechanical processes. Drivers of mechanical sea ice break-up include surface winds, currents, and waves which apply stresses to the ice that if strength is exceeded, will cause cracks to form and propagate within the ice (Jones et al., 2016). Changes in sea surface slope due to tides can result in body forces on the ice, which may contribute to break-up (Druckenmiller et al., 2009). The relative contributions of different stressors to mechanical break-up is highly region-dependent and are not well constrained for Admiralty Inlet. The definition of sea ice break-up may depend on the user and the type of information desired. Shorefast ice break-up has been defined as the first day on which ice movement is detected (Petrich et al., 2012). Other studies have defined break-up as the first date when the averaged ice concentration for a region is 5/10ths or less (Gagnon and Gough, 2005), or the last day when ice was present in a grid cell (Galley et al., 2012). Inuit communities may define the start of break-up based on access to the sea (e.g. first day of boating activity (Petrich et al., 2012)). Break-up definitions depend on the spatial scale in question and the resolution of information available, and are closely related to the specific user needs.

2.4.1 Thermal Processes

During the melt season, increased air temperature, solar radiation and oceanic heat input cause ice temperature to increase to the melting point (Yang et al., 2016b). Snow and ice meltwater on the upper ice surface may collect to form melt ponds if drainage is prevented. Melt ponds reduce the albedo of the ice surface (Table 2.1), allowing more heat to be absorbed, leading to more melt (Webster et al., 2015). Oceanic heat input to the underside of the ice may also cause thinning (Kirillov et al., 2015) and the amount of input heat necessary to completely melt the ice depends on the thickness of the ice. Snow has a low thermal conductivity, meaning that it is relatively diﬃcult to transfer heat through it. In areas with thick snow layers, the

15 2. Literature Review sea ice is insulated by the snow layer, which may prevent melt (Cheng et al., 2008).

Table 2.1: The albedo of typical sea ice surface types (Perovich and Polashenski, 2012).

Surface Albedo Open Water 0.07 Bare Sea Ice 0.55 Melt Ponds 0.32 - 0.6 Snow 0.85

Melting occurs mainly at the top surface of the ice, where thermal gradients between the ice and the atmosphere cause heat to be absorbed when air temperatures rise. Additionally, incoming solar radiation may be absorbed, reflected, or transmitted through the top surface of the ice. The amount of radiation absorbed and reflected depends on the type of surface that is exposed: snow has a higher albedo than ice causing more reflection, while dust and other impurities in the ice provide bases for absorption to occur (Nolin, 2017). Melt ponds, which have a lower albedo than snow or ice, form when the ice surface melts, and allow more radiation to be absorbed, causing further melting, and expansion of the melt pond. Other factors contributing to ice decay include oceanic heat fluxes to the bottom surface, biological factors, tides, and mechanical disruption. The thermal decay of sea ice leads to many changes in the physical properties of the ice. Warming and melting of ice leads to the enlargement of brine channels, allowing for more brine and meltwater to drain through the ice. The structural properties of ice are also highly dependent on the temperature of ice, as warmer temperatures will change the crystallography of the ice. Even before the visible signs of melting are present, when ice temperatures increase, the strength of ice will decrease considerably (Shokr and Sinha, 2015). As the mechanical strength of ice decreases during thermal decay, the ice may become more susceptible to mechanical break-up due to the action of wind or waves. Timco and Johnston (2002) have shown that the relative strength of sea ice can decrease by as much as 90% as the melt

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Figure 2.5: Normalized borehole strength of sea ice (green) plotted against mean daily air temperatures (red) in Resolute, NU for landfast first-year sea ice during the ice decay season in 2000 (from Timco and Johnston, 2002). season progresses (Figure 2.5). Their measurements were made at Resolute Bay, only about 350 km from Admiralty Inlet. As the surface warms, temperature gradients between the top and bottom surface of the ice decrease, and less heat will be conducted to the surface. Eventually, the temperature profile throughout the ice will become isothermal, and a temperature inversion may occur, where surface ice temperatures become warmer than bottom ice temperatures. Depending on the salinity of ice, different sections of the ice will melt at different temperatures, leading to non-uniform decay throughout the ice (Bitz and Lipscomb, 1999). Melting will continue until all the ice decays, or the season

17 2. Literature Review changes and freezing begins again. The models used to describe the thermodynamic growth of sea ice can range from the simplest case of cooling at the ocean-atmosphere interface leading to freezing and ice growth throughout the winter (Leppäranta, 1993; Petrich et al., 2012), to complex three-dimensional models used in global climate models (Hunke et al., 2015). The complexity of the model needed depends on the environmental conditions themselves. In some regions, a simple one-dimensional heat transfer model can suﬃciently describe the physical system, whereas in other regions more complex thermodynamic and dynamic processes must be considered. All thermodynamic models are trying to solve some variation of the heat conduction equation (Leppäranta, 1993):

%/%C(8 , 28 ,)) = ∇ · (8∇)) + @ (2.3) where t is time, 8 is the density of ice, 28 is the speciﬁc heat capacity of ice, T is the ice temperature, 8 is the heat conductivity of ice, and q is an internal source term (e.g. solar radiation penetrating into the ice). Generally horizontal thermal gradients in ice are neglected, so only vertical temperature gradients are considered. The boundary conditions are:

C>? : 8 %)/%I = &) (2.4)

1>CC>< : ) = )5 (2.5)

The temperature gradient at the ice-atmosphere interface is equal to the heat

fluxes at the surface (Q)), and the bottom ice temperature is fixed at the salinity- dependent freezing point of sea water. Finally, ice growth can be determined from the balance of heat fluxes at the bottom surface by the latent heat released from freezing sea water:

8 !3/3C = 8 · %)/%I|1>CC>< − &F (2.6)

18 2. Literature Review where L is the latent heat of freezing, H is the ice thickness, and QF is the heat flux from the water to the ice. The surface energy budget is the main controlling factor in thermodynamic sea ice growth, although oceanic heat fluxes can be significant in certain regions as well. The energy budget is composed of long-wave (&;F) and short-wave (&BF) incoming and outgoing radiation, and latent (&;) and sensible (&B) heat fluxes. Incoming short-wave radiation is modulated by the changes in the amount of incoming sunlight to the surface of the Earth, which fluctuates significantly in the high latitude regions where sea ice is most commonly found. Incoming short- and long-wave radiation is modulated by clouds. Both short- and long-wave radiation may be absorbed, reflected, or transmitted at the surface of the ocean or sea ice, and, depending on which surface the radiation interacts with, will affect how the energy from the radiation is partitioned.

2.4.2 Mechanical Processes

Mechanical sea ice break-up may be caused by a variety of physical processes, and may result in different break-out processes (Figure 2.6). Depending on where ice breaks out relative to bottomfast ice or grounded ice ridges, break-out events may be considered drift-out (floating ice past the bottomfast ice), break-out (grounded ridges and floating ice break-out), or break-away (only floating ice breaks off). In Admiralty Inlet, the most important break-out process is likely drift-out, which will be referred to here as break-up or a break-out event, caused by surface wind and ocean current drag forces acting on the ice, but waves and sea surface slope may also play a role. The dominant process affecting break-up will depend on the characteristics of the region in question. Winds blowing on the upper ice surface may cause sea ice to converge and form pressure ridges, or diverge and break apart, depending on the

19 2. Literature Review

Figure 2.6: Break-out processes in Chukchi Sea from Druckenmiller (2011). Drift-out events occur when floating fast ice separates from bottom fast ice, break-out events occur when grounded ice becomes unfastened and drifts away from the shore, and break-away events occur then the floating extension detaches from the grounded ice zone. direction of the wind in relation to surrounding coasts or other stabilizing points in the ice (Itkin et al., 2017). Currents can apply under-ice drag, and waves and tides may cause changes in sea level causing the overlying ice to bend and crack (George et al., 2004). Landfast ice covers that are exposed to large bodies of open ocean can undergo rapid break-up due to bending stresses caused by ocean waves (Crocker and Wadhams, 1988). The effect of sea surface slope on break-up has not been studied extensively, but rough estimates suggest that it is not a significant contributor (Jones et al., 2016). In shallow water, pressure ridges incorporated into the landfast ice may become grounded and act as stabilizing points preventing ice motion (Jones et al., 2016). If significant stabilizing forces from pressure ridges or attachment points to the coast are present, the ice must melt and decay in place before dynamic forces such as wind or waves cause it to break-up. One study of the break-up of landfast ice in Alaska exhibiting both thermal and mechanical break-up processes suggested

20 2. Literature Review that the decay and ungrounding of pressure ridges was the predominant process leading to break-up in years when mechanical break-up occurred (Petrich et al., 2012). In Admiralty Inlet, the shoreline likely provides the primary stabilizing force for sea ice, and the eﬀects of the interaction between the ice and the shore on break-up will need to be investigated.

2.5 Modelling Sea Ice Dynamics

The drift of pack ice has been studied extensively (Thorndike et al., 1975; Hibler, 1979; Hunke et al., 2015; Heorton et al., 2018). The momentum equation at the ice/ocean boundary layer can be given by (Lemieux et al., 2016a):

u < = − × < 5 + 0 + F + + Δ · − <6Δ> C k u 1 (2.7) where C is the total derivative, u is vector velocity of the mean flow, t is time, − − 5 = 2$B8=) is the Coriolis parameter ($ = 7.292×10 5 s 1 is Earth’s angular rotation speed, and ) is latitude), k is the unit vector aligned with the z axis of the coordinate system, 0/F/1 are the wind, current, and basal stresses respectively, is the internal ice stress tensor, g is gravitational acceleration, and > is the sea surface height. The left-hand side of equation 2.7 makes up the ‘total (material) derivative’ of the mean ice flow, composed of the rate of change of the flow with time at fixed point, and change of the flow due to advection. The right-hand side of equation 2.7 is composed of the effect of the Coriolis force on the flow, the external stresses acting on the ice (wind, current, basal), the divergence of the internal ice stress, and the pressure gradient force due to changes in sea surface slope. Wind and current stresses can be described by the following equation:

G = G 2G |DG |DG (2.8)

21 2. Literature Review where the subscript x can indicate either wind or current, is the wind or current stress, G is the air or water density, 2G is the drag coefficient, |DG | is the magnitude of the wind or current velocity, and DG is either the u- or v- component of wind/current. Different forces become relevant at different spatial and temporal scales of interest. The seasonal cycle can also affect oceanic drift, as greater damping of wave stresses occurs during the winter due to ice presence preventing motion (Schulz-Stellenfleth and Lehner, 2002). Large-scale atmospheric oscillations such as the North Atlantic Oscillation or the Arctic Oscillation affect the large-scale wind patterns, and the dominant stage of oscillation will determine these large-scale patterns (Tivy et al., 2011). Until very recently landfast sea ice has generally not been included or accounted for in large scale drift models, and the prediction of landfast break-up has proved challenging due to the difficulty in defining break-up and the number of processes that contribute to the event. There are several stages that go into the development of geophysical models. First, detailed observations of the process in question are needed to describe the process, determine the range of possible outcomes, establish what variables would be useful to model, and identify potential causal relationships between the variables (Weiss et al., 2007; Asplin et al., 2012). Simple box models can be developed when a basic understanding of the relationships between the most essential variables in the system being modelled are established (e.g. Yang et al., 2016a). Further model development adds complexity to the model, introducing more variables and more relationships between variables (Lemieux et al., 2015). To evaluate the skill of the model, model results need to be validated by observations (Lemieux et al., 2016b). A problem in many applications of geophysical modelling is that different processes are important at different spatial and temporal scales. Large-scale sea ice models used in GCMs such as the Los Alamos sea ice model (CICE) (Hunke et al., 2015) and the Louvain-la-Neuve sea ice model (LIM3) (Vancoppenolle et al.,

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2012) operate at scales relevant to the study of interactions between sea ice and the global climate, but may not be appropriate for operational sea ice forecasting in Northern communities. Environment Canada has developed the Regional Ice Prediction System (RIPS) at 1/12° spatial resolution (Lemieux et al., 2016b), which produces 48 hour forecasts of sea ice concentration, ice velocity, and internal ice pressure in the Arctic Ocean, the North Atlantic, and the ice-infested waters around Canada. However, it has been shown that the RIPS model overestimates sea ice melt and does not simulate landfast ice well (Lemieux et al., 2016b). Recent work has tried to improve simulations of landfast ice by adding parametrizations of processes related to landfast ice, or by changing the material properties of sea ice. In large-scale models, parametrizations of tensile strength (König Beatty and Holland, 2010), basal stress (Lemieux et al., 2016a), and tides (Lemieux et al., 2018) have been implemented to improve landfast ice simulations with varying success. Different processes govern the configuration of landfast ice in different regions in the Arctic depending on the geography and oceanography of the region, which must be taken into account when trying to model landfast ice on a regional scale. Pack ice is often modelled as individual ice floes with no tensile strength between individual floes, but the addition of ice tensile strength has been used as a parametrization of the grounding of ice ridges (König Beatty and Holland, 2010). Others have used a combination of tensile and shear strength in the form of the Mohr-Coulomb yield curve to model the shear strength of ridge keels (Druckenmiller, 2011), or the fracture of landfast ice (Plante et al., 2020).

2.6 Sea Ice Rheology

The eﬀects of a force applied to an object is modiﬁed by the area to which it is applied. Generally, the forces that will be described in this report are external forces which are applied from sources outside a body. The measure of the force

23 2. Literature Review applied per unit area is stress (), and descriptions of the effects of stresses applied to materials is what will be used for most of the descriptions throughout the rest of this report. When a stress is applied to a material, the material as a whole may move, or be displaced, or the material may deform, where parts of the material may move relative to other parts of the material (Mellor, 1983). A dimensionless quantity used to describe the displacement per unit length is strain (). Stresses and strains may change with time, and variations of these quantities with respect to time are called stress rates and strain rates. Stresses may be compressive, tensile, or in shear. If a material deforms along one axis in either compression or tension, a strain will also result in the perpendicular direction. The ratio of lateral strain to longitudinal strain is known as Poisson’s ratio and is about 0.33 for sea ice (Timco and Weeks, 2010). Stresses may be applied in one dimension (the simplest case), or in two or three dimensions. Similarly, strains can occur in a material in three dimensions. Some materials are isotropic, where the direction of stress application does not affect the response of the material, whereas other materials are anisotropic, where the direction of stress application affects the response of the material (Mellor, 1983). Normal stresses are applied in a direction normal to the plane on which the stress acts, and shear stresses are applied in a direction parallel to the plane on which the stress acts. The applied stresses can be described by a stress tensor which defines the components of stress in a given coordinate system. Mechanical models of sea ice make assumptions about the rheological (deformation) properties of sea ice. The two common rheologies used are the viscous-plastic (VP) rheology (Hibler, 1977) and the elastic-viscous-plastic rheology (Hunke and Dukowicz, 1997; Hunke, 2001), which treat sea ice as a fluid with a high viscosity. The elasto-brittle Girard et al. (2011) and Sinha model (Sinha, 1984) treat ice as a solid, which accommodates stress by multi-scale fracturing and frictional sliding (Dansereau et al., 2016), as opposed to flowing like a fluid. Constitutive equations

24 2. Literature Review

Figure 2.7: Stress and strain relationships with time for Burger’s model. When a 4 stress () is applied from t0 to t1, the material will experience elastic strain ( ) as soon as the stress is applied, and will continue to deform due to transient creep as the stress is sustained. After the stress is removed at t1, the elastic strain is 3 immediately relieved, and gradually the delayed elastic strain ( ) is recovered. E Permanent viscous elastic strain ( ) remains in the material (from Xu et al., 2019). deﬁne the rheological properties of a material. The rheological properties of materials determine the relationship between stress, strain, and time of a material (Mellor, 1983) (Figure 2.7). When stresses are applied to solid materials, the material will deform in some way. The strain response depends on the material type, the magnitude and direction of the stress, and the length of application of stress. Ice in all its forms is a solid that exists in the natural environment at temperatures relatively close to its melting point, while most materials used in engineering applications are used at temperatures far from their melting point (Mellor, 1983). Near the melting point, most materials lose their brittle characteristics, but ice maintains these characteristics, and is an anomalous material that exhibits both brittle and creep characteristics (Xu et al., 2019). The three main rheological properties of materials are: elasticity, viscosity, and plasticity. In elastic materials strain is related to stress directly through the elastic modulus, and this type of strain is recoverable once the stress is removed, and is modelled as a spring. The elastic modulus is the coeﬃcient of proportionality between stress and in strain, and may also be called Young’s modulus (E) (Mellor, 1983). Viscous materials are modelled using dashpots, and the rate of change of

25 2. Literature Review strain with time (strain rate) is proportional to stress. Plastic materials experience no strain until a critical yield stress (k) is reached, where the material strain will increase indefinitely at indeterminate speed while stress remains along the yield curve (Mellor, 1983). A block lying on a plane with dry friction between the two is used to represent plasticity in rheological models. Viscous and plastic strain are non-recoverable (Xu et al., 2019). Ice exhibits a combination of these properties, and the dominant properties exhibited depend on the physical environment, stress rate and time scale of events. Burger’s model (Figure 2.8) is an example of a visco-elastic material with transient creep. In this model, the total strain in a material is the sum of the elastic (4), viscous (E), and delayed elastic (3) strain. The elastic strain acts immediately when a load (stress) is applied, followed by transient creep, which is a combination of the viscous and delayed elastic strain (Figure 2.7). Delayed elastic strain (also called primary or recoverable creep) is strain that grows slowly to a maximum when a persistent stress is applied to a material, and is recovered when the load is removed (Timco and Weeks, 2010). When the load is removed, the viscous strain will not be recovered. Sinha’s model for ice deformation (Sinha, 1978, 1979, 1984) is implemented in the FEM developed by McKenna et al. (in revision), which can be represented as the Burger’s model. In VP and EVP models, there are two regions where the strain can respond to stress: the ductile and plastic region. When the internal stresses are less than the maximum stresses the material can accommodate defined by the ’ellipse yield curve’, the material will behave viscously, with relatively small deformations. When the internal stresses reach the yield curve, the internal stresses remain on the yield curve, and the material enters the plastic region where it will flow with relatively large, irreversible deformations (Hunke, 2001). In brittle material models, the ice will deform in response to stresses until reaching some yield criteria (e.g. Mohr-Coulomb, Tresca), which define the maximum uniaxial and/or shear stresses

26 2. Literature Review

Figure 2.8: Burger’s model of visco-elastic material is composed of an elastic strain 4 E component ( ) represented as a spring, a viscous strain component ( ), which 3 is represented as a dashpot, and a delayed elastic strain component ( ), which is represented as a spring and dashpot in parallel. The three strain components (elastic, viscous, and delayed elastic) are connected in series (from Xu et al., 2019). the material can accommodate through deformation before fracturing (Girard et al., 2011).

