Reliability-Based Sea-Ice Parameters for Design of Offshore Structures

December, 2015

Abstract: The intent of this study was to supplement the ISO 19906 Standard: Petroleum and Natural Gas Industries - Arctic Offshore Structures (i.e., the Normative). This supplement provides additional sea-ice information, for US waters in both the Chukchi and Beaufort seas, in a format consistent with the philosophy of the Normative. Currently, implementation of ISO 19906 in US waters is questionable due the lack of sea- ice design criteria. Appendices B.7 (Beaufort Sea) and B.8 (Chukchi Sea) of ISO 19906 are intended to provide this information but the data is not in a format consistent with the philosophy of the Normative – i.e., a reliability (probability)-based format. A full complement of design values for the regions covered in B.7 and B.8 is required to implement the normative provisions and, ultimately, produce a safe and reliable offshore structural design that can successfully survive demands from sea-ice. The work here included an extensive literature review and detailed analysis of sixteen (16) seasons of under-ice measurements from lease sites in the Chukchi and Beaufort seas. The analyses have further characterized ice cover and identified the most acute values for certain ice features. Also included in this study is a means to identify a critical keel depth with a low probability of being exceeded (conversely a high reliability of not being exceeded/failing) in a particular timeframe. The study concluded with an assessment of the suitability of the current ISO 19906 recommendations for estimating global ice actions (forces) on offshore structures. The latter included commentary on possible steps for refining the current standard of practice cited in ISO 19906.

Executive Summary

The project completed the scope set forth under contract E13PC00020 from BSEE; the following objectives were completed:  Obtain sea ice data of good quality and sufficient quantity  Conduct a literature review  Compute statistics for relevant sea ice parameters  Determine limit state values for applicable parameters if data was sufficient to do so. In addition to completing the objectives established in the contract the following additional objectives were also completed:  Produce ice velocity roses  Provide a probabilistic means for calculating critical pressure ridge keel depth  Examine how the ISO 19906 computes ridge loading on vertical structures  Compare theoretical ridge loads to recorded ridge loads in the Beaufort Sea  Investigate the ice strength coefficient, CR  Use recorded loadings in the Beaufort Sea to suggest alternative values of CR Overall, this project produced new information that should be able to be easily implemented by industry or regulatory agencies for the Beaufort and Chukchi Seas. Specifically there are reported values and findings that are of particular significance:  The ridge keel draft in the Beaufort and Chukchi Seas can be described by a Weibull Distribution, as presented by Eq. 4.2.3.1 with a threshold value, μ, of six meters. o Beaufort Sea: Shape parameter, α = 2.70 o Beaufort Sea: Scale parameter, β = 0.99 o Chukchi Sea: Shape parameter, α = 2.37 o Chukchi Sea: Scale parameter, β = 1.02  There appears to be a majority presence of FY ridges in both seas due to the presence of a modal keel width.  Modal ridge keel angles were found: o Beaufort Sea: 33.7° o Chukchi Sea: 32.5°  There appears to be no significant relationship between keel depth and speed.  From Figure 6.3 and Figure 6.4 it can be seen that, using the probability theory approach, the critical keel depth increases with service life. The annual exceedance probability approach is independent of service life and considers an event on an annual basis as opposed to a service life basis.

In comparison to other studies found this project had a large amount of quality data for analysis, making the results significant. A major component of this study was to verify suggested values for various sea- ice parameters provided in annexes B.7 and B.8 of the ISO 19906. Table ES.1: Beaufort Sea ISO 19906 Sea Ice Conditions; values in bold indicate results from this study (Reproduced from International Organization for Standardization, 2010, Table B.7-4)

Average Range of Parameter Annual Value Annual Values Sea Ice Late September First Ice October to late October Occurrence Early July to Last Ice July mid-August Landfast Ice Thickness 1.8 1.5 to 2.3 Level Ice (m) (FY) Floe Thickness (m) 1.8 1.5 to 2.3 Rafted Ice Rafted Ice Thickness (m) 3 2.5 to 4.5 Sail Height (m) 5 3 to 6 Rubble Fields Length (m) 100 to 1,000 100 to 1,000 3 to 6 Sail Height (m) 5 1 to 7 Ridges 15 to 28 Keel Depth (m) 25 6 to 30 Water Depth Range (m) 20 15 to 30 Stamukhi Sail Height (m) 5 to 10 up to 20 Level Ice (SY Ice Thickness (m) 3 to 6 2 to 11 & MY) Floe Thickness (m) 5 2 to 20 Sail Height (m) Significant Significant Keel Depth (m) 20 10 to 35 Rubble Fields (SY & MY) Average Sail Height (m) 2 to 5 3 to 6 Length Annual Maximum 750 50 to 2,300 (m) Ice Movement Speed in Nearshore (m∙s-1) 0.06 0.04 to 0.2 0.06 to 1.0 Speed in Offshore (m∙s-1) 0.08 0 to 1.5 Icebergs/Ice Islands Size Mass 10 ND Months Present Poorly Known Poorly Known Frequency Number per Year Poorly Known Poorly Known Maximum Number per Rare Rare Month

Table ES.2: Chukchi Sea ISO 19906 Sea Ice Conditions; values in bold indicate results from this study (Reproduced from International Organization for Standardization, 2010, Table B.8-4)

Region Northeastern Parameter Average Range of Annual Annual Values Value Late October to First Ice November Early December Occurrence Mid-June to Late Last Ice July August Level Ice Landfast Ice Thickness (m) 1.5 1.3 to 1.7 (FY) Floe Thickness (m) 0.7 to 1.4 0.7 to 1.8 Rafted Ice Rafted Ice Thickness (m) 1.0 to 2.0 1.0 to 3.0 Sail Height (m) 2 1 to 3 Rubble 300 to Fields Length (m) 300 to 1,000 1,000 1 to 3 Sail Height (m) 2 1 to 6 Ridges (FY) 8 to 15 Keel Depth (m) 10 6 to 26 Water Depth Range (m) None None Stamukhi Sail Height (m) None None Level Ice Floe Thickness (m) 2 to 4 2 to 6 (SY & MY) Ridges (SY Sail Height (m) 1 to 2 1 to 3 & MY) Keel Depth (m) 4 to 8 4 to 10 Ice Speed in Nearshore (m∙s-1) 0.1 to 0.2 0.1 to 0.3 Movement Speed in Offshore (m∙s-1) 0.2 to 0.3 0.2 to 0.3 0 to 1.1

Referencing Table ES.1 and 2, the most significant findings are the ice speed and pressure ridge depth. It should also be noted that this study was confined to information for the offshore environment. The near-shore features shown on the table were not studied. It was not possible to distinguish between first year and multi-year ice from the available data. However, it is likely the Chukchi ice is almost entirely first year ice. The reason for this is a particular mechanism must set up for multi-year ice features to travel from the Canadian Beaufort to the Chukchi Sea. The BSEE studies on freeze-up in the region elaborate on the conditions required for MY ice to travel from the Beaufort. Pressure ridge statistics from the Beaufort Sea data exhibited more dispersion than the Chukchi data. However, data from both seas passed statistical goodness-of-fit tests. It is speculated that MY features, more common in the Beaufort Sea, could be the source of the increased ‘spread’ of the Beaufort data. Based on the results of this study, it is likely that FY pressure ridges will govern the ultimate and possible the abnormal limit states for global ice action on offshore structures in the Chukchi lease areas. For the Beaufort, FY ridges may control the ultimate limit state. Based on experience and information from other studies, MY features may control global ice forces in the Beaufort Sea as the occurrence of these features in more frequent. A means of estimating a critical pressure ridge depth for both seas was derived from the data and is presented in this study. The utility of this information is that it can be used to identify depth at which interference with construction may occur (e.g., well head depth); it can be used to identify a limit-state pressure ridge feature; it can be used to inform decisions regarding burial depth of subsea pipelines. The tables below provide guidance on critical pressure ridge depth on an annual basis as well as a lifetime basis. Service lives are defined in terms of keels passing a given point, a year of service corresponding to the average number of keels in a season for both the Beaufort and Chukchi Sea data used in this study. The “T=100” line represents the critical keel depth based on an annual probability of occurence equal to 0.01 which is independent of service life. Given the availability of the sea-ice data, the study team elected to further study certain aspects of the ISO 19906 document as this was a convenient next step and did not represent any additional cost to the project. In particular, the team explored the suitability of ISO 19906 guidelines for calculating global ice actions (total force from ice on an offshore structure). It was initially found that when estimating pressure ridge loads using the ISO 19906 standard the magnitudes were extremely high, far larger than anything recorded for FY ridges. When this was further investigated by using measured parameters from recorded events and theoretically computing the load, it was still found that the

Figure ES.1: Beaufort Sea Critical Keel Depth as a Function of Service Life

Figure ES.2: Chukchi Sea Critical Keel Depth as a Function of Service Life theoretical action was much greater than the recorded action. While there was not sufficient data to come to a firm conclusion, it appears that the ISO 19906 is conservative

when computing ridge loading but may not be conservative for FY level ice loading. From the literature reviewed for this project it also seems that the ice strength parameter, CR, is not well understood or agreed upon. Furthermore, an investigation into MY ridges and ice was not conducted, which could have an impact on CR. From the results CR values of 1.62 and 3.36 MPa, the weighted average of the CR values, are recommended for FY ridges and FY level ice, respectively. Further research into the computation of ridge loading, particularly with respect to the consolidated layer, would be of great benefit and is advisable. The results of Monte Carlo simulation of global ice forces indicates that while the strength of ice composing a pressure ridge is less than that of level ice, FY pressure ridge features in the Chukchi sea will likely cause governing (in terms of engineering design) global ice forces on offshore structures sited in that sea.

Table of Contents

Page List of Figures ...... xiv

List of Tables ...... xxi

List of Appendices ...... xxiii

Acknowledgments ...... xxv

Chapter 1: Introduction ...... 1

1.1 Background ...... 1

1.2 Objective ...... 2

1.3 Data Collection ...... 3

1.4 Data Processing ...... 3

1.5 Presentation of Results ...... 4

Chapter 2: Literature Review ...... 5

2.1 Beaufort Sea ...... 5

2.2 Chukchi Sea ...... 6

2.3 Measurement of Ice Draft and Keel Depth ...... 8

2.4 Sea Ice Morphology ...... 10

2.4.1 First-Year Ice ...... 10

2.4.2 Multi-Year Ice ...... 11

Page

2.4.3 Pressure Ridges ...... 11

2.4.4 Level Ice ...... 13

2.4.5 Rafted Ice ...... 13

ix 2.4.6 Stamukhi ...... 14

2.4.7 Rubble Ice ...... 15

2.4.8 Icebergs and Ice Islands ...... 15

2.5 Reliability Engineering ...... 16

2.6 ISO 19906 Design Philosophy ...... 17

2.7 Arctic Structure Design ...... 18

2.8 Pressure Ridge Statistics ...... 19

2.8.1 Pressure Ridge Keel Draft Statistics ...... 19

2.8.2 Pressure Ridge Keel Width Statistics ...... 21

2.8.3 Pressure Ridge Keel Angle Statistics ...... 22

2.8.4 Pressure Ridge Keel Spacing Statistics ...... 22

2.8.5 Pressure Ridge Sail Statistics ...... 24

2.9 Ice Velocity ...... 25

2.10 Sea Ice Engineering Properties ...... 25

2.11 Sea Ice Loads on Structures ...... 27

2.12 Changing Ice Conditions ...... 34

Chapter 3: Data ...... 35

3.1 Overview ...... 35

3.2 Data Collection ...... 37

Page

3.3 Pressure Ridge Keel Identification ...... 43

3.4 Level Ice Identification ...... 48

3.5 Other Ice Identification ...... 52

x Chapter 4: Data Analysis ...... 55

4.1 Overview ...... 55

4.2 Probability Density Functions ...... 55

4.2.1 Gamma Distribution ...... 56

4.2.2 Exponential Distribution ...... 57

4.2.3 Weibull Distribution ...... 58

4.2.4 Lognormal Distribution ...... 59

4.3 P-Value Testing of PDFs ...... 59

4.4 Pressure Ridge Keel ...... 61

4.4.1 Keel Identification Starting Threshold Value ...... 61

4.4.2 Pressure Ridge Keel Draft ...... 63

4.4.3 Pressure Ridge Keel Width ...... 71

4.4.4 Pressure Ridge Keel Angle ...... 74

4.4.5 Pressure Ridge Keel Velocity ...... 75

4.4.6 Pressure Ridge Keel Spacing ...... 78

4.5 Ice Velocity ...... 83

4.6 Level Ice ...... 84

4.7 Other Ice ...... 86

Chapter 5: Results...... 89

Page

5.1 Pressure Ridge Keel ...... 89

5.1.1 Pressure Ridge Keel Draft ...... 89

5.1.2 Pressure Ridge Keel Width ...... 90

xi 5.1.3 Pressure Ridge Keel Angle ...... 91

5.1.4 Pressure Ridge Keel Velocity ...... 92

5.1.5 Pressure Ridge Keel Spacing ...... 94

5.2 Ice Velocity ...... 95

5.3 Level Ice ...... 97

5.4 Other Ice ...... 100

Chapter 6: Implementation ...... 101

6.1 ISO 19906 Comparison ...... 101

6.1.1 Beaufort Sea ...... 101

6.1.2 Chukchi Sea ...... 104

6.2 Pressure Ridge Keel Depth Probabilities ...... 106

6.2.1 Pressure Ridge Keel Depth Probability Calculation ...... 110

6.3 Limit State Ice Actions ...... 115

6.3.1 Consolidated Layer Force ...... 115

6.3.2 Keel Force ...... 118

6.3.3 Horizontal FY Ridge Action ...... 121

6.3.4 Monte Carlo Simulation ...... 121

6.3.5 Beaufort Sea Results ...... 122

6.3.6 Chukchi Sea Results ...... 124

Page

6.3.7 Molikpaq Ridge Comparison ...... 125

6.3.8 CR Determination from Molikpaq FY Ridges ...... 129

6.3.9 CR Determination from Molikpaq FY Level Ice...... 135

xii 6.3.10 Impact of CR on Caisson Weight...... 138

6.3.11 Determination of Governing Condition ...... 141

Chapter 7: Recommendations ...... 143

7.1 Pressure Ridge Keels ...... 143

7.1.1 Keel Spacing ...... 143

7.1.2 Keel Age ...... 143

7.2 Level Ice ...... 144

7.3 Other Ice ...... 144

7.4 Ridge Consolidated Layer ...... 144

7.5 Ridge Actions ...... 145

7.5.1 Ice Strength Coefficient CR ...... 145

7.5.2 Keel Action Fk ...... 145

Chapter 8: Conclusions ...... 147

8.1 General ...... 147

8.2 Findings ...... 148

8.3 ISO 19906 Implementation ...... 149

References ...... 151

Appendices ...... 167

xiii List of Figures

Page Figure 2.1: Map of the Beaufort Sea ...... 5 Figure 2.2: Map of the Chukchi Sea ...... 7 Figure 2.3: Ice Thickness ...... 9 Figure 2.4: Pressure Ridge Diagram ...... 12 Figure 2.5: Stamukhi Diagram ...... 15 Figure 2.6: Typical Demand/Capacity Plot ...... 17 Figure 2.7: Offshore Caisson Structure Site Map ...... 28 Figure 2.8: Tarsiut Caisson Profile ...... 30 Figure 2.9: SSDC Beaufort Sea ...... 31 Figure 2.10: CRI Beaufort Sea...... 32 Figure 2.11: Molikpaq Caisson Structure Beaufort Sea ...... 33 Figure 3.1: Site Map ...... 37 Figure 3.2: Typical IPS and ADCP Mooring Diagram...... 39 Figure 3.3: Spatial Conversion Algorithm ...... 41 Figure 3.4: Spatial Ice Profile ...... 42 Figure 3.5: Keel Shadowing Illustration ...... 44 Figure 3.6: Keel Identification Algorithm ...... 46 Figure 3.7: Level Ice Identification Algorithm ...... 50 Figure 3.8: Other Ice Identification Algorithm ...... 52 Figure 4.1: Starting Threshold P-Value Test Summary ...... 62 Figure 4.2: 2005-06 Site A Stacked Keel Shapes ...... 64 Figure 4.3: Keel Draft Histogram ...... 65 Figure 4.4: Shifted Keel Draft Histogram ...... 66 Figure 4.5: Keel Draft Exponential Probability Plot ...... 68 Figure 4.6: Keel Draft Weibull Probability Plot ...... 69 Figure 4.7: Keel Width Exponential Probability Plot ...... 71

xiv Page Figure 4.8: Keel Width Weibull Probability Plot ...... 72 Figure 4.9: Keel Width Lognormal Probability Plot ...... 72 Figure 4.10: Beaufort Keel Width Modal Analysis Plot ...... 74 Figure 4.11: Keel Angle Determination ...... 75 Figure 4.12: Keel Speed Exponential Probability Plot ...... 76 Figure 4.13: Keel Speed Weibull Probability Plot ...... 76 Figure 4.14: Keel Speed Lognormal Probability Plot ...... 77 Figure 4.15: Keel Speed v. Draft ...... 78 Figure 4.16: 2005-06 Site A Keel Spacing ...... 79 Figure 4.17: Keel Spacing Weibull Probability Plot ...... 81 Figure 4.18: Keel Spacing Lognormal Probability Plot ...... 81 Figure 4.19: 2005-06 Site A Ice Velocity Rose ...... 84 Figure 4.20: Level Ice Distribution ...... 85 Figure 4.21: 2005-06 Site A January Level Ice Draft ...... 86 Figure 4.22: 2005-06 Site A Other Ice Histogram ...... 87 Figure 5.1: 2005-06 Site A Keel Totals by Month ...... 89 Figure 5.2: Beaufort Sea Diagrammatic Keel Width/Angle ...... 91 Figure 5.3: Chukchi Sea Diagrammatic Keel Width/Angle ...... 92 Figure 5.4: Beaufort Keel Speed v. Draft ...... 93 Figure 5.5: Chukchi Keel Speed v. Draft ...... 93 Figure 5.6: Keel Spacing...... 94 Figure 5.7: Beaufort Site Ice Velocity Rose ...... 96 Figure 5.8: Chukchi Site Ice Velocity Rose...... 97 Figure 5.9: Monthly Level Ice Growth ...... 99 Figure 5.10: 2005-06 Site A Other Ice Histogram ...... 100 Figure 6.1: Keel Depth Probability v. Depth ...... 107 Figure 6.2: CDF Corresponding to P(D) ...... 109

xv Page Figure 6.3: Beaufort Sea Critical Keel Depth as a Function of Service Life...... 112 Figure 6.4: Chukchi Sea Critical Keel Depth as a Function of Service Life ...... 113 Figure 6.5: Beaufort Limit State Actions ...... 123 Figure 6.6: Chukchi Limit State Actions ...... 125 Figure 6.7: Recorded Molikpaq Ridge Load v. Computed Ridge Load ...... 129