2.7 Finite Element Modelling

Numerical models of geophysical processes are used to solve complex partial differential equations over space and time to evaluate the relationships between physical quantities and to answer research questions that cannot be solved using analytical models or in-situ observations. Finite difference, finite element, and finite volume methods are common numerical methods used to discretize partial differential equations to be solved using computer algorithms, each with their advantages and disadvantages (Kaliakin, 2002). In this thesis, a numerical model of sea ice mechanics using the finite element method will be used to study the effect of wind and current forces on sea ice deformation. Several FEMs of sea ice exist, such as Finite-Element Sea Ice Model (FESIM) (Danilov et al., 2015), and another developed by Lietaer and Fichefet (2008), which have been used to study large-scale sea ice-ocean dynamics. The principles of

27 2. Literature Review

finite element modelling involve taking an area of interest or domain (e.g. the Arctic Ocean), and dividing the area into many ’elements’ of a specified shape (e.g. rectangle, triangle) depending on the finite element method used, creating a mesh (Kaliakin, 2002). Elements are composed of ’nodes’, and adjacent elements are connected at nodal points. Once the area is divided into a mesh, the equations governing the physical quantities of interest (e.g. Hooke’s Law for stress and strain) can be discretized into a series of vector equations for each node and solved simultaneously for an unknown quantity (e.g. displacement), accounting for the relationship of all the elements within the domain in the unknown quantity. If the system has the ability to evolve over time, the time domain is divided into time steps of a specified length, and the governing equations are solved at each time step. Normally, to be able to derive a unique solution from a partial differential equation, appropriate initial and boundary conditions must be applied (Kaliakin, 2002). Initial conditions set the configuration of the system before the numerical method is executed, and boundary conditions constrain the solution. There are two main types of boundary conditions: Dirichlet and Neumann. Dirichlet boundary conditions specify the value of a quantity at the boundary of a domain. The most commonly used Dirichlet boundary that is used in landfast ice modelling is the ’no-slip’ condition, where displacements are fixed at zero at the shorelines (Hunke and Dukowicz, 1997). Neumann boundary conditions specify the value of the derivative of a quantity at the boundary of a domain. For large-scale sea ice modelling, a set of equations including the momentum equation, constitutive law, and conservation of ice thickness and ice concentration are solved using the FEM. The FEM used in this work by McKenna et al. (in revision) uses finite element methods to solve only the sea ice constitutive law; the momentum equation is not solved, so ice advection is not modelled, only small-scale ice deformations. Different constitutive models for sea ice have been implemented in FEMs, which include some combination of elastic, viscous, and plastic material

28 2. Literature Review properties (e.g. Hibler, 1979; Sinha, 1984; Hunke and Dukowicz, 1997; Girard et al., 2011), which were discussed in Section 2.6. The McKenna et al. (in revision) model uses Sinha’s model for ice deformation (Sinha, 1978, 1979, 1984) to describe the ice material properties.

29 3 Geography of Admiralty Inlet

3.1 Admiralty Inlet

This thesis aims to better understand the processes leading to sea ice break-up in Admiralty Inlet by studying the environmental factors which may affect break-up to improve our predictive capacity for when break-up may occur. Admiralty Inlet is located on the northern part of Baffin Island (NU) at roughly 72°03’N 86°00’W and runs roughly northeast-southwest (Figure 3.1). The inlet is about 260 km long and 43 km wide at its mouth, where it opens to Lancaster Sound to the north, one of the main eastern entries into the Northwest Passage. Along the eastern shore, several waterways extend out of Admiralty Inlet including (from north to south): Elwin Inlet, Baillarge Bay, Victor Bay, Adams Sound, Levasseur Inlet, and Moffet Inlet, and the southern portion ends at Jungersen Bay. Steep vertical cliffs rising up to 300 m above the sea surround Admiralty Inlet, with some lower slopes also present, and water depths can reach up to 800 m (Figure 3.1). The region was carved by the last glaciation 8,500 years ago, with Precambrian rock overlain with sedimentary strata and belts of Precambrian material (Douglas, 1970). Landfast ice is seasonally present here for up to 10 months of the year, with freeze-up occurring in October, and break-up in late-June or July (Galley et al., 2012). This region is highly biologically productive (Fallis et al., 1983; Crawford and Jorgenson, 1990; Nunavut Department of Environment, 2010), and is an important region culturally and economically for nearby communities such as Ikpiarjuk (Arctic Bay). Lancaster Sound, Admiralty Inlet, and eastern Baffin Bay were designated as the Tallurutiup Imanga National Marine Conservation Area in 2019.

30 3. Geography of Admiralty Inlet

Lancaster Sound

Elwin Inlet

Baillarge Bay

Admiralty Inlet Strathcona Sound

Adam's Sound

Field Sites Main Site Site 2 Cameras

Figure 3.1: Topography and bathymetry of Admiralty Inlet and adjacent waterways from Jakobsson et al. (2012). Contour lines indicate 20 m elevation/depth, index contours indicate 100 m elevation/depth. Inset shows location of Admiralty Inlet (black square) within Canada. Locations of ﬁeld sites used in this study are indicated on the map and in the map legend. .

31 3. Geography of Admiralty Inlet

Arctic Bay is located in Adams Sound, and is a settlement that started as a Hudson’s Bay Company (HBC) post in 1936. The current population of Arctic Bay is about 900 (StatsCanada, 2016), and is largely Inuit. Arctic Bay has a mixed economy with contributions from both subsistence activities such as wildlife harvest of seals, narwhal, and arctic char, and formal economic activities such as mining (Nanasivik mine from 1976-2002 and Mary River Mine 2014-present) and tourism (Ford et al., 2010). The ﬂoe edge in Admiralty Inlet is an important area for hunting seal and narwhal, and is a place where families go camping (Furgal et al., 2002; Ford et al., 2010). Recent changes in the Arctic climate (Stroeve et al., 2014; Serreze and Meier, 2019) have led to increasingly unpredictable weather and unstable sea ice (Laidler et al., 2009; Ford et al., 2010), which pose challenges for Inuit communities and have highlighted the need to understand the causes of these changes to facilitate adaptation.

3.2 Meteorology

Admiralty Inlet is in an Arctic climate zone with extremely cold winters and mean temperatures below 0 °C between September and May, with up to 6000 freezing degree days. The sun remains above the horizon from March 17 to September 23 and the sun remains below the horizon from November 12 to January 29. Observational meteorological data is not available at the ﬂoe edge in Admiralty Inlet, but weather data at the Arctic Bay airport is available from 2000-present, about 15 km inland from Admiralty Inlet. Climate normal data is available from Environment and Climate Change Canada (ECCC) for Nanisivik, about 30 km inland to the north-east of Admiralty Inlet and at about 640 m above sea level (Figure 3.2). The record maximum temperature at Nanisivik is about 20 °C in July and record minimum temperature is about -55 °C in February. Precipitation is generally low year round, but the greatest precipitation occurs in July and August with total precipitation up

32 3. Geography of Admiralty Inlet

Figure 3.2: Temperature and precipitation climate normal data for 1981-2010 at Nanisivik, NU at 641.9 m elevation. (ECCC) to 50 mm in these months. The dominant wind direction in Arctic Bay is SE-NW, with the strongest winds generally coming from the south. Monthly average wind speeds in Arctic Bay range from 1.4 m/s to 4 m/s, with stronger winds occurring more consistently in the summer months. The strongest winds that occur during the winter are caused by storms. Due to the topography around Arctic Bay, the wind conditions at Arctic Bay may not reﬂect the wind conditions in Admiralty Inlet, which is mostly unobstructed by topography.

3.3 Oceanography

Water depths in Admiralty Inlet are generally deep throughout the inlet and range from 0 m at the coasts, to up to 800 m in the centre of the Inlet (Figure 3.1). These water depths prevent the formation of grounded pressure ridges, meaning that the only attachment points for the sea ice are along the east and west coasts of

33 3. Geography of Admiralty Inlet

Admiralty Inlet and islands found within the inlet. A 30 m mixed layer forms at the surface of Admiralty Inlet during the winter, which lies above relatively warm and saline Atlantic Water. Surface temperatures are at the freezing point (∼-1.8 °C) through winter, which may rise in the summer after the ice has melted. Consistent with Arctic oceanographic conditions, water temperatures increase with depth in Admiralty Inlet to about 0 °C. Surface water salinities may increase during the winter due to brine rejection from the sea ice, and will decrease as the melt water from melting sea ice dilutes the surface waters (Rudels, 2015).

3.3.1 Tides and Currents

Little historical data is available on the currents in Admiralty Inlet. Anecdotal evidence and Fallis et al. (1983) have suggested that surface currents in Admiralty Inlet move in a counterclockwise gyre, with incoming waters moving along the western shore, and outgoing waters flowing along the eastern shore. Current speeds throughout the inlet are thought to be low. However, measurements at Cape Crawford (northwest mouth to Admiralty Inlet) indicated a mean speed of 27.7 cm/s and a maximum speed of 90.5 cm/s, and a net flow south from Lancaster Sound along the western shore of Admiralty Inlet (Fissel and Wilton, 1978). Measurements at our field site in Admiralty Inlet in June 2019 showed surface currents less than 10 cm/s. More in-situ data is necessary to determine the current patterns in Admiralty Inlet. The principal lunar semi-diurnal (M2) tide is the dominant tide in Admiralty Inlet, but a weak six hour (M4) tidal signal is also observed in the current record. The tidal range is about 1 m, but may increase to 2 m during a spring tidal cycle.

34 3. Geography of Admiralty Inlet

3.3.2 Sea Ice

Sea ice in Admiralty Inlet begins to form in October, creating a continuous landfast ice cover throughout the winter. In recent years, break-up has begun in late- June/early-July, and most of the ice in the inlet disappears by the end of July. Galley et al. (2012) found a significant trend toward landfast onset occurring later from 1983-2009 (1.4 weeks/decade), but no significant trend towards earlier break-up using Canadian Ice Service regional weekly ice charts. The sea ice regime in Admiralty Inlet is affected by the sea ice in Lancaster Sound, which forms a landfast ice cover throughout the winter in some years, while in other years the ice in Lancaster Sound is mobile throughout the winter (Gorman, 1988). If sea ice is landfast in Lancaster Sound, ice motion is prevented within the inlet and no floe edge forms. In this ice regime the sea ice in Admiralty Inlet will melt and disintegrate in place in the summer. Usually sea ice in Lancaster Sound is mobile, creating a floe edge at the intersection between Admiralty Inlet and Lancaster Sound, which progresses south throughout the break-up season as ice floes break off the northern floe edge and float out into Lancaster Sound (Fallis et al., 1983). Ice thickness in Admiralty Inlet has been measured up to 2.2 m in May in areas of rafting (Gorman, 2001). The average ice thickness of seasonal landfast ice in the Canadian Arctic Archipelago has been observed to be about 2 m (Howell et al., 2016). Ice ridging at the shoreline occurs due to the tides moving the ice towards and away from the shore can produce ridges several meters tall, but otherwise the ice surface in Admiralty Inlet is generally flat with small ridges (<2 m) occurring infrequently. The ice salinity in late spring is around 5 ppt. Sea ice in Admiralty Inlet forms in October, and reoccurring cracks a couple of meters wide form in the winter running across the inlet, usually associated with entry points into other waterways feeding into Admiralty Inlet (e.g. Elwin Inlet,

35 3. Geography of Admiralty Inlet

Baillarge Bay, Adams Sound) (Gorman, 2001). These cracks are relatively stable throughout the winter, which may change in size with the tides, but in the spring are thought to become points of instability where ice floes can break off, with the floe edge gradually progressing south as ice floes break off at the northern part of the floe edge.

36 4 Methods

To study the factors governing landfast ice break-up and their relative importance (Objectives 1 and 2), a combination of field work (Section 4.1) and finite element modelling (Section 4.2) methods were used. A case study of a break-out event in 2019 was observed and reconstructed using a FEM (Section 4.3) to evaluate whether the model was able to effectively model the break-out event, and determine what variables were most useful for predicting break-out (Objective 3).

4.1 Field Work Overview

Field work for this project occurred between May 24 - June 6, 2019 and was based out of Ikpiarjuk, Nunavut. Day trips on the ice in Admiralty Inlet were conducted to deploy instruments to take time series measurements of meteorological and oceanographic variables prior to the break-up period. Most data were collected at the main field site, which was located at 73.29°N, 85.34°W on the sea ice in Admiralty Inlet about 30 km north of Ikpiarjuk and 7 km from the eastern shore of Admiralty Inlet (Figure 3.1). At this site, a weather station, Acoustic Doppler Current Profiler (ADCP), and Sea Ice Mass Balance Array (SAMS) were deployed to take time series measurements of various atmospheric and oceanographic variables (Figure 4.1). Time lapse cameras were deployed on shore at 73.29°W, 85.15°W, and 73.48°N, 84.17°W. Instruments were deployed on May 27 and 30, 2019, and were recovered from the sea ice on June 22, 2019. Cameras were recovered on August 2 and 9, 2019. Additionally, an ice thickness measurement, ice core, CTD cast, and current profile were taken at the main field site on May 27, 2019. A CTD and current profile were also taken at 73.29°N, 85.50°W on May 30, 2019. See Figure 3.1 for

37 4. Methods locations of the ﬁeld site and where measurements were taken in Admiralty Inlet and Table 4.1 for a summary of the dates of data collection. A report of the ﬁeld work conducted in Admiralty Inlet in 2019 can be found at Loewen et al. (2019).

Figure 4.1: Main ﬁeld site in Admiralty Inlet after instrument deployment on May 30, 2019. Left to right: ADCP in ABS pipe frozen into ice attached to orange buoy, yellow SAMS data logger, automated weather station with two anemometers at diﬀerent heights, and air temperature and relative humidity sensor.

4.1.1 Oceanographic Conditions

Current Measurements

Surface currents may change both spatially and temporally (Shirasawa, 1986), so both point and time series measurements of surface currents in Admiralty In- let were collected in two locations to provide estimates of ocean currents to verify data with WebTide, a tidal modelling tool developed by Bedford Insti- tute of Oceanography (https://inter-l01.dfo-mpo.gc.ca/sites/bio/science/

38 4. Methods

Table 4.1: Start and end dates for data collection from the 2019 ﬁeld season in Admiralty Inlet.

Instrument/Measurement Start Date End Date Comments Ice Core May 27, 2019 N/A One core sample collected CTD Cast May 27, 2019 N/A Single profiles May 30, 2019 Infinity Current Profile May 27, 2019 N/A Single Profiles May 30, 2019 ADCP May 30, 2019 June 22, 2019 Valid data only from May 30 - June 1, 2019 SAMS May 27, 2019 June 22, 2019 - Weather Station May 27, 2019 June 22, 2019 - Time Lapse Camera 1 May 30, 2019 August 9, 2019 Deployed at Sujartalik Time Lapse Camera 2 June 6, 2019 August 2, 2019 Deployed at Elwin Inlet research-recherche/ocean/webtide/index-en.php), which was used as input into the FEM (Section 4.2). Profiles of surface currents were measured at 1 Hz at the main site and another 5 km southwest of the main field site using JFE Infinity AEM-USB Electromagnetic Current Meter (Infinity) on May 27 (15:10-15:24) and May 30 (15:55-16:10) using a similar method as in Shirasawa (1986). The average current velocity at seven different depths from 2 to 15 m was measured by holding the instrument at each depth for 2 minutes. Current speeds at each depth were calculated by identifying the times when the instrument was held steady at each measurement depth and averaging the measurements within each time block. Measured velocities had an accuracy of 1 cm/s and a resolution of 0.02 cm/s. Continuous measurements of currents at the main field site in the upper 24 m of the inlet were collected using a 3-beam 1 MHz Nortek Aquadopp Acoustic Doppler Current Profiler (ADCP). On May 30, 2019 the ADCP contained within a custom mount using two ABS pipes was deployed downward-facing through a hole in the ice so that the instrument transducers were situated just below the bottom ice surface. Ocean current speed and velocity were measured by the ADCP by sending acoustic waves through the water every 900 s (15 minutes). Currents measurements

39 4. Methods were made starting 0.4 m below the instrument transducers at 1 m intervals to 24.4 m below the ice surface. Data were collected until the instrument was recovered on June 22, 2019, although in post-processing it was discovered that reliable data were only available from May 30 - June 1, 2019. Weak returns of the acoustic signal were thought to have been caused by meltwater pooling at the underside of the ice surface, preventing acoustic waves from being eﬀectively transmitted through the water column. ADCP data were processed in MATLAB. The current data were transformed from beam coordinates to xyz coordinates by the instrument software, and the xyz coordinates were further transformed to align the y axis to true north based on the instrument orientation at deployment. The instrument magnetometer did not indicate any change in orientation of the instrument throughout the deployment period. The accuracy of water velocity was 1 % of the measured value, and the vertical velocity precision was 0.5 cm/s and the horizontal velocity precision was 1.4 cm/s based on the conﬁguration of the instrument.

CTD Casts

Ocean heat flux to the underside of ice can suppress ice growth and/or cause melting to the ice (Kirillov et al., 2015). The magnitude of oceanic heat flux to ice depends on the difference between the ocean mixed layer temperature and the melting point of ice (-1.8 °C). To estimate ocean heat flux to ice, measurements of temperature and salinity with depth at two locations in Admiralty Inlet were collected using a RBR XR620 and an Idronaut Ocean Seven 304 CTD (conductivity, temperature, depth) profiler following the methods described in Halverson et al. (2017). The instruments were manually lowered through holes in the ice at 50 - 75 cm/s to a maximum depth of 300 - 450 m. The accuracy and resolution of the RBR and Idronaut temperature, conductivity, and pressure sensors are shown in Table 4.2. Issues were suspected with the pressure sensor on the Idronaut.

40 4. Methods

Table 4.2: Accuracy and resolution of RBR XR620 and Idronaut Ocean Seven 304 CTDs. Measurement Instrument Accuracy Resolution RBR 0.002 °C <0.00005 °C Temperature Idronaut 0.002 °C 0.0001 °C RBR 0.003 mS/cm 1 S/cm Conductivity Idronaut 0.003 mS/cm 0.3 S/cm RBR 0.05% full scale (F.S.) <0.001 % F.S Pressure Idronaut 0.05 % F.S. 0.0015 % F.S.

WebTide

Since valid ADCP data were only available for two days, the WebTide Arctic model (Dunphy et al., 2005) was used to estimate currents during break-up for the realistic case described in Section 4.3. The output u and v components of currents from WebTide near the location the ADCP was deployed were saved and compared with the ADCP data by computing the coeﬃcient of determination (R2) for the current speeds and directions for the two datasets.

4.1.2 Meteorological Conditions

Weather Station

A weather station was set up at the main field site which included two Davis Vantage Pro2 anemometers and one Davis Vantage Pro2 air temperature/relative humidity sensor to evaluate the effects of the meteorological conditions during the break-up season and to provide reasonable estimates for wind inputs to be used in finite-element modelling of break-up. The two anemometers were installed at 90 cm and 252 cm above the ice surface, and the temperature/humidity sensor was 150 cm above the ice surface, where the snow depth was approximately 14 cm. Wind on a north-south axis was thought to dominate in Admiralty Inlet so the anemometers were oriented east-west to reduce eddy effects from the tripod

41 4. Methods pole. To collect measurements, a Cryologger (https://github.com/adamgarbo/ Cryologger_Automatic_Weather_Station), an open-source Arduino-based data logger and telemeter, sampled the temperature, humidity, wind speed and direction, and battery voltage every 5 minutes and saved this information to a microSD card. At the end of every hour, the samples were averaged and the hourly data was transmitted via the Iridium satellite network hourly and was posted in near real-time at cryologger.org/arctic-bay-data/. MATLAB was used for further analysis, and wind direction and speed were converted to east-west (u) and north-south (v) components. Wind speeds measured at the surface were scaled to 10 m winds using the one-seventh power law following Hussain (2002).

Numerical Weather Models

Since meteorological data from the field was only available for a short amount of time, observations from the Arctic Bay airport and various numerical weather model reanalysis products were compared with the available field data to determine whether these data products could be used when field data was unavailable. Wind speed and direction were the most important variables to compare, as these variables were necessary for input into the FEM. 10 m wind velocity component field data from Admiralty Inlet was compared with National Centre for Environmental Predictions (NCEP; NCEP Reanalysis data provided by the NOAA/OAR/ESRL PSL, Boulder, Colorado, USA, from their website at https://psl.noaa.gov/) sub-daily (6 hour) 1000 hPa u and v wind data, hourly 10 m u and v winds from European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 Reanalysis (Generated using Copernicus Climate Change Service information (2020)), and hourly data available from Environment and Climate Change Canada at the Arctic Bay airport (Climate ID 2400404). The R2 values were used to evaluate how well different data products could be used to model winds in Admiralty Inlet in the absence of field data.

42 4. Methods

4.1.3 Sea Ice Geophysics

In-situ Measurements

Sea ice strength properties were derived using ice thickness, temperature, and salinity from in-situ measurements. A single ice core provided information about ice thickness, temperature, and salinity, and continuous measurements of sea ice thickness and temperature were collected using a Scottish Association for Marine Science Research Services Ltd Sea Ice Mass Balance Array (SAMS) using a through ice thermistor chain. A 170 cm long ice core was taken at the main field site on May 27, 2019 with a 9 cm diameter Kovacs corer following Eicken et al. (2010). Immediately after removing the ice core from the corer small holes were drilled into the core at 10 cm intervals and thermometers were inserted to measure the ice temperature profile. The ice core was then subsampled into 5 cm sections at 15 cm intervals which were subsequently melted for bulk salinity measurements using the Idronaut CTD and a YSI Pro Plus. The SAMS consisted of a thermistor array connected to a data logger which transmitted data in real-time via Iridium satellites. The thermistor chain was deployed through a hole in the ice at the main field site. Each thermistor sensor was separated by 2 cm, and the top node of the thermistor chain was at the upper ice surface (snow-ice interface at node 1). The ice thickness at the time of deployment was approximately 160 cm, so the ice-water interface was at approximately node 80. The snow thickness was approximately 14 cm. The SAMS recorded ice temperatures every 6 hours, and data were transmitted by Iridium satellite.

43 4. Methods

Calculating Ice Properties

Estimates of sea ice properties were used to model realistic responses of sea ice to external forces during break-up. Ice temperature (T8), porosity ()), and strain rate have been identified to be significant factors affecting sea ice strength (Timco and Weeks, 2010). During the springtime, rising air temperatures lead to increasing ice temperatures and porosity, decreasing the strength of the ice (Timco and Johnston, 2002).

Ice porosity ()) and ice tensile strength (C; in MPa) were calculated using equations from Timco and Weeks (2010):

49.185 1 = (8 + 0.532 (4.1) |)8 |

) = 1 + 0 (4.2)

−0.6455 C = 4.278) . (4.3)

where 1 is the relative brine volume S8 is the ice salinity in ppt, ice temperature

(T8) is in °C, and 0 is the relative air volume. First year sea ice is assumed to have no relative air volume (Richter-Menge and Jones, 1993), and the brine volume of the ice was estimated using equation 4.1 and salinity data from the ice core and temperature data from the SAMS. The tensile strength throughout the break-up season was then estimated using equation 4.3. Timco and Johnston (2002) used a similar method for estimating sea ice ﬂexural strength during the melt season, but tensile strength is more relevant for evaluating mechanical break-up.

44 4. Methods

4.2 Finite Element Modelling

A FEM of sea ice was used to understand the response of ice due to external forcing from winds and currents. The FEM used for these studies was developed by Richard McKenna and was implemented and adapted for the work presented here. This model uses a 2D mesh composed of irregularly-shaped four node quadri- lateral elements to represent a solid ice continuum in plane stress. An explicit numerical scheme is used to solve the equation of motion, assuming static equilibrium (i.e. negligible acceleration of the material due to the application of a load). The equation of motion used in this model is:

[ ]{D} = {0 } + {F } + {< } + {A } (4.4) where K is the stiffness matrix which is related to the material properties of the ice at each element, u is the displacement at each node, 0 and F are the air (wind) and water (current) drag forces applied to each node, < is the load applied to each node due to internal stresses, and A is the reaction force, which is relevant only for nodes with boundary conditions. At each time step, this equation is inverted to solve for displacement. Each element may be assigned different material properties including: ice thickness, ice temperature, grain size, and density, which are considered to be uniform throughout the element. The standard material properties used in model runs are shown in Table 4.3. At each time step, the displacement, velocity, and reaction force are calculated for each node. Four Gauss points in the interior of each element are where the stresses and strains of each element are calculated at each time step. Temporally- and spatially-varying wind and current forces may be applied to the ice to determine the effects of these forces on the ice. Elastic, viscous, and delayed elastic deformation material behaviours are included

45 4. Methods

Table 4.3: Input ice property model parameters

Property name Value Units Comments Ice thickness (h) 1.60 m Field data Ice temperature (T8) -2 °C Field data Ice grain size (d) 0.003 m McKenna et al. (in revision) Air drag coefficient (c0) 0.001 [] Turnbull et al. (2017) Water drag coefficient (cF) 0.005 [] Vancoppenolle et al. (2012) Ice density (8) 900 kg/m3 McKenna et al. (in revision) Young’s Modulus (Y) 8.1985 x 109 Pa Mellor (1983) in this model, which was adapted from a model of ice deformation developed by Sinha (Sinha, 1978, 1979, 1984) to multiaxial loading situations. Elastic strain is instantaneously recoverable strain, viscous strain is permanent creep deformation, and delayed elastic strain is deformation along grain boundaries which is recovered slowly after the removal of a load. Internal stresses are related to elastic strain, and the total strain of an element is defined by the change in its displacement. The constitutive equations for strain from Sinha’s model include:

= 4 + 3 + E (4.5) where is the total axial strain, 4 is elastic strain, 3 is delayed elastic strain (primary creep), and E is viscous strain (secondary creep), which are given by:

4 = / (4.6)

2131 /= = ( ){ − 4G?[−(0) C)1 ]} 3 3 1 1 (4.7)

= E = ¤E1C( ) (4.8) 1 where t is time, is uniaxial stress, E is Young’s modulus, 21 is a constant, d is the ice grain size, 31 is a unit grain diameter constant, 0)1 is a temperature dependent

46 4. Methods

constant, ¤E1 is a temperature dependent secondary creep coeﬃcient, 1 is a unit stress, and n is the creep exponent. The parameter values for Sinha’s model are given in Table 4.4 A Gaussian quadrature method is used to integrate stresses and strains throughout each element. The FEM was calibrated to Sinha’s model which was derived from physical experiments. For further details on the equations and numerical methods used in the FEM, see Section 2.7 or McKenna et al. (in revision).

Table 4.4: Ice parameter values in Sinha’s model.

Property name Value Units

Delayed elastic constant (21) 9 [] −1 Temperature dependent constant (0)1) ∼0.00025 B −7 −1 Secondary creep coeﬃcient (¤E1) ∼1.76 × 10 B Unit grain diameter (31) 0.001 m 6 Unit stress (1) 1 × 10 Pa Creep exponent (n) 3 []

To ensure the model cases examined in this thesis were well posed and modelled realistic situations, appropriate inputs and boundary conditions were applied to the mesh. Boundary conditions may be applied by prescribing (e.g. fixing at 0) displacements and/or forces at certain nodes in the mesh. In the experiments described in this work, zero displacement at the boundary nodes is the only boundary condition applied. Boundary nodes which have fixed displacements will generate a reaction force. At nodes with boundary conditions, reactions forces will be generated, which act equal and opposite to the sum of the applied loads to each node (i.e. winds and currents). For the sensitivity and idealized model runs described in Sections 4.2.1 and 4.2.2, a mesh representing Admiralty Inlet was developed using a coast shapefile from the CIS as an outline for the inlet, and a meshing script from the FEM was used to create the nodes and elements based on the outline shape. The nodes along the east and west coasts of Admiralty Inlet were fixed at zero displacement (no motion at the shores). The northern extent of the mesh was chosen from the average location

47 4. Methods of the northern ice edge at the end of May seen in MODIS imagery. The southern extent of the mesh was chosen as an approximate location of a cross-inlet lead.

4.2.1 Sensitivity Analysis

A series of simulations were conducted to determine the ideal spatial and temporal resolution for conducting simulations, and for determining whether or not the solution is stable for different resolutions. An ideal spatial resolution should capture all the small scale variations in the stress and strain curves within the vicinity of the coastline, while an ideal temporal resolution would allow the ice to react realistically to perturbations in external forces in combination with reasonable run times. Spatial resolution may have an effect on the results of the model because of the unrealistic wind and current patterns in a coarse mesh or unresolved features at the shoreline (Lietaer and Fichefet, 2008). Mesh resolutions of 10 x 10 elements, 25 x 25 elements, 50 x 50 elements, and 75 x 75 elements were tested to determine the most effective and computationally efficient resolution. The highest resolution that could be accommodated using the available computing power was 75 x 75 elements. The mean of maximum principal stress within the elements found in the four grey regions 1-4 in Figure 4.2 for each spatial resolution were calculated and compared with the 75 x 75 element case. Based on the results (Section 4.2.1), a standard resolution of 50 x 50 elements (∼1.1 km length) was selected for all further numerical simulations. Temporal resolution may also have an effect on the model results, in particular, if the time step is too large, the model may become numerically unstable, and produce unrealistic results (Hunke and Dukowicz, 1997). To evaluate the appropriate time step to be used, model cases with time steps of 0.5 s, 1 s, 2 s, and 5 s were run where the wind direction changed abruptly from 45 ° SW to 45 ° SE at 1800 s in the simulation. The displacement, maximum principal stress, and reaction force at location b (see

48 4. Methods

Lancaster Sound

Elwin Inlet

Baillarge Bay Fixed Nodes Horizontal Crack Mesh Outline Averaging Polygons Node Locations Admiralty Inlet Plotting Locations

Figure 4.2: Mesh outline and locations where the maximum principal stress values were averaged for diﬀerent regions of the grid (grey boxes) in the sensitivity tests (1-4) and idealized cases (1-5). The location of the cross-inlet crack used in GS_50_50_hc is shown in blue. The locations of the ﬁxed shoreline nodes are shown in red. Brown points are node and approximate element locations which are used for plotting in Section 5.2 and are used to show representative output of the model.

Figure 4.2) was plotted for each case and qualitatively compared to determine the most eﬀective time step. Based on the results (Section 4.2.1), a standard of 1 s was chosen for all further numerical simulations.

4.2.2 Idealized Simulations

To test the response of the ice under diﬀerent conditions, idealized simulations were run with diﬀerent inputs. These simulations use the shoreline of Admiralty Inlet as an outline (Figure 4.2). Inlets extending from the eastern shore of Admiralty Inlet such as Elwin Inlet were not included in these simulations. For most model

49 4. Methods simulations, the displacements at the nodes at the east and west shores (red lines in Figure 4.2) were fixed at zero to prevent motion at the shorelines. The nodes at northern and southern extents of the model mesh were ’free nodes’, and free boundary conditions were applied to those nodes. Different combinations of wind and current input, and ice properties were applied to each of the different scenarios to quantify the effects of different inputs on the ice. The reference case (GS_50x50_standard) was run for 21600 s with a 1 s time step. The output for this case was stable around 10800 s, so further simulations were run only until 10800 s with a 1 s time step. The different scenarios are summarized in Tables 4.5 and 4.6, where ’GS’ refers to the model element resolution (’grid size’).

Table 4.5: Material properties for experiments were ice thickness (h), ice temperature (T8), and Young’s modulus (Y) were changes from the standard case. Model case names are deﬁned by the spatial resolution (’GS_50x50’) and the material property changed (’mpropXX’).

Case Name h (m) T8 (°C) Y (GPa) GS_50x50_standard 1.6 -2 8.2 GS_50x50_mpropT 1.6 -10 8.2 GS_50x50_mpropH 1.0 -2 8.2 GS_50x50_mpropY1 1.6 -2 6.5 GS_50x50_mpropY2 1.6 -2 9.0

Changes in material properties such ice temperature, ice thickness, or Young’s modulus may have significant effects on the response of ice to environmental forces due to the effect of these properties on the strain response of the ice (see equations 4.5-4.8). Several model cases were run while changing these properties as described in Table 4.5, to examine the effect of these properties on ice displacement and internal stresses. Winds and ocean currents are the main environmental drivers of ice stress in narrow straits (Rallabandi et al., 2017). To test the hypothesis that wind speed and direction are significant drivers of break-up in Admiralty Inlet, several model experiments were run to test the effect of wind speed and direction on ice stress.

50 4. Methods

Table 4.6: Description of idealized simulations. Model case names are deﬁned by the spatial resolution (’GS_50x50’) and main environmental input(s).

Casename D0 (m/s) WD (°) D2 (m/s) CD (°)TC>C GS_50x50_standard 5 225 0.00 0 21600 GS_50x50_10ms 10 225 0.00 0 10800 GS_50x50_15ms 15 225 0.00 0 10800 GS_50x50_20ms 20 225 0.00 0 10800 GS_50x50_sinwind 0 - 20 225 0.00 0 10800 GS_50x50_NEwind 5 45 0.00 0 10800 GS_50x50_NWwind 5 315 0.00 0 10800 GS_50x50_SEwind 5 135 0.00 0 10800 GS_50x50_current 0 0 0.04 225 10800 GS_50x50_wind-current 5 225 0.04 225 10800 GS_50x50_wind-diﬀcurr 5 225 0.04 45 10800 GS_50x50_wind-sincur 5 225 0 → 0.1 225 10800 GS_50x50_hc 5 225 0.00 0 10800

* D0 = wind speed, WD = wind direction, D2 = current speed, CD = current direction, TC>C = total number of time steps

Wind speeds of 5, 10, 15, and 20 m/s produce a wind stress of 0.03, 0.13, 0.29, and 0.52 Pa, respectively, using equation 2.8, assuming an air density of 1.3 kg/m3 and air drag coefficient of 0.001. Wind directions were changed in NEwind, NWwind, and SEwind, which are indicated in Table 4.6 in meteorological coordinates. Current speeds of 0.04 m/s were used in the cases with currents unless otherwise noted, which corresponds to a current stress of 0.008 Pa using equation 2.8, assuming a water density of 1025 kg/m3 and current drag coefficient of 0.005. In GS_50x50_wind-current, the wind and current were pointing in same direction, while in GS_50x50_wind-diffcur the wind and current were pointing in opposite directions. GS_50x50_wind-sincur had wind and current pointing in same direction, and current speeds increased from 0 to 0.01 m/s over one hour following a sine function. Wind and current stresses were applied to each node and scaled to be proportional to the area of the elements associated with the node using shape functions, which express the geometry of the element. Winds and currents may change in space and

51 4. Methods time, which can complicate the analysis, but for these idealized cases, the speeds and directions of the winds and currents were constant in space and time unless otherwise noted. Cracks that form in the winter extend across Admiralty Inlet and may grow into leads in the spring are locations where break-up is more likely to occur. Assuming the leads are completely open, the effect of cross-inlet leads on the model results were evaluated by eliminating a portion of the mesh (i.e. elements below the blue line in Figure 4.2) and applying a 5 m/s SW wind throughout the model run GS_50x50_hc. Outputs include displacement, stress, stain, and reaction force at each element or node in the mesh. These outputs change in space and time, as the response of the ice is contingent on configuration of the ice and the time history of forces acting on the ice. The maximum principal stresses were averaged over regions 1-5 shown in Figure 4.2 after 10800 s for each case to evaluate how the principal stresses changed between different cases. The regions were defined so a 3 x 3 element square of the lowest resolution case (10 x 10 elements) could fit into each region. Reaction forces occurred at nodes along the shorelines which were fixed to have no displacement, and represent a combination of physical forces acting at the shoreline such as frozen tidal leads or grounded ridges. The total force keeping the ice attached to the coast was estimated by summing the reaction forces along the coast and dividing by the length of the coast. The sum of the x and y components of reaction forces at both shores at each time step is equal to the sum of the x and y components of the environmental (wind and current) forces applied over the entire mesh at that time step. The direction of the reaction forces may act to oppose the motion of the ice towards a fixed point (e.g. shore or structure), or may act as a resisting force to prevent the ice from pulling away from a fixed point. The x component of reaction force in the global coordinate system was considered to act perpendicular to the shore, and the y component of the reaction force in the

52 4. Methods global coordinate system was considered to act parallel to the shore. Variations in the shoreline mean this assumption is not always correct.