Figure 6.8: CR Estimate from Molikpaq FY Ridges ...... 133

Figure 6.9: Consolidated Layer Load with Variation of CR ...... 134

Figure 6.10: CR Molikpaq Analysis ...... 137 Figure 6.11: FY Level Ice Weight Determination ...... 140 Figure 6.12: FY Ridge Weight Determination ...... 140 Figure A.1: Beaufort Sea Keel Draft Histogram ...... 167 Figure A.2: Chukchi Sea Keel Draft Histogram ...... 168 Figure A.3: Beaufort Sea Keel Draft Exponential Plot ...... 168 Figure A.4: Beaufort Sea Keel Draft Weibull Plot ...... 169 Figure A.5: Chukchi Sea Keel Draft Exponential Plot ...... 169 Figure A.6: Chukchi Sea Keel Draft Weibull Plot ...... 170 Figure A.7: 2005-06 Site A Keel Totals by Month ...... 170 Figure A.8: 2005-06 Site B Keel Totals by Month ...... 171 Figure A.9: 2006-07 Site A Keel Totals by Month ...... 171 Figure A.10: 2006-07 Site B Keel Totals by Month ...... 172 Figure A.11: 2007-08 Site A Keel Totals by Month ...... 172 Figure A.12: 2007-08 Site K Keel Totals by Month ...... 173 Figure A.13: 2007-08 Site V Keel Totals by Month ...... 173 Figure A.14: 2009-10 Site A Keel Totals by Month ...... 174 Figure A.15: 2009-10 Site V Keel Totals by Month ...... 174 Figure A.16: 2009-10 Burger Keel Totals by Month ...... 175 Figure A.17: 2009-10 Crackerjack Keel Totals by Month ...... 175

xvi Page Figure A.18: 2010-11 Site A Keel Totals by Month ...... 176 Figure A.19: 2010-11 Site V Keel Totals by Month ...... 176 Figure A.20: 2010-11 Burger Keel Totals by Month ...... 177 Figure A.21: 2010-11 Crackerjack Keel Totals by Month ...... 177 Figure B.1: Beaufort Sea Diagrammatic Keel Width/Angle 179 Figure B.2: Chukchi Sea Diagrammatic Keel Width/Angle ...... 179 Figure C.1: 2005-06 Site A Ice Velocity Rose 181 Figure C.2: 2005-06 Site B Ice Velocity Rose ...... 182 Figure C.3: 2006-07 Site A Ice Velocity Rose ...... 182 Figure C.4: 2006-07 Site B Ice Velocity Rose ...... 183 Figure C.5: 2006-07 Site K Ice Velocity Rose ...... 183 Figure C.6: 2007-08 Site A Ice Velocity Rose ...... 184 Figure C.7: 2007-08 Site K Ice Velocity Rose ...... 184 Figure C.8: 2007-08 Site V Ice Velocity Rose ...... 185 Figure C.9: 2009-10 Site A Ice Velocity Rose ...... 185 Figure C.10: 2009-10 Site V Ice Velocity Rose ...... 186 Figure C.11: 2009-10 Burger Ice Velocity Rose ...... 186 Figure C.12: 2009-10 Crackerjack Ice Velocity Rose ...... 187 Figure C.13: 2010-11 Site A Ice Velocity Rose ...... 187 Figure C.14: 2010-11 Site V Ice Velocity Rose ...... 188 Figure C.15: 2010-11 Burger Ice Velocity Rose ...... 188 Figure C.16: 2010-11 Crackerjack Ice Velocity Rose ...... 189 Figure D.1: 2005-06 Site A Level Ice Distribution ...... 191 Figure D.2: 2005-06 Site B Level Ice Distribution ...... 192 Figure D.3: 2006-07 Site A Level Ice Distribution ...... 193 Figure D.4: 2006-07 Site B Level Ice Distribution ...... 194 Figure D.5: 2006-07 Site K Level Ice Distribution ...... 195

xvii Page Figure D.6: 2007-08 Site A Level Ice Distribution ...... 196 Figure D.7: 2007-08 Site K Level Ice Distribution ...... 197 Figure D.8: 2007-08 Site V Level Ice Distribution ...... 198 Figure D.9: 2009-10 Site A Level Ice Distribution ...... 199 Figure D.10: 2009-10 Site V Level Ice Distribution ...... 200 Figure D.11: 2009-10 Burger Level Ice Distribution ...... 201 Figure D.12: 2009-10 Crackerjack Level Ice Distribution ...... 202 Figure D.13: 2010-11 Site A Level Ice Distribution ...... 203 Figure D.14: 2010-11 Site V Level Ice Distribution ...... 204 Figure D.15: 2010-11 Burger Level Ice Distribution ...... 205 Figure D.16: 2010-11 Crackerjack Level Ice Distribution ...... 206 Figure E.1: Beaufort Other Ice Draft 207 Figure E.2: Chukchi Other Ice Draft ...... 208 Figure E.3: 2005-06 Site A Other Ice Draft ...... 208 Figure E.4: 2005-06 Site B Other Ice Draft ...... 209 Figure E.5: 2006-07 Site A Other Ice Draft ...... 209 Figure E.6: 2006-07 Site B Other Ice Draft ...... 210 Figure E.7: 2006-07 Site K Other Ice Draft ...... 210 Figure E.8: 2007-08 Site A Other Ice Draft ...... 211 Figure E.9: 2007-08 Site K Other Ice Draft ...... 211 Figure E.10: 2007-08 Site V Other Ice Draft ...... 212 Figure E.11: 2009-10 Site A Other Ice Draft ...... 212 Figure E.12: 2009-10 Site V Other Ice Draft ...... 213 Figure E.13: 2009-10 Burger Other Ice Draft ...... 213 Figure E.14: 2009-10 Crackerjack Other Ice Draft ...... 214 Figure E.15: 2010-11 Site A Other Ice Draft ...... 214 Figure E.16: 2010-11 Site V Other Ice Draft ...... 215

xviii Page Figure E.17: 2010-11 Burger Other Ice Draft ...... 215 Figure E.18: 2010-11 Crackerjack Other Ice Draft ...... 216

xix

List of Tables

Page Table 2.1: Offshore Caisson Site Information ...... 29 Table 3.1: Dataset Details ...... 36 Table 3.2: Keel Identification Summary ...... 47 Table 3.3: Level Ice Identification Summary ...... 51 Table 3.4: Other Ice Identification Summary ...... 53 Table 4.1: Keel Draft PDF Parameters ...... 67 Table 4.2: Keel Draft P-Value Summary ...... 70 Table 4.3: Keel Spacing PDF Parameters ...... 80 Table 4.4: Keel Spacing P-Value Summary ...... 82 Table 5.1: Keel Draft Weibull Parameter Summary ...... 90 Table 5.2: Keel Spacing Lognormal Parameters ...... 95 Table 5.3: Ice Type Percentages ...... 98 Table 6.1: Beaufort Sea ISO 19906 Sea Ice Conditions ...... 102 Table 6.2: Chukchi Sea ISO 19906 Sea Ice Conditions ...... 104 Table 6.3: Ice Properties Summary ...... 120 Table 6.4: Summary of FY Ridge Events on the Molikpaq ...... 126 Table 6.5: Molikpaq Input Parameters ...... 128 Table 6.6: Horizontal Action Variation ...... 130

Table 6.7: CR Molikpaq Ridge Analysis ...... 132

Table 6.8: Molikpaq FY Level Ice CR Analysis ...... 136

xxi

xxii List of Appendices

Page Appendix A: Pressure Ridge Keel Draft ...... 167

Appendix B: Pressure Ridge Keel Width ...... 179

Appendix C: Ice Velocity ...... 181

Appendix D: Level Ice ...... 191

Appendix E: Other Ice ...... 207

xxiii

xxiv Acknowledgments

I am grateful to both Shell Offshore Incorporated (Shell) and ASL Environmental Sciences Inc. (ASL) for sharing sea ice data from lease areas in the Beaufort and Chukchi Seas. I am also appreciative of the instruction and guidance of Dr. Andrew Metzger (University of Alaska Anchorage) and Dr. Hajo Eicken (University of Alaska Fairbanks) throughout the entire process. Furthermore, I am greatly indebted to Dr. Andy Mahoney (University of Alaska Fairbanks), who provided immeasurable help understanding all matters concerning sea ice and Matlab© coding. I would also like to thank the Bureau of Safety and Environmental Enforcement (BSEE), who provided funding and support throughout the project. This work was supported by funding from the Bureau of Safety and Environmental Enforcement, Alaska OSC Region, Anchorage, Alaska, under contract E13PC00020.

xxv

xxvi Chapter 1: Introduction

1.1 Background

The Beaufort and Chukchi Seas are located off the north and north-western coasts of Alaska respectively. Much research and exploration has been conducted by industry in these areas and it seems probable that vast hydrocarbon reservoirs exist in these regions. Due to the highly volatile nature of hydrocarbon prices recently there has been a renewed interest in developing these reservoirs by both the oil companies and the American government (Timco & Frederking, 2009). However, since both seas lie in the Arctic Ocean there are various engineering challenges that must be overcome in order to responsibly develop these resources.

One of the most immediate and pertinent engineering challenges is the presence of sea ice. Sea ice has a major impact on how offshore structures will be designed and constructed in these regions, yet for such an important topic, readily available information on current conditions is sparse (Timco & Johnston, 2002). The majority of literature on this topic is from the 1970’s and 1980’s. Due to the ever-changing nature of the climate and sea ice, having the most recent information is crucial to providing a safe, functional, and cost effective structure.

While industry stakeholders may wish to develop hydrocarbon infrastructure in the Beaufort and Chukchi Seas, it is also important to consider the environmental impact potential accidents may have on these regions. The Beaufort coast provides a critical habitat for several species essential to the subsistence lifestyle of Arctic native populations (Dunton, Weingartner, & Carmack), while the Chukchi Sea is one of the most biologically productive regions in the world ocean due to its nutrient-rich makeup (Grebmeier, Cooper, Feder, & Sirenko, 2006). If a hydrocarbon spill were to occur in these regions it would be disastrous for the entire Arctic ecosystem. An offshore structure improperly designed for the existing sea ice conditions in the region would create a legitimate risk of a spill event occurring. 1 This is a major reason why government agencies have been established to monitor offshore development. Chief among these agencies are the Bureau of Safety and Environmental Enforcement (BSEE) and the Bureau of Ocean Energy Management (BOEM). Among other duties, these agencies are tasked with regulating and monitoring offshore development in the Beaufort and Chukchi Seas. Thus it is critical to have some reference for sea ice conditions in these regions, as they provide the demands on offshore structures (Kovacs A. , 1983). For this reason BSEE is considering the adoption of the ISO 19906 Standard: Petroleum and Natural Gas Industries – Arctic Offshore Structures (i.e., the Normative) as a standard for Arctic offshore structure design.

The ISO 19906 is a design normative that was developed to address design requirements and assessments for all offshore structures used by the petroleum and natural gas industries worldwide (International Organization for Standardization, 2010). The ISO 19906 contains sea ice parameters for both the Beaufort and Chukchi Seas, among many others. However, some of the information in the Normative is inconsistent or has been omitted. Many important design values are not present in the Normative and not all of the given values follow the same mandated reliability based design philosophy. It is important that, before the ISO 19906 is implemented, design values are present and consistent.

1.2 Objective

When designing an offshore structure in either the Beaufort or Chukchi Seas it is critical that the design engineer have access to accurate environmental information to compute structural loads. Due to these seas being part of the Arctic Ocean the most pertinent design load is caused by various sea ice features. The goal of this study was to characterize the physical features of sea ice in these regions using a probability based approach when possible. Furthermore, an examination of the calculation of ice actions was conducted.

2 1.3 Data Collection

The primary data for this project was provided by Shell Offshore Incorporated (Shell). Shell had contracted ASL Environmental Sciences Incorporated (ASL) to collect and preliminarily process both sea ice draft, the distance from the waterline to the bottom of the ice, and velocity data. Beginning in 2005, ASL deployed ice profiling sonar (IPS) and acoustical Doppler current profiler (ADCP) moorings to measure ice draft and velocity at a variety of different sites in both the Beaufort and Chukchi Seas. The IPS measures ice draft by identifying the acoustic echo from the bottom of the ice and computing the distance based on the time it takes the echo to travel (Melling, Johnston, & Riedel, 1995). The ADCP works by determining the motion of an underwater acoustic target by measuring the Doppler shift of the echo returned from it along four separate acoustic beams (Melling, Johnston, & Riedel, 1995). More details about these instruments are provided in the Data section.

Altogether ASL had six sites: four in the Beaufort Sea and two in the Chukchi Sea. In the Beaufort Sea, the moorings at the four sites recorded full datasets for parts of five seasons, 2005-2008 and 2009-2011. In the Chukchi Sea, the moorings at the two sites recorded full datasets for parts of two seasons, 2009-2011. Each dataset consisted of a draft and velocity time series file for an individual site during an independent year long period, or season. This provided a more than adequate amount of information to make a statistical model of different sea ice features.

1.4 Data Processing

The first step in processing the data was performed by ASL before it was delivered to the project team. In order to obtain accurate measurements it is important to incorporate many different factors such as temperature, pressure, and tilt of the IPS (Melling, Johnston, & Riedel, 1995). Furthermore, the change in the density and sound speed profiles within the water column of the IPS must be taken into account (Melling, Johnston, & Riedel, 1995). This preliminary processing of the raw data also included 3 adjusting for erroneous data points, mooring drift over time, and adjusting for errors in the start and end time records (Fissel, et al., 2010). This process is examined further in the Data section.

The next step was to interpolate the draft time series datasets with their respective velocity time series datasets to produce a dataset of evenly spaced draft values. While the ice draft dataset had measurements at regular time intervals, due to the irregular motion of the ice the drafts were unevenly spaced. By incorporating the velocity time series and using a cubic interpolation an evenly spaced spatial was created. The resulting spatially defined dataset contained draft values all separated by one meter (Fissel, et al., 2010). This process is examined further in the Data section.

Now that a consistent series of interpolated datasets had been created, the individual ice features needed to be discerned. For this a suite of interactive software was developed to accurately compile and analyze the data. Utilizing the Matlab© and Mathematica software packages, several programs were written and tested to automate the bulk of the computations. This suite identified different sea ice features such as level ice, pressure ridge keels, and ice that was neither level or ridge ice. Additional statistical analyses were performed on the resulting data. The purpose of the analyses was to enable estimation of critical ice features from information that was available. The specifics of these processes are discussed in the Data Analysis and Results sections.

1.5 Presentation of Results

The results for this project are displayed in a multitude of formats. Emphasis has been placed on trying to present these results in a simple manner that is clear and concise. Results, such as probability density functions, are presented both graphically and numerically. When possible the results are displayed diagrammatically to give the reader a sense of the scale of the results.

4 Chapter 2: Literature Review

2.1 Beaufort Sea

The Beaufort Sea is part of the greater Arctic Ocean and is located along the northern coast of Alaska and the north-western coast of Canada. Between both the American and Canadian regions the Beaufort Sea roughly covers an area from 69° N to 75° N and 125° W to 152° W. The depth of the seafloor in the Beaufort Sea varies greatly, from two meters near shore to several thousand further from shore (see Figure 2.1) (International Organization for Standardization, 2010).

Figure 2.1: Map of the Beaufort Sea (International Organization for Standardization, 2010, Figure B.7-1)

5 Of particular importance to sea ice conditions are the climate and hydrology of the region. The Beaufort Gyre is a major circulatory system of the Arctic Ocean in which the long-term average ice drift forms a clockwise pattern around a persistent region of high pressure known as the Beaufort High. In the southern Beaufort Sea the ice therefore typically drifts westward past the coast of Alaska, driven by prevailing easterly or northeasterly winds. This drift pattern transports ice into U.S. waters from the Canadian high Arctic, where some of the oldest, thickest sea ice in the northern hemisphere is found. These winds can cause large segments of sea ice to converge against the coast leading to deformation and the dynamical creation of thick ice in the form of ridges (Mahoney A. R., 2012).

From an engineering standpoint, sea ice in the Beaufort Sea can differ significantly from that found in the Chukchi Sea. The Beaufort Gyre, as mentioned previously, transports some of the oldest and thickest ice in the Arctic into the Beaufort from the Canadian Archipelago. This, along with other conditions, leads the Beaufort Sea to retain significant perennial ice cover (Mahoney A. R., 2012). Along with this perennial ice cover is landfast ice. Landfast ice is by definition attached to the shoreline and remains stationary for extended periods of time. In the Beaufort Sea landfast ice is not present year round, usually developing in September or October and retreating in June (Mahoney A. , Eicken, Gaylord, & Shapiro, 2007; Mahoney A. R., Eicken, Gaylord, & Gens, 2014). Lastly, the seasonal ice zone occupies the area between the perennial ice zone and landfast ice. This zone is mostly composed of FY ice and its extent varies greatly depending on the time of year (International Organization for Standardization,

2010).

2.2 Chukchi Sea

The Chukchi Sea is part of the greater Arctic Ocean and is located between the north-eastern edge of Asia and the north-western edge of North America. To the west of the Chukchi Sea lies the East Siberian Sea; to the east the Beaufort Sea; to the south the

6 Bering Sea; and to the north the Arctic Basin. The Chukchi Sea covers a large expanse and thus is usually broken into four regions (see Figure 2.2) (International Organization for Standardization, 2010).

Figure 2.2: Map of the Chukchi Sea (International Organization for Standardization, 2010, Figure B.8-1)

Of particular importance to the formation and movement of sea ice in the Chukchi Sea is the climate and hydrography of the region. Strong winds can occur in the Chukchi Sea, from a variety of different directions, which has a direct impact on the movement and deformation of sea ice in the region. Due to the many different currents present in the Chukchi Sea ice conditions can vary greatly between regions. For instance, the warm flow from the Pacific Ocean to the south can quickly melt the sea ice in region three,

7 while the sea ice in region four may melt more slowly due to the colder flow from the Arctic Ocean (International Organization for Standardization, 2010).

Lastly, it is important to describe the ice conditions in the Chukchi Sea. In general, the Chukchi Sea is entirely covered by ice from November or December until May or June. Since the Chukchi Sea is connected to the Pacific Ocean there is a net northward transport of heat which enhances the early loss of ice in the region (Woodgate, Weingartner, & Lindsay, 2010). This, in part, causes the sea ice in the Chukchi Sea to be, in general, newly grown each year. Furthermore, the winds in the Chukchi create sections of open water in leads, which are linear openings in the ice formed either between floes or at the coast (Mahoney A. R., 2012).

In order for landfast ice to extend into the deeper water of the Chukchi Sea the area must be anchored by grounded ridges (Mahoney A. R., Eicken, Gaylord, & Gens, 2014). While the Chukchi Sea is much shallower than the Beaufort Sea on average, within approximately 25 kilometers of the coast the depth of the Chukchi Sea is deeper than the Beaufort (Mahoney A. R., Eicken, Gaylord, & Gens, 2014). Since the seafloor is relatively deep near the coast of the Chukchi there also is not a large presence of grounded pressure ridges.

2.3 Measurement of Ice Draft and Keel Depth

Throughout the history of sea ice research there have been a variety of methods employed to obtain relevant sea ice data. However, before an explanation of this can be done, first one must have a solid grasp on the terms associated with how sea ice thickness is measured. The thickness of a segment of sea ice can effectively be separated into two components: ice draft and ice freeboard. Ice draft consists of the thickness of sea ice below the waterline. This is typically what is measured by underwater methods. Conversely, ice freeboard consists of the thickness of sea ice above the waterline. The overall ice thickness is the total of these two components (see Figure 2.3).

Figure 2.3: Ice Thickness

Initial exploration of the Arctic Ocean by the United States began in 1947 with the diesel-battery submarine the U.S.S. Boarfish, which recorded the first successful dive under sea ice in the Chukchi Sea. With the advent of nuclear powered submarines further distances could be traversed, opening the Arctic up for a rapid expanse in exploration. In 1957 the U.S.S. Nautilus, a nuclear powered submarine, cruised 1,300 miles under the sea ice, a first for United States nuclear powered submarines. In order to pilot and record sea ice draft data a series of forward, upward, and downward looking sonars were employed (Lyon, 1961). After the voyage of the U.S.S. Nautilus more sea ice draft data began to be collected in various waters. For example, in 1976 the U.S.S. Gurnard (SSN- 662) collected 1,400 kilometers of data from the Beaufort Sea (Wadhams & Horne, 1980), which was used to look at a number of different ice features. The identification of keel features is similar to that employed today, which is explained in detail in the Data section.

During the late 1970’s and early 1980’s moored self-contained upward looking sonar began to be used to acquire underside topographic measurements of sea ice. Typically, these moorings include an ice profiling sonar (IPS) and acoustic Doppler 9 current profiler (ADCP) (Melling, Johnston, & Riedel, 1995). The workings of these instruments are elaborated on in the Data section of this paper. With the increased cost efficiency and applicability of these instruments in acquiring data they have become a common method for data acquisition in contemporary times (Melling, Johnston, & Riedel, 1995).

2.4 Sea Ice Morphology

The morphology of sea ice in the Beaufort and Chukchi Seas is a wide and complex topic. For this work it is easiest to divide sea ice into three broad categories: pressure ridge, level ice, and other ice. While there certainly are more categories of sea ice, such as ice islands and rafted ice, for the objective of this project only these three broad categories are examined in great detail. Furthermore, it is important to divide sea ice into first-year (FY) and multi-year (MY) ice. While the data used in this study primarily pertains to FY ice, it is important to understand the difference between the two ice types due to their different mechanical engineering properties.

2.4.1 First-Year Ice

FY ice is defined as ice that has not yet existed through one summer. In the Beaufort and Chukchi Seas, FY ice that forms at the beginning of winter typically reaches a thickness of 1.5 to 1.8 meters, though FY ice that begins forming later will be thinner. As sea ice grows, it rejects salt into the ocean beneath, but some salt remains in the ice, encapsulated within liquid brine pockets. Depending on the temperature and growth rate of the ice, this brine volume can represent a bulk salinity of 4 to 12 psu (practical salinity unit) and result in ice porosities of one to ten percent. Due to this, FY ice is typically rather thin and not well developed. Since this ice has only been present for less than one season it is usually relatively porous and has a high salinity. Recently there has been an increase in the number of articles and reports concerning FY ice. This is

10 due to the dramatic shift in climate in the Arctic region, which has drastically changed the ratio of FY ice to MY ice (Wadhams & Toberg, 2012).

2.4.2 Multi-Year Ice

MY ice is defined as ice that has survived one or more summers, though some terminology draws a distinction between MY ice and second year (SY) ice. Due to growth during successive winters, MY ice can grow to greater thicknesses than FY ice. Melt processes in the summer result in a reduction in both salinity and porosity as fresh meltwater flushes brine pockets and refreezes the following winter. Due to its lack of salt, this melt water refreezes more readily and without the porosity of ice formed from saltwater. This combination of low porosity and salinity can greatly increase the strength of MY ice relative to FY ice. MY ice is common in the literature from the 1970’s and 1980’s, however it has become increasingly rare in the Arctic due to the dramatic losses of perennial ice in recent decades (Wadhams & Toberg, 2012).

2.4.3 Pressure Ridges

A pressure ridge is a deformed ice feature composed of blocks of ice piled above and below the waterline. Pressure ridges are formed by convergent deformation of ice cover due to factors such as wind and ocean current. The breaking of existing sea ice cover occurs in some combination of compression and shear, the balance of which has an impact on the characteristics of the ridge. As the existing sea ice cover fractures and deforms, blocks of ice are forced beneath the ice cover. These blocks begin to stack together, forming the keel of the pressure ridge. Simultaneously, blocks also stack above the waterline, forming the sail of the pressure ridge. Ridges formed during winter can consolidate to a certain depth below the waterline over time, due to conduction of heat into the cold atmosphere (see Figure 2.4) (Ekeberg, Høyland, & Hansen, 2014).

Figure 2.4: Pressure Ridge Diagram (Reproduced from Strub-Klein & Sudom 2012, Figure 1)

An important aspect of pressure ridges, especially in an engineering context, is whether they are defined as FY or MY ridges. During its first winter an ice ridge is designated as a FY ridge. However, if a ridge manages to survive one or more summer seasons then it is considered a MY ridge (Ekeberg, Høyland, & Hansen, 2014). What separates a FY ridge from a MY ridge is the degree to which it has consolidated. As with brine pockets in MY ice, the voids between ice blocks in a FY pressure ridge can be flushed with fresh meltwater, which refreezes and deepens the consolidated layer. A FY ridge can be thought of as a collection of ice blocks bound together by a weak bond via consolidation (Kovacs, Weeks, Ackley, & Hibler III, 1973). However, a MY ridge can be thought of as an almost solid piece of ice (Kovacs, Weeks, Ackley, & Hibler III, 1973). Since the MY ridge has survived at least a full summer and winter season

12 the blocks have had ample time to freeze together and consolidate into one solid unit. Furthermore, as the ridge consolidates its salinity and porosity decrease,

thereby increasing its strength (Kovacs, Weeks, Ackley, & Hibler III, 1973). This designation between FY and MY ice can have a dramatic impact on the design of offshore structures.

2.4.4 Level Ice

Level ice is a term used to describe sea ice that has not been mechanically thickened through deformation like a pressure ridge. The thickness of level ice is therefore controlled by thermodynamic processes and can be related to the age and growth rate of the ice. In the absence of mechanical deformation, level ice can therefore be identified by the uniformity of its thickness or draft (Melling & Riedel, 1995). The specific thickness of a level ice segment is limited by the number of freezing degree days in a season (International Organization for Standardization, 2010). Overall, there are not a large number of articles that deal with the distribution of level ice in the Arctic. This most likely is due to the fact that level ice is not thought to be the controlling condition for offshore structure design. However, most sources seem to indicate that the majority of an ice floe area consists of level ice (Wadhams & Horne, 1980).

2.4.5 Rafted Ice

There have been two types of rafted ice structures observed: simple rafted and finger rafted. Simple rafting occurs when two ice sheets interact along a straight edge and one sheet overrides the other. Finger rafting occurs when the interacting sheets fracture along lines perpendicular to their interacting edge and form fingers. Alternate fingers are then over-thrust and underthrust, leaving an interlocked structure. Multiple rafting actions may also occur, producing thick sea ice features. While the bonds between the layers are initially weak they can strengthen over time to produce a consolidated ice sheet (Babko, Rothrock, & 13 Maykut, 2002; Bailey, Sammonds, & Feltham, 2012). It has been found that rafted ice often is located near pressure ridges (International Organization for Standardization, 2010).

Due to the absence of a keel or sail, rafted ice can be difficult to distinguish from level ice without in situ observations. However, rafted ice is a design condition that should be taken into consideration when designing offshore structures in the Arctic.

2.4.6 Stamukhi

Stamukhi, a collection of stamukha, is a formation of grounded ice piles and ridges in the seafloor. Stamukha generally occur when an ice pressure ridge moves from a location with a deep seafloor to an area with a shallow seafloor. As the pressure ridge enters the shallow region the keel of the ridge typically does not deform. Instead the ridge creates an indentation in the seabed and forms a large scour as it moves. This scouring can affect undersea utilities such as oil pipelines (see Figure 2.5) (International Organization for Standardization, 2010).

Figure 2.5: Stamukhi Diagram (Reproduced from "Stamukha Drawing" by Lusilier - Own work. Licensed under CC BY-SA 3.0 via Wikimedia Commons – http://commons.wikimedia.org/wiki/File:Stamukha_Drawing.svg#/media/File:Stamukha_ Drawing.svg

2.4.7 Rubble Ice

Rubble ice forms mechanically, similarly to pressure ridges. Rubble ice can form from floe deformation or when the ocean swells. For rubble ice the debris does not stack to a large extent and the draft generally remains shallow. Thus the rubble ice is not consistent enough in draft to be classified as level ice, yet generally not deep enough in draft to be classified as a pressure ridge (National Oceanic and Atmospheric Administration, n.d.). Due to its relatively shallow draft rubble ice is not considered a primary design event for offshore structures; however its impact should be considered (International Organization for Standardization, 2010).

2.4.8 Icebergs and Ice Islands

Icebergs and ice islands are important design features to consider for offshore design. An iceberg is a large freshwater ice body that calves off from a 15 glacier. Icebergs can survive for many years in Arctic regions and present a hazard not only to structures but also ships in the region. An ice island is similar to an iceberg, except that it is usually larger and may have been calved from an ice shelf. Besides being created in nature ice islands can also be constructed artificially. Icebergs and ice islands in the Beaufort and Chukchi Seas are rare events that are not well understood (International Organization for Standardization, 2010).

2.5 Reliability Engineering

Due to the large variations of sea ice parameters and the changing conditions in the Arctic it is not realistic to establish deterministic ice features, ice events, or ice actions. However, some values for ice actions (ice forces) must be established to design offshore structures. One way to address a nondeterministic problem is with the likelihood of the occurrence of an event, or its occurrence frequency. The occurrence frequency, a number from zero to one, may be defined as how frequently an event occurs in a large number of trials or experiments. This method requires an appropriately large sample to study the frequency of occurrences of an event (Ross S. , 2002). Reliability shall be defined as:

“The ability of an item to perform a required function, under given

operational conditions, for a stated period of time.” (Høyland & Rausand, 2004)

Reliability engineering is a broad topic that includes not only the determination of design loading but also the reliability of materials and what type of failure mode will occur. There already is an extensive body of knowledge regarding material failure and failure modes (Timco & Weeks, 2010).

Reliability engineering for load determination is essentially trying to make an educated guess using probability on what future loading may be applied based on historical data. Often, this requires the analysis of data related to the load demands on a 16 structure to determine load conditions with a low probability of being exceeded. Such low probability events may be determined by statistical means, sometimes in terms of return periods, or by using probability theory to establish threshold events with a low probability of exceedance in some timeframe (see Figure 2.6).

Figure 2.6: Typical Demand/Capacity Plot

2.6 ISO 19906 Design Philosophy

The ISO 19906 has an inherent design philosophy for offshore structures that follows the reliability based engineering method described above. The ISO 19906 however examines limit states to determine what magnitudes of loads should be considered. The four limit states considered by the ISO 19906 are: ultimate limit state (ULS), service limit state (SLS), fatigue limit state (FLS), and abnormal limit state (ALS) (International Organization for Standardization, 2010).

17 The ULS ensures that over the design life of the structure there is an acceptably low probability of actions that may cause significant structural damage. The ULS considers both local and global actions. The SLS is where the structure loses the capability to perform adequately under normal use. The FLS considers the cyclic or repeated actions due to ice actions, such as compressive and flexural ice failure. Lastly, the ALS considers abnormal ice events. In this case the structure is permitted to suffer some structural damage. However, the structure should have enough reserve strength to keep from losing complete integrity (International Organization for Standardization, 2010).

All of the limit state design values are associated with a specific probability, as stipulated by the ISO 19906. The SLS shall be designed for events with an annual exceedance probability not greater than 10-1, or 10%. The ULS shall be designed for events with an annual exceedance probability not greater than 10-2, or 1%, based on linear elastic methods of structural analysis. The ALS shall be designed for events with an annual exceedance probability not greater than 10-4, or 0.01%, based on non-linear methods of structural analysis (International Organization for Standardization, 2010). For the purposes of this project the FLS shall be omitted.

2.7 Arctic Structure Design

While there are definitely challenges to designing offshore structures in the Arctic environment the general design process is similar to a regular structure. First, a designer must consider the conditions the structure is subjected to, such as location and operating times. Next, they must determine which loading conditions, such as snow or sea ice, should be considered. The designer then selects or computes the loading on the structure, in this case due to sea ice. Upon calculating the forces that will be applied to the structure, the engineer must determine the limit states and begin to design members and connections accordingly.

18 2.8 Pressure Ridge Statistics

Since pressure ridges are commonly considered the design event for offshore structures in ice covered waters there has been much effort expended to develop probabilistic models to predict pressure ridge characteristics (Ekeberg, Høyland, & Hansen, 2014). Since the ISO 19906 uses the draft of the keel as the primary input design value, most of the statistical analysis has been devoted towards that value. However, while less common, there are probabilistic models that examine other keel characteristics such as width, spacing, and angle. There also has been research conducted into determining the properties of the sail of the ridge. While not as critical as the keel, these properties are examined in the literature review since some play a role in the ice action calculations.

2.8.1 Pressure Ridge Keel Draft Statistics

Due to their importance in the design of offshore Arctic structures there is a plethora of literature available on ridge keel draft statistics. Of particular note are the works by Wadhams (2011), Davis (1995) and Fissel (2010), which are all relatively recent.

Wadhams examined 204 kilometers of draft data collected in the Fram Strait and Beaufort Sea during the 2007 season. This included an area of extensive research near this project’s area of interest, at approximately 73° N and 146° W. After determining which ice features were pressure ridges Wadhams applied reliability methods to determine extreme events. Wadhams showed that a negative exponential probability density function (PDF), which represents a stochastic process of ridge production, was an excellent fit for his data. This is consistent with the findings of other researchers and seems to be generally accepted within the scientific community (Ekeberg, Høyland, & Hansen, 2014; Hibler III, Weeks, & Mock, 1972; Obert & Brown, 2011; Wadhams P. , 1983; Wadhams & Davy, 1986; Wadhams P. , 2011). 19 Davis examined 729 ridges that were greater than five meters deep from geographically distinct regions between Greenland and Svalbard during a 1987 study. While Davis was not seeking to determine the extreme design events for pressure ridges, he did fit a PDF to the pressure ridge keel data. Unlike Wadhams, Davis found that a lognormal distribution was a better fit than a negative exponential. While the region of these ridges does not coincide with the regions of this project, it is important to note this work since it is one of the few to suggest this distribution (Davis & Wadhams, 1995).

Lastly, Fissel examined ridges from an extensive dataset. The dataset consisted of multiple seasons at two sites in the Chukchi Sea, which made for a dataset of over 1,800 keels. When looking at keels with a draft greater than 13 meters it was found that a three parameter Weibull distribution produced favorable results (Fissel, et al., 2010).

The three articles above illustrate that there are a variety of methods and PDFs to fit ridge keel data. Some of these authors looked at all keels greater than five meters (Davis & Wadhams, 1995) when analyzing the data while others looked at only those greater than 13 meters (Fissel, et al., 2010). All of these authors found different distributions fit their data relatively well.

Along with the statistical models of sea ice pressure ridge keels the greatest keel draft recorded is also of great interest. From the literature examined for this project it was found that the deepest keel observed was 47 meters. The location of this keel was not present in the literature examined. There also was an extremely large sail observed in the Beaufort Sea and using ratios between the sail and keel a draft of 57 meters was inferred for a FY ridge (Kovacs, Weeks,

Ackley, & Hibler III, 1973).

20 2.8.2 Pressure Ridge Keel Width Statistics

The width of a pressure ridge keel is another important factor in offshore structural design in the Arctic. Most seem to agree that the width of a keel is somewhat dependent on the depth of the keel (Sudom, Timco, Sand, & Fransson, 2011). While some probabilistic models have been fit to keel width data, it is more common to see keel width to depth ratios and average or statistical mode values.

Timco (1997), using a dataset of 112 FY ridges located in the Beaufort and Baltic Seas, reported a ratio of keel width to keel depth of approximately 3.9 for FY ridges (Timco & Burden, 1997). Using a dataset of 64 ridges located in the Beaufort Sea and Queen Elizabeth Island region Timco (1997) reported a ratio of keel width to keel depth of approximately 3.3 for MY ridges (Timco & Burden, 1997). Davis (1995) however did not report his findings in terms of ratios. Davis fit a lognormal distribution to the keel width dataset and found a mean keel width of 72.8 meters and a mode of 65 meters for both FY and MY ridges in geographically distinct regions between Greenland and Svalbard during a 1987 study (Davis & Wadhams, 1995). This value is different than that reported by Sudom (2011). Sudom reported a mean keel width value of 37 meters for FY ridges and a range from 35 to 79 meters for MY ridges. Sudom (2011) examined 262 FY ridges and 85 MY ridges from various locations in the Arctic Ocean (Sudom, Timco, Sand, & Fransson, 2011). Ekeberg (2014) reported in the Fram Strait a mean observed keel width of 28 meters for 30,186 keels, which can be described with a lognormal distribution (Ekeberg, Høyland, & Hansen, 2014).

It can be observed from the examples above that there is considerable variation in the reported keel widths. While a general magnitude of keel width can be determined, it seems that there is no determinant range. The ISO 19906 only gives an angular relationship of 26° from horizontal to determine the keel width

21 based on keel depth, which works out to a 4.1:1 width to depth ratio for isosceles triangular keels (International Organization for Standardization, 2010).

2.8.3 Pressure Ridge Keel Angle Statistics

Due to the variable nature of sea ice finding a consistent angle of repose for ridge keels is difficult. While there have been some studies to examine the angle of repose of a keel, most are limited and only present a mean observed value. Example values are described to develop an understanding of the general range one should expect for a keel angle of repose.

Due to the friction and wear on MY ice ridges, there is usually a distinction made between the angle values for FY and MY ridges. Kovacs (1972) reported FY keel angles between 20 and 55°, with an average of 33° from data gathered in the Bering, Chukchi, and Beaufort Seas (Davis & Wadhams, 1995). Strub-Klein however reported a mean keel angle of 28° for over 300 FY ridges in various seas in the Arctic Ocean, including the Beaufort and Chukchi Seas, between 1971 and 2014 (Strub-Klein & Sudom, 2012). For both FY and MY ridges Davis (1995) reported ridge angle values from 8 to 36°, with a mean of 23.2° and a modal value of 18° for 729 ridges between Greenland and Svalbard. Davis (1995) also found that the data for ridge angles followed a lognormal distribution (Davis & Wadhams, 1995). From the ISO 19906 the prescribed angle for a keel is 26° from horizontal (International Organization for Standardization, 2010).

2.8.4 Pressure Ridge Keel Spacing Statistics

The spacing of pressure ridge keels is another topic that has been extensively studied. Of particular interest are the works by Hibler (1972), Mock (1972) and Wadhams (1986) since they examined data from the Beaufort Sea.

22 These articles studied the distribution of the spacing between ridge keels and looked to apply PDFs to the data.

Hibler examined ridge spacing in the Central Arctic Basin and Beaufort Sea using sonar data from submarine voyages. Looking at numerous datasets, which had a total of 18,906 keels, Hibler came to the conclusion that for the ridge spacing a Poisson distribution was valid, which implies that a negative exponential probability density function is applicable for ridge spacing (Hibler III, Weeks, & Mock, 1972).

Mock examined ridge features in the Beaufort Sea via aerial photographs taken during 1969 and 1971. By analyzing the data using goodness-of-fit tests Mock determined that the keel spacing most closely followed a negative exponential model. However, in his article Mock did note that there were significant deviations from the model, especially for close spacings (Mock, Hartwell, & Hibler III, 1972).

In 1986 Wadhams further investigated the statistics of keel spacing and came to a different conclusion than either Hibler or Mock. Using a 637 kilometer segment from a set of 1976 data in the Beaufort Sea Wadhams analyzed which PDFs would best fit the spacing data. From his research Wadhams concluded that the fit was much improved when using a three-parameter lognormal distribution. To further confirm this model Wadhams also tested it on a variety of different datasets. He found that all fit the distribution well (Wadhams & Davy, 1986).

While the authors used the same general method to come to their conclusions, they got slightly different results. Looking through further literature in this field it seemed that the lognormal distribution was generally accepted. Examples of the lognormal distribution to describe keel spacing can be found in Davis (1995), Sear (1992), and Key (1989).

23 2.8.5 Pressure Ridge Sail Statistics

While most pressure ridge features use a PDF to describe the feature, when analyzing the sail of a pressure ridge the majority of the literature uses simple ratios or equations between the keel depth and sail height. However, depending on the dataset used many of the various researchers found slightly different results. A few of these ratios are examined.

Timco and Burden (1997) reported that for sea ice in the Beaufort Sea they found mean ratios of keel depth to sail height of 4.46 for FY ridges and 3.34 for MY ridges, although it should be noted that there was significant scatter in the results (Timco & Burden, 1997). This is similar to the keel depth to sail height ratios reported by Tucker III (1989). Tucker III found a ratio of 4.5 for FY ridges and 3.2 for MY ridges (Davis & Wadhams, 1995). More recently Sudom (2011) used a dataset from various seas in the Arctic Ocean to determine ratios. Sudom found that the keel depth to sail height ratio was 4.35 for FY ridges and 3.60 for MY ridges (Sudom, Timco, Sand, & Fransson, 2011).

From the examples above it is important to note that while different, the ratios of keel depths to sail heights are relatively close. Even though these researchers used datasets from different seas, during different years, they all found ratios remarkably close. While this project did not directly measure sail height, due to the data collection method, the literature provides valuable information for the ice action calculation component of this project.

Along with the statistical models of sea ice pressure ridge sails the greatest sail height recorded is also of interest. From the literature examined for this project it was found that the highest sail recorded was 12.8 meters in the Beaufort Sea (Kovacs, Weeks, Ackley, & Hibler III, 1973).

24 2.9 Ice Velocity

While there are many different articles that have velocity measurements for different sea ice features, there were none found in this study that attempted to examine ice velocities in the probabilistic sense. In most cases the author simply examined how the velocity of ice features varied at different times of the year (Belliveau, Bugden, Eid, & Calnan, 1989). Another common general analysis of sea ice velocities was to present the average velocity or present a compass-rose plot to show the direction and magnitude of the ice (Fissel, et al., 2010).

2.10 Sea Ice Engineering Properties

When designing an offshore structure in the Arctic it is necessary to not only know the geometric properties of sea ice features but also the material properties. Material properties include compression strength, tensile strength, modulus of elasticity, and many others. The material properties of sea ice allow the design engineer to calculate the magnitude of the loads and forces applied to the structure.

Since sea ice material properties are so vital to design, there has been much effort to research them. The article A review of the engineering properties of sea ice by Timco (2010) presents the most complete findings on material properties for sea ice that was found during this literature review. The article contains findings from many different publications in this field and presents a well-rounded source of information. A few of the sea ice properties that have a particular application to this project are examined further in depth.

One property that is of interest is the angle of internal friction of sea ice. The angle of internal friction is a measure of the ability of a material to resist shear stress. The range of published sea ice rubble internal friction angle varies from 10 to 80°. However, this property is hard to distinguish since it is hard to differentiate between the contributions of the angle of internal friction and the consolidated layer to shear strength.

25 Generally accepted values range from 20 to 40° (International Organization for Standardization, 2010).

Cohesion is another property of interest. Cohesion is a measure of how “together” a material acts. For example, after a keel has impacted a structure and completely broken into separate blocks, it can be said that there is no cohesion between the units. On average the cohesion of a FY ridge keel ranges from 5 to 7 kPa (International Organization for Standardization, 2010).

The porosity of a keel feature is also important when calculating ice forces. The porosity of sea ice is determined as the overall fractional void volume (Leppäranta, Lensu, Kosloff, & Veitch, 1995). Using the equations presented in Timco (2010) the volume of the air and brine can be calculated and used to compute the porosity (Timco & Weeks, 2010). However, the ISO 19906 also gives reported values from collected literature. The Normative states that keel porosity ranges from 10 to 50% and usually increases with depth (International Organization for Standardization, 2010).

The density of sea ice is also needed to compute ice forces. For FY ice, the ice above the waterline has in situ values that range from 0.84 to 0.91 Mg∙m-3. Values ranging from 0.90 to 0.94 Mg∙m-3 have also been reported for ice below the waterline. As described by Timco (2010) a value of 0.92 Mg∙m-3 should serve as a reasonable estimate for ice density of FY ice. Timco (2010) also found that for MY ice the average densities of the complete ice sheet were between 0.910 and 0.915 Mg∙m-3 (Timco & Weeks, 2010).

However, the ISO 19906 prescribes slightly different sea ice density values. The Normative prescribes densities of 0.840 to 0.910 Mg∙m-3 for FY ice above the waterline and 0.720 to 0.910 Mg∙m-3 for MY ice above the waterline. It also has densities ranging from 0.900 to 0.920 Mg∙m-3 for both FY and MY ice below the waterline (International Organization for Standardization, 2010).

26 2.11 Sea Ice Loads on Structures

Sea ice loads on a structure, the forces that the sea ice exerts on the structure, are critical for the design of offshore structures in the Arctic. While there are many different sources to theoretically determine the force a pressure ridge exerts on a structure, there are few studies that have collected in situ data. For this project the works of Dalane (2015) and Timco (2009) are examined to show recorded pressure ridge loads on actual structures.

Dalane (2015) looked to create sea ice loads that modeled actual conditions in a controlled environment. To do this, Dalane produced laboratory ice ridges using a saline solution and set up a “floater” in a 78 meter long, 10 meter wide, and 2.5 meter deep ice tank. A floater, in this case a Sevan FPU-Ice model, is a floating circular structure that is moored to the bottom of a tank, which has a movable false bottom. This floater has various sensors to measure different variables. In order to create the impact between floater and ice ridge, the false bottom moves the floater, attached via mooring, into the ridge. Upon impact the floater measures forces. While the article looked at many different topics, of particular interest to this project were the forces applied. Dalane reported scaled forces that ranged from 50.6 to 156.9 MN corresponding to simulated ice ridges (Dalane, Aksnes, & Løset, 2015).

While the findings from Dalane (2015) were valuable it is important to note that these are scaled values found in a controlled environment. Of greater significance were the findings by Timco (2002, 2004, 2009), which examined the ice loads on caisson structures in the Beaufort Sea. Timco looked at a total of five caisson structures in the Beaufort Sea during the 1980’s. These five structures are: Tarsiut Caisson, Single-Steel Drilling Caisson (SSDC), Caisson-Retained Island (CRI), Molikpaq, and the Glomar Beaufort Sea I (CIDS). While each of these offshore structures provided varying degrees of information, all give some idea of what type of structures may be present in the Arctic (see Figure 2.7 and Table 2.1).