4.2.3 Stress Analysis

The internal stress of the ice was used to evaluate the eﬀects of diﬀerent external forcings on ice around break-up. To analyze the stress state of the ice, the normal (8) and shear ( 89) stress components of each element were converted to the principal components of stress (1,2). In this conversion, the shear stresses are eliminated by rotating the original coordinate system by angle ? (Figure 4.3). The conversion of the xx, yy, and xy components of stress to principal stresses is performed using the following equations:

r GG + HH GG − HH 2 2 , = + GH (4.9) 1 2 2 2

2 GH C0=(2?) = (4.10) GG − HH By converting to the principal components of stress, the pure compressive and tensile stresses exerted on each ice element were computed. Tensile stresses were considered positive, and compressive stresses were considered negative. The maximum principal stresses of each element was then compared with a tensile strength threshold, indicating the strength of the ice (Maximum Normal Stress Criterion). Elements whose stress exceeded the threshold were identiﬁed as likely candidates for yielding or fracture. The tensile strength used for further analysis of FEM output was assumed to be 25 kPa (Tremblay and Hakakian, 2006), however there is much uncertainty in the correct value of tensile strength to be used. Other failure criterion may also be used (e.g. Mohr-Coulomb), with similar results. This topic will be discussed in further detail in section 6.1.3.

53 4. Methods

Figure 4.3: Transformation of stresses in a given coordinate system to principal stresses (from eFunda, 2020). Left: normal (8) and shear (89) stresses in given coordinate system. Right: principal stresses (1,2) by transforming the original coordinate system by the angle (?).

4.3 Break-up in 2019

4.3.1 Visual Observations

Visual observations throughout sea ice break-up in 2019 were collected using two time-lapse cameras placed at diﬀerent locations on the shore of Admiralty Inlet to provide supplementary information about environmental conditions during break-up. On May 30, 2019 one camera was deployed on the eastern shore of Admiralty Inlet between Strathcona Sound and Baillarge Bay in a place called Sujartalik. The camera was placed about 250 m from the shore at 15 m elevation facing west towards the large lead in the ice. The second camera was deployed on June 6 by members of the Arctic Bay Nauttiqsuqtiit (Guardians) on the southern corner at the mouth of Elwin Inlet looking north towards Lancaster Sound during break-up. Both cameras took photos every 15 minutes, and were recovered in early August 2019. Images from each camera were stitched together to create time-lapse

54 4. Methods videos, which were analyzed to identify the timing of break-out events and other visual cues for break-out events such as the condition of the shore lead, or the presence/size of pre-existing leads.

4.3.2 Modelling Break-up

A model run with a realistic configuration of ice extent and environmental conditions was developed to simulate a break-out event in Admiralty Inlet which occurred on June 28, 2019. The ice configuration, including the approximate ice edge and lead locations were derived from a Sentinel-2 image from June 24, 2019 and a MODIS image from June 19, 2019 (Figure 4.4). Wind speed and directions at 10 m were taken from 12 grid point locations in the northern part of Admiralty Inlet from ERA5 from 5.5 hours before to half an hour after the break-out event occurred. Current speed and directions were taken from 6 points on the northern part of Admiralty Inlet from WebTide from 5.5 hours before to half an hour after break-up occurred. Break-up timing was estimated to have occurred at 02:30 UTC from the time lapse imagery (Section 5.3.1). The mesh was 40 x 40 elements for this experiment, and the mean area of the elements was 1.4 km2, a similar resolution to the standard cases. This case was designed to model the configuration of environmental and ice conditions as closely as possible to those in Admiralty Inlet on June 24, 2019 to determine what factors may have contributed to this break-up event. Shore leads were not modelled explicitly, although they were observed in the time-lapse imagery. The magnitude and direction of reaction forces at the shoreline were used to evaluate interactions between the ice and the shore. The southern extent of the mesh was chosen as the first major lead south of the floe edge that could be identified from synthetic aperture radar (SAR) satellite imagery around the time of break-up. Model output used to evaluate this break-up event included internal ice stresses and reaction forces along the shoreline. The tensile ice strength at this advanced

55 4. Methods

WebTide Markers ERA5 Locations Mesh Outline

Figure 4.4: Outline of mesh used for the realistic case, locations of ERA5 grid points (green diamonds) for wind, and WebTide markers (blue circles) for current. Pre-existing lead where break-out occurred is shown in red. Sentinel-2 image from June 24, 2019 (left) and MODIS image from June 19, 2019 (right) are shown in the background. melt state was estimated to be 25 kPa (Tremblay and Hakakian, 2006), and locations where the internal ice stress within an element exceeded the assumed ice strength were thought to have experienced prior fracture. Reaction forces along the shoreline provided an indication of the forces at the shoreline necessary to prevent ice from deforming relative to the shoreline. Although an exact measure of shoreline strength is not known, this output provides an estimate of the order of magnitude of forces acting along the shoreline.

56 5 Results

5.1 Field Work

5.1.1 Meteorological Conditions

Meteorological conditions in Admiralty Inlet from May 28 - June 23, 2019 are shown in Figure 5.1. Air temperatures during this period ranged from -6.9 to 7.0 °C, with a mean temperature of 0.7 °C. Temperatures had regular diurnal variations, and there was a shift from air temperatures consistently below zero before June 11 (dashed line in Figure 5.1), to consistently above zero after June 11, which may have led to melting at the surface of the ice. Wind speeds in Admiralty Inlet measured by the weather station ranged from 0 to 10.4 m/s, with a mean wind speed of 3.6 m/s. Wind directions were primarily north-south, with winds from the south over 30 % of the time, and 17 % of the time from the north (Figure 5.2). Comparing modelled meteorological data from NCEP and ERA5 at a grid point close to where the weather station was deployed and at the same time as the ﬁeld data show that modelled data did not always agree with observed data at mid-Admiralty Inlet. ERA5 data showed wind predominately in the north-south direction, but a higher frequency of northerly winds, rather than southerly winds (Figure 5.2). NCEP data was predominately south-east - north-west, and was biased towards wind speeds higher than was observed by the weather station. Modelled air temperatures from NCEP and ERA5 generally followed the observed air temperatures. Air temperatures measured at the Arctic Bay airport were generally warmer than the air temperatures measured on the ice in Admiralty Inlet.

57 5. Results

Figure 5.1: Time series of air temperatures (a) and wind speeds (b) in Admiralty Inlet from the weather station deployed May 28 - June 23, 2019. Arctic Bay airport data from Environment and Climate Change Canada, and reanalysis data from NCEP and ERA5. Vertical dashed line indicates date after which air temperatures remain consistently above 0 °C.

Scatterplots of weather station data scaled to 10 m with modelled products shows little correlation between the wind speed and direction between the two data sets (Figure 5.3). ERA5 wind data had the highest correlation coefficients with the weather station data with R2 values of 0.08 for wind speed and 0.01 for wind direction. NCEP had the lowest R2 values of 0.03 for wind speed and 0.001 for wind direction. Arctic Bay Airport had a similar R2 value for wind direction as ERA5, but a slightly lower R2 value for wind speed at 0.05. Arctic Bay airport is found on Adams Sound, east of Admiralty Inlet, and is surrounded by hills which may influence the air flow in this region. Section 6.1.1 will discuss some of the reasons the reanalysis products did not correlate well with observed data in Admiralty Inlet, and the implications of this.

58 5. Results

Figure 5.2: Wind roses from Admiralty Inlet Weather Station (a), Arctic Bay Airport (b), ERA5 (c), NCEP (d). Directions indicate direction wind comes from, and colours indicate wind speed in each direction. Length of bars in each direction indicate the frequency occurrence of wind speed and direction as a percentage in time of the whole time series. Black dashed line indicates approximate orientation of northern part of Admiralty Inlet where the weather station was located.

59 5. Results

Figure 5.3: Correlation of wind speed (a-c) and direction (d-f) between Admiralty Inlet weather station (Wx Station) and ERA5 (a, d), NCEP (b, e), and Arctic Bay Airport (Env Canada) data (c, f).

5.1.2 Oceanography

CTD casts were taken in two different locations in Admiralty Inlet, one on May 27 and another on May 30. Profiles were taken using both the Idronaut and RBR, however only the Idronaut collected data successfully at both locations. The lower boundary of the surface mixed layer is usually indicated by significant changes in temperature and salinity (Kaiser, 1978). In both profiles shown in Figure 5.4, the temperature and salinity values from the Idronaut are averaged over a 35 point (5 s) moving average filter. The boundary of the surface mixed layer occurs around

60 5. Results

Figure 5.4: Temperature (a) and salinity (b) proﬁles from the Idronaut CTD on May 27 and May 30, 2019 in Admiralty Inlet. Inset zooms in on temperature and salinity proﬁles from the surface (0 m) to 50 m depth. Dashed line at 25 m on inset indicates depth of surface mixed layer. Only downcasts are plotted here and data were averaged over 35 samples (5 s).

25 m depth, indicated by the dashed line in the inset. The average salinity of the mixed layer was 31.5 ppt, which corresponds to a freezing point of about -1.73 °C. The average temperature of the mixed layer was -1.7 °C, indicating that the water temperatures were nearly cold enough for ice growth to occur, and there would have been very little ocean heat flux to the underside of the ice. Current profiles of near surface currents below sea ice in Admiralty Inlet were measured on May 27 and May 30, 2019 from the Infinity current meter (Figure

61 5. Results

5.5). The weakest currents occurred near the ice-water interface, and current speed increased with depth up to ∼ 7 m from the surface, but didn’t exceed 4 cm/s in either profile. Tidal charts from the Hydrologic Survey of Canada indicated that the time when the Infinity profiles were taken was around the peak of high tide, when current speeds are expected to be the lowest. If the profiles had been taken during the transition between high and low tide, the current speeds might have been higher.

Figure 5.5: Current speeds from the Inﬁnity current meter on May 27 and May 30, 2019.

The mean ADCP surface (0.4 - 5.4 m depth) current magnitude when valid data was available was 0.04 m/s, and surface current magnitudes ranged from 0 m/s to 0.09 m/s. The v component was higher in magnitude than the u component (Figure 5.6a), which was expected as the inlet is oriented approximately NE-SW

62 5. Results which would affect the direction of fluid flow. The u component of current speed was mainly positive (to the east), regardless of the position of the tidal cycle. Diurnal tidal signals could be seen in surface currents in Admiralty Inlet up to about 12 m depth from the time series of valid current speeds from the ADCP (not shown). A one-sided amplitude spectrum from the u and v components of current speeds averaged from 0.4 - 5.4 m (Figure 5.6b) showed a significant peak at 2 cycles/day in the v spectrum and to a lesser extent in the u spectrum. This corresponds to the 12 hour, M2 tide.

Figure 5.6: Current speeds (a) and single-sided amplitude spectrum (b) for current speeds averaged between 0.4 m and 5.4 m from the ADCP. v (solid) indicates the north-south component and u (dashed) indicates the east-west component.

63 5. Results

Since ocean currents were only measured for a short time before break-up, using a modelled product can give an estimate for currents in Admiralty Inlet during break-up. In general, current speeds were similar between WebTide and the ADCP, and WebTide was able to capture the tidal signal measured by the ADCP (Figure 5.7a). When the currents came from the south, Webtide and the ADCP agreed well, but when currents came from the north, currents from Webtide came more from the west, while measured currents were more from the east (Figure 5.7b). The R2 value for both current speed and direction was 0.2.

Figure 5.7: Current speed (a) and direction (b) from the ADCP and Webtide from May 30 - June 1, 2019 in UTC.

64 5. Results

5.1.3 Sea Ice Strength

The temperature and salinity throughout an ice core is shown in Figure 5.8. The mean ice temperature was -1.8 °C and the average salinity was 4.8 ppt. At the time of ﬁeld work, air temperatures were around zero, and ice temperatures were close to isothermal, which was also measured by the SAMS. A time series of the mean ice temperature throughout the SAMS deployment is shown in Figure 5.9a, and average temperatures rise above the melting point of sea ice around June 11, 2019.

Figure 5.8: Ice temperature (a) and salinity (b) proﬁles from an ice core taken at the ﬁeld site in Admiralty Inlet on May 27, 2019. Salinity values were measured using both the Idronaut and YSI Salinometer.

65 5. Results

The tensile strength of sea ice in Admiralty Inlet was estimated to decline from 210 kPa to 120 kPa in the month leading up break-up (Figure 5.9b) using equation 4.3 due to increases in mean ice temperature. Note that the equations used to calculate ice tensile strength may not be accurate at these temperatures. In addition, the ice was assumed to have no air-filled pores, but as ice warms and brine pockets drain, air pockets may become significant during the melt season (Frantz et al., 2019). The equation for ice tensile strength used here is based on laboratory measurements of ice strength and may need to be scaled to be used in large-scale applications (Dempsey et al., 1999), which is why these values differ greatly from the assumed tensile strength of the ice used in analysis of the FEM output. Scaling of ice strength will be discussed in further detail in Section 6.1.3. The values of tensile strength given here illustrate how much the tensile strength of ice can decline during the melt season (∼ 43%), and likely declined further up to the time of break-up.

66 5. Results

Figure 5.9: (a) Time series of mean ice temperatures from SAMS thermistor chain, and modelled brine volume from Timco and Weeks (2010). Dashed line indicates melting point of sea ice. (b) Time series of ice strength (C) from equation 4.3 using salinities from the ice core taken during ﬁeld work.

67 5. Results

5.2 Finite Element Modelling

In-situ data was only available for a short period before break-up. The following modelling studies allowed different ice and environmental configurations to be tested to determine how they may affect break-up.

5.2.1 Sensitivity Studies

Spatial Sensitivity

The means and medians of maximum principal stress within regions 1 - 4 of the mesh shown in Figure 4.2 were similar between the different mesh resolutions (Figure 5.10). The 50 x 50 element case was most similar to the 75 x 75 element, and different regions of the mesh had different magnitudes of standard deviations due to irregularities in the mesh which result in varying responses to wind stress. Figures comparing the displacement, total strain, and stress at different model resolutions at a single time step are shown in Appendix A. These results justify the use of the 50 x 50 element case for further simulations. The mean element length in the 50 x 50 element case was 1.1 km.

Temporal Resolution

There was little qualitative diﬀerence between the displacement (U), reaction force (F), and maximum principal stress (PS) at location b (see Figure 4.2) for the diﬀerent temporal resolutions after an abrupt change in wind direction at 1800 s (Figure 5.11). Convergence of model output occurred with decreasing time step (Figure 5.11a), and Figure 5.11b, c illustrates numerical instability at higher time steps. Time steps larger than 10 s were computationally unstable. A 1 s time step was used for further modelling studies to balance computational stability with memory considerations.

68 5. Results

Figure 5.10: Box plots of maximum principal stresses at each of the four corners of the mesh at 10 x 10 (black), 25 x 25 (red), 50 x 50 (blue), and 75 x 75 (purple) element resolutions. The mean for each location and resolution are shown as blue diamonds.

69 5. Results

Figure 5.11: Time series of displacement (U), reaction force (F), and maximum principal stress (PS1) for changing temporal resolutions (dt) when wind direction changed abruptly at t = 1800 s. Diﬀerent line colours indicate the time series at the same node/element for diﬀerent temporal resolutions.

70 5. Results

5.2.2 Numerical Experiments

The idealized simulations described in this section were compared against a standard case with 50 x 50 element spatial resolution, 1 s time step, and model run length of 21600 s (6 hours). Winds were 5 m/s, 45° from the SW, and there was no current stress in this case. An average of the stresses within the ﬁve regions shown in Figure 4.2 at time step 10800 were calculated for all the numerical experiments described in the following sections, and are summarized in Table 5.1.

Table 5.1: Mean and standard deviation of maximum principal stress (PS1) within diﬀerent regions for diﬀerent model runs at t = 10800 s unless otherwise noted. Tension is positive, compression is negative. Bold values indicate maximum stress for each case.