27 28

Figure 2.7: Offshore Caisson Structure Site Map

Table 2.1: Offshore Caisson Site Information

Structure Site Year(s) Map Number Latitude Longitude Tarsiut Tarsiut N-44 1982-83 1 69.8969 -136.1942 Caisson Unviluk P-66 2 70.2633 -132.3120 1982-84 Kogyuk N-67 3 70.1139 -133.3300 SSDC Phoenix 4 70.7169 -150.428 1986-88 Aurora 5 70.1092 -142.785 Kadluk O-07 1983-84 6 69.7800 -136.0205 CRI Amerk O-09 1984-85 7 69.9822 -133.5142 Kaubvik I-43 1986-87 8 69.8761 -135.4225 Tarsiut P-45 1984-85 9 69.9156 -136.4180 Amauligak I-65 1985-87 10 70.0778 -133.8044 Molikpaq Amauligak F-24 1987-89 11 70.0547 -133.6300 Isserk I-15 1989-90 12 69.9122 -134.2992

The Tarsiut Caisson was the first caisson-type structure used in the Arctic. While it did drill wells during the 1981-82 season, during the winter of 1982-83 it was left to study ice interaction at the Tarsiut N-44 site. The Tarsiut Caisson consisted of four individual concrete caissons each ten meters in length. These caissons formed a square pattern, which created an inner core. They were placed on a subsea berm that came within six meters of the water surface, while the inner core was further filled with dredge material. This formed a structure that was approximately 100 meters across at the water line and had a vertical outer surface (see Figure 2.8) (Timco & Johnston, 2002).

Figure 2.8: Tarsiut Caisson Profile (Reproduced from Timco & Johnston, 2002, Figure 9)

While the Tarsiut Caisson did experience a number of ice actions, the information was not complete and several assumptions were often made when calculating the loads. The four best events, as defined by Timco (2004), consisted of FY rubble ice loading. The peak load of these was 240 MN (Timco & Johnston, 2004).

The SSDC was a caisson structure owned and operated by Canmar. The SSDC was a heavily modified super tanker 162 meters long, 53 meters wide, and 25 meters high, with all sides vertical. Like the Tarsiut-Caisson the SSDC also rested on a submerged berm. The SSDC was deployed in the Canadian Beaufort from 1982-84 at the Uviluk P-66 and Kogyuk N-67 sites. From 1986-88 the SSDC was deployed in the American Beaufort at the Phoenix and Aurora Sites. The only sites where reliable ice load measurements were taken was in the American Beaufort (see Figure 2.9) (Timco & Johnston, 2002).

Figure 2.9: SSDC Beaufort Sea (Timco & Johnston, 2002, Figure 13, reproduced with permission)

From the information gathered at the American Beaufort sites 13 quality load events were determined. It is important to note that the SSDC was surrounded by a rubble field at these sites. From the data gathered the peak load, 74 MN, was generated from a FY 1.65 meter ice feature at the Phoenix site (Timco & Johnston, 2004).

The CRI was a caisson structure deployed in the Canadian Beaufort from 1983- 87. Throughout its use the CRI was stationed at the Kadluk O-07 site from 1983-84, the Amerk O-09 site from 1984-85, and the Kaubvik I-43 site from 1986-1987. The CRI consisted of eight individual caissons in an octagonal pattern. Each individual caisson was 43 meters long, 12.2 meters high, and 13.1 meters wide. Using two pre-stressed bands of steel wire cable to hold the caissons together a central core was constructed. This central core was 92 meters across and filled with sand. Each face of the octagon was approximately 49.2 meters wide, while each flat was approximately 118 meters across. The outside face of the structure was inclined 30° from vertical (see Figure 2.10) (Timco & Johnston, 2002).

Figure 2.10: CRI Beaufort Sea (Timco & Johnston, 2002, Figure 27, reproduced with permission)

While there were a number of ice load measurements made the investigators did not use local pressure values to determine a global load on the CRI (Timco & Johnston, 2004). Using the results of the Implementation section with local pressure values would not be useful for this project.

The Molikpaq structure was deployed in the Canadian Beaufort from 1984-89. Throughout its use the Molikpaq was stationed at the Tarsiut P-45 site from 1984-85, the Amauligak I-65 site from 1985-87, the Amauligak F-24 site from 1987-89, and the Isserk I-15 site from 1989-90. The Molikpaq consisted of an octagonal steel annulus on which sat the structure deck. This steel annulus was filled with sand to provide horizontal resistance. The caisson itself had outside dimensions of 111 meters at its base and 86 meters at its deck, with an overall height of 33.5 meters. When deployed at a set down draft of 20 meters the caisson had a waterline diameter of 90 meters. At this deployment draft the Molikpaq had walls 8° off vertical through the waterline and 23° off vertical

32 from 3.5 meters to 15 meters below mean sea level, with a flare out of about 40° thereafter. This caused the consolidated layer of ridges to interact with a near vertical face, while the keel portion primarily interacted with the 23° face (see Figure 2.11) (Wright & Timco, 2001).

Figure 2.11: Molikpaq Caisson Structure Beaufort Sea (Timco & Johnston, 2004, Figure 4, reproduced with permission)

The Molikpaq structure collected a plethora of quality data during its deployment. Most importantly it was able to capture loading from FY ice ridges. The peak recorded ridge load of 89 MN was caused by a ridge with a one meter sail, drifting at 0.1 meters per second, impacting the 105 meter side. This event, along with the 22 other provided ridge interaction events, gave good numbers to compare calculated values to. Furthermore, loads of up to 140 MN were reported for FY level ice interactions with the Molikpaq (Wright & Timco, 2001).

33 Lastly, the CIDS was a structure operated in the American Beaufort Sea. However, in this literature review ice loading values were not discovered for the structure (Timco & Johnston, 2004). This structure did provide any useful information for this project.

2.12 Changing Ice Conditions

Numerous studies about sea ice features in the project domain were carried out in the 1970s, 1980s, and in the most recent several years. However, there was little activity during the interval between these two eras. As of late, there is a consensus that the annual temperature regime has and is changing (i.e. “climate change”). One must take into account the applicability of previous studies in light of recent climatic changes.

For instance, Wang (2009) theorized that there could be an increased September sea ice reduction over the next 25 years. He also stated that there will be a decrease in sea ice thickness, as MY ice becomes rare and is replaced with FY ice. These changes in ice coverage and ice type can have a large impact on offshore structures and shipping in the Arctic (Wang & Overland, 2009).

Another example of changing ice conditions can be found in Wadhams (2011). In this article Wadhams examined an ice draft dataset from the Fram Strait in 2007 and compared it to a similar dataset from 1976. Wadhams found that a decrease in mean draft of 32% occurred over 31 years in this region. This is a drastic change over such a period of time and clearly shows that the Arctic sea ice conditions are constantly evolving and changing (Wadhams, Hughes, & Rodrigues, 2011).

34 Chapter 3: Data

3.1 Overview

In order to analyze sea ice parameters in a reliability based analysis for offshore structure design, data for a statistical sample of ice parameters needed to be obtained. This data needed to have an acceptably large number of entries to be statistically significant. For this project the draft and velocity of sea ice were of particular interest. Field work was not part of the scope of work for the project. The intent of the project was to collect existing samples of sea ice parameters.

Data from recent studies was acquired for Shell by ASL Environmental Sciences Inc. (ASL) and provided by Shell as a collection of annual datasets for different mooring locations in the Beaufort and Chukchi Seas. Each annual dataset consisted of ice draft and velocity time series measured by moored IPSs and ADCPs, respectively. The raw sensor data was processed following methods described by (Melling, Johnston, & Riedel, 1995) and (Fissel, et al., 2010). The physical collection of the data is examined in greater depth in the Data Collection section.

Altogether the data covered seven seasons and six mooring sites, for a total of 16 yearlong datasets of ice draft and velocity. Table 3.1 shows details for each dataset, while Figure 3.1 provides a map of site locations.

35 Table 3.1: Dataset Details. Days included are when both the IPS and ADCP were simultaneously operational and where length does not include periods of open water.

Season Region Site Days Length (km) Site A 328 1,974 2005-06 Beaufort Site B 330 1,989 Site A 248 1,775 2006-07 Beaufort Site B 223 2,131 Site K 250 1,866 Site A 250 2,198 2007-08 Beaufort Site K 256 2,185 Site V 257 2,340 Site A 284 1,303 Beaufort Site V 284 1,955 2009-10 Burger 201 2,096 Chukchi Crackerjack 204 2,194 Site A 228 1,824 Beaufort Site V 168 1,329 2010-11 Burger 214 3,257 Chukchi Crackerjack 215 2,901

Figure 3.1: Site Map

3.2 Data Collection

To collect the draft and velocity data two upward looking sonars were deployed. The first was an ice profiling sonar (IPS). This device measured ice draft data to an estimated accuracy of +/- 0.05 meters every one to two seconds using an acoustic beam (Fukamachi, et al., 2006). While the acoustic beam measured the distance to the sea ice above, a pressure sensor on the device determined the depth of the IPS. The IPS used an algorithm to identify the echo of the acoustic beam and then calculated the draft of the ice based on how quickly the sound travelled back through the seawater. It is important to note that an assumed value is used for the speed sound travels through the water. The IPS then recorded when the measurement was taken and the draft of the measurement (Fissel, et al., 2010; Melling, Johnston, & Riedel, 1995; Melling, Johnston, & Riedel, 1995). The IPS also recorded the tilt of the instrument and the surrounding pressure. These parameters were also incorporated to modify the draft readings to increase accuracy (Melling, Johnston, & Riedel, 1995). 37 Along with the IPS is the ADCP, a complex, microprocessor-controlled echo sounder that is used to determine the motion of sea ice (Melling, Johnston, & Riedel, 1995). The ADCP measured velocity by detecting the Doppler shift in acoustic frequency from the transmitted acoustic pulses of the backscattered pulse returns. The ADCP took measurements every 30 minutes for the full deployment. While this project exclusively used the measurements of the sea ice velocity, it is also possible for the ADCP to record water current (Fissel, et al., 2010).

Both the IPS and ADCP were deployed via ship and moored to the sea floor during the summer open water season. They stayed moored on the sea floor for close to a full 12 months at a time, internally collecting and storing data until retrieval. Once they were retrieved by the ship the next summer season, the data was downloaded. It is important to note ASL then made adjustments to this data before it was sent to the project team, such as accounting for erroneous or extraneous data points and correcting for the drift of the instrument’s internal clock (see Figure 3.2).

Figure 3.2: Typical IPS and ADCP Mooring Diagram (Reproduced from Fissel, et al., 2010, Figure 2-2)

For the data provided it was necessary to convert from time dependent data to spatially dependent data. This was done by using both the IPS and ADCP datasets. First, the velocity data was linearly interpolated over the IPS draft data, to assign a velocity value to all draft values. Using these interpolated velocity values the distance and direction that the draft measurements moved was calculated. This made the distance between draft measurements known. Lastly, to develop a pseudo-spatial series where each ice draft measurement would be evenly separated by one meter, a cubic spline 39 interpolation was performed between values (Mahoney A. R., et al., 2015). With this new spatial draft dataset all sites, no matter the season, could be compared (see Figure 3.3 and Figure 3.4).

Figure 3.3: Spatial Conversion Algorithm

41 2005-06 Site A Spatial Ice Draft Profile 0 10

Draft (m) 20 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 ) 10 42

Draft (m 20 0 70 75 80 85 90 95 100 105 110 115 120 125 130 ) 10

Draft (m 20 135 140 145 150 155 160 165 170 175 180 185 190 195 Distance Along Profile (km) Figure 3.4: Spatial Ice Profile

3.3 Pressure Ridge Keel Identification

With datasets spatially defined in terms of draft it was possible to develop an algorithm to identify pressure ridge keel features on the underside of the ice. The algorithm used had been extensively vetted in the scientific community and widely employed (Ekeberg, Høyland, & Hansen, 2014; Fissel, et al., 2010; Melling & Riedel, 1996; Wadhams P. , 1992). However, there was variability of the input parameters throughout the literature so a further investigation of these parameters was undertaken.

The first part of the algorithm was to import the spatially defined draft data, set the starting threshold of a keel, ending threshold of a keel, and a value for the Rayleigh Criterion. The spatially defined draft data was what had been computed from the given preprocessed time series data. The starting threshold defines a minimum draft value that an ice feature must exceed to be considered a keel. The ending threshold defines a draft value where a keel is considered to begin and end. The α parameter is the Rayleigh Criterion, a value that looks at slope reversal in a segment identified as a keel, which indicates the ending of a keel that does not go below the end threshold. Essentially, simply using just the start and end thresholds to identify keels could lead to instances of keel shadowing where two keels close together would be counted as a single unit. The purpose of the α value was to eliminate this by looking for a noticeable reversal of keel slope over a keel segment defined by the starting and ending thresholds (see Figure 3.5).

Figure 3.5: Keel Shadowing Illustration (Reproduced from Wadhams & Horne, 1980, Figure 9)

It is important to note that while there are many examples in the literature of these parameters being selected, there is much variability in the starting threshold value. Both the α and ending threshold values seemed to be fairly consistent throughout the literature. An α value of 0.5 and ending threshold value of two meters was selected based on previous work (Ekeberg, Høyland, & Hansen, 2014; Fissel, et al., 2010; Wadhams & Davy, 1986). The selection of the starting threshold value however varied from values as low as two meters to as high as 13 meters (Davis & Wadhams, 1995; Fissel, et al., 2010; Wadhams & Davy, 1986).

The keel identification program first processed through the spatially defined draft data and found keels based on the starting and ending thresholds. Next, the maximum keel depth between these points was identified. Then the keel beginning and end points were redefined by finding the beginning and end of the keel based on the maximum depth point and end threshold. After this, the α value was employed to eliminate keel shadowing by separating any shadowed keels. Lastly, a check was done to correct for any keels that slightly overlapped one another. From this an output file was produced that displayed the maximum keel draft, maximum keel location, keel width, separation of keels based on maximum draft point, keel start location, and keel end location. The

44 output file was written in a comma-separated value (.csv) file. This output file was critical for all future analyses (see Figure 3.6 and Table 3.2).

Figure 3.6: Keel Identification Algorithm

46 Table 3.2: Keel Identification Summary; where the starting keel threshold is six meters

Keel Identification Summary

Number of Keels Maximum Keel Season Region Site Identified Draft (m)

Site A 5,391 24.36 2005-06 Beaufort Site B 5,614 25.00 Site A 4,198 25.08 2006-07 Beaufort Site B 3,365 23.00 Site K 3,730 25.69 Site A 3,208 25.46 2007-08 Beaufort Site K 2,459 23.56 Site V 4,043 25.60 Site A 3,505 23.55 Beaufort Site V 5,297 29.38 2009-10 Burger 4,121 26.05 Chukchi Crackerjack 4,680 23.98 Site A 2,492 25.39 Beaufort Site V 2,882 22.73 2010-11 Burger 5,766 24.13 Chukchi Crackerjack 4,993 19.50

Beaufort Sea Sites 46,184 29.38 Chukchi Sea Sites 19,560 26.05

47 3.4 Level Ice Identification

While the methodology for the identification of pressure ridge keels was well established in the scientific community, there were a variety of different methods employed to identify level ice. For this project an algorithm using the standard deviation of the sea ice draft values over a predefined minimum length was used to identify segments of level ice. While other methods were examined, particularly looking at the mode of the draft over a predefined minimum length, the results from the standard deviation method best fit the expected distribution of level ice over the entire ice floe.

First, the spatial draft data was imported into the algorithm. It is important to note that the algorithm was established so that datasets could only be run individually. For example, it would be incorrect to combine all 16 datasets and run them through the algorithm. However, it would be correct to run each dataset individually through the program to obtain results. Along with the draft data, the distance between draft measurements was a necessary input. From the spatial draft datasets it was known that all draft values were one meter apart.

Next, three major parameters were established for the algorithm to identify level ice segments. The first of these parameters was the minimum length of a level ice segments. The second was the maximum standard deviation of ice draft over a length. Lastly, the maximum draft value to be considered in the level ice analysis was necessary. For the purposes of this project the minimum length was set to 50 meters, the maximum standard deviation set to 0.1 meters, and the maximum draft considered was 30 meters.

From the literature there was little guidance on how to select the parameter values for the identification of level ice segments. In order to select parameters that would produce results that made logical sense a series of trials were run using varying parameter values. The set of values chosen were those that produced a sensible overall percentage of level ice cover for the dataset.

48 As the algorithm ran it computed both the mean and standard deviation of the draft in segments of sea ice. Thus the running mean and running standard deviation were established for ice segments. The running standard deviation was then compared to the input maximum standard deviation of 0.1 meters. From this the midpoints of the level ice segments were found and consequently used to identify the complete level ice segment. With the entire segment now defined it was possible to find both the beginning and end points of the level ice segment. As an output the program recorded the beginning and end points of the level ice segment, segment mean, segment mode, and segment standard deviation in a .csv file (see Figure 3.7 and Table 3.3).

Figure 3.7: Level Ice Identification Algorithm

50 Table 3.3: Level Ice Identification Summary

Level Ice Identification Summary Level Ice Length Level Ice Percentage Season Region Site (km) of Total Ice Site A 428 21.67% 2005-06 Beaufort Site B 604 30.38% Site A 700 39.42% 2006-07 Beaufort Site B 917 43.03% Site K 764 40.93% Site A 1,045 47.56% 2007-08 Beaufort Site K 1,166 53.38% Site V 1,166 49.82% Site A 470 36.04% Beaufort Site V 725 37.07% 2009-10 Burger 938 44.77% Chukchi Crackerjack 1,052 47.94% Site A 693 37.99% Beaufort Site V 486 36.54% 2010-11 Burger 1,437 44.12% Chukchi Crackerjack 1,477 50.90%

Beaufort Sea Sites 9,162 - Chukchi Sea Sites 4,904 -

It is important to note that the algorithm did not differentiate between FY level ice and MY ice that may have been identified as level through the algorithm. While most FY level ice was identified in the literature as ice with a draft up to two meters (Melling & Riedel, 1995), MY level ice is typically much thicker due to its greater time to develop thermodynamically and also exhibits greater spatial variability in thickness due to summer processes. Thus, it was challenging to differentiate between level MY ice and thick FY rubble without additional in situ observations. It is therefore possible that some of the thicker floes identified as level ice were MY ice floes, but it is not certain.

51 3.5 Other Ice Identification

In comparison to the algorithms to determine pressure ridge keels and level ice, the algorithm to identify other ice was relatively simple. Using the total spatial draft dataset for the entire floe, the dataset for pressure ridge keels, and the dataset for the level ice segments, by process of elimination the “other” ice segments were identified. The range of individual keels and range of level ice segments were combined and used to eliminate the ranges in the total draft dataset. From this the remaining ranges were used to establish the other ice draft segments. The other ice segments could be composed of all manner of different ice features such as rubble fields, rafted ice, and MY ice to name a few (see Figure 3.8 and Table 3.4).

Figure 3.8: Other Ice Identification Algorithm

52 Table 3.4: Other Ice Identification Summary

Other Ice Identification Summary Other Ice Length Other Ice Percentage of Season Region Site (km) Total Ice Site A 1,256 64.39% 2005-06 Beaufort Site B 1,107 56.50% Site A 881 50.46% 2006-07 Beaufort Site B 1,059 50.38% Site K 918 49.91% Site A 942 43.52% 2007-08 Beaufort Site K 864 40.10% Site V 970 42.16% Site A 626 48.87% Beaufort Site V 1,001 52.09% 2009-10 Burger 979 47.48% Chukchi Crackerjack 944 43.80% Site A 1,009 55.99% Beaufort Site V 731 55.83% 2010-11 Burger 1,590 49.55% Chukchi Crackerjack 1,244 43.63%

Beaufort Sea Sites 11,363 - Chukchi Sea Sites 4,756 -

54 Chapter 4: Data Analysis

4.1 Overview

With all of the data processed and ice features identified as either pressure ridge keel, level ice segment, or other ice segment, analyses were conducted for each feature. Drawing from the categories presented in the ISO 19906 similar parameters were investigated using several different techniques.

4.2 Probability Density Functions

When using a nondeterministic approach the implementation of PDFs was chosen to describe the uncertainty of the data. The general analysis process consisted of producing a histogram of the data being analyzed and then applying various PDFs to the plot, as well as inspecting associated probability plots. From this, candidate PDFs where chosen and a goodness-of-fit analysis was applied to the data to determine the PDF with the best fit. For this project four primary PDFs were utilized and examined. These were the exponential, gamma, Weibull, and lognormal distribution functions. The exponential, gamma, and Weibull are of a particular family of PDFs and thus are closely related (Matlab©).

55 4.2.1 Gamma Distribution

The gamma probability density function is a two parameter function that models sums of exponentially distributed random variables. The gamma distribution, as characterized by Mathematica, can be described by Eq. 4.2.1.1:

0 (Eq. 4.2.1.1)

where:

 α – shape parameter  β – scale parameter  μ – location parameter

The shape and scale parameters were defined using the data; then histograms, probability plots, and goodness-of-fit tests were used to assess the suitability of the PDF for describing the uncertainty in the data. The determination of these parameters was found from internal commands in either the Matlab© or Mathematica software packages (Wolfram).

56 4.2.2 Exponential Distribution

The exponential probability density function is a single parameter function that is a special case the gamma distribution. The exponential distribution is found by setting the α variable in the gamma distribution equal to one. The exponential distribution is special because of its utility in modeling events that occur randomly over time (Matlab©). The exponential distribution, as characterized by Mathematica, can be described by Eq. 4.2.2.1:

0 (Eq. 4.2.2.1)

where:

 λ – any real positive number that helps fit the distribution to the data  μ – location parameter

The λ parameter was defined using the data; then histograms, probability plots, and goodness-of-fit tests were used to assess the suitability of the PDF for describing the uncertainty in the data. The determination of this parameter was found from internal commands in either the Matlab© or Mathematica software packages (Wolfram).

57 4.2.3 Weibull Distribution

The Weibull probability density function, in the context of this paper, is a three parameter function which is closely related to both the exponential and gamma distributions. The Weibull distribution, as characterized by Mathematica, can be described by Eq. 4.2.3.1:

0 (Eq. 4.2.3.1)

where:

 α – shape parameter  β – scale parameter  μ – location parameter

58 4.2.4 Lognormal Distribution

The lognormal distribution, in the context of this paper, is a two parameter function whose logarithm has a normal distribution. The lognormal distribution, as characterized by Matlab©, can be described by Eq. 4.2.4.1:

|, (Eq. 4.2.4.1) √

where:

 μ –logarithmic mean  σ – logarithmic standard deviation

The logarithmic mean and logarithmic standard deviation parameters were defined using the data; then histograms, probability plots, and goodness-of-fit tests were used to assess the suitability of the PDF for describing the uncertainty in the data. The determination of these parameters was found from internal commands in either the Matlab© or Mathematica software packages (Wolfram).