Casename PS1 NW (kPa) PS1 mid (kPa) PS1 NE (kPa) PS1 SW (kPa) PS1 SE (kPa) GS_50x50_standard 0.39 0.27 0.30 0.17 0.30 0.15 0.45 0.16 0.31 0.18 GS_50x50_mpropH 0.65 0.48 0.67 0.31 0.61 0.29 0.78 0.30 0.56 0.39 GS_50x50_mpropT 0.38 0.23 0.22 0.15 0.24 0.13 0.42 0.15 0.28 0.13 GS_50x50_mpropY1 0.37 0.22 0.20 0.13 0.21 0.11 0.41 0.13 0.27 0.09 GS_50x50_mpropY2 0.41 0.31 0.44 0.22 0.40 0.19 0.51 0.20 0.37 0.29 GS_50x50_10ms* 1.6 1.2 1.7 0.77 1.5 0.74 2.0 0.75 1.4 1.0 GS_50x50_15ms* 4.0 3.1 6.3 2.4 4.9 2.3 5.3 2.4 4.1 3.8 GS_50x50_20ms* 7.7 6.3 16.0 6.4 11.0 5.4 12.0 6.2 10.0 10.0 GS_50x50_sinwind 7.4 6.1 16.0 6.4 11.0 5.1 11.0 6.1 9.9 10.0 GS_50x50_NEwind 0.09 0.18 0.29 0.11 0.20 0.15 0.34 0.26 0.39 0.18 GS_50x50_NWwind 0.12 0.13 0.11 0.02 -0.02 0.08 0.25 0.07 -0.06 0.13 GS_50x50_SEwind 0.11 0.12 0.16 0.07 0.24 0.10 -0.06 0.09 0.31 0.13 GS_50x50_current 0.09 0.05 0.04 0.03 0.04 0.02 0.10 0.03 0.07 0.02 GS_50x50_wind-current 0.50 0.36 0.45 0.22 0.42 0.21 0.58 0.22 0.41 0.26 GS_50x50_wind-diﬀcurr 0.28 0.18 0.19 0.11 0.19 0.10 0.32 0.12 0.22 0.11 GS_50x50_wind-sincur 1.0 0.76 1.1 0.49 0.97 0.47 1.3 0.48 0.90 0.62 * Average maximum principal stress at t = 1800 s.

71 5. Results

Standard Case

A time series plot of the displacement, reaction force, principal stress, and principal strain for the standard case at one element at location a (see Figure 4.2) is shown in Figure 5.12. Initially, elastic strain and delayed elastic strain dominated material deformation, but after approximately 1800 s (black vertical dashed line in Figure 5.12), the importance of delayed elastic strain decreased signiﬁcantly, and viscous strain became more important, which is several orders of magnitude smaller than elastic and delayed elastic strain. After three hours, approximately 90% of the maximum principal stress at six hours was modelled in all elements in the standard case. The rest of the idealized simulations were run for three hours unless otherwise noted, with the same material properties as the standard case except for the cases with mprop in the case name, but with variable wind and current forces and one case (GS_50x50_hc) modelled leads by removing elements from the mesh south of a cross-inlet lead. Understanding patterns in maximum principal stress throughout the mesh in the standard case provides a reference for understanding changes in maximum principal stress due to variable material properties and environmental stresses. Regions of tensile (positive) stress are of interest here due to the potential for ice fracture if internal stress exceeds the tensile strength of the ice, while compressive stress may lead to ice ridging, which is not as relevant for studying break-up. After six hours of constant 5 m/s wind from SW, the western side of the mesh was mainly in tension, with the highest stress magnitudes closest to the shore (Figure 5.13). A region of weak compressive stresses formed in the middle of the inlet closer to the eastern side. A combination of tensile and compressive stresses occurred along the eastern shore, and stress was sensitive to protrusions of the shore, a feature which is described further in Section 5.2.3. The northwestern extent of the mesh had some compressive stresses, and tensile stresses formed near the two corners of

72 5. Results

Figure 5.12: Time series of (a) displacement (U), (b) reaction force (F), (c) maximum principal stress (PS1), and (d) maximum principal strain (E1) for the standard case at one location (see point a in Figure 4.2). Black vertical dashed line indicates the time when viscous strain begins to dominate over elastic and delayed elastic strain. the southern extent of the mesh, although it was unclear if the stresses modelled in these regions were realistic, or artifacts of the boundary conditions.

73 5. Results

Figure 5.13: Principal stresses for standard case at t = 21600. Maximum principal stress (PS1) contours shown in the background of the mesh. Compressive (black) and tensile (red) stress tensors of maximum and minimum principal stress superimposed on contours. Arrow shows direction of 5 m/s wind.

Material Properties

Several model runs were conducted testing the effect of modifying ice thickness, ice temperature, and Young’s modulus as shown in Table 4.5 on model output. Material properties govern two main properties of sea ice: ice strength (Section 5.1.3), and the internal stress and strain response of the ice to applied forces. The following experiments investigated the effect of changing the latter property. Increasing the ice thickness increases the momentum of the element, which resulted in reduced displacement and internal stress when the ice thickness was 1.6 m (standard case) compared to when the ice thickness was 1.0 m (Figure 5.14a, black and blue lines). Decreasing the ice temperature decreases the delayed elastic creep constant, which increases the delayed elastic strain. Ice at lower temperatures is stiffer (i.e. less susceptible to deformation), which resulted in decreased displacements and stresses over time for the case where the ice temperature was -10 ° C (red line)

74 5. Results compared to the standard case where the ice temperature was -2 ° C (black line). Changing the ice thickness had the largest effect on the model output. Young’s modulus is the main parameter governing the stiffness matrix used in the FEM, which affects the response of the ice to applied forces. Decreasing Young’s modulus decreases the ratio of stress to strain (Timco and Weeks, 2010), which decreased the overall stress after three hours compared to the standard run (Figure 5.14b, green line). Conversely, increasing Young’s modulus increases the stress to strain ratio, which increased the overall stress within an element compared to cases with lower Young’s modulus (Figure 5.14b, purple line).

Figure 5.14: Time series of displacement (U) and maximum principal stress (PS) with changing material properties. Diﬀerent line colours indicate the time series at the same node/element for diﬀerent material properties. Displacements and principal stresses are plotted at a node and element at the northeast section of the mesh (see point b in Figure 4.2 for location). T8 indicates ice temperature, h8 indicated ice thickness, Y indicates Young’s modulus.

75 5. Results

The largest range in maximum principal stress between the different cases occurred in the middle of the northern part of the mesh (Table 5.1, PS1 mid). Changing Young’s modulus while fixing the other material properties produced a range of maximum principal stress from 0.20 - 0.67 kPa, a 108 % difference. Increasing the ice thickness from 1.0 m to 1.6 m reduced the maximum principal stress by 76 %. Reducing the ice temperature by 8 °C decreased the maximum principal stress by 31 %. Increasing Young’s modulus by 38 % increased the maximum principal stress by 120 %. In all cases, the maximum principal stresses were quite low, less than 1 kPa on average, much lower than the assumed ice strength. In all cases, nodal displacements were initially high due to the elastic response of the ice, although after about 300 s, displacements grew at a much slower rate (Figure 5.14a). Principal stresses initially spiked, especially for the case with decreased ice temperature (Figure 5.14b). This initial spike in stress was relaxed by the viscous and delayed elastic strain, which then grew over time after 600 s. For most of the model runs, principal stresses grew almost directly proportional to the displacements (Figure 5.14).

Wind Speed and Direction

Several model runs showed the eﬀect of changing the wind speed and direction on the location and magnitude of principal stresses. Increasing the wind speed linearly increased the displacements and principal stress exponentially (Figure 5.15). Wind speeds above 15 m/s sustained for longer than 3600 time steps caused instabilities in the model, producing stresses that went to inﬁnity. Higher wind speeds became unstable more quickly. In Figure 5.15, numerical instabilities can be seen in the 20 m/s case around 2100 s. This is likely because FEMs are designed for small displacements, but at higher wind speeds, nodal displacements exceeded 50 cm. Irregularities in the mesh at the northwest corner of the mesh may also have caused instabilities in the model. Over time, the 5 and 10 m/s cases reached an equilibrium

76 5. Results state where there were negligible changes in displacement and stress magnitudes, whereas instabilities can be seen in Figure 5.15 after t = 2100 s in the 20 m/s case.

Figure 5.15: Time series of displacement (U) and maximum principal stress (PS1) with increasing wind speed. Displacements and principal stresses are plotted at a node and element at the northeast section of the mesh (see point b in Figure 4.2 for location).

When the wind speed was increased but the wind direction was kept the same, a region of high tensile stress formed initially near the bend along the west shore, which spread northeast towards the middle of the floe edge. This effect can be observed in the animation in Appendix B for the standard case, and when wind speed is increased, with greater stress magnitudes and larger stress centres form. Another centre of tensile stresses occurred at the NE corner of the mesh, which combined with other stress centres at the northern floe edge. The magnitude of principal stresses increased from an average of 0.37 kPa in the NW corner in the standard (5 m/s) case, to 7.7 kPa in the 20 m/s case after 1800 s (Table 5.1, standard

77 5. Results case at t = 1800 s not shown). A region of high compressive (negative) stresses occurred near the eastern shore almost directly across the inlet from the region of high tensile stresses which can be seen in the standard case (Figure 5.13), but the magnitude of compressive stresses increased with increasing wind speed. In all stable cases, ice stresses caused by wind stresses alone were never large enough to exceed the assumed ice tensile strength (25 kPa), but regions with high tensile stresses have a greater potential to be regions where break-up potentially occurs. As speeds increased linearly from 0 to 20 m/s over 3 hours in GS_50x50_sinwind, principal stresses increased exponentially (Figure 5.16), but reached different magnitudes than in the cases with a sustained wind speed. The mean principal stress in the NE corner when the wind speed was 5 m/s, 10 m/s, and 15 m/s in GS_50x50_sinwind were 0.14 kPa, 1.1 kPa, and 4.1 kPa respectively, smaller than they were after half an hour of constant wind speed for these cases (Table 5.1). The other corners of the mesh showed similar patterns in stresses. Since the wind direction did not change, the locations of stresses did not change significantly between the constant wind speed case and increasing wind speed cases, just the magnitudes. If the ice strength was assumed to be 25 kPa, fracture could have occurred when the wind speed was at least 15 m/s (Figure 5.16). Wind direction affected the deformation of the ice relative to the shore, which changed the distribution of stresses and reaction forces, but did not substantially affect their magnitudes. Winds in Admiralty Inlet are primarily along inlet (NE - SW) (Section 5.1.1), but it has been noted that wind directions have become more variable in Admiralty Inlet in recent years (Ford et al., 2010). Winds from the east resulted in higher tensile stress in elements along the eastern shore, and compression tended to occur along the western shore (Figure 5.17b, c). Winds from the west resulted in higher tensile stress in elements along the western shore, and compression along the eastern shore (Figure 5.17a, b). NE winds produced similar results in maximum principal stress to SE winds in the middle of the northern part of the inlet, but larger

78 5. Results

Figure 5.16: Maximum principal stress (PS1) at the element with the maximum stress in the mesh (a) and wind speed (b) for GS_50x50_sinwind. Dashed line in (a) indicates the assumed ice strength. diﬀerences in magnitude between the two cases occurred on the western sides of the inlet (Table 5.1).

Ocean Currents

Currents in Admiralty Inlet ranged from 0 - 0.1 m/s (Section 5.1.2), resulting in current stresses that range from 0 - 0.05 Pa, about the same magnitude as the smallest wind stress. The average current speed measured in Admiralty Inlet was 3.6 cm/s, corresponding to a current stress of 0.007 Pa using equation 2.8. Current stresses acting on ice in Admiralty Inlet may only be important when wind stress is small. Currents had less of an eﬀect on ice stress than wind forces due to the lower magnitudes of currents observed when ice is present. With an average current of

79 5. Results

Figure 5.17: Maximum principal stress magnitudes and tensors for standard case (a), NE wind (b), NW wind (c), SE wind (d) at time step 10800. Arrows show the direction of wind at 5 m/s for each case. Tensile stresses are positive (red), compressive stresses are negative (blue). Distribution and locations of maximum tensile and compressive stresses changes depends on the direction of wind.

80 5. Results

0.04 m/s, the maximum mean stress was only 0.10 kPa, compared to 0.45 kPa for 5 m/s wind at the SW corner for both cases (Table 5.1). Current and wind forces in the same (opposite) direction increased (decreased) stress from the standard case almost linearly (i.e. equivalent to adding the stress from wind forced simulation and currents-only simulation together) (Table 5.1).

Leads

Removing elements south of the location of a cross-inlet lead (blue line, Figure 4.2) aﬀected the magnitude and distribution of stresses relative to the standard case, even though wind speed and direction were unchanged (Table 5.2). This case was numerically unstable after approximately 3000 s, but before numerical instabilities dominated, tensile stresses increased at the northwest corner of the mesh, and the region of compressive stresses in the middle of the mesh seen in the standard case was reduced in the cross-inlet lead case (Figure 5.18).

Table 5.2: Mean and standard deviation of maximum principal stress (PS1) within diﬀerent regions for diﬀerent model runs at t = 1800 s.

Casename PS1 NW (kPa) PS1 mid (kPa) PS1 NE (kPa) GS_50x50_standard 0.37 0.20 0.17 0.13 0.19 0.11 GS_50x50_hc 0.76 0.46 0.37 0.26 0.40 0.23

Displacements increased when the southern part of the mesh was eliminated. The maximum displacement of any node in the standard case was 1.1 cm near the middle of the floe edge. At the same node in GS_50x50_hc, the maximum displacement was 2.6 cm, more than double the displacement from the standard case. The location of maximum displacement was similar between the two cases, and the pattern of displacement near the floe edge was similar between the two cases (not shown). However, displacements at the southern extent of GS_50x50_hc were much higher and in a different direction from the standard case. In both cases,

81 5. Results

Figure 5.18: Maximum principal stress magnitudes and tensors for standard case (a), cross-inlet lead (b) at t = 1800 s. Tensile stresses are positive (red), compressive stresses are negative (blue). Magnitudes and distribution of stresses change when the mesh extent changes.

82 5. Results

Table 5.3: Reaction forces per unit length along the east and west shores at t = 10800 s and the percentage of reaction forces at each shore. Arrows show the direction of the reaction force relative to the shore. For example, down (south) arrows indicate the shore is preventing northward movement.

|AG=_ | |AG=_, | Casename Dir FAG= [%] Dir FAG= , [%] [N/m] _ [N/m] _ GS_50x50_standard 482 ↓ 53 496 ↓ 47 GS_50x50_10ms* 1953 ↓ 54 1952 ↓ 46 GS_50x50_15ms* 4467 ↓ 55 4302 ↓ 45 GS_50x50_20ms* 8025 ↓ 55 7551 ↓ 45 GS_50x50_sinwind 7968 ↓ 55 7616 ↓ 45 GS_50x50_NEwind 482 ↑ 53 496 ↑ 47 GS_50x50_NWwind 560 ← 62 404 ← 38 GS_50x50_SEwind 560 → 62 404 → 38 GS_50x50_current 118 ↓ 51 132 ↓ 50 GS_50x50_wind-current 607 ↓ 53 617 ↓ 47 GS_50x50_wind-diﬀcurr 357 ↓ 53 374 ↓ 48 GS_50x50_wind-sincur 1257 ↓ 54 1264 ↓ 46 GS_50x50_hc* 564 ↓ 56 524 → 45 * Reaction force at t = 1800 s. displacements increased away from the shore to a maximum near the middle of the inlet, but in GS_50x50_hc the displacements increase at a higher rate of change away from the shore than in the standard case.

5.2.3 Reaction Forces

The proportion and direction of reaction forces along each coast was sensitive to changes in the magnitude and direction of external forces, and the extent of the mesh. In the standard case, the proportion of reaction forces to total environmental forces at the eastern shore was 53 %, and along the western shore was 47 %, when the wind was 5 m/s from the southwest. Reaction forces keeping the ice fixed at the shore increased as wind speed increased, as expected (Table 5.3). Adding currents did not significantly affect the magnitude or proportion of reaction forces along each shore, as the current forces were small relative to the wind forces.

83 5. Results

The proportion of reaction forces at the east and west shores changed when the wind speed or direction changed (Table 5.3). Changing the wind direction while maintaining wind speed changed which shore had the greater proportion of reaction forces, but changing the v component of wind (north or south), while keeping the u component (east or west) constant did not affect the magnitude of the reaction forces (Table 5.3). When the wind was from the NW or SE, the reaction force was stronger along the eastern shore, with the same magnitude but different directions, whereas reaction forces were stronger along the western shore when the wind direction was from the SW and NE directions. Winds from the SW or SE increased the reaction forces closer to the floe edge, where break-out events are more likely to occur (not shown). The main difference between reactions forces due to changes in wind direction was the net direction of the reaction force along each shore (Table 5.3). Winds from the SW and NE predominately produced reaction forces alongshore, while winds from the NW and SW predominately produced reaction forces perpendicular to shore. This result may have implications for break-up in Admiralty Inlet, where only certain wind directions may permit an ice floe to navigate out of the inlet. Eliminating elements south of an assumed location of a cross-inlet lead changed the relative magnitudes of reaction forces between each shore slightly (Table 5.3). The force per unit length also increased in the cross-inlet lead case compared to the standard case because the reaction forces were distributed over a shorter distance along each shore, even though the environmental forces would have also decreased. Stresses and reaction forces were sensitive to shore line irregularities (Figure 5.19). Protrusions in the shore led to stronger tensile stresses downwind, and compressive stresses upwind of the protrusion. Reaction forces changed direction and magnitude accordingly to account for the relative changes in motion between the ice and the shoreline. These irregularities in the shoreline may be important for stabilizing the ice until the ice has melted out enough from the shore, or the environmental forces

84 5. Results acting on the ice allow the ice to navigate around these features.

Figure 5.19: Close-up of maximum principal stresses (PS1) and reaction forces along eastern shore with irregular shoreline at time step 10800 s for the standard case. Large black arrow indicates wind direction. Arrows along shoreline indicate reaction force magnitude and direction. Red (positive) contours indicate tensile stresses, blue (negative) contours indicate compressive stresses.

85 5. Results

5.3 Break-up 2019

The first major spring break-up event of sea ice in Admiralty Inlet occurred between June 27-28, 2019. During this event, a large ice floe broke off just north of Elwin Inlet on the eastern shore, along a pre-existing lead which ran across the inlet to the western shore ∼ 8 km south of Cape Crauford. This break-out event was identified to have occurred at approximately 22:30 local time on June 27, 2019 (02:30 June 28, 2019 UTC) from the time lapse camera located near Elwin Inlet (see Figure 3.1 for camera location). Five and a half hours before the break-out event happened, reanalysis data from ERA5 indicated winds in the region ranged between 0 - 8 m/s, with stronger winds on the eastern side of the inlet, and weaker winds on the western side of the inlet (Figure 5.20). Winds were initially mainly southerly, but around the time of break-up, winds on the western side of the inlet changed to northerly, while winds on the eastern side of the inlet remained northerly.

Figure 5.20: Time series of wind speed (a) and direction (b) from 12 ERA5 grid points in Admiralty Inlet from 5.5 hours before break-up to half an hour after. Time of break-up indicated by the vertical black dashed line.

86 5. Results

According to WebTide predictions of tides in Admiralty Inlet and tidal charts for Arctic Bay from the Canadian Hydrographic Service, the peak of high tide occurred just before the time of break-up, where sea surface elevations were at their highest and falling, and ocean current speeds were at a minimum (Figure 5.21). Before the break-out event occurred, currents were coming in from the north, but as the tide changed, the current direction changed to ﬂowing out of the inlet (coming from the south) (Figure 5.21). This break-out event occurred 4 days before a new moon, which usually corresponds with a spring or stronger tide.

Figure 5.21: Time series of current speed (a) and direction (b) from 6 WebTide markers in Admiralty Inlet from 5.5 hours before break-up to half an hour after. Time of break-up indicated by black dashed line.

The average wind speed at the time of break-up was 2.44 m/s, and the average current speed was 0.02 m/s. These values correspond with a wind stress of 0.008 Pa, and current stress of 0.002 Pa from equation 2.8. The length of the ice from the ice edge to where the lead where break-out started was about 30 km. The total wind and current force acting over length of the ice ﬂoe that broke out was 240 N/m and 60 N/m. Using a similar analysis for failure in tension as Druckenmiller (2011)

87 5. Results assuming an ice thickness of 1.6 m and a tensile strength of 25 kPa (Tremblay and Hakakian, 2006), the ratio of the stress acting on the ice to the strength of the ice would be 0.006 and 0.002 for wind and current stresses respectively. This indicates that neither stress would have been strong enough to overcome the tensile strength.

5.3.1 Time Lapse Imagery

The time lapse cameras showed the evolution of melt ponds and the deterioration of ice at the shoreline throughout June until the ice was completely clear from Admiralty Inlet by mid-July. Links to the videos of the time-lapse cameras can be found in Appendix C and D. The field of view of the camera from Sujartalik contained a large lead which extended across the inlet. Melt ponds formed around June 9, 2019, and ice at the shore started to move around June 27, 2019. The landfast ice in the field of view of this camera started to move around July 2, 2019, and the ice was completely cleared from the camera field of view on July 6, 2019, with drifting ice passing through periodically until July 15, 2019. A major break-out event occurred in northern Admiralty Inlet on June 27, 2019 (Figure 5.22) and this event was captured in the field of view of the camera near Elwin Inlet. The opening of a large lead can be seen near the horizon on June 28, 2019, 02:30 UTC (June 27, 2019 11:30 EDT) from this camera. Several weeks before break-up, melt ponds formed on the ice in Admiralty Inlet, which continued to grow throughout the month as above-zero air temperatures were maintained. Initially, a tidal crack allowed vertical motion of the ice as water level rose and fell with the tides below the ice, but horizontal motion wasn’t able be accommodated as there may have been some frozen leads along the shoreline preventing horizontal motion (Figure 5.22, top-right). Over time, melting at the shoreline increased until a significant amount of open water was present, allowing lateral motion of ice along the shoreline, and suggesting that the ice was not entirely landfast during this time

88 5. Results

Figure 5.22: Left: Sentinel 2 image on June 29, 2019 with locations of cameras and approximate camera ﬁeld of view. #1 indicates the camera at Sujartalik, and #2 indicates the camera at Elwin Inlet. Top-right: photo from time lapse camera at Elwin Inlet at 19:00 EDT on June 7, 2019. Bottom-right: photo from time lapse camera at Elwin Inlet at 19:00 EDT on June 30, 2019. Note substantial expansion of the shore lead in the bottom image.

(Figure 5.22, bottom-right). The ice floe that broke away broke along a pre-existing lead located several kilometers from the shore at Elwin Inlet, and ice was completely cleared from the field of view by July 10, 2019 at the Elwin Inlet camera. The cross-inlet lead where the ice floe broke off cannot be seen clearly in the time lapse photos before the break-out event, but when break-out occurs, the opening of the lead can be seen clearly in the band of open water that occurs between the nearshore ice and the ice floe that broke away. This lead can also be seen in high-resolution SAR imagery in the days before the break-out event occurred. In the week before break-up occurred, ERA5 air temperatures in Admiralty Inlet rose from an average of ∼0 °C on June 22, to greater than 7 °C on the day break-up occurred (not shown). During that time, deterioration of the shore lead was observed in the time lapse camera, and small ice floes became mobile between the shore and the ice extension across the shore lead. There were likely few grounded

89 5. Results ridges, and hence few points anchoring the ice in place, making it more susceptible to even small wind and current forces causing the ice to detach from the shore.

5.3.2 Modelling Break-up

A realistic case for modelling break-up in the FEM was designed to evaluate the conditions during the break-out event in June 2019 described in the previous section. The maximum stress at the end of the run were around 0.77 kPa at the SE corner which did not exceed the assumed ice strength. A concentration of stresses started at the southeastern shore, which progressed to the northwestern corner and spread across the ﬂoe edge (Figure 5.23, Appendix E). Alternating regions of compressive and tensile stresses were modelled along the western shore around the time of break- up, which are likely due to the slight curve in the western shore. Tensile stresses occurred in the middle of the shore near the peak of the curvature, surrounded by compressive stresses north and south of the peak as ice deformed away from the peak of the shore. During the time of break-up, wind forces were more signiﬁcant than current forces (Figure 5.24) and just before the estimated time of break-up (02:00 June 28, 2019 UTC), the wind force comprised 82 % of the total force acting on the ice, while the currents comprised only 18 % of the total force acting on the ice. The mean wind speed at break-up was 2.4 m/s, with southeasterly winds on the eastern side of the inlet, and northwesterly winds on the western part of the inlet (Figure 5.23). The mean current speed at break-up was 0.02 m/s, approximately from the south. Reaction forces were stronger along the eastern shore than the western shore by 4.9 times. The total reaction force at break-up along the eastern shore was 11.5 MN towards the east (ice deforming away from shore), and 0.78 MN towards the south-east (ice deforming north slightly towards the shore) along the western shore.

90 5. Results

Figure 5.23: Maximum principal stress for the realistic case at time step 19800 (02:30 on June 28, 2019 UTC). Tensile stresses are positive (red), compressive stresses are negative (blue). Black arrows wind direction at 02:30 June 28, 2019 UTC from ERA5.

While nowhere in the mesh did the internal stresses exceed the ice strength, the patterns of stresses and reaction forces did support the general pattern of break- up observed from satellite and time-lapse imagery. Elements along the eastern shore were in tension, and the reaction forces on the east shore were the strongest and to the south-east, indicating the ice was deforming towards the north-west. As seen in Figure 5.22, break-out occurred mainly along the eastern side of the inlet. Immediately after the ice ﬂoe began to move away from the shore, it broke into several pieces however, there was no evidence in the model to indicate these subsequent fractures would have occurred. In the hour before break-up occurred, both wind and current direction and magnitude changed. Magnitudes decreased for both, but more importantly, after about 01:00, current direction was to the north, which was more conducive to break-

91 5. Results

Figure 5.24: Total and sum of wind (F0) and current (FF) force magnitudes in the realistic case throughout the whole mesh (a) and normalized mean directions (colours correspond to legend entries in a) (b), and reaction forces along each coast (E = east coast; W = west coast) (c), and normalized net direction of reaction force along each coast (colours correspond to legend in c) (d) from 21:00 June 27, 2019 to 03:00 June 28, 2019 UTC. Black dashed line indicates the time of break-up. up. Initially, reaction forces along both shores were towards the north, but after a slight lag in the change in direction of environmental forces, the reaction forces along both shores were towards the south, indicating that there was a response in the ice due to the change in wind direction. The mechanisms for break-up in Admiralty Inlet in 2019 are discussed in further detail in Section 6.3.

92 6 Discussion

6.1 Environmental Forcing in Admiralty Inlet

6.1.1 Meteorology

As air temperatures in Admiralty Inlet warmed above the melting point of ice throughout June 2019, ice temperatures rose accordingly (Section 5.1). As ice warms, brine pockets increase in size to maintain phase equilibrium between the H2O molecules and sea salt ions (Petrich and Eicken, 2009). The increase in ice temperature and brine volume causes significant decreases in the ice flexural, compressive, and tensile strength (Timco and Johnston, 2002, this study). Observations of wind speed and direction were not available when break-up occurred in Admiralty Inlet, but they were available for the month preceding break-up and were compared with reanalysis products from NCEP and ERA5, and observations from the Arctic Bay Airport. Overall, there was very little correlation between the observed wind speeds and directions with these data sets (Figure 5.3). The spatial resolution of NCEP and ERA5 reanalysis products may not be high enough to resolve the topography of Admiralty Inlet, which has steep cliffs along the shore in some locations, which likely have a large influence on the wind speed and direction in this region. The topography around the Arctic Bay airport also influences the winds, making the winds in that location different than within the inlet, and thus unusable as a proxy for winds in Admiralty Inlet. While no data product was able to exactly match observations of winds within the inlet, wind speeds and directions from ERA5 had the highest R2 values, with 0.08 for wind speed, and 0.01 for wind direction, and was used to force the realistic

93 6. Discussion case model run of break-up (Section 4.3). Finding accurate reanalysis and forecast atmospheric products in the Arctic is a challenge due to the low coverage of conventional data available at high latitudes to assimilate into atmospheric models (Lawrence et al., 2019). Several atmospheric reanalysis products were validated against in-situ data of air temperature, humidity, and wind speed in Fram Strait by Graham et al. (2019), and ERA5 had the best correlation in mean wind speed and air temperature. Reanalysis products have been found to perform poorly over Arctic sea ice, but better for lower latitudes and over oceanographic settings (Cullather et al., 2016). The issue of the questionable accuracy of modelled winds need to be kept in mind when interpreting model results for the realistic case that was forced using modelled winds.

6.1.2 Surface Currents

The presence of ice reduces surface current speeds due to the reduced ability for wind fetch to influence surface currents (Weingartner et al., 2017). Measured current speeds were relatively low (0 - 5 cm/s), which is typical for the Arctic (Kwok et al., 2013), although currents may be higher in straits in the Arctic (Davis et al., 2019). At Cape Crauford, located at the boundary between Lancaster Sound and Admiralty Inlet, 10 m currents with maximum speeds of 90 cm/s were recorded, with a mean speed of 27.7 cm/s (Fissel and Wilton, 1978). Current speeds measured at Cape Crauford were likely higher than the ones we measured in Admiralty Inlet due to the proximity of Cape Crauford to Lancaster Sound, where the mean flow is on the order of 30 cm/s (Fissel and Wilton, 1978), while our measurements of currents were further into Admiralty Inlet, and surface currents may have dissipated due to ice-ocean interactions. A comparison of observations of currents in Admiralty Inlet with Webtide current predictions found that the tidal fluctuations in tidal speed and direction

94 6. Discussion in Webtide corresponded reasonably well with the observations (R2 = 0.2), except when the currents were coming from the north: Webtide predicted currents came from the north-east, while the ADCP observations suggested they came from the north-west (Figure 5.7). Webtide current data in the Arctic has been validated using ADCP data from Barrow Strait (Dunphy et al., 2005), and Webtide was found to be effective in modelling currents in that location. It is important to note that the time series of currents measured in Admiralty Inlet was not long enough to effectively separate the tidal component from mean flow. Since Webtide only models tidal variations in currents, it is unknown whether the difference between our current observations and Webtide were due to inaccuracies in Webtide, or due to other signals in our current observations.

6.1.3 Sea Ice Strength

Sea ice strength is a difficult quantity to measure and evaluate during the melt season. During break-out events, the flexural, tensile, and shear strength of sea ice are likely the most relevant measures of ice strength. Flexural strength prevents the ice from breaking due to changes in sea surface height, which may be substantial as the tidal range in Admiralty Inlet is 1 - 2 m (Canadian Hydrographic Service, 2019). Ice may fail in shear when the ice is subject to biaxial tensile and compressive stresses, which may occur when forces in different directions act on the ice. Tensile strength is relevant when environmental forces such as wind and currents act to pull the ice apart, and away from the shore. A wide range of values of tensile strength can be found in the literature, from 800 kPa from in-situ ice cores (Richter-Menge and Jones, 1993) to 25 kPa (Tremblay and Hakakian, 2006) from remote sensing techniques, while values for tensile strength used in sea ice models range from 0.6 kPa to 28 kPa (Plante et al., 2020). Ice strength is dependent on ice thickness, porosity, and temperature (Timco and Weeks, 2010), and there is thought to be a strong scale effect

95 6. Discussion on ice strength (Dempsey et al., 1999). In large-scale sea ice models, such as LIM and CICE, the tensile ice strength has been assumed to be a proportion of the compressive strength (Lemieux et al., 2016a), or to have no tensile strength at all such as in the case of pack ice, although this scheme is unsuitable for modelling landfast ice (Lietaer and Fichefet, 2008). Yield curves such as the ellipse curve (e.g. Hibler, 1979) or Mohr-Coulomb yield criterion (e.g. Dansereau et al., 2017) are often used in sea ice models to determine when the ice strength has been exceeded. König Beatty and Holland (2010) were the first to test the implementation of tensile strength in a dynamic sea ice model, which was used to parametrize grounding of ice ridges in shallow water and the resistance of landfast ice to offshore winds in deep water. Ice fracture can be caused by different failure mechanisms depending on the applied forces and the ice type (e.g. pack ice vs. continuous ice sheet) (Schreyer et al., 2006), which makes the application and interpretation of proper yield criteria difficult. Break-up in Admiralty Inlet occurs in late-June, early-July, when the ice is significantly ponded, and has likely lost much of its strength (Timco and Johnston, 2002). The calculated tensile strength decreased from 180 kPa to 120 kPa over the month of June (Figure 5.9) using the mean ice temperature from the SAMS and equations 4.1 and 4.3. Equation 4.3 only accounts for changes in brine volume on tensile strength, and equation 4.1 is known to be inaccurate during ice decay (Timco and Weeks, 2010). Predicted brine volumes reached 270 ppt, but according to work by Frantz et al. (2019), late melt stage ice can have a porosity of 500 ppt. If this is the case in Admiralty Inlet, and assuming the ice thickness remained constant, the estimated tensile strength would have been 89 kPa using equation 4.3. Dempsey et al. (1999) suggested that laboratory-scale measures of ice tensile strength should be scaled √ by 1/ ! for in-situ applications, where L is the characteristic length. Assuming a characteristic length (L) of 300 m (Dammann et al., 2018), a representative value for large scales, this would result in a tensile strength of 5.1 kPa. These rough

96 6. Discussion calculations illustrate the diﬃculty in applying an accurate ice strength criterion to determine where tensile fracture may occur in sea ice. No matter what the assumed ice strength, very few of the idealized cases resulted in internal ice stresses that exceeded ice tensile strength. This suggests that either the ice would have had to have been very weak during this time, or that the fracturing of ice may not be an important factor during break-up except when very strong forces are applied to the ice over sustained periods of time.

6.2 Numerical Experiments

The various factors affecting break-up studied in the numerical experiments can be broadly separated into two different categories: environmental factors (factors that are external to the ice), and ice properties and configuration (properties that are internal to the ice) (Figure 6.1). Winds and currents apply drag forces to the ice which generally operate at different magnitudes, but elicit similar responses in the ice. Thermodynamics is an environmental factor that was not modelled explicitly and includes a variety of processes, but implicitly affects ice properties and configuration through warming and melting of ice. Modifying the ice properties (i.e. ice temperature, ice thickness, Young’s Modulus) affects the mechanical response of ice to stresses, but the configuration of the ice (i.e. leads) may also affect ice stresses, and plays an important role in break-up in Admiralty Inlet. The factors associated with break-up that were investigated in the numerical experiments and will be discussed in detail in the following sections.

6.2.1 Material Properties

Ice thickness had the greatest eﬀect on ice deformation out of all the material properties tested in the numerical experiments. Level ice thickness measured in Admiralty Inlet in May 1999 and 2000 (Gorman, 2001) and May 2019 ranged from

97 6. Discussion

Factors affecting break-up

Environmental Ice Properties/ Factors Configuration

Thermodynamics Leads Young’s Modulus (Air/Water (Shore/ Current Wind Temperatures, Cross-Inlet) Solar Radiation) Speed Speed

Ice Temperature Ice Thickness Current Wind Direction Direction

Figure 6.1: Summary of the factors affecting break-up which were investigated in the numerical modelling experiments. Current/wind speed/direction discussed in Section 6.2.2. Thermodynamics affects all the factors under ’Ice Prop- erties/Configuration’, and is discussed in Sections 6.2.1, 6.2.3, and 6.2.4. Leads discussed in Sections 6.2.3 and 6.2.4. Ice temperature, ice thickness, and Young’s Modulus are discussed in Section 6.2.1. Items in the third level of the hierarchy with the same colour are considered to be in the same subcategory within the level.