4.3 P-Value Testing of PDFs

To determine which PDF best fit the respective data two different methods were employed. The first was a qualitative method which involved creating a probability plot from the parameters of the distribution and observing how close the data was with the distribution. The second method was quantitative. This involved using a goodness-of-fit test on the data and generating an associative p-value. This p-value was compared to the established significance level, five percent, and also compared between distributions.

59 Just as there are a plethora of different PDFs to fit to data, there are also numerous tests to determine goodness-of-fit. Goodness-of-fit tests including the Anderson-Darling test, Kolmogorov-Smirnov test, Lilliefors test, and Cramér-von Mises test were all considered. After comparing values for a few datasets it was determined that the Cramér- von Mises (CVM) criteria was the most applicable for this project. The Cramér-von Mises test has been shown to sometimes be more powerful against a large class of alternate hypotheses than tests such as the Kolmogorov-Smirnov (Arnold & Emerson, 2011), thereby increasing its usefulness for this project.

The Cramér-von Mises test for a single sample dataset can be described by Eq. 4.3.1 (Arnold & Emerson, 2011):

∙ (Eq. 4.3.1)

where:

 W2 – Cramér -von Mises test criterion  n – number of entries

 F0(x) – values drawn from a specified distribution

 Fdata(x) – empirical distribution function of the sample

The Cramér-von Mises test calculates a p-value by computing the area between the theoretical distribution cumulative probability plot and the cumulative data. If this area is large, then the p-value will be small and vice versa. Using a standard significance level of five percent it was determined if a theoretical distribution fit a dataset.

60 4.4 Pressure Ridge Keel

Since the pressure ridge keel is considered one of the most important topics for sea ice loading on offshore structures (Ekeberg, Høyland, & Hansen, 2014) the majority of the analysis effort was spent there. In order to accurately describe, and later extrapolate, keel conditions the actual keel feature was broken into areas of interest. Drawing from the ISO 19906, and an assortment of other literature, keel draft, width, angle, velocity, and spacing were chosen to be analyzed.

4.4.1 Keel Identification Starting Threshold Value

Before an analysis of the pressure ridge keel could be begin a starting threshold value, as described in the Data section, had to be selected. From the literature reviewed there were a variety of different starting threshold values, ranging from 2 to 13 meters (Davis & Wadhams, 1995; Fissel, et al., 2010; Wadhams & Davy, 1986). However, it seemed that these values were chosen somewhat arbitrarily (Wadhams P. , 2011). For this project a less arbitrary method was attempted to select a starting threshold value.

To determine a starting threshold value a series of trials were conducted. Using all of the individual datasets, keels were identified using starting threshold values of four, five, six, seven, and nine meters. It is important to note that by increasing the starting threshold parameter the number of keels identified decreased.

Next, the exponential and Weibull PDFs were fit to the keel draft values and a Cramér-von Mises goodness-of-fit test was used. This produced p-values for all 16 datasets, for each of the five starting thresholds, giving a total of 80 p- values for each distribution. These p-values were then plotted see if a trend would emerge between the datasets (see Figure 4.1).

61 62

Figure 4.1: Starting Threshold P-Value Test Summary

As seen in Figure 4.1 there seems to be a significant jump in p-value between the six and seven meter starting thresholds. The implication being that all ice features with a draft of six meters or more conformed to a single PDF. It is important to note that not all of the datasets displayed this particular behavior; however it seemed to be a general trend. For this project, all ice features with a draft of six meters or more were considered pressure ridge keels. The project team determined that a value of six meters provided a great enough p-value, while still providing plenty of ridge draft data and making physical sense. This seemed to be an improvement over previous methods for determining the starting threshold, which had previously been chosen relatively arbitrarily (Wadhams P. , 2011).

4.4.2 Pressure Ridge Keel Draft

To analyze the keel draft data a nondeterministic reliability approach was utilized. First, the data was analyzed for an entire season at a single site. The first segment of this analysis included taking the data and using it to create a histogram of keel drafts. Next, various PDFs, primarily the exponential, gamma, and Weibull distributions, were applied to the histogram. These distributions were used to create probability plots. Then, the PDFs were tested using a Cramér-von Mises goodness-of-fit test. Using the results of the goodness-of-fit testing across all datasets a consistent PDF, the Weibull distribution, was selected. The Weibull distribution either met or exceeded the significance level of five percent in almost all cases. Once this was completed the seasonal data was broadly examined on a per month basis. After applying this methodology to one site for one season the same process was repeated for the remaining 15 datasets. Furthermore, the datasets per sea were combined and underwent the same process.

First, an initial plot was produced from the program to display qualitatively how the drafts of the keels were generally distributed. The figure took all of the measured drafts along each keel, not just the maximum draft, and

63 plotted them. The closer the colorful segment was to the origin of the x-axis, the lesser in width the keels were. However, if the colorful segment was large horizontally, it indicated that the keels had large widths (see Figure 4.2).

2005-06 Site A Stacked Keel Shapes 0

15 Draft (m)

25 -100.0 -50.0 0.0 50.0 100.0 Distance From Deepest Point on Keel (m)

Figure 4.2: 2005-06 Site A Stacked Keel Shapes

Figure 4.2 serves two important purposes. First, it allows the user to quickly determine if the keels are exceptionally large or exceptionally small. Secondly, it allows the user to determine if there are a large portion of asymmetrical keels. A large amount of asymmetrical keels would cause the colorful segment of the plot to shift greatly to one side. This would likely indicate that there is a natural phenomenon causing this shift, which would warrant further investigation. During the analysis of the datasets for this project large amounts of asymmetry were not encountered.

64 After the initial qualitative figure was produced to check for glaring irregularities, such as extremely wide or dominantly asymmetrical keels, a histogram was produced for the data. The histogram used keel depth bin sizes of 0.5 meters and plotted keel depths from 6 to 30 meters, since keels are defined in this work as ice features with a draft of six meters or greater and no keels were observed in excess of 30 meters (see Figure 4.3).

2005-06 Site A Keel Draft 0.35

0.3

0.25

0.2

0.15 Fraction(-)

0.1

0.05

0 6 10 15 20 25 30 Keel Depth (m)

Figure 4.3: Keel Draft Histogram

With keel draft histograms produced for each dataset distributions could begin to be fit. It is important to note that Matlab© has a limitation with its distribution fitting that forces the user to shift the histogram to the origin to obtain accurate parameter values. Once the correct parameters have been obtained and limit state values have been determined it is vital to add this shift back in to the limit state values (see Figure 4.4).

65 2005-06 Site A Shifted Keel Histogram 0.4

0.35

0.3

0.25

0.2

Fraction (-) 0.15

0.1

0.05

0 0 5 10 15 20 25 30 [Keel Depth - 6] (m)

Figure 4.4: Shifted Keel Draft Histogram

With the various distributions applied to the keel draft data parameters were determined using Mathematica (see Table 4.1).

66 Table 4.1: Keel Draft PDF Parameters; where the μ is six meters

Keel Draft PDF Parameter Summary Exponential Gamma Weibull Season Region Site λ α β α β Site A 0.32 1.01 3.09 1.01 3.12 2005-06 Beaufort Site B 0.32 0.99 3.19 1.00 3.16 Site A 0.41 1.00 2.41 1.00 2.41 2006-07 Beaufort Site B 0.50 0.97 2.06 0.98 1.99 Site K 0.44 0.93 2.43 0.96 2.23 Site A 0.32 1.07 2.87 1.06 3.16 2007-08 Beaufort Site K 0.34 1.08 2.70 1.06 2.99 Site V 0.37 1.04 2.60 1.03 2.73 Site A 0.36 1.07 2.61 1.06 2.85 Beaufort Site V 0.37 0.98 2.76 0.99 2.70 2009-10 Burger 0.40 1.06 2.34 1.04 2.53 Chukchi Crackerjack 0.38 1.01 2.60 1.01 2.64 Site A 0.38 0.89 2.90 0.92 2.50 Beaufort Site V 0.43 1.01 2.29 1.01 2.33 2010-11 Burger 0.44 1.00 2.29 1.00 2.28 Chukchi Crackerjack 0.49 1.08 1.92 1.06 2.11

Beaufort Sea Sites 0.37 0.99 2.75 0.99 2.70 Chukchi Sea Sites 0.43 1.03 2.29 1.02 2.37

With the applicable PDFs selected and their parameters found the next step was to determine which PDF best fit the data. To do this first a qualitative analysis was conducted using probability plots, followed by a quantitative p-value analysis. The probability plots provided a quick reference to determine not only if a PDF accurately fit the data but also where the PDF was accurate in the dataset.

Examining the two sample probability plots presented, one would expect that the Weibull distribution would be a better quantitative fit than the exponential distribution. Not only that, but by examining the plots closely one can see that for 67 the larger draft values the Weibull distribution clearly provided a better representation than the exponential. Since this project is primarily concerned with determining the limit states values, values that present the greater engineering risk, the tail end of the distribution is critical. It is also important to note that the probability plots below reflect the shift that was described previously. Any values derived from these plots should account for this shift and thus increase the draft by six meters (see Figure 4.5 and Figure 4.6).

2005-06 Site A Keel Draft Exponential Probability Plot

0.9999

0.9995 0.999

0.995 0.99 Probability 0.95 0.9 0.75 0.5 0.25 0.01 0 5 10 15 [Draft Data - 6] (m)

Figure 4.5: Keel Draft Exponential Probability Plot

68 2005-06 Site A Keel Draft Weibull Probability Plot

0.99990.999 0.99 0.9 0.75 0.5 0.25 0.1 0.05

Probability 0.01 0.005

0.001 0.0005

0.0001

-3 -2 -1 0 1 2 10 10 10 10 10 10 [Draft Data - 6] (m)

Figure 4.6: Keel Draft Weibull Probability Plot

While probability plots provided an excellent tool with which to qualitatively assess a comparison between a PDF and data, a quantitative method is more rigorous and may be compared to acceptance criterion. To analyze the PDFs goodness-of-fit the Cramér-von Mises test was used to obtain a p-value for each distribution. The p-values were then compared between distributions to see which one was most accurate based on the test (see Table 4.2).

69 Table 4.2: Keel Draft P-Value Summary

Keel Draft PDF P-Value Summary Exp. Gamma Weibull Season Region Site CVM CVM CVM Best Fit P-Value P-Value P-Value Site A 0.6568 0.6148 0.5667 Exp. 2005-06 Beaufort Site B 0.3896 0.4453 0.3819 Gamma Site A 0.8729 0.8461 0.9086 2006-07 Beaufort Site B 0.3568 0.8390 0.9753 Weibull Site K 0.0475 0.9278 0.9966 Site A 0.0029 0.0675 0.1850 2007-08 Beaufort Site K 0.0140 0.1091 0.1906 Weibull Site V 0.0487 0.1225 0.1784 Site A 0.0007 0.0000 0.0492 Beaufort Weibull Site V 0.7792 0.9941 0.9976 2009-10 Burger 0.0426 0.4340 0.6684 Chukchi Weibull Crackerjack 0.6384 0.7225 0.7591 Site A 0.0010 0.2723 0.7046 Weibull Beaufort Site V 0.7142 0.6918 0.6285 Exp. 2010-11 Burger 0.4945 0.5367 0.5547 Chukchi Weibull Crackerjack 0.0027 0.1234 0.2717

Beaufort Sea Sites 0.0246 0.1282 0.0847 Gamma Chukchi Sea Sites 0.0694 0.2633 0.3421 Weibull

From Table 4.2 it can be observed that in general the Weibull distribution produced the most accurate fit to the data using the Cramér-von Mises criterion. While there were some datasets where an exponential or gamma distribution produced a more accurate fit, in general the increase in accuracy was slight. It is interesting to note that for the dataset 2009-10 Beaufort Site V that an exponential distribution best fit the data. This could potentially be due to the shorter length of this dataset, as shown in Table 3.1. To make the limit state results consistent and

70 reproducible the Weibull distribution was chosen to represent all datasets. From the results presented in Table 4.2 this seemed like a logical simplification.

4.4.3 Pressure Ridge Keel Width

Initially a nondeterministic probability based approach was employed to try to fit PDFs to the keel width data. However, it was found that the PDFs did not consistently fit the data accurately. Upon examining the qualitative probability plots it was easily deduced that the chosen PDFs did not accurately reflect the trends of the data. Once this was determined a modal analysis was employed to produce results that would make sense (see Figure 4.7 - Figure 4.9).

2005-06 Site A Keel Width Exponential Probability Plot

0.9999

0.9995 0.999

0.995 0.99 Probability 0.95 0.9 0.75 0.5 0.25 0.01 0 200 400 600 800 1000 1200 Keel Width (m)

Figure 4.7: Keel Width Exponential Probability Plot

71 2005-06 Site A Keel Width Weibull Probability Plot

0.99990.999 0.99 0.9 0.75 0.5 0.25 0.1 0.05

Probability 0.01 0.005

0.001 0.0005

0.0001

0 1 2 3 4 10 10 10 10 10 Keel Width (m)

Figure 4.8: Keel Width Weibull Probability Plot

2005-06 Site A Keel Width Lognormal Probability Plot 0.9999 0.99950.999 0.995 0.99 0.95 0.9 0.75 0.5 0.25 Probability 0.1 0.05 0.01 0.005 0.00050.001 0.0001 0 1 2 3 4 10 10 10 10 10 Keel Width (m)

Figure 4.9: Keel Width Lognormal Probability Plot

72 Conceptually a modal method employed here seemed reasonable since due to the limitations of the IPS and ADCP there was no way to know at which orientation a keel passed over the instruments. The keel could have passed over the instruments perfectly perpendicular, which would represent the true width of the keel. It is also possible that the keel could have passed over the instruments nearly parallel, which would greatly increase the width of the keel. For keels passing over the mooring at small angles, approximately 15º or less from an orthogonal approach, only a small increase in recorded width was expected. These measurements near the true width were thought to represent the mode of the data.

To analyze the mode of the width data, a general method to determine the relationship between keel draft and width needed to be established. For every width data point there was a corresponding maximum draft data point. To divide the keel width data into segments, ranges of keel drafts one meter wide were chosen. Thus the associative width values for the respective draft values were segmented (see Figure 4.10).

73 Beaufort Modal Keel Width At Draft 6 m & 7 m 600

500

400

300

No. of Keels 200

100

0 0 50 100 150 200 Keel Width (m)

Figure 4.10: Beaufort Keel Width Modal Analysis Plot

The histograms, as represented above, were for all the keels in either the Beaufort or Chukchi Seas. Using a collection of these histograms a modal keel width value was determined. This modal value was used to represent the “true” width of the keel, based on the conceptual reasoning previously discussed.

4.4.4 Pressure Ridge Keel Angle

Using the results from the pressure ridge keel width analysis a general keel angle was be estimated. Knowing the modal keel width associated with each bin of keel depth, relative values were determined and plotted. It is important to note that this analysis examined keel widths determined from keel draft bins with a width of one meter. While there was an investigation into using larger bin widths, they did not have a significant impact on the results and have thus been omitted (see Figure 4.11).

Figure 4.11: Keel Angle Determination

In Figure 4.11 the green line represents the keel width values that would be determined using the ISO 19906 prescribed keel angle of 26°. The plot indicates that actual keel angles are greater than those prescribed in the ISO 19906; resulting in a narrower keel. Using a linear regression for the data in both seas, keel angles were determined for the Beaufort and Chukchi Seas, respectively. Due to the large sample size of keels in this project it seemed probable that these values were representative of true keel characteristics. Diagrammatic representations of these values are shown in the Results section.

4.4.5 Pressure Ridge Keel Velocity

Initially a nondeterministic reliability based approach was employed to fit PDFs to the keel velocity data. However, it was found that the PDFs did not consistently fit the data accurately. Upon examining the qualitative probability plots it was deduced that the chosen PDFs did not accurately reflect the trends of the data. Once this was determined a different analysis method was employed (see Figure 4.12 - Figure 4.14).

75 Beaufort Keel Speed Exponential Probability Plot

0.9999

0.9995 0.999

0.995

Probability 0.99

0.95 0.9 0.75 0.5 0.25 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Keel Speed (m/s)

Figure 4.12: Keel Speed Exponential Probability Plot

Beaufort Keel Speed Weibull Probability Plot

0.99990.999 0.99 0.9 0.75 0.5 0.25 0.1 0.05 0.01 0.005 Probability 0.001 0.0005 0.0001

-6 -4 -2 0 2 10 10 10 10 10 Keel Speed (m/s)

Figure 4.13: Keel Speed Weibull Probability Plot

76 Beaufort Keel Speed Lognormal Probability Plot

0.9999 0.999 0.99 0.95 0.9 0.75 0.5 0.25

Probability 0.1 0.05

0.0001

-6 -4 -2 0 2 10 10 10 10 10 Keel Speed (m/s)

Figure 4.14: Keel Speed Lognormal Probability Plot

The first step in analyzing the keel velocity data was to determine how fast each keel was moving at the moment it passed over the mooring. To determine this speed a point was chosen on either side of the keel. Knowing both the distance between these points and the time it took for both to pass over the mooring, the speed could be interpolated and then applied to the keel. Locations five meters before and after the keel were used to estimate the speed of the keel.

Once all of the keel speeds for a sea had been estimated, bins were created based on the draft of the keel. Using the keel draft bins both the median and mean speed of the keels were determined. To properly visualize this all values were plotted. From this analysis it was determined that there was no significant change in keel speed due to keel draft. This ran counter to the initial hypothesis where it was thought that deeper keels would move more slowly than shallow keels due to increased ocean drag (see Figure 4.15).

Figure 4.15: Keel Speed v. Draft

4.4.6 Pressure Ridge Keel Spacing

The process to analyze keel spacing data was similar to that of keel draft. A histogram was first produced showing the relative distribution of different pressure ridge keel spacing. In general, there was a high concentration of keel spacing data less than 1,000 meters and a smattering of keel spacing values greater than 1,000 meters. It is important to note while there were spacing values much greater than 1,000 meters, they were not common and thus the x-axis was truncated for a better visual display. Various PDFs were then fit to the histogram in an attempt to model the data. Next, qualitative probability plots were produced for the PDFs to see if they fit the data. Lastly, the Cramér-von Mises p-value was calculated for the PDF (see Figure 4.16).

78 2005-06 Site A Keel Spacing 0.025

0.02

0.015 Fraction 0.01

0.005

0 0 100 200 300 400 500 600 700 800 900 1000 Keel Spacing (m)

Figure 4.16: 2005-06 Site A Keel Spacing

From these histograms it appeared that it was plausible to fit a PDF to the data. For the keel spacing data the gamma, Weibull, and lognormal PDFs were fit to the data. The exponential distribution was excluded in this report but was briefly examined. The exponential distribution did not seem to even remotely fit the data and thus was excluded. Table 4.3 shows the parameters found for each PDF.

79 Table 4.3: Keel Spacing PDF Parameters

Keel Spacing PDF Parameter Summary Gamma Weibull Lognormal Season Region Site α β α β μ σ Site A 0.74 435.1 0.77 252.1 4.97 1.07 2005-06 Beaufort Site B 0.72 398.2 0.76 223.5 4.83 1.09 Site A 0.66 548.4 0.72 260.1 4.96 1.13 2006-07 Beaufort Site B 0.36 1531.0 0.71 406.7 5.35 1.25 Site K 0.61 723.2 0.70 291.8 5.06 1.15 Site A 0.69 485.6 0.74 239.9 4.93 1.04 2007-08 Beaufort Site K 0.57 849.7 0.68 291.4 5.08 1.11 Site V 0.65 537.0 0.81 293.6 5.12 1.08 Site A 0.75 466.7 0.77 267.8 5.05 1.02 Beaufort Site V 0.76 404.6 0.78 250.0 4.94 1.12 2009-10 Burger 0.47 967.2 0.73 345.1 5.21 1.22 Chukchi Crackerjack 0.56 786.4 0.67 278.7 4.98 1.22 Site A 0.35 1827.2 0.65 385.1 5.27 1.29 Beaufort Site V 0.58 737.8 0.74 327.3 5.16 1.21 2010-11 Burger 0.54 995.3 0.66 323.5 5.12 1.25 Chukchi Crackerjack 0.50 1112.6 0.65 306.2 5.07 1.25

Beaufort Sea Sites 0.67 576.3 0.73 279.2 5.04 1.13 Chukchi Sea Sites 0.55 911.3 0.67 312.3 5.09 1.24

After the PDFs had been fit to the data qualatitive probability plots were produced (see Figure 4.17 and Figure 4.18).

80 2005-06 Site A Keel Spacing Weibull Probability Plot

0.9999 0.999 0.99 0.9 0.75 0.5 0.25 0.1 0.05 Probability 0.01 0.005

0.001 0.0005

0.0001

0 1 2 3 4 5 10 10 10 10 10 10 Data

Figure 4.17: Keel Spacing Weibull Probability Plot

2005-06 Site A Keel Spacing Lognormal Probability Plot 0.9999 0.9995 0.999 0.995 0.99

0.95 0.9 0.75

0.5

Probability 0.25 0.1 0.05

0.01 0.005 0.001 0.0005 0.0001 0 1 2 3 4 5 10 10 10 10 10 10 Data

Figure 4.18: Keel Spacing Lognormal Probability Plot

81 From examining Figure 4.17 and Figure 4.18 it appeared that the lognormal PDF most closely represented the keel spacing data, which was fairly consistent throughout all the datasets. To further support this argument p-values were produced using the Cramér-von Mises goodness-of-fit test (see Table 4.4).