0.8 m to 1.6 m. Air temperature in Admiralty Inlet remained consistently above zero by mid-June, which likely led to melting of the ice and reduction of the ice thickness (Figure 5.1). Some basal melting may have been measured by the SAMS, when temperatures at nodes that were initially in the ice rose above the melting point of ice, although melt rates in Admiralty Inlet were not derived in this study. Basal melt rates can range from 1 - 2 mm of melt per day (Lei et al., 2018), to several cm per day (Launiainen and Cheng, 1998) during the spring, depending on the atmospheric and oceanic heat ﬂuxes to the ice. Landfast ice in the Arctic reaches a maximum thickness of ∼2 m in late-April to late-May in several locations in the Arctic (Bilello, 1980; Howell et al., 2016), and completely decays/break-up by mid-July, a period of about 2 months where ice properties can change dramatically. Temporal and spatial variability of ice thickness was not examined in this thesis,

98 6. Discussion but reducing the ice thickness parameter increased the modelled internal ice stress (Table 5.1). Ice stress increased in the thinner ice case because the applied forces were distributed over a smaller ice volume. All measures of ice strength would be reduced with thinner ice, and the combination of increased stress and reduced ice strength would suggest that ice thinning or regions in Admiralty Inlet with thinner ice may be areas where ice fracture is more likely to occur. Petrich et al. (2012) found that landfast ice failed preferentially below melt ponds where the ice had either melted completely or weakened enough to fail under moderate forces, but regions of unponded level ice did not fracture during break-up. Melt ponds extensively covering the ice surface by mid-June were seen in the time lapse imagery (Appendix C, D), and may have contributed to the subsequent break-up of the ice floe that detached from the shore on June 27, 2019 due to weakening of the ice. Colder ice temperatures reduced displacements and stresses slightly in the simulation, which is expected as colder ice is stronger due to smaller brine inclusions (Frantz et al., 2019). Ice temperature also affects the creep properties of ice (Mellor and Testa, 1969), where higher temperatures result in a higher creep rate, leading to more deformation. This may explain the higher stresses within warmer ice (Table 5.1), as the warmer ice accommodates applied forces by increased viscous deformation in the ice, and internal stress is proportional to strain in the model used here. Changes in ice temperature likely have more of an effect on the strength of the ice than on short-term ice deformations. Changes in Young’s modulus had modest effects on displacement and stress, although divergence in output between the model runs with different values for Young’s modulus becomes more apparent over time in Figure 5.14. Initial differences in displacement and stress between the different cases would be due to the differences in the elastic response of the ice due to the change in Young’s modulus. Over time, delayed elastic strain would become more significant, which is indirectly related to Young’s modulus due to its effect on the internal stress of each

99 6. Discussion element. Young’s modulus tends to decrease with brine volume (Timco and Weeks, 2010), which was shown to vary substantially during ice decay in Section 6.1.3. Progressively reducing Young’s modulus has been used as a method for implicitly modelling how cracks and faults affect ice mechanical properties (Girard et al., 2011) and may be relevant here for modelling inhomogeneities in the ice surface, and the propagation of cracks. Changing material properties (e.g. ice thickness, temperature) has the double effect of changing the ice’s response to external force, while also changing the ice strength, both of which affect the susceptibility of ice to fracture and break-up. These numerical experiments were highly idealized, and the effect of changing multiple material properties at once was not tested. However, these results suggest that the FEM was most sensitive to ice thickness, and this parameter should be initialized as accurately as possible in the FEM for modelling break-up. The FEM was also sensitive to Young’s modulus, which would tend to decrease during melt, decreasing ice deformation. It is unclear whether the opposing effects of decreased ice thickness and Young’s modulus on ice deformation would negate their effects in the model results if both properties were changed, and this could be a subject for further study.

6.2.2 Winds and Currents

Linear increases in wind and current speeds led to an exponential increase in the displacements and stresses within the ice (Table 4.6), as expected due to the squared power dependence of environmental stress on wind and current speed (Equation 2.8). The distribution of stress depended mainly on the direction of the wind. It’s important to note that the internal stress distributions changed over time and increasing the environmental stress magnitude caused the rate of propagation of stress within the mesh to change.

100 6. Discussion

Wind and current direction may affect whether an ice floe is pushed out of the inlet or not. Depending on if the winds and currents act in the same or opposite directions, the net direction of environmental forces acting on the ice may be different than either component. Environmental stresses are added linearly to the ice, so the relative contribution of the current or wind stress is not as important as the net environmental stress that is applied. It is generally assumed that offshore winds, or in the case of narrow straits, along-inlet winds, are more likely to cause break-out events to occur (Jones et al., 2016; Rallabandi et al., 2017). Cross-inlet winds likely do not have a significant effect on the motion of the ice during the winter due to the constraint of the land boundaries of the inlet, but may have more of an effect during the melt season when sufficient melt has occurred at the shores. Using a discrete element model, Konietzky et al. (2018) found that increases in wind speed could drastically reduce the area of landfast ice area in the Kara Sea, and changes in wind direction could modify the configuration of landfast ice in that region. The results from the numerical experiments show that the configuration of both the magnitude and direction of environmental forces can have a substantial effect on resultant ice deformation. In general, winds had a greater effect on sea ice stress than currents due to the greater range of wind magnitudes that can occur within Admiralty Inlet, despite water having a higher drag coefficient than air. This is likely because the current speeds input into the model in most cases were low (0.07 m/s), which were typical for what was observed in Admiralty Inlet before break-up occurred. Much is unknown about the spatial and temporal variability of currents in Admiralty Inlet, so there is the possibility that currents near the mouth of Admiralty Inlet are stronger and may contribute more significant stresses to ice near the floe edge. The magnitude of wind and current stress necessary to cause ice to break-up depends on the strength of the ice, and the area of ice in question (i.e. the larger the landfast ice area, the greater the magnitude of wind and current stress necessary

101 6. Discussion to cause break-up). In most of the idealized cases with winds and currents, the resultant ice stresses would not have been high enough to lead to ice fracture (Table 5.1). This result is supported by Dammann et al. (2018), who suggested that wind and current forces have limited effect on landfast ice stresses based on ice stresses derived from synthetic aperture radar (SAR) interferometry. Jones et al. (2016) showed examples of break-out events that occurred when environmental (wind and current) stresses were both low and high. If a break-out event occurred when environmental stresses were low, preconditioning of the ice due to compacting of ice keels and the enlarging of tidal cracks due to flexural failure of the ice were suggested to have played a role in break-out in that study. The possibility of preconditioning of the ice in Admiralty Inlet due to pre-existing cross-inlet and shore leads is discussed in Section 6.2.3. In the standard case where 5 m/s winds from the southeast for 6 hours resulted in a maximum stress of 1.3 kPa within one element. At this element, 90 % of this stress was achieved after 3.6 hours, suggesting that after a certain time interval, environmental forces acting at a constant speed and direction will not result in substantial deformations in the ice. External stress is relieved by strain and in the FEM used here, the total strain of an element is composed of elastic, delayed elastic (primary creep), and viscous (secondary creep) strain. With sustained external stress, the elastic and delayed elastic components of strain can become maximized, and if further external stress is applied, only viscous strain can relieve the applied stress, which is several orders of magnitude smaller than the elastic and delayed elastic components of strain. Body strain causes internal stress, so when viscous strain dominates, strain changes little over time, and thus stress does as well. Viscous strain may become significant over seasonal time scales (Dammann et al., 2016), but on the time scale of break-up (hours to days), viscous strain is insignificant, and we are more interested in elastic deformations in ice.

102 6. Discussion

6.2.3 Cross-Inlet Leads

Cracks and leads were not modelled explicitly, but the southern extent of the mesh was reduced by removing elements south of an assumed cross-inlet ’lead’ location so the conditions acting on an ice sheet preconditioned for break-up due to the presence of cross-inlet leads could be examined. Although this case was numerically unstable, at a time when the model was thought to be stable, the maximum principal stresses were greater in the case with a lead than the standard case (Table 5.2). Reducing the area of the mesh would have decreased the net environmental forces acting on the mesh, but the geometry of the two meshes was very different. The ratio of boundary nodes to free nodes along the extents of the mesh were much reduced in the lead case, which may have contributed to the numerical instability, but may have also given the mesh more freedom to deform, resulting in increased stresses. The reaction forces per unit length of the shoreline also increased relative to the standard case, likely because the length of shore the environmental forces were acting over was reduced, increasing the reaction force per unit length of the remaining shoreline. More work is needed to study the effect of different ice configurations on ice deformation, but preliminary results suggest that the distribution and concentration of stresses can change substantially with changes in ice configuration.

6.2.4 Reaction Forces and the Shoreline

The total sum of the reaction forces from both coasts is equivalent to the net environmental forces acting over the whole mesh, and the proportion of reaction forces acting on one shore or the other is an indicator of the forces acting to separate the ice from the shore. The direction and proportion of reaction forces along the east or west shore was highly sensitive to the wind direction (Table 5.3). Changing the extent of the mesh in the lead case had an eﬀect on the net direction of the

103 6. Discussion reaction forces along the western shore, which may have been due to the change in the geometry of the mesh, where a greater portion of the mesh was oriented perpendicular to the direction of the wind, whereas in the standard case both shores on the bottom portion of the mesh were oriented almost parallel to the direction of the wind, which is reflected in the net direction of the reaction force for that case. Reaction forces represent a number of grounding forces that maintain landfast ice including bottomfast ice (ice frozen to the seafloor) and grounded pressure ridges. In Admiralty Inlet, the general shape of the shore may act as a physical barrier for ice motion, depending on the direction of external forces and the net motion of the ice. Anchoring strength has been estimated to range from < 0.01 kPa to 2 kPa in Alaska by Mahoney et al. (2007a), but Lemieux et al. (2016a) predicted basal stress associated with grounding of 0 to 0.2 Pa without tides, and 0 to 0.26 Pa with tides in a pan-Arctic ice-ocean model, which is several orders of magnitude less than what Mahoney et al. (2007a) found. Basal stress estimated by Lemieux et al. (2016a) was smaller than those estimated by Mahoney et al. (2007a) because the method of calculating the basal stress and the scales of the two studies were very different (Pan-Arctic vs. local). Jones et al. (2016) estimated the grounding strength of the ice on the sea floor in Alaska in February which was on the order of 6.6 x 104 kN from ice ridge coupling with the sea floor, which was approximately 4.4 kPa over their 15 km study area. This value (6.6 x 104 kN) is larger than the net reaction forces modelled for 5 m/s winds along one shore of Admiralty Inlet (2.5 - 2.8 x 104 kN). Grounded ridges are less likely to form in Admiralty Inlet due to the steep nearshore bathymetry, so grounding forces were likely lower in Admiralty Inlet than in Alaska, although more work is necessary to quantify this. The magnitude and direction of reaction forces were sensitive to irregularities at the coast (Figure 5.19), which may indicate that protrusions of the shore may play a role in stabilizing landfast ice. Downwind of a protrusion, compressive stresses form in the ice and reaction forces act to resist ice deformation towards the shore,

104 6. Discussion while tensile stresses and reaction forces keeping the ice in place act upwind of a protrusion. The FEM does not model advection of the ice, but for ice downwind of a protrusion to be able to break-up, either environmental forces would need to act to move the ice away from the shore, or the shore lead would need to have widened suﬃciently for ice to navigate easily around the protrusion. Preconditioning of the ice for break-up through melting at the shoreline has been suggested to play a signiﬁcant role for break-up in Alaska by weaken attachment to the shore by Mahoney et al. (2007b). During late spring in Admiralty Inlet there may be little to no resistive forces acting to keep the ice in place due to shoreline melt, which may explain why the ice broke out in 2019, even though environmental forces were very weak. This hypothesis will be discussed more in the next section.

6.3 Break-Up 2019

There are three main factors that may delay break-up in Admiralty Inlet: the internal strength of the ice, interactions between the ice and the shore, which may include grounded ridges, frozen tidal cracks, or bottomfast ice, and length of continuous ice from the Northern ice edge in Admiralty Inlet. Preconditioning of the ice before the break-out event in 2019 was likely critical to allow the ice to become mobile. Processes involved in preconditioning of the ice may have included the formation of cracks and leads across the inlet or along the shorelines due to melting, ﬂexural failure due to changes in sea surface slope or waves, or tensile failure due to winds or currents. Around the time of break-up, some pack ice from Lancaster Sound came up against the ice edge in Admiralty Inlet, and may have applied shear forces locally to the ice at the ﬂoe edge. A month before break-up occurred, ice at the shoreline was not able to move freely, as was seen in the time lapse imagery. Water depths in Admiralty Inlet are more than 20 m less than a kilometer away from the shore, meaning that grounded

105 6. Discussion ridges are not a key stabilizing feature in this region, like they are for maintaining landfast ice along the north shore of Alaska (Jones et al., 2016), but may provide stabilizing points where they do occur in Admiralty Inlet. Floating offshore ice was separated from nearshore bottomfast ice by a tidal crack located a few meters from the shore, which was initially very narrow, and only allowed vertical motion of the floating ice due to changes in sea surface height. As air temperatures rose, significant ponding formed on the surface of the ice, and more importantly, substantial nearshore melting occurred, widening the tidal crack and allowing small ice blocks to move freely between the shore and the ice floe during high tide. River runoff may have also contributed to nearshore melting by introducing warm water under the ice, and has been found to play a role in the detachment of landfast ice in Alaska (Weingartner et al., 2017). Although only a small part of the shore was within view of the time lapse cameras, it is likely that melting along the shore occurred along the both coasts of Admiralty Inlet up to the northern floe edge. Initially, the grounded nearshore ice would have resisted forces pulling the ice away from the shore (e.g. wind, current, tides). Over time, the anchoring forces attaching the ice to the shore were likely weakened or eliminated. Once enough melting occurred at the shoreline, even a small pulling force may have been able to initiate a break-out event, which is likely what happened in Admiralty Inlet in 2019. During this break-out event, all the ice within the view of the camera moved, indicating that any previously anchored ice had already become detached, or any remaining anchoring forces were overcome by the environmental forces. The extent of preconditioning along the shoreline necessary to allow the ice to move likely depends on the extent and thickness of bottomfast and grounded ice. Empirical models of the number of melting degree days necessary before break-up can occur have been developed for different locations of the Arctic based on historical analysis of break-up (Petrich et al., 2012; Bell, 2017), and similar approaches could be

106 6. Discussion applied here to estimate the amount of melting necessary to precondition the ice for break-up. Thermodynamic models could also be used to simulate nearshore ice melt using physical principals, and could account for atmospheric, oceanic, and sediment heat fluxes to the ice (Leppäranta, 1993). For ice to move out of Admiralty Inlet, resistance to ice motion at both the shores and across the inlet must be overcome. Leads extending across Admiralty Inlet are known to form regularly in various locations throughout the inlet throughout the winter (Gorman, 2001), although the exact cause of these leads is not known. These leads form in approximately the same locations each year and may be caused by regular changes in sea surface slope which form throughout the inlet. In the winter, these leads open and close with changes in the tide, but in the spring, atmospheric and oceanic heating may cause these leads to expand and remain open, allowing ice north of the lead to become mobile. Once the shoreline attachments of the ice are removed, mechanisms related to ice arching may be relevant due to the study of break-up in Admiralty Inlet due to its geometry. Once the ice becomes detached from the shore, it may still remain within the inlet if it is ’jammed’ in to the inlet due to irregularities along the shore. In this case, the wind and current forces may have to act in an appropriate direction to allow the ice to maneuver out of the inlet. Some models of ice arching processes use the tensile and shear strength of the ice to apply a yield criterion (e.g. Mohr-Coulomb, ellipse yield curve), to determine where the ice may break-up if internal ice stress exceeds the yield curve (Dumont et al., 2009; Dansereau et al., 2017). The deterioration of the attachment of ice at the shore and the presence of cross-inlet leads provides some explanation for why the break-out event occurred when it did. Initially, the cross-inlet and shore leads may have been partially frozen, preventing horizontal ice motion. As was shown in the idealized cases, sustained wind speeds greater than 15 m/s and/or a combination of offshore wind and currents over the entire ice floe would have been necessary to cause the internal

107 6. Discussion strength of the ice to exceed the ice strength and initiate ice fracture. On June 10 - 12, 2019 wind speeds up to 10 m/s were observed and up to 20 m/s were modelled by reanalysis products in Admiralty Inlet (Figure 5.1b). However, air temperatures before that event were still near or below 0 °C (Figure 5.1a), and melting was likely not to have been initiated yet, so the ice strength would have still been fairly high at that time, and fracture would have been more difficult to initiate. Sustained above-zero air temperatures in the later part of June initiated the formation of surface melt ponds and warming of the ice, which would have reduced the ice strength, but following the strong wind event in mid-June, wind speeds were not very high for the rest of the month. Existing plane of weakness would have been necessary for the ice to break-up under weak environmental forces. This explains why internal ice stresses modelled in the realistic case did not reach any reasonable estimate of ice tensile strength (Figure 5.23), and why the ice broke-up even when environmental forces were at a minimum (Figure 5.24). While ice fracture was likely not what initiated break-up of the main ice floe, further break- up of the ice floe (Figure 5.22) may have been due to the existence of pre-existing locations of weakness or fracture in the detached ice floe, or additional sources of stress (e.g. waves, torque) applied to the ice after it became mobile causing the internal ice stress to exceed the ice strength. While internal ice stresses from the FEM were not able to suggest break-up, reactions forces at the shoreline were more useful indicators for break-up, which provided an estimate for the attachment forces necessary to keep ice in place at the time of break-up, and the net direction of deformation of the ice due to environmental stresses. Physically, the reaction forces represent a combination of resistive forces that may occur along the shoreline: grounded ridges, bottomfast ice, or protrusions in the shoreline. In the six hours before the break-out event was observed, the environmental forces acting on the ice floe that broke off were twice what they were when break-out actually occurred (Figure 5.24a). While

108 6. Discussion the attachment forces at the shore likely did not change significantly during that time, both the wind and current directions changed significantly around the time break-out occurred (Figure 5.24b) to directions more conducive to move ice out of the inlet. Initially, the net wind direction was towards the northeast, but the currents were towards the south. The wind force magnitudes were greater than the current force magnitudes, but as seen in the reaction force directions at the shorelines (Figure 5.24d), the net deformation of the ice was towards the south — into the inlet. Around 02:00 on June 28, 2019, the net direction of the reaction forces along both shorelines switched to predominately towards the southeast, indicating the net deformation of the ice was toward the northwest — out of the inlet. Satellite imagery shows the ice floe that broke away during this time drifted away from the eastern shore of Admiralty Inlet and rotated counterclockwise out of the inlet. At the time the ice broke out, nearly all the reaction forces were associated with the eastern shore, and there were negligible reaction forces along the western shore (Figure 5.24c), which supports general motion of the ice during break-up. Further work is necessary to determine if a criterion for reaction forces at the shore could be determined to predict future break-out events, but using the reaction forces in combination with the other environmental conditions present during break-up are useful for interpreting the break-out event in 2019. Other field and modelling studies of the break-up of landfast sea ice have identified similar processes and patterns related to break-out events in different places in the Arctic. Jones et al. (2016) studied breakout events in Barrow, Alaska, and found that for break-out events in February and March, the ice may have been preconditioned for break-out due to changes in water level, compacting the grounded ridges, and reducing their anchoring strength. These break-out events happened mid-winter, when air temperatures were far below zero, so ice strength was likely near its maximum, and thermal effects likely did not play a role in

109 6. Discussion these events. Petrich et al. (2012) found that break-up in Alaska was not associated with unusually strong winds, but strong oﬀshore winds were usually associated with mechanical break-up in this region, which agrees with our hypothesis that wind direction plays an important role in break-up. In the Kara Sea, ice bridges are suggested to have formed due to attachment of ice to the coast (Olason, 2016), although the speciﬁc attachment mechanisms were not described.