Table 4.4: Keel Spacing P-Value Summary

Keel Spacing PDF P-Value Summary Gamma Weibull Lognormal Season Region Site CVM CVM CVM P-Value P-Value P-Value Site A 1.0E-14 1.0E-14 5.2E-10 2005-06 Beaufort Site B 9.7E-15 2.9E-15 3.3E-12 Site A 3.3E-15 6.8E-15 6.1E-09 2006-07 Beaufort Site B 9.3E-15 7.8E-16 3.5E-06 Site K 3.2E-15 1.5E-14 2.8E-09 Site A 1.9E-15 7.5E-15 4.9E-06 2007-08 Beaufort Site K 9.2E-15 1.4E-14 2.5E-07 Site V 5.2E-15 3.8E-15 2.1E-04 Site A 6.1E-15 1.3E-14 4.9E-07 Beaufort Site V 1.2E-14 2.1E-15 7.6E-05 2009-10 Burger 7.7E-15 7.7E-15 8.4E-05 Chukchi Crackerjack 2.2E-15 8.8E-15 2.2E-07 Site A 9.5E-15 3.1E-15 2.9E-07 Beaufort Site V 8.9E-16 9.8E-15 6.9E-05 2010-11 Burger 9.4E-15 8.4E-15 5.9E-12 Chukchi Crackerjack 3.8E-15 4.9E-15 2.6E-10

Beaufort Sea Sites 1.5E-14 2.1E-14 1.1E-14 Chukchi Sea Sites 1.8E-14 9.4E-15 1.1E-16

The Cramér-von Mises p-values from the lognormal PDF, while they did not pass the significance level of 0.05, seemed to provide the best fit for the keel 82 spacing data. Table 4.4 shows that in general the lognormal PDF provided a fit with p-values orders of magnitude closer to 0.05 than the gamma or Weibull PDFs.

4.5 Ice Velocity

To gain an understanding of ice movement patterns it is important to examine how all the ice moves in terms of direction and magnitude. A common method of presenting this is with an ice velocity rose. An ice velocity rose functions similarly to a wind rose, showing both the direction and speed at which the ice is moving. It is important to note that for this application the “leaving” direction was used. That is to say the direction presented is that which the ice segment was travelling once it had passed over the mooring, not before.

From previously published literature on both the Beaufort and Chukchi Seas it was expected that the ice velocity rose would show dominant movement patterns. For the Beaufort Sea it was expected that the ice would move primarily east and west, approximately parallel to the nearby Alaska coastline. For the Chukchi Sea it was expected that the ice movement would be more evenly distributed due to the greater distance of the moorings to the coastline and vary from season to season (International Organization for Standardization, 2010). Ice velocity roses for sites in both the Beaufort and Chukchi Seas are shown in the Results section of this report (see Figure 4.19).

83 2005-06 Site A Ice Velocity Rose

Ice Speeds (cm/s) 25% I  120 S 20% 100  I < 120 S 15% 80  I < 100 S 10% 60  IS < 80 5% 40  IS < 60 20  I < 40 S W 0% E 0  IS < 20

Figure 4.19: 2005-06 Site A Ice Velocity Rose

4.6 Level Ice

For the analysis of level ice the first step was to examine the ice type distribution for an entire dataset. From the literature on level ice it was expected that a significant portion of the dataset would be level ice (Wadhams & Horne, 1980). It was also expected that the moorings in the Chukchi Sea would observe more level ice than those in the Beaufort Sea due to the zone of strong ice deformation found near the coast in the latter (Mahoney & Eicken; Reimnitz & Barnes, 1974). Upon analyzing the ice type distribution everything looked reasonable. Next it was necessary to examine the distribution of level ice on a monthly basis (see Figure 4.20).

84 2005-06 Site A Level Ice Distribution 3 400 Mean Median 350 2.5 Lower 5% Upper 5% 300 2 250

1.5 200

33.3% 150 1 56.1%

100 Ice Drift Distance (km) Level Ice ThicknessLevel Ice (m) 32.0% 0.5 54.6% 15.3% 50 0.0% 16.4% 7.8% 3.2% 1.7% 0.7% 1.9% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure 4.20: Level Ice Distribution

Figure 4.20 shows the general monthly distribution of level ice for an individual dataset. The light gray areas represent the ice drift distance that passed over the mooring during a given month, as measured by the vertical axis to the right. The dark gray areas represent what fraction of that ice drift distance was level ice, with the exact percentage shown above the gray area. The various lines that cross the figure are explained in the legend and their values can be determined by using the vertical axis to the left. This figure succinctly shows how level ice varies from month to month and what some representative values are.

85 Along with the level ice distribution figure monthly histograms were produced for level ice draft. A discussion of these histograms is presented in the Results section (see Figure 4.21).

2005-06 Site A Level Ice, January 0.45 Monthly Level Ice Track = 10.3 km 0.4

0.35

0.3

0.25

0.2 Fraction (-) Fraction 0.15

0.1

0.05

0 0 1 2 3 4 5 6 7 Level Ice Draft (m)

Figure 4.21: 2005-06 Site A January Level Ice Draft

4.7 Other Ice

Other ice was not extensively examined as it was difficult to know what type of ice features it actually represented. A sample figure of a typical histogram produced by the draft of other ice over a season is presented in the Results section and is also shown here. A monthly analysis of other ice was not conducted (see Figure 4.22).

86 2005-06 Site A Other Ice Draft 0.1 Other Ice Track = 1263 km

0.08

0.06

0.04 Fraction (-)

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure 4.22: 2005-06 Site A Other Ice Histogram

88 Chapter 5: Results

5.1 Pressure Ridge Keel

One important result of the pressure ridge keel analysis was the occurrence of keels at a particular location per month. Knowing when keels occur at a site can impact construction schedules and operation of an offshore structure. Full results are presented in Appendix A (see Figure 5.1).

2005-06 Site A Keels By Month 1400

1200

1000

800

600

Number of Number Keels 400

200

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure 5.1: 2005-06 Site A Keel Totals by Month

5.1.1 Pressure Ridge Keel Draft

From the analysis of keel draft a series of PDFs were fit to the data. After careful consideration it was determined that the Weibull PDF was best suited to represent the distribution of keel drafts. Examining each dataset individually, and

89 combining the data to examine the seas as a whole, PDF parameters were determined (see Table 5.1).

Table 5.1: Keel Draft Weibull Parameter Summary; see Eq. 4.2.3.1 for Weibull PDF form

Keel Draft Weibull Parameter Summary Weibull Season Region Site α β Site A 1.01 3.12 2005-06 Beaufort Site B 1.00 3.16 Site A 1.00 2.41 2006-07 Beaufort Site B 0.98 1.99 Site K 0.96 2.23 Site A 1.06 3.16 2007-08 Beaufort Site K 1.06 2.99 Site V 1.03 2.73 Site A 1.06 2.85 Beaufort Site V 0.99 2.70 2009-10 Burger 1.04 2.53 Chukchi Crackerjack 1.01 2.64 Site A 0.92 2.50 Beaufort Site V 1.01 2.33 2010-11 Burger 1.00 2.28 Chukchi Crackerjack 1.06 2.11

Beaufort Sea Sites 0.99 2.70 Chukchi Sea Sites 1.02 2.37

5.1.2 Pressure Ridge Keel Width

From the analysis of keel width it was found that a nondeterministic approach would be inadequate for an accurate analysis. It seemed that a modal

90 analysis better suited the data. This in itself is a result, since previous literature typically used PDFs or ratios to describe keel width. Another important result from the keel width analysis was that there appeared to be a linear relationship between keel width and keel depth, indicating that the majority of ridges were fairly triangular in cross section. This also deviated from the literature and could potentially indicate an increase in the presence of FY ridges.

5.1.3 Pressure Ridge Keel Angle

From the analysis of keel width and depth empirical keel angles of 33.7° and 32.5° were found for the Beaufort and Chukchi Seas respectively. These values were determined from the linear regression of the data, presented in Figure 4.11. A diagrammatic example of this is shown (see Figure 5.2 and Figure 5.3).

Figure 5.2: Beaufort Sea Diagrammatic Keel Width/Angle

Figure 5.3: Chukchi Sea Diagrammatic Keel Width/Angle

Figure 5.2 and Figure 5.3 show how the change of the keel angle can impact the width of the keel. Using an arbitrary keel draft of 15 meters it is apparent that the width of the keel greatly shrinks with a slight increase in angle. This could have a serious impact on how keel forces are calculated for offshore structure design. This is an indication that the ISO 19906 keel angle may be conservative.

5.1.4 Pressure Ridge Keel Velocity

From the velocity analysis an interesting conclusion was reached between ridge depth and speed. The analysis did not suggest that there was a relationship between keel draft and keel speed. The data suggested that keel speed is independent of keel draft, which ran counter to the initial hypothesis (see Figure 5.4 and Figure 5.5).

Figure 5.4: Beaufort Keel Speed v. Draft

Figure 5.5: Chukchi Keel Speed v. Draft

93 5.1.5 Pressure Ridge Keel Spacing

The result from the keel spacing analysis was the development of histograms for the data and fitting PDFs to the data. In general, there was a high concentration of keel spacing data less than 1,000 meters and a smattering of keel spacing values greater than 1,000 meters. It is important to note while there were spacing values much greater than 1,000 meters, they were not common and thus the x-axis was truncated for a better visual display. Figure 5.6 serves as an example of the histograms produced, while Table 5.2 summarizes the lognormal PDF parameters for the data (see Figure 5.6 and Table 5.2).

2005-06 Site A Keel Spacing 0.025

0.02

0.015 Fraction 0.01

0.005

0 0 100 200 300 400 500 600 700 800 900 1000 Keel Spacing (m)

Figure 5.6: Keel Spacing

94 Table 5.2: Keel Spacing Lognormal Parameters

Keel Spacing PDF Parameter Summary Lognormal Season Region Site μ σ Site A 4.97 1.07 2005-06 Beaufort Site B 4.83 1.09 Site A 4.96 1.13 2006-07 Beaufort Site B 5.35 1.25 Site K 5.06 1.15 Site A 4.93 1.04 2007-08 Beaufort Site K 5.08 1.11 Site V 5.12 1.08 Site A 5.05 1.02 Beaufort Site V 4.94 1.12 2009-10 Burger 5.21 1.22 Chukchi Crackerjack 4.98 1.22 Site A 5.27 1.29 Beaufort Site V 5.16 1.21 2010-11 Burger 5.12 1.25 Chukchi Crackerjack 5.07 1.25

Beaufort Sea Sites 5.04 1.13 Chukchi Sea Sites 5.09 1.24

5.2 Ice Velocity

A useful result from the ice velocity analysis was the development of ice velocity roses. These plots are important because they show which way the ice predominantly travels and its magnitude. The results from this analysis made sense given the position of the moorings. For locations in the Beaufort Sea dominant east and west direction movements were observed. This is sensible since these moorings were located close to the shore. For locations in the Chukchi Sea there was a much more distributed movement

95 pattern. This was expected since these moorings were located farther from shore. Full results are presented in Appendix C (see Figure 5.7 and Figure 5.8).

2005-06 Site A Ice Velocity Rose

Ice Speeds (cm/s) 25% I  120 S 20% 100  I < 120 S 15% 80  I < 100 S 10% 60  IS < 80 5% 40  IS < 60 20  I < 40 S W 0% E 0  IS < 20

Figure 5.7: Beaufort Site Ice Velocity Rose

96 2009-10 Burger Ice Velocity Rose

Ice Speeds (cm/s) 20% I  90 S 16% 80  I < 90 S 12% 70  IS < 80 8% 60  IS < 70 4% 50  IS < 60 40  I < 50 S W 0% E 30  IS < 40

20  IS < 30

10  IS < 20

0  IS < 10

Figure 5.8: Chukchi Site Ice Velocity Rose

5.3 Level Ice

Two important results were obtained for level ice in the Beaufort and Chukchi Seas. The first was the general percentage of level ice in a dataset (see Table 5.3).

97 Table 5.3: Ice Type Percentages

Ice Type Percentages Season Region Site Keel Ice % Level Ice % Other Ice % Site A 13.98 21.67 64.39 2005-06 Beaufort Site B 13.13 30.38 56.50 Site A 10.15 39.42 50.46 2006-07 Beaufort Site B 6.60 43.03 50.38 Site K 9.17 40.93 49.91 Site A 8.93 47.56 43.52 2007-08 Beaufort Site K 6.54 53.38 40.10 Site V 8.05 49.82 42.16 Site A 15.13 36.04 48.87 Beaufort Site V 10.85 37.07 52.09 2009-10 Burger 7.78 44.77 47.48 Chukchi Crackerjack 8.28 47.94 43.80 Site A 6.04 37.99 55.99 Beaufort Site V 7.65 36.54 55.83 2010-11 Burger 6.34 44.12 49.55 Chukchi Crackerjack 5.48 50.90 43.63

As can be seen the majority of ice cover was either level ice or other ice. This result generally agrees with published literature. It is important to note that in Table 5.3 the sum of the percentages equals a value larger than 100%. This is due to small irregularities in the program where the tail ends of draft values identified as level ice may also be identified as the tail end of a pressure ridge keel. Due to this it should be expected that all of the values are slightly above 100%.

Secondly, monthly histograms of level ice draft were produced. These histograms provide valuable information on the distribution of level ice thickness, which may be important for any operations that take place on the ice. These histograms depict how the ice changes from month to month (see Figure 5.9).

2009-10 Burger Level Ice, Jul-Oct 2009-10 Burger Level Ice, November 2009-10 Burger Level Ice, December 0.8 Monthly LI Track = 0 m Monthly LI Track = 152662 m Monthly LI Track = 350502 m 0.7 0.6 0.5

0.4

Fraction (-) 0.3

0.2

0.1

0 2009-10 Burger Level Ice, January 2009-10 Burger Level Ice, February 2009-10 Burger Level Ice, March 0.8 Monthly LI Track = 183986 m Monthly LI Track = 79589 m Monthly LI Track = 59719 m 0.7

0.6

0.5

0.4 99

Fraction (-) 0.3

0.2

0.1

0 2009-10 Burger Level Ice, April 2009-10 Burger Level Ice, May 2009-10 Burger Level Ice, June 0.8 Monthly LI Track = 73841 m Monthly LI Track = 41135 m Monthly LI Track = 1525 m 0.7

0.6

0.5

0.4

Fraction (-) 0.3

0.2

0.1

0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Level Ice Draft ( m ) Level Ice Draft ( m ) Level Ice Draft ( m )

Figure 5.9: Monthly Level Ice Growth

5.4 Other Ice

For other ice the only results obtained were seasonal histograms for other ice draft. Other ice segments could potentially be composed of all manner of different ice features such as rubble fields, rafted ice, and MY ice to name a few. Full results are presented in Appendix E (see Figure 5.10).

2005-06 Site A Other Ice Draft 0.1 Other Ice Track = 1263 km

0.08

0.06

0.04 Fraction (-)

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m) Figure 5.10: 2005-06 Site A Other Ice Histogram

100 Chapter 6: Implementation

6.1 ISO 19906 Comparison

As stated in the Introduction section of this paper, the ISO 19906 contains sea ice parameters for both the Beaufort and Chukchi Seas. However, some of this information is either inconsistent with the Normative or has been omitted. In order to provide more information a comparison between various parameters was conducted.

6.1.1 Beaufort Sea

Table 6.1 shows the sea ice parameters currently recorded in the ISO 19906 for the Beaufort Sea, along with the updated values found from this study.

101 Table 6.1: Beaufort Sea ISO 19906 Sea Ice Conditions; values in bold indicate results from this study (Reproduced from International Organization for Standardization, 2010, Table B.7-4)

Average Range of Parameter Annual Value Annual Values Sea Ice Late September First Ice October Occurrenc to late October e Early July to Last Ice July mid-August Landfast Ice Thickness 1.8 1.5 to 2.3 Level Ice (m) (FY) Floe Thickness (m) 1.8 1.5 to 2.3 Rafted Ice Rafted Ice Thickness (m) 3 2.5 to 4.5 Rubble Sail Height (m) 5 3 to 6 Fields Length (m) 100 to 1,000 100 to 1,000 3 to 6 Sail Height (m) 5 1 to 7 Ridges 15 to 28 Keel Depth (m) 25 6 to 30 Water Depth Range (m) 20 15 to 30 Stamukhi Sail Height (m) 5 to 10 up to 20 Level Ice Ice Thickness (m) 3 to 6 2 to 11 (SY & MY) Floe Thickness (m) 5 2 to 20 Sail Height (m) Significant Significant Rubble Keel Depth (m) 20 10 to 35 Fields (SY Average Sail Height (m) 2 to 5 3 to 6 & MY) Length Annual Maximum 750 50 to 2,300 (m) Speed in Nearshore (m∙s-1) 0.06 0.04 to 0.2 Ice 0.06 to 1.0 Movement Speed in Offshore (m∙s-1) 0.08 0 to 1.5 Icebergs/Ice Islands Size Mass 10 ND Months Present Poorly Known Poorly Known Frequency Number per Year Poorly Known Poorly Known Maximum Number per Rare Rare Month 102 From the analysis of data present for this study the following recommendations can be made to Table 6.1:

 Ridges o Sail Height (m) – 1 to 7 . Note that sail height was inferred from keel depth by using a keel depth to sail height ratio of 4.5 (Davis & Wadhams, 1995; International Organization for Standardization, 2010; Timco & Burden, 1997) o Keel Depth (m) – 6 to 30 . Weibull Distribution, as shown in Eq. 4.2.3.1  Shape Parameter, α – 0.99  Scale Parameter, β – 2.70  Ice Movement o Speed in Offshore (m∙s-1) – 0.0 to 1.5

103 6.1.2 Chukchi Sea

Table 6.2 shows the sea ice parameters currently recorded in the ISO 19906 for the Chukchi Sea, along with the updated values found from this study.

Table 6.2: Chukchi Sea ISO 19906 Sea Ice Conditions; values in bold indicate results from this study (Reproduced from International Organization for Standardization, 2010, Table B.8-4)

Region Northeastern Parameter Average Range of Annual Annual Values Value Late October to First Ice November Early December Occurrence Mid-June to Late Last Ice July August Level Ice Landfast Ice Thickness (m) 1.5 1.3 to 1.7 (FY) Floe Thickness (m) 0.7 to 1.4 0.7 to 1.8 Rafted Ice Rafted Ice Thickness (m) 1.0 to 2.0 1.0 to 3.0 Sail Height (m) 2 1 to 3 Rubble 300 to Fields Length (m) 300 to 1,000 1,000 1 to 3 Sail Height (m) 2 1 to 6 Ridges (FY) 8 to 15 Keel Depth (m) 10 6 to 26 Water Depth Range (m) None None Stamukhi Sail Height (m) None None Level Ice Floe Thickness (m) 2 to 4 2 to 6 (SY & MY) Ridges (SY Sail Height (m) 1 to 2 1 to 3 & MY) Keel Depth (m) 4 to 8 4 to 10 Speed in Nearshore (m∙s-1) 0.1 to 0.2 0.1 to 0.3 Ice 0.2 to 0.3 Movement Speed in Offshore (m∙s-1) 0.2 to 0.3 0 to 1.1

104 From the analysis of data present for this study the following recommendations can be made to Table 6.2:

 Ridges o Sail Height (m) – 1 to 6 . Note that sail height was inferred from keel depth by using a keel depth to sail height ratio of 4.5 (Davis & Wadhams, 1995; International Organization for Standardization, 2010; Timco & Burden, 1997) o Keel Depth (m) – 6 to 26 . Weibull Distribution, as shown in Eq. 4.2.3.1  Shape Parameter, α – 1.02  Scale Parameter, β – 2.37  Ice Movement o Speed in Offshore (m∙s-1) – 0.0 to 1.1

105 6.2 Pressure Ridge Keel Depth Probabilities

Given the distribution of keel depths from a sample of pressure ridges conforms to

a PDF corresponding to the random number, P(D), a critical keel depth, Dc, can be described by Eq. 6.2.1.

(Eq. 6.2.1)

For any keel depth, D, from a sample of pressure ridges the probability of that keel depth being at or shallower than the critical keel depth is described by Eq. 6.2.2.

(Eq. 6.2.2)

Conversely, the probability of any keel being as deep as, or deeper than, the critical keel depth is described by Eq. 6.2.3.

1 (Eq. 6.2.3)

A visual representation of Eq. 6.2.1 - 6.2.3 is shown (see Figure 6.1).

106 P D

P Dc D Dc

Figure 6.1: Keel Depth Probability v. Depth

For a succession of pressure ridges moving over a particular geographic point, the passage of each ridge over that point is defined as an “event” in a Bernoulli Trial, where the probability of “success” for any ridge passing over the point is described by Eq. 6.2.4.

1 (Eq. 6.2.4)

107 The probability of r successes in n trials may be determined from the Binomial Distribution described by Eq. 6.2.5.

! | 1 (Eq. 6.2.5) !!

where:

 n – number of pressure ridges in a sample  r – may be interpreted as the number of ridges that have a keel

depth equal to or deeper than the critical keel depth Dc from a sample of n pressure ridges

For a mandated value of P(r|n) it is necessary to determine the corresponding

value of pex, and then refer back to P(D) in order to estimate the critical keel depth, Dc. For a prescribed value corresponding to P(1|n), that is, the probability of one ridge with a keel depth greater than or equal to Dc during n events (n pressure ridges passing over a given geographical point), the Binomial Distribution resolves to Eq. 6.2.6.

1| 1 (Eq. 6.2.6)

Similarly, the probability of zero occurrences in n events resolves to Eq. 6.2.7.

0| 1 (Eq. 6.2.7) 108 The P(0|n) equation, Eq. 6.2.7, may be rearranged (see Eq. 6.2.8).

10| (Eq. 6.2.8)

By use of the cumulative density function (CDF), C(D), corresponding to P(D), it is possible to estimate critical keel depth, Dc, corresponding to the mandated value for P(0|n) (see Figure 6.2).

C D

C Dc

D Dc

Figure 6.2: CDF Corresponding to P(D)

109 6.2.1 Pressure Ridge Keel Depth Probability Calculation

For a condition where 4,000 pressure ridge features with keel depths at or deeper than six meters, and an imposed P(0|n) value of 0.99, an estimate of the critical keel depth can be determined assuming the distribution of the keel depths conforms to a PDF of the following form, with the following parameters (see Eq. 6.2.1.1).

(Eq. 6.2.1.1) ,

where:

 α – Weibull distribution shape parameter, set to 1.04236  β – Weibull distribution scale parameter, set to 2.5379  μ – Weibull distribution location parameter, set to 6 meters

Thus, Eq. 6.2.8 can be written as:

10| 10.99 0.00000251258

110 The CDF for P(D) can be expressed by Eq. 6.2.1.2.

0 (Eq. 6.2.1.2) 1

Using the values presented in Eq. 6.2.9 and Figure 6.2 the corresponding value on the C(D) curve is 0.99999748741 while the corresponding value for Dc is approximately 35.7 meters. If it is assumed that, on average, 4,000 keel events occur annually over a 20 year service life, then Dc for P(0|80,000) is approximately 42.0 meters. Figure 6.3 and Figure 6.4 show plots of the critical keel depth for a range of service lives in the Beaufort and Chukchi Seas.

111

Figure 6.3: Beaufort Sea Critical Keel Depth as a Function of Service Life

112

Figure 6.4: Chukchi Sea Critical Keel Depth as a Function of Service Life

Service lives are defined in terms of keels passing a given point, a year of service corresponding to the average number of keels in a season for both the Beaufort and Chukchi Sea data used in this study.

For comparison, the keel draft that has a 0.01 chance of being exceeded in any one year was calculated as well. This corresponds to the 100 year annual probability of exceedance and corresponds to a probability represented by Eq. 6.2.1.3.

∙ (Eq. 6.2.1.3)

where:

 N – number of years of data

113  n – total number of data points  T – return period, in this case 100 years

Using the CDF as before, this corresponds to a critical keel depth of approximately 35.7 meters for the Chukchi Sea. This number is similar to the 37.4 meter value found by Fissel (2010), which used a 13 meter starting threshold, μ, during calculation (Fissel, et al., 2010).

114 6.3 Limit State Ice Actions

To estimate pressure ridge forces on a structure the methodology described in the ISO 19906 was utilized. The Normative breaks the ridge calculation into two parts, the consolidated layer force and the unconsolidated keel force. Due to the high variability of different parameters a Monte Carlo simulation was employed to estimate the upper bound horizontal ridge action on the structure.

6.3.1 Consolidated Layer Force

As stated in section A.8.2.4.5.1 of the ISO 19906, an estimate of the consolidated layer action component can be determined from the instructions given in section A.8.2.4.3, with the use of section A.8.2.4.3.3 for estimating consolidated layer parameters (International Organization for Standardization, 2010). Assuming that the structure being subjected to the ridge load is vertical to the waterline, the instructions present in section A.8.2.4.3.2 can be used to estimate the ice crushing action caused by the consolidated layer. By slightly adjusting some of the symbols of the ISO 19906 equations, for clarity purposes, Eq. 6.3.1.1 can be used.

∙ (Eq. 6.3.1.1)

where:

 Fc – horizontal action component of consolidated layer (MN)

 pG – ice pressure averaged over nominal contact area associated with global action (MPa)

2  AN – nominal contact area (m ) 115 Furthermore, the nominal contact area, AN, term can be further deconstructed (see Eq. 6.3.1.2).

∙ (Eq. 6.3.1.2)

where:

2  AN – nominal contact area (m )

 hc – thickness of the consolidated layer (m)  w – projected width of structure (m)

While the projected width of the structure, w, and consolidated layer thickness, hc, are two parameters that can be determined from the design scenario, the ice pressure, pG, must be calculated separately (see Eq. 6.3.1.3).

(Eq. 6.3.1.3)

116 where:

 pG – ice pressure averaged over nominal contact area associated with global action (MPa)

 CR – ice strength coefficient (MPa)

 hc – thickness of consolidated layer (m)

 h1 – reference thickness equal to one meter  n – empirical coefficient equal to -0.16  w – projected width of structure (m)  m – empirical coefficient equal to:

o (-0.50 + hc/5), for hc < 1.0 m

o -0.30, for hc ≥ 1.0 m

From the input parameters most everything can usually be easily

determined except the ice strength coefficient, CR. Without the information to probabilistically determine CR, a deterministic number had to be used. The ISO 19906 suggests values of 2.8 MPa for the Arctic, 2.4 MPa for the sub-Arctic, and 1.8 MPa for temperate regions (Palmer & Croasdale, 2013). Since both the Beaufort and Chukchi Seas are in the Arctic region, a value of 2.8 MPa seemed most appropriate. However, it should be noted that this value is for an extreme level ice event (ELIE) and potentially includes some magnification due to the compliance of the structure in the referenced data (International Organization for

Standardization, 2010). Without any other information on this factor a CR of 2.8 MPa was utilized for ridge analysis.

117 6.3.2 Keel Force

To estimate the action of the ridge keel on a vertical structure the equations presented in section A.8.2.4.5.1 of the ISO 19906 can be used. Eq. 6.3.2.1 shows the general keel horizontal action equation.

21 (Eq. 6.3.2.1)

where:

 Fk – keel horizontal action component (MN)

 μϕ – passive pressure coefficient (-)  w – projected width of structure (m)

-3  γe – effective buoyancy (MN∙m )  c – apparent keel cohesion (MPa)

Furthermore, the passive pressure coefficient, μϕ, and effective buoyancy,

γe, can be described by Eq. 6.3.2.2 and Eq. 6.3.2.3 respectively.

45° (Eq. 6.3.2.2)

118 where:

 μϕ – passive pressure coefficient (-)  ϕ – angle of internal friction (°)

(Eq. 6.3.2.3)

where:

-3  γe – effective buoyancy (MN∙m )  e – keel porosity

-3  ρw – water density (kg∙m )

-3  ρi – ice density (kg∙m )  g – gravity (m∙s-2)

As examined in the Literature Review there is some information regarding the properties needed to compute the keel action component, Fk. For this analysis any property with a range of values was described by a uniform random variable (URV) between the minimum and maximum values. For the cohesion, c, of the keel a URV with a range from 5 to 7 kPa was used. For the angle of internal friction, ϕ, of the keel a URV with a range from 20 to 40° was selected. For the porosity, e, of the keel a URV with a range from 20 to 50% was used. All of these values are based on the information presented in section A.8.2.8.8 of the ISO -3 19906. The water density, ρw, was taken to be 1,027 kg∙m . Lastly, for the ice -3 density, ρi, of the keel a URV with a range from 900 to 920 kg∙m was selected

119 based on the information presented in section A.8.2.8.10 of the ISO 19906 (see Table 6.3) (International Organization for Standardization, 2010).

Table 6.3: Ice Properties Summary

Ice Properties Summary Property Symbol Units Lower Bound Upper Bound Cohesion c kPa 5 7 Angle of Internal ϕ (°) 20 40 Friction Porosity e % 20 50

Water -3 ρw kg∙m 1,027 Density -3 Ice Density ρi kg∙m 900 920

For the draft of the keel the results from the ridge depth analysis were used. Essentially, random ridge depths were generated based on the Weibull parameter values determined in the Data Analysis section. This produced slightly different Fk values based on which sea was examined.

120 6.3.3 Horizontal FY Ridge Action

To calculate an estimated total horizontal force the sum of the consolidated layer force and unconsolidated keel is computed. There are two important items to note about this summation. First, it excludes any contribution from the sail (International Organization for Standardization, 2010), since the sail is made of loose blocks and is relatively small in volume. Second, using the methodology previously presented this will represent an upper bound estimate. Eq. 6.3.3.1 shows the equation to calculate the upper bound estimate of the horizontal action caused by a FY ridge.

(Eq. 6.3.3.1)

where:

 FR – upper bound estimation of horizontal action (MN)

 Fc – horizontal action component of consolidated layer (MN)

 Fk – keel horizontal action component (MN)

6.3.4 Monte Carlo Simulation

Due to the large amount of variability in the numerous variables when calculating the upper bound horizontal action estimate a Monte Carlo simulation was used. A Monte Carlo simulation is the act of approximating an expectation by the sample mean of a function of simulated random variables (Anderson E. C., 1999). Basically, a large number of trials are run using the variables randomly

121 selected. With enough trials the Monte Carlo method invokes the laws of large numbers to approximate expectations. For the purposes of this project a Monte Carlo simulation using 1,000,000 trials was used, unless otherwise stated.

6.3.5 Beaufort Sea Results

Using the Weibull parameters for the ridge draft in the Beaufort Sea a Monte Carlo simulation was conducted to identify the SLS, ULS, and ALS horizontal actions for a structure. For the purposes of the simulation the projected width of the structure, w, was arbitrarily set to 100 meters. Also, the thickness of

the consolidated layer, hc, was established as an URV with a range from 0 to 6 meters, since this most likely represented the realistic lower and upper bounds of the consolidated layer (Strub-Klein & Sudom, 2012). Since there was little information on the thickness of the consolidated layer this seemed like the best

way to present realistic values. Since an alternate value for CR was not presented in the ISO 19906, a value of 2.8 MPa was used.

From the Monte Carlo simulation FR values of 574, 622, and 654 MN

were found for the SLS, ULS, and ALS respectively in the Beaufort Sea. Fc

values of 572, 620, and 626 MN and Fk values of 11, 33, and 112 MN were found for the SLS, ULS, and ALS respectively (see Figure 6.5).

122 Beaufort Sea Limit State Ice Actions, w = 100 m 0.02

0.018

0.016

0.014

0.012

0.01

0.008 Fraction (-)

0.006

0.004

0.002 ULS 0 0 100 200 300 400 500 SLS600 ALS700 800 Horizontal Action F (MN) R

Figure 6.5: Beaufort Limit State Actions

It is important to note the shape produced by the Monte Carlo simulation.

There clearly is a steep decline in probability at approximately FR equal to 620 MN. This decline is due to how the consolidated layer of the ridge was established. Using the model, only ridges six meters deep or larger were considered, while the consolidated layer uniformly varied between zero and six meters. Since the contribution of the keel was minimal for smaller ridges, the linearly increasing pattern is seen up until approximately 620 MN. However, in order to have FR values greater than 620 MN there must be a significant contribution from the keel, thus a deep keel, and a highly developed consolidated layer. Since the Weibull PDF predicts large ridges as an uncommon occurrence, and the consolidated layer uniformly varies, it becomes increasingly rare for a deep ridge to develop with a thick consolidated layer.

123 6.3.6 Chukchi Sea Results

Using the Weibull parameters for the ridge draft in the Chukchi Sea a Monte Carlo simulation was conducted to identify the SLS, ULS, and ALS horizontal actions for a structure. For the purposes of the simulation the projected width of the structure, w, was arbitrarily set to 100 meters. Also, the thickness of

way to present realistic values. Since an alternate value for CR was not presented in the ISO 19906, a value of 2.8 MPa was used.

From the Monte Carlo simulation FR values of 573, 621, and 643 MN

were found for the SLS, ULS, and ALS respectively in the Chukchi Sea. Fc values

of 572, 620, and 626 MN and Fk values of 10, 25, and 83 MN were found for the SLS, ULS, and ALS respectively (see Figure 6.6).

124 Chukchi Sea Limit State Ice Actions, w = 100 m 0.02

0.018

0.016

0.014

0.012

0.01

0.008 Fraction (-)

0.006

0.004

0.002 SLS ALS 0 0 100 200 300 400 500 600ULS 700 800 Horizontal Action F (MN) R

Figure 6.6: Chukchi Limit State Actions

6.3.7 Molikpaq Ridge Comparison

In addition to using a Monte Carlo simulation to estimate SLS, ULS, and ALS horizontal action values the project team also chose to simulate recorded ridge events and examine how precisely the ISO 19906 methodology matched the recorded forces. To do this the research by Wright & Timco (2001) was heavily utilized. This publication contained measurements for 23 FY ridges impacting the Molikpaq in the Beaufort Sea over two years. Observations of the ridges included their sail height, peak load, and failure mode among many others (see Table 6.4).

125 Table 6.4: Summary of FY Ridge Events on the Molikpaq (Reproduced from Wright & Timco, 2001)

Surrounding Width of Ridge Sail Ice Drift Peak Ridge Sheet Thickness Loading Height (m) Speed (m∙s-1) Load (MN) (m) (m) 0.8 0.10 60 30 0.9 0.42 75 52 0.5 1.0 0.13 105 44 1.1 0.10 105 42 0.7 0.75 75 45 0.8 0.10 60 39 0.8 0.10 105 89 0.9 0.42 75 43 0.9 0.10 105 68 1.0 0.9 0.10 105 66 1.0 0.13 105 67 1.0 0.13 105 54 1.0 0.13 105 37 1.1 0.10 105 55 1.1 0.10 105 50 0.8 0.10 105 88 0.9 0.42 75 56 1.5 0.9 0.10 75 60 1.0 0.13 105 70 1.1 0.30 60 46 0.9 0.42 75 72 2.0 1.1 0.20 75 81 2.5 1.3 0.10 60 75

Using the information provided in Table 6.4 a series of Monte Carlo simulations were conducted using the specifics for each loading event. It was assumed that since the sides of the Molikpaq were near vertical that an analysis for forces on a vertical side would be accurate. Using the sail height a ridge depth was inferred using published a ridge depth to sail height ratio of 4.5 (Davis & 126 Wadhams, 1995; International Organization for Standardization, 2010; Timco & Burden, 1997). It should be noted that there was significant scatter shown in the results of Timco & Burden (1997). However, this value is what was included in the ISO 19906 and thus was utilized for the analysis. From the surrounding ice sheet thickness a consolidated layer thickness was determined using the published ratios of 1.5 to 2.0. (International Organization for Standardization, 2010; Timco

G. , Frederking, Kamesaki, & Tada, 1999). An ice strength coefficient, CR, value of 2.8 MPa was used per the ISO 19906 (see Table 6.5 and Figure 6.7).

127 Table 6.5: Molikpaq Input Parameters

Molikpaq Input Parameters Peak Width of Keel ULS Computed Load h h Ridge Loading Depth c, lower c, upper - Recorded Load (m) (m) Load FR (m) (m) (MN) (MN) (MN) 60 2.25 1.20 1.60 30 130.5 100.5 75 2.25 1.35 1.80 52 174.1 122.1 105 2.25 1.50 2.00 44 252.9 208.9 105 2.25 1.65 2.20 42 274.5 232.5 75 4.50 1.05 1.40 45 141.1 96.1 60 4.50 1.20 1.60 39 131.0 92.0 105 4.50 1.20 1.60 89 209.8 120.8 75 4.50 1.35 1.80 43 174.8 131.8 105 68 231.9 163.9 4.50 1.35 1.80 105 66 231.9 165.9 105 67 253.6 186.6 105 4.50 1.50 2.00 54 253.6 199.6 105 37 253.6 216.6 105 55 275.1 220.1 4.50 1.65 2.20 105 50 275.1 225.1 105 6.75 1.20 1.60 88 212.3 124.3 75 56 176.4 120.4 6.75 1.35 1.80 75 60 176.4 116.4 105 6.75 1.50 2.00 70 255.8 185.8 60 6.75 1.65 2.20 46 173.0 127.0 75 9.00 1.35 1.80 72 179.4 107.4 75 9.00 1.65 2.20 81 211.5 130.5 60 11.25 1.95 2.60 75 204.3 129.3

128

Figure 6.7: Recorded Molikpaq Ridge Load v. Computed Ridge Load

Both Table 6.5 and Figure 6.7 show that the computed action for the ULS action was vastly greater than the recorded value for FY ridges on the Molikpaq. While some magnification was expected since the recorded loads did not occur at the ULS, otherwise the Molikpaq structure would fail, the degree of magnification appeared excessively large.

6.3.8 CR Determination from Molikpaq FY Ridges

From the results of the Molikpaq FY ridges and the Monte Carlo simulation it seemed that the computed actions vastly overestimated the recorded ridge load. This was inconsistent with what others have found (Dalane, Aksnes, & Løset, 2015; Spencer & Morrison, 2014). From the analysis it became obvious that the main contributing factor to the load, especially at the ridge depths examined, was from the consolidated layer (see Table 6.6).

129 Table 6.6: Horizontal Action Variation

Horizontal Action Variation, w = 100 m F (MN) F (MN) F (MN) F /F Keel Depth (m) c k R k c ULS ULS ULS ULS 6 5.4 620.3 0.87% 7 7.5 620.4 1.21% 8 10.0 620.8 1.61% 9 12.8 621.4 2.07% 10 16.0 622.2 2.58% 11 19.6 623.3 3.16% 12 23.6 624.7 3.80% 13 27.9 626.1 4.50% 14 32.7 627.9 5.27% 15 37.8 630.0 6.10% 16 43.3 632.3 6.99% 17 49.3 634.9 7.94% 18 620 55.6 637.8 8.96% 19 62.3 641.0 10.05% 20 69.3 644.7 11.18% 21 77.0 648.7 12.42% 22 85.1 653.1 13.72% 23 93.5 658.0 15.07% 24 102.2 662.9 16.47% 25 111.2 668.6 17.93% 26 121.1 674.5 19.52% 27 131.1 681.1 21.14% 28 141.5 687.7 22.82% 29 152.4 695.0 24.57% 30 163.8 702.7 26.40%

Table 6.6 was created using a Monte Carlo simulation, with the consolidated layer thickness, hc, set as a URV from 0 to 6 meters. In an attempt to produce values

130 that more closely resembled the recorded Molikpaq data the consolidated layer

force equation, Fc, was further examined.

From the equation to determine the horizontal action component of the

consolidated layer, Fc, it seemed most likely that the overestimation was originating from the ice strength coefficient, CR. As mentioned in the ISO 19906

this term likely provides some amplification to the Fc term. Without information to further analyze a more accurate value for CR the project team attempted to

estimate CR using the Molikpaq FY ridge data. Using the ridge events a Monte

Carlo simulation was run to try and empirically determine a CR value. This was done by combining Eq. 6.3.1.1 - 6.3.1.3 and then rearranging terms to solve for

CR (see Eq. 6.3.8.1).

(Eq. 6.3.8.1) ∙

where:

 CR – ice strength coefficient (MPa)

 Fc – horizontal action component of consolidated layer (MN)

 h1 – reference thickness equal to one meter

 hc – thickness of the consolidated layer (m)  n – empirical coefficient equal to -0.16  m – empirical coefficient equal to:

o (-0.50 + hc/5), for hc < 1.0 m

o -0.30, for hc ≥ 1.0 m  w – projected width of structure (m)

131 A Monte Carlo simulation was conducted to identify the SLS, ULS, and

ALS CR values for the structure. For the purposes of this simulation the projected width of the structure, w, was set to values of 60, 75, or 105 meters. Also, the thickness of the consolidated layer was established as an URV with a range from the minimum and maximum value at the width, based on the available data and a consolidated layer thickness to surrounding level ice thickness ratio of 1.5 to 2.0.

The horizontal action component of the consolidated layer, Fc, was established as an URV with a range from the minimum and maximum peak recorded loads at the respective width (see Table 6.7).

Table 6.7: CR Molikpaq Ridge Analysis

CR Ridge Analysis Molikpaq FY Ridge Analysis w (m) 60 w (m) 75

hc (m) 1.20 - 2.60 hc (m) 1.05 - 2.20

Fc (MN) 30 - 75 Fc (MN) 43 - 81 Data Points 4 Data Points 7 SLS 1.46 SLS 1.54 CR CR (MPa) ULS 1.85 (MPa) ULS 1.88 ALS 2.04 ALS 2.04 w (m) 105

hc (m) 1.20 - 2.20

Fc (MN) 37 - 89 Data Points 12 SLS 1.15 CR ULS 1.39 (MPa) ALS 1.51

132 Figure 6.8 shows an example of this simulation at the 105 meter width while

Figure 6.9 depicts how the loading varies with different CR values.

CR Estimate from Molikpaq FY Ridges 0.18

0.16

0.14

0.12

0.1

0.08 Fraction (-) 0.06

0.04

0.02

SLS ULS ALS 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 CR (MPa)

Figure 6.8: CR Estimate from Molikpaq FY Ridges

133

Figure 6.9: Consolidated Layer Load with Variation of CR

From Figure 6.9 it can be seen that using an empirical CR value brought the action values closer to the recorded values. A CR value of 1.8 MPa was also included because it was mentioned by the ISO 19906 as an ELIE factor for the

Baltic Sea. This CR value of 1.8 MPa was also quite close to the CR value estimated from the ridges on the 60 and 75 meter faces. While 1.39 MPa is by no means a definitive value to use for CR at the ULS, at 105 meters, it does seem to present values that are closer to reality.

Using the results of this analysis of CR a new simulation was performed on the arbitrarily defined 100 meter wide caisson structure previously discussed.

Using the ULS CR value of 1.39 MPa, since this was derived from the 105 meter width (~100 meters), the ULS total horizontal action, FR, was 305 and 304 MN for the Beaufort and Chukchi Seas respectively. This is a significant decrease from the previous ULS values for the Beaufort and Chukchi Seas when CR was set to 2.8 MPa per the Normative.

134 6.3.9 CR Determination from Molikpaq FY Level Ice

After looking at the resulting CR values from the FY ridges that impacted the Molikpaq, segments of FY level ice were examined in a similar fashion. For this the work of Timco (2004) was extensively used. In particular, FY level ice events from the Molikpaq at the Amguligak I-65 site that had a crushing primary ice failure mode were utilized. Altogether this gave 40 quality events to estimate

CR with.

A Monte Carlo simulation was conducted to identify the SLS, ULS, and

ALS CR values for the structure at different values for the projected width, w. Also, the thickness of the FY level ice, h, was established as an URV, along with the recorded horizontal action component F. Since the level ice horizontal action equation also used Eq. 6.3.1.1, Eq. 6.3.8.1 was used to calculate CR (see Table 6.8).