6.4 Sources of Error

In any computational model, resolving features in high-resolution leads to high computer memory requirements, which needs to be taken into consideration when designing numerical experiments. Increasing the model resolution increases the computer memory needed to store the output and model runtime exponentially. As was shown in Figure 5.19, internal ice stresses and reaction forces were sensitive to irregularities in the shoreline, and many shoreline features were not resolved in the meshes used for the numerical experiments. Having a high enough resolution mesh to resolve these features is important for accurately modelling ice-shore interactions, which may prevent the ice from breaking out. There are many unknowns about the winds and currents at northern Admiralty Inlet, as the strength and direction may be variable, and there may be eddy effects due to the changing topography and bathymetry where the mouth of Admiralty Inlet opens into Lancaster Sound. This, in combination with low confidence in modelled environmental products (especially winds, Section 5.1.1), means understanding break-up processes and elucidating the exact causes of a specific break-out event are difficult. Modelled environmental data is useful for estimating environmental conditions when observations are not available, but care must be taken when using modelled data and making conclusions about results from this data, as compounding errors may affect results.

110 6. Discussion

The ice tensile strength during melt is not well defined but is a key parameter for evaluating ice fracture. Few measurements of geophysical-scale ice strength during the melt season are available due to the difficulty of measuring this parameter logistically and accurately. The equations used to estimate tensile strength from measured ice temperatures may not be valid at high ice temperatures (Timco and Weeks, 2010), and may not represent ice tensile strength at geophysical scales anyway. Depending on what realistic values of ice tensile strength should be, the ice may be more susceptible to fracture than initially thought. In several of the idealized cases, numerical instabilities caused model output to produce unrealistic results. Approximation errors are inherent in numerical models (Kaliakin, 2002), but numerically unstable model cases magnify these errors over time. Typically, temporal and spatial resolutions must satisfy a stability criterion for a numerical method to be stable (e.g. Courant–Friedrichs–Lewy condition), although often the stability criterion cannot easily be explicitly defined, and stability is often determined using heuristic approaches (Kaliakin, 2002). One potential reason for the numerical instabilities may have been due to the strong curvature along the northern part of the western coast, which resulted in irregular element shapes, which affects the stability of the solution. Most of the cases that were numerically unstable were associated with increased wind speeds. Higher wind speeds result in higher stresses acting on the ice and larger deformations in the ice, which could have increased the irregularity of the element shapes on the northwestern side of the mesh. The cross-inlet lead case was also numerically unstable, which may have also been because of the irregularity of element shapes near the northwestern coast. Although wind speeds were not very strong in this case (5 m/s), the ratio of fixed nodes/free nodes was much reduced in this case, and much of the regular part of the mesh south of the bend in the western coast were removed, which may have magnified the effect of the irregular coast on the solution. More work is necessary to identify the exact causes of the numerical instabilities but

111 6. Discussion regularizing the mesh elements near the northwestern coast may improve results.

6.5 Model Limitations

The processes related to landfast sea ice break-up are complex, and while many of these processes were examined using the FEM, several key processes were not included in the model which may be relevant to break-up. In FEM used in this study, only wind and current forces were applied to the ice, but other forces, such as sea surface slope, may also play a role in break-out events. In addition, the FEM model was only designed to model small-scale deformations of ice but cannot model the advection of ice. This means that the trajectory of an ice floe that has broken off from a stable ice sheet cannot be predicted using this model. The effects of changes in sea surface slope due to tide or waves were not included in the FEM but can cause the ice to break in flexure (Jones et al., 2016). Leads extending across Admiralty Inlet form in mid-winter likely due to tidal changes in sea surface height are locations where break-out events are more likely to occur. Some break-out events may occur during periods of spring tide, where changes in sea surface height are at their greatest, and ice floes may drift out of the inlet under gravity. This force is not included in the model, but for an ice floe 50 km x 30 km − and assuming a sea surface slope () of 0.5 × 10 6 m/m estimated from Webtide sea surface elevations at different points in Admiralty Inlet, the stress on the ice cover due to gravity ( BBB = −8 ℎ8 6)(Druckenmiller et al., 2009) would approximately 0.007 Pa, and would exert a force over the whole ice floe on the order of magnitude of 10 MN, a similar order of magnitude of the wind and current forces (Figure 5.24a), and may play a role in break-up. Currently, no criterion was applied in the model to respond to instances when the ice stress exceeded ice strength. Ice stress only exceed ice strength in a few model runs, but such events did occur during sustained high wind stresses, where elements

112 6. Discussion near the northern and southern extents of the mesh exceeded the assumed ice strength over time. When internal stress exceeds strength, failure occurs, and stresses are redistributed (Wilchinsky et al., 2010), a process which is not currently captured in the model. Several approaches could be used to deal with cases for localized regions where ice stress exceeded ice strength, but before break-up occurred. A damage parameter could be applied to the Young’s modulus for elements where stress exceeded strength (e.g. Girard et al., 2011), or a full implementation of fracture dynamics could be introduced (e.g. Schreyer et al., 2006).

113 7 Conclusions

Although landfast ice makes up only 12% of all sea ice in the Northern Hemisphere (Li et al., 2020), it is critically important because it occupies the region between mobile pack ice and the shore — a region of strategic importance to many animals and to the Inuit who use it as a platform for transportation and traditional activities such as hunting. Proper parametrization of landfast ice is also important for large-scale ice models, but because of its relatively small extent, it has received much less study than drifting sea ice. The break-up processes of landfast ice in particular have received little attention, in part because the processes controlling break-up are numerous, poorly understood, and vary substantially between different locations. The first and second objectives of this study were to identify and determine the relative importance of the processes that control mechanical sea ice break-up in Admiralty Inlet. A visco-elastic FEM was used to calculate the stress states and patterns of stresses in the ice under simulated driving force regimes. The key factors contributing to the break-up of landfast ice in Admiralty Inlet that were studied here include: wind and current speed and direction, ice material properties (thickness, temperature, Young’s modulus), and the configuration of the ice (i.e. presence of cross-inlet leads). Model results showed that changes in ice thickness had the greatest effect on stress states, followed by Young’s modulus, then ice temperature. The net direction of environmental forces acting on the ice had a large effect on the distribution of stresses throughout the ice, while changing the magnitude of environmental forces affected the magnitude of ice stresses. Under typical conditions of winds and currents, the maximum principal stress modelled in the ice in space and time was on the order of 1 kPa. The tensile strength of ice during advanced stages of melt is highly uncertain, but here it was estimated to be

114 7. Conclusions on the order of 25 kPa. This suggests that large-scale fractures are not generated by specific wind or current events which then lead to break-up, but pre-existing cracks and leads must exist in the ice before break-up can occur. Pre-existing leads that run completely across the inlet in various locations, along with the development of shore leads on both sides of the inlet, are likely what control break-up in Admiralty Inlet. Once cross-inlet leads are developed, they offer little resistance to driving forces pushing ice out of the inlet. For break-up to occur, contact of ice with the shore must be reduced until local failure at the shoreline can occur under driving forces. Grounding of pressure ridges may occur very locally in the nearshore regions in Admiralty Inlet, which may help stabilize the ice, but play a much less important role in break-up here than in regions where water depth is shallow and gently sloping. Once attachments at both the shores and across the inlet are sufficiently deteriorated, ice floes can drift out of the inlet under minimal driving forces. Internal decay and subsequent weakening of the ice as air temperatures rise during the spring makes the ice more susceptible to further fracture due to stress once an ice floe has detached from stable ice. Small deviations in the coastline direction were shown to be areas of high localized stress and may be important pinning points which resist ice movement until the adjacent ice is sufficiently eroded. In general, the FEM showed that high tensile stresses occur when the wind is blowing offshore and high compressive forces occur when the wind is onshore. This is, in part, an artifact of the model since the boundary conditions at the ice-shore interface are fixed to have zero displacement. In reality, these tensile stresses may cause the ice to move away from the shore, increasing the size of the shore lead and removing some of the resistance to motion of the ice mass. High compressive stress against a shore may result in some deformation of ice (e.g. crushing, rubbling, ridging, or ice push), which would temporarily increase the contact of the ice to the shore, but would lead to further opening of the shore lead when the wind direction changed.

115 7. Conclusions

Additional factors that may play a role in break-up include sea surface slope and waves. The magnitude of the forces due to sea surface slope are thought to be less than those from winds and tidal currents, but may be significant in some break-up events. Wave-induced fracture at the floe edge may be important in removing ice locally but does not contribute significantly to major break-up events. The final objective of this study was to demonstrate the effectiveness of a FEM for modelling landfast ice break-up using a break-up event in Admiralty Inlet in June 2019 as a case study. Satellite imagery, and reanalysis and modelled products were used to initialize and force the FEM to simulate a break-out event in Admiralty Inlet in June 2019. Around the time of break-up, both wind and current forces decreased, but their directions changed, acting to push ice away from contact with the east coast which freed the floe to rotate and move out of the inlet. The FEM was successfully able to generate patterns of stress that were consistent with the observed motion of the ice during break-up in 2019. It is not possible to determine how effective the FEM is as a tool for predicting future break-up events by studying only one break-up event. Analysis of many more years of break-up events would be necessary for this. However, few models exist currently which predict the break-up of landfast ice, and this study shows the potential for an FEM to identify indicators for break-up. This study has highlighted the importance of preconditioning of ice before break- out events can occur, which has been identified previously by Petrich et al. (2012) and Jones et al. (2016). In Admiralty Inlet, the main preconditioning mechanisms include the existence of a cross-inlet lead, and sufficient deterioration of shoreline attachments. Preconditioning of the ice is a necessary, but not sufficient condition for break-up to occur in Admiralty Inlet, as driving forces must also act on the ice in a direction which allows the ice floe to navigate out of the inlet. Increased warming in the Arctic may enhance ice preconditioning and lead to break-up earlier in the season, while changing wind patterns may facilitate break-out events if they allow

116 7. Conclusions ice to move out of the inlet. Monitoring the state of cross-inlet and shore leads near the mouth of Admiralty Inlet through high-resolution satellite imagery or other means may help identify the risk of break-up in Admiralty Inlet for local ice users in the absence of predictive break-up models. The knowledge gained from this study about processes related to the break-up of landfast ice in a narrow strait contributes to the existing knowledge of landfast ice break-up. Many field studies of landfast sea ice break-up have focused on the north coast of Alaska (e.g. Mahoney et al., 2007a; Petrich et al., 2012; Jones et al., 2016), but a few of the critical processes related to break-up in Alaska are irrelevant in Admiralty Inlet due to the differences in coastal geography between the two regions. The main differences between the two regions are the lack of grounded ridges in Admiralty Inlet, and the heightened importance of coastal geometry for stabilizing ice in Admiralty Inlet. Some of the processes related to the stability of ice arches in narrow straits may be relevant here, such as dependence on the applied forcing and geometry of the strait for stability. However, previous studies of ice arching processes (e.g. Dumont et al., 2009; Rallabandi et al., 2017; Plante et al., 2020) have focused on ice arches formed from the interlocking of discrete ice floes, while in Admiralty Inlet, a continuous ice sheet forms, which may affect the mechanisms for ice stability. This work has raised many questions about the processes related to break-up in Admiralty Inlet, and how they may change from year to year. The processes affecting break-up in Admiralty Inlet may also be relevant for other locations in the Canadian Arctic Archipelago, where many constrained waterways can be found, and further work elucidating the general processes related to break-up may be useful for various regions in the Arctic.

117 7. Conclusions

Recommendations

To improve the ability to predict future break-out events, preconditioning of the ice needs to be included implicitly or explicitly, or taken into account when interpreting model results. Empirical (Petrich et al., 2012) or thermodynamic melt (Leppäranta, 1993) models could be developed or incorporated into existing models to simulate the deterioration of ice at the shoreline. Large-scale sea ice models currently in use (e.g. Vancoppenolle et al., 2012; Hunke et al., 2015) are typically run at spatial and temporal resolutions too coarse to model break-up processes at a regional scale, and often do not model landfast ice processes well. Additionally, the plastic flow yield criterion that is typical in these models is not suitable for modelling landfast ice break-up. Brittle fracture mechanics could be implemented to model localized fracture (Dansereau et al., 2016), and evolving boundary conditions at the shoreline could be developed to better represent the development of shore leads. Knowledge of ice tensile strength during melt and accurate meteorological and oceanographic forecast data are critical for predicting break-up. Little information is currently available about the tensile strength of ice during the melt season, and this is an important subject for further study. Reanalysis products of meteorological conditions, especially winds, did not correlate well with observations in Admiralty Inlet, and the accuracy of forecast products were not evaluated at all. For break-up to be predicted accurately using numerical modelling, both the physics of a sea ice model, and the input into the model, must represent the air-ice-ocean environment effectively. Analysis of historical data and additional field data of spatial and temporal changes of ice properties and meteorological and oceanographic conditions could be used to better understand the processes leading to break-out events. Data capturing the temporal and spatial variability of winds and currents in Admiralty

118 7. Conclusions

Inlet around break-out events are important to validate reanalysis products to evaluate the validity of using these products to understand historical break-out events. Additional information about how shoreline conditions change throughout the spring would provide critical information about the shoreline attachment forces that potentially need to be overcome before break-out events can occur. Time lapse imagery can provide easy-to-interpret information about conditions at the shore, but high-resolution satellite imagery may provide information about the large-scale stability of ice using SAR interferometry (e.g. Dammann et al., 2019). Only one break-out event was analyzed in detail in this study, but interpreting more break-out events using the FEM could provide a range of estimates of environmental and reaction forces that occur at the shore to make more general conclusions about the necessary and suﬃcient criteria for break-up to occur. Evaluating the attachment at the coast could provide insight to the condition of the coast during break-up. An explicit parametrization of pre-existing leads is currently in development to be implemented in the McKenna et al. (in revision) FEM which would facilitate studies of the eﬀect of cross-inlet and shore leads. In addition, analyzing historical break-out events using satellite imagery is planned for this project, which will identify reoccurring patterns or modes of break-up in Admiralty Inlet. Changes in the Arctic climate are expected to continue for the foreseeable future (Vincent, 2020), which will require ongoing adaptation by Inuit communities to safely continue traditional practices involving sea ice. This research corroborates existing Inuit knowledge of processes leading to break-up in Admiralty Inlet, and shows how these processes can be included in numerical models to predict landfast ice break-up. Adaptation to Arctic climate change will require innovation on many fronts, and this research advances the potential for using numerical models as a tool to assess the risk of landfast ice break-up.

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135 Appendices

Appendix A: Spatial Resolution Sensitivity

Figure A.1: Displacement magnitudes and vectors for 10 x 10 element (a), 25 x 25 element (b), 50 x 50 element (c), 75 x 75 element (d) resolutions at time step 10800. Note the displacement vector arrows are scaled diﬀerently for each spatial resolution. Arrows beside each mesh show the direction of wind at 5 m/s for each case.

136 Appendix

Figure A.2: Maximum principal stress magnitudes and tensors for 10 x 10 element (a), 25 x 25 element (b), 50 x 50 element (c), 75 x 75 element (d) resolutions at time step 10800. Arrows beside each mesh show the direction of wind at 5 m/s for each case. Tensile strains are positive (red), compressive strains are negative (blue).

137 Appendix

Figure A.3: Maximum principal total strain magnitudes and tensors for 10 x 10 element (a), 25 x 25 element (b), 50 x 50 element (c), 75 x 75 element (d) resolutions at time step 10800. Arrows beside each mesh show the direction of wind at 5 m/s for each case. Tensile strains are positive (red), compressive strains are negative (blue).

138 Appendix

Appendix B: Animation of Standard Case Principal

Stresses

Animation of the principal stresses in the GS_50x50_standard case throughout the model run. Contours in the background indicate the magnitudes of maximum principal stresses, where red contours indicate tensile stresses and blue contours indicate compressive stresses. Stress tensors of maximum and minimum principal stresses are overlaid on the contours. Red tensors indicate tensile stress and black tensors indicate compressive stress. Link: https://youtu.be/9c-I-hr_1O4

Appendix C: Time Lapse Video : Sujartalik

This time lapse imagery was captured during the break-up season in Admiralty Inlet from May 30, 2019 to August 9, 2019 at Sujartalik (Location #1 in Figure 5.22). Link: https://youtu.be/YcWtCmWIllg

Appendix D: Time Lapse Video : Elwin Inlet

This time lapse imagery was captured during the break-up season in Admiralty Inlet from June 6, 2019 to August 02, 2019 at the south-west corner of Elwin Inlet (Location #2 in Figure 5.22). Link: https://youtu.be/yx6A05xO6Oc

139 Appendix

Appendix E: Animation of Realistic Case Principal

Stresses

Animation of the principal stresses for the realistic case throughout the model run. Contours in the background indicate the magnitudes of maximum principal stresses, where red contours indicate tensile stresses and blue contours indicate compressive stresses. Stress tensors of maximum and minimum principal stresses are overlaid on the contours. Red tensors indicate tensile stress and black tensors indicate compressive stress. Arrows indicate magnitude and direction of ERA5 winds. Link: https://youtu.be/BtNCqbqjvZQ

140