135 Table 6.8: Molikpaq FY Level Ice CR Analysis

CR Analysis Molikpaq FY Level Ice Analysis w (m) 105 w (m) 95 h (m) 0.8 h (m) 0.7 - 0.8 F (MN) 79 - 104 F (MN) 60 - 87 Data Points 5 Data Points 8 SLS 2.44 SLS 2.33 CR CR (MPa) ULS 2.50 (MPa) ULS 2.46 ALS 2.50 ALS 2.52 w (m) 75 w (m) 60 h (m) 0.6 - 1.2 h (m) 0.6 - 1.2 F (MN) 50 - 110 F (MN) 34 - 80 Data Points 16 Data Points 11 SLS 3.30 SLS 2.87 CR CR ULS 3.98 ULS 3.49 (MPa) (MPa) ALS 4.32 ALS 3.79

It is important to note that this analysis, similarly to the ridge analysis, had little information to estimate CR with. In order to compare the results of the CR analysis for keels to that for level ice Figure 6.10 was produced.

136

Figure 6.10: CR Molikpaq Analysis

From Figure 6.10 it can be observed that CR values for FY level ice are significantly higher, especially at the ULS or ELIE state, than that prescribed by the ISO 19906. However, it can also be observed that the CR values for ridges are significantly lower than that prescribed by the ISO 19906 or calculated from the

FY level ice segments. Also on this plot is the ULS CR value of 3.6 MPa, suggested by Spencer (2014). From the plot it can be seen that the CR value found by Spencer more closely resembles the results from the Molikpaq FY level ice analysis, although it does not agree with the keel analysis. It does appear that there is some significant difference between the FY level ice and FY ridge actions that is not accounted for in the ISO 19906. This should be further investigated.

Intuitively the result of having different CR values for both FY level ice and FY ridges seems plausible. When calculating the horizontal action of the

137 consolidated layer or a level ice segment Eq. 6.3.1.1 is used. Since this equation does not use any material properties, it would seem that ice property differences are not accounted for. The differences in the properties of FY level ice and the consolidated layer could potentially be reflected in the CR parameter. However, the ISO 19906 does not provide measures to readily deal with this matter. Additional data and analysis is needed to test this hypothesis.

6.3.10 Impact of CR on Caisson Weight

To demonstrate the significance of the ice pressure coefficient, CR, a simple example was constructed. Using an arbitrarily defined steel caisson structure varying FY level ice and FY ridge ULS ice actions were applied. Using the actions a required weight was determined to keep the caisson from

overturning or sliding. The change in weight for differing values of CR demonstrated the importance of the ice pressure coefficient.

The steel caisson structure used for this example was square, 105 meters wide. The caisson sat on a sand berm on the seafloor and had an overall height of 50 meters. To determine ice forces for FY level ice segments Monte Carlo simulations were conducted with a URV ice thickness from 0 to 2 meters. Three

Monte Carlo simulations were run for CR values of 2.50, 2.80, and 3.60 MPa, corresponding to the empirically determined, ISO 19906 mandated, and Spencer (2014) suggested values. This resulted in ULS FY level ice forces of 224, 251, and 323 MN respectively.

To determine ice forces for FY ridges Monte Carlo simulations were conducted with a URV consolidated layer thickness from 0 to 6 meters. Two

Monte Carlo simulations were run for CR values of 1.39 and 2.80 MPa, corresponding to the empirically determined and ISO 19906 mandated values.

This resulted in ULS consolidated layer forces, Fc, of 316 and 657 MN respectively. 138 Both the FY level ice and FY ridge ice actions were applied at the top of the caisson structure, to be conservative. The overturning moment and sliding forces were then determined using the ULS ice actions. Using a moment arm equal to the height of the caisson, 50 meters, overturning moments of 11,200, 12,550, and 16,150 MN∙m were determined for FY level ice ULS actions corresponding to CR values of 2.50, 2.80, and 3.60 MPa. Overturning moments of 15,800 and 32,850 MN∙m were determined for FY ridge ULS actions corresponding to CR values of 1.39 and 2.80 MPa. The sliding force for all events was equal to the ice action.

To determine the weight needed to keep the caisson from overturning or sliding basic statics was utilized. Using a resisting moment arm half the width of the structure, or 52.5 meters, the weight needed to resist overturning was determined. For FY level ice weights of 320, 359, and 461 MN were determined. For FY ridges weights of 451 and 939 MN were determined. In all cases a factor of safety (FS) of 1.5 was applied.

To determine the weight needed to keep the caisson from sliding first a coefficient of static friction, μs, between steel and sand was needed. For this example a value of 0.55 was chosen (Leijnse, 2010). Using a μs of 0.55 and a FS of 1.5 the weight needed to resist sliding was determined. For FY level ice weights of 611, 685, and 881 MN were determined. For FY ridges weights of 862 and 1,792 MN were determined (see Figure 6.11 and Figure 6.12).

139

Figure 6.11: FY Level Ice Weight Determination

Figure 6.12: FY Ridge Weight Determination

140 From Figure 6.11 and Figure 6.12 it can be seen that different CR values produce vastly different weights needed to resist overturning and sliding. This difference in weight can have a significant impact on the type of construction and cost for the caisson structure. It should be noted that this example did not take into account the effects of vibration or liquefaction.

6.3.11 Determination of Governing Condition

To try and further apply the results of the CR analysis and ISO 19906 methodology for calculating horizontal actions caused by sea ice, an investigation was pursued to determine if a FY level ice or a FY ridge event provided the controlling horizontal action. The ULS horizontal actions for both scenarios were examined.

Using the CR values obtained a Monte Carlo simulation was run for the Beaufort Sea using a hypothetical 105 meter wide caisson structure. For the FY level ice simulation the level ice thickness, h, was set as a URV with a range from

0 to 2 meters. The CR value was set to 2.50 MPa for FY level ice and 1.39 MPa for FY ridges, using the results from analysis of FY ridges and level ice on the Molikpaq. These values are shown in Table 6.7, Table 6.8, and Figure 6.10. All material property values are shown in Table 6.3 and the thickness of the

consolidated layer, hc, is a URV from 0 to 6 meters.

For the FY level ice the simulation produced a ULS horizontal action of 224 MN. For the FY ridge the simulation produced a ULS consolidated layer

horizontal action, Fc, of 316 MN and a ULS ridge keel horizontal action, Fk, of 34

MN. Overall, the total ULS horizontal action, FR, was 318 MN. From this analysis the governing design scenario for the ULS horizontal action was from the FY ridge.

141

Chapter 7: Recommendations

7.1 Pressure Ridge Keels

With the limitations of one-dimensional draft data it was difficult to further analyze keel draft, width and velocity; however, using two-dimensional data could provide further information on these parameters. From the one-dimensional data more information could potentially be gathered on keel spacing and keel age. Keel spacing is important in engineering design because there is the potential that multiple deep keels could impact an offshore structure in rapid succession. This could change the ice action considerations and overall design of the structure. Also, keel age, FY or MY, is an important factor in design. Older keels have different ice properties which generally make them stronger and more of a structural threat.

7.1.1 Keel Spacing

The keel spacing analysis for this project built on previous research by Hibler (1972), Mock (1972), and Wadhams (1986). However, what may be more interesting is to separate the keel spacing based on pressure ridge keel draft. For instance, having a six meter keel closely follow a 25 meter keel would be a vastly different design scenario than having two 25 meters keels impact a structure in succession. By establishing a minimum keel depth to use to analyze keel spacing more relevant results could potentially be determined.

7.1.2 Keel Age

From the data obtained it was impossible to reliably distinguish FY keels from MY keels. However, FY and MY keels have vastly different ice properties and geometric features. Knowing whether a keel is FY or MY is an important aspect of structural design and further researching keels based on age would be a valuable endeavor. One potential research route might be to use the geometric shape and smoothness of the ridge to attempt to determine if a ridge is FY or MY. 143 Also, more information on the material properties of MY ice would be of value in the engineering community. These materials properties would likely either have to be gathered in situ or in a laboratory setting.

7.2 Level Ice

The primary topic of further research concerning level ice is to determine what features were being detected as level with drafts greater than two meters. These segments could potentially be large swaths of level MY ice, shallow pressure ridge keels with extremely flat bottoms, or smooth rafted ice. Without further analysis effort and outside resources, making these distinctions is extremely difficult. However, due to the differences in material properties between MY and FY ice it would be valuable to identify these features.

7.3 Other Ice

While the analysis and results of other ice features were only marginally examined in this project, this does not mean that they are irrelevant to offshore structure design. While this project did not have the resources, such as satellite imagery, necessary to further analyze other ice features these resources do exist. With a further analysis of satellite images and other resources, features in other ice could potentially be discerned and described using probability theory. This may include features such as rafted or MY ice.

7.4 Ridge Consolidated Layer

It was seen that the thickness of the consolidated layer was a primary feature needed to calculate ridge actions (see section on Implementation). However, from the literature review little information was found on specific measurements of the consolidated layer, with the best source being Strub-Klein (2012). While this is understandable due to the difficultly in measuring this parameter, the lack of information nevertheless presents a challenge. Further research and data collection into the 144 consolidated layer of ridges in the Beaufort Sea, and especially the Chukchi Sea, would be valuable. If a probabilistic model could be constructed using the consolidated layer values for these seas it would be helpful in obtaining design values. This methodology has been used before, for the Barents Sea, and is presented in Strub-Klein (2012) (Strub- Klein & Sudom, 2012).

7.5 Ridge Actions

As shown in Chapter 6 it can also be seen that there was little agreement between recorded FY ridge actions and estimated FY ridge actions. By conducting this analysis two potential issues with the methodology were hypothesized.

7.5.1 Ice Strength Coefficient CR

When examining the horizontal action a FY ridge exerts on a structure it was determined that the primary contributor to the action was the force due to the

consolidated layer, Fc. Thus, to significantly impact the action magnitude of the

overall action, FR, the force due to the consolidated layer must be examined.

While there is little supporting evidence presented in the ISO 19906 to determine the validity of the coefficients n and m, it is stated in the Normative that

a CR value of 2.8 MPa could potentially include some magnification (International Organization for Standardization, 2010). While this project attempted to

determine a refined value for CR, with limited data it is difficult to give a concrete

answer. Before using CR it should be better understood and further researched. While there are papers that examine this, the most prominent discovery during this project being Spencer (2014), more research on this would be advisable.

7.5.2 Keel Action Fk

When examining the action of the ridge keel on a structure a few curiosities were discovered. First, the velocity at which the keel travels does not

145 appear accounted for in the action formulas. One would think that this would be an important parameter to include, especially since some properties of ice are strain rate dependent (Jones, 1997). Second, the width of the keel does not seem to have an impact in the formulation, which is also noted by Dalane (2015) and Sudom (2013) (Dalane, Aksnes, & Løset, 2015; Sudom & Timco, 2013). While some average width may or may not be accounted for in the formulas, it does seem strange that by the formulas presented a 12 meter deep ridge, 24 meters wide yields the same horizontal action as a 12 meter deep ridge, 100 meters wide. While further examining these formulas was outside the scope of this project, it would seem that further research needs to be done.

146 Chapter 8: Conclusions

8.1 General

The project completed the scope set forth under contract E13PC00020 from BSEE; the following objectives were completed:

 Obtain sea ice data of good quality and sufficient quantity  Conduct a literature review  Compute statistics for relevant sea ice parameters  Determine limit state values for applicable parameters

In addition to completing the objectives established in the contract the following additional objectives were also completed:

 Produce ice velocity roses  Examine how the ISO 19906 computes ridge loading on vertical structures  Compare theoretical ridge loads to recorded ridge loads in the Beaufort Sea

 Investigate the ice strength coefficient, CR  Use recorded loadings in the Beaufort Sea to suggest alternative values of

Overall, this project produced new information that should be able to be easily implemented by industry or regulatory agencies for the Beaufort and Chukchi Seas.

147 8.2 Findings

Specifically there are reported values and findings that are of particular significance:

 The ridge keel draft in the Beaufort and Chukchi Seas can be described by a Weibull Distribution, as presented by Eq. 4.2.3.1 with a threshold value, μ, of six meters. o Beaufort Sea: Shape parameter, α = 2.70 o Beaufort Sea: Scale parameter, β = 0.99 o Chukchi Sea: Shape parameter, α = 2.37 o Chukchi Sea: Scale parameter, β = 1.02  There appears to be a majority presence of FY ridges in both seas due to the presence of a modal keel width.  Modal ridge keel angles were found: o Beaufort Sea: 33.7° o Chukchi Sea: 32.5°  There appears to be no significant relationship between keel depth and speed.  From Figure 6.3 and Figure 6.4 it can be seen that, using the probability theory approach, the critical keel depth increases with service life. The annual exceedance probability approach is independent of service life and considers an event on an annual basis as opposed to a service life basis.

In comparison to other studies found this project had a large amount of quality data for analysis, making the results significant.

148 8.3 ISO 19906 Implementation

It was initially found that when estimating pressure ridge loads using the ISO 19906 standard the magnitudes were extremely high, far larger than anything recorded for FY ridges. When this was further investigated by using measured parameters from recorded events and theoretically computing the load, it was still found that the theoretical action was much greater than the recorded action. While there was not sufficient data to come to a firm conclusion, it appears that the ISO 19906 is conservative when computing ridge loading but may not be conservative for FY level ice loading. From the literature reviewed for this project it also seems that the ice strength parameter,

CR, is not well understood or agreed upon. Furthermore, an investigation into MY ridges

and ice was not conducted, which could have an impact on CR. From the results CR values of 1.62 and 3.36 MPa, the weighted average of the CR values, are recommended for FY ridges and FY level ice, respectively. Further research into the computation of ridge loading, particularly with respect to the consolidated layer, would be of great benefit and is advisable.

149

150 References

Abarbanel, H., Koonin, S., Levine, H., MacDonald, G., & Rothaus, O. (1992). Statistics of Extreme Events with Application to Climate. The MITRE Corporation, McLean.

Amundrud, T. L., Melling, H., & Ingram, R. G. (2004, June 04). Geometrical constraints on the evolution of ridged sea ice. Journal of Geophysical Research, 109(C06005). doi:10.1029/2003JC002251

Anderson, E. C. (1999, October 20). Monte Carlo Methods and Importance Sampling. 1 - 8.

Anderson, T. W. (1962, April 12). On the Distribution of the Two-Sample Cramer-von Mises Criterion. The Annals of Mathematical Statistics, 1148 - 1159.

Arnold, T. B., & Emerson, J. W. (2011, December). Nonparametric Goodness-of-Fit Tests for Discrete Null Distributions. The R Journal, 3(2), 34 - 39.

Babko, O., Rothrock, D. A., & Maykut, G. A. (2002, August 29). Role of rafting in the mechanical redistribution of sea ice thickness. Journal of Geophysical Research, 107(No. C8), 27-1 - 27-14. doi:10.1029/1999JC000190

Bailey, E., Sammonds, P. R., & Feltham, D. L. (2012, June 6). The consolidation and bond strength of rafted sea ice. Cold Regions Science and Technology, 83 - 84, 37 - 48. doi:10.1016/j.coldregions.2012.06.002

Barber, D. G., Galley, R., Asplin, M. G., Abreu, R., Warner, K.-A., Pućko, M., . . . Julien, S. (2009, December 24). Perennial pack ice in the southern Beaufort Sea was not as it appeard in the summer of 2009. Geophysical Research Letters, 36(L24501). doi:10.1029/2009GL041434

Belliveau, D. J., Bugden, G. L., Eid, B. M., & Calnan, C. J. (1989, December 13). Sea Ice Velocity Measurements by Upward-Looking Doppler Current Profilers. Journal of Atmospheric and Oceanic Technology, 7, 596 - 602.

151 Bishop, G. C., & Chellis, S. E. (1989, July 25). Fractal Dimension: A Descriptor of Ice Keel Surface Roughness. Geophysical Research Letters, 16(No. 9), 1007 - 1010. doi:10.1029/GL016i009p01007

Bjerkås, M. (2007). Review of Measured Full Scale Ice Loads to Fixed Structures. 26th International Conference on Offshore Mechanics and Arctic Engineering. San Diego.

Blanchet, D. (1997, July 11). Ice loads from first-year ice ridges and rubble fields. Canadian Journal of Civil Engineering, 25, 206 - 219. doi:10.1139/l97-073

Bonnemaire, B., & Bjerkås, M. (n.d.). Ice Ridge-Structure Interaction Part I: Geometry and Failure Modes of First-Year Ice Ridges. Norwegian University of Science and Technology, Trondheim.

Bourke, R. H., & Garrett, R. P. (1986, July 18). Sea Ice Thickness Distribution in the Arctic Ocean. Cold Regions Science and Technology, 13, 259 - 280. doi:10.1016/0165-232X(87)90007-3

Bourke, R. H., & Paquette, R. G. (1989, January 15). Estimating the Thickness of Sea Ice. Journal of Geophysical Research, 94(No. C1), 919 - 923. doi:10.1029/JC094iC01p00919

Carstens, T. (1980). Working Group on Ice Forces on Structures. International Association for Hydraulic Research Section on Ice Problems. Hanover: UNITED STATES ARMY.

Comfort, G., Singh, S., & Dinovitzer, A. (1997). Limit Force Ice Loads and Their Significance to Offshore Structures in the Beaufort Sea. The International Society of Offshore and Polar Engineers, (pp. 686 - 692). Honolulu.

Coon, M. D. (1995). Sea Ice Stress Research. Northwest Research Associates, Inc., Bellevue.

Cox, G., & Richter-Menge, J. (1985). Triaxial Compression Testing of Ice. ASCE Arctic '85. San Francisco.

152 Dalane, O., Aksnes, V., & Løset, S. (2015). A Moored Arctic Floater in First-Year Sea Ice Ridges. Journal of Offshore Mechanics and Arctic Engineering, 137, (011501-1)-(011501-8). doi:10.1115/1.4028814

Davis, N. R., & Wadhams, P. (1995). A Statistical Analysis of Arctic Pressure Ridge Morphology. Journal of Geophysical Research, 100(NO. C6), 10,915-10,925.

Dorris, J. F., & Austin, J. S. (1985). The Uniaxial Mechanical Response of Multi-Ridge Ice.

Dunton, K. H., Weingartner, T., & Carmack, E. C. (n.d.). The nearshore western Beaufort Sea ecosystem: Circulation and importance of terrestrial carbon in arctic coastal food webs.

Ekeberg, O.-C., Høyland, K., & Hansen, E. (2014). Ice ridge keel geometry and shape derived from one year of upward looking sonar data in the Fram Strait. Cold Regions Science and Technology, 109, 78-86.

Fissel, D. B., Marko, J. R., Ross, E., Kwan, T., & Egan, J. (n.d.). Upward Looking Sonar- based Measurements of Sea Ice and Waves.

Fissel, D. B., Mudge, T. D., Borg, K., Sadowy, D., Budd, K., Lawrence, J., . . . Bard, A. (2010). Analysis of Ice and Metocean Measurements, Chukchi Sea 2009-2010.

Fissel, D., Chave, R., & Buermans, J. (2009). Real-Time Measurement of Sea Ice Thickness, Keel Sizes and Distributions and Ice Velocities Using Upward Looking Sonar Instruments.

Flato, G. M., & Hibler III, W. D. (1995). Ridging and strength in modeling the thickness distribution of Arctic sea ice. Journal of Geophysical Research, 100(C9), 18,611- 18,626.

Frederking, R., & Timco, G. W. (1986). Field Measurements of the Shear Strength of Columnar-Grained Sea Ice. IAHR Ice Symposium 1986. Iowa City.

Fukamachi, Y., Mizuta, G., Ohshima, K. I., Takenobu, T., Kimura, N., & Wakatsuchi, M. (2006). Sea ice thickness in the southwestern Sea of Okhotsk revealed by a 153 moored ice-profiling sonar. Jounral of Geophysical Research, 111(C09018), 2156 - 2202. doi:10.1029/2005JC003327

Gordon, R. L. (1996). Acoustic Doppler Current Profiler: Principles of Operation, A Practical Primer.

Grebmeier, J. M., Cooper, L. W., Feder, H. M., & Sirenko, B. I. (2006). Ecosystem dynamics of the Pacific-influenced Northern Bering and Chukchi Seas in the Amerasian Arctic. Progress in Oceanography, 331-361.

Heinonen, J. (2004). Constitutive Modeling of Ice Rubble in First-Year Ridge Keel.

Hibler III, W. D. (1980). Modeling a Variable Thickness Sea Ice Cover. Monthly Weather Review, 1943-1973.

Hibler III, W. D., & Mock, S. J. (1974). Classification and Variation of Sea Ice Ridging in the Western Arctic Basin. Journal of Geophysical Research, 79(18), 2735- 2743.

Hibler III, W. D., Weeks, W. F., & Mock, S. J. (1972). Statistical Aspects of Sea-Ice Ridge Distributions. Journal of Geophysical Research, 77(30), 5954-5970.

Hoare, R. D., Danielewicz, B. W., & Pilkington, G. R. (1980). An Upward-Looking Sonar System to Profile Ice Keels for One Year.

Hopkins, M. A. (1994, August 15). On the ridging of intact lead ice. Journal of Geophysical Research, 99(No. C8), 16,351 - 16,360.

Hopkins, M. A. (1996). The effects of individual ridging events on the ice thickness distribution in the Arctic ice pack. Cold Regions Science and Technology, 24, 75- 82.

Hopkins, M. A. (1998). Four stages of pressure ridging. Journal of Geophysical Research, 103(C10), 21,883-21,891.

154 Hopkins, M. A., Hibler III, W. D., & Flato, G. M. (1991). On the Numerical Simulation of the Sea Ice Ridging Process. Journal of Geophysical Research, 96(C3), 4809- 4820.

Høyland, A., & Rausand, M. (2004). Reliability Theory Models and Statistical Methods. Hoboken, New Jersey, United States: John Wiley & Sons, Inc.

Høyland, K. V. (2002). Consolidation of first-year sea ice ridges. Journal of Geophysical Research, 107(NO. C6), (15-1)-(15-16). doi:10.1029/2000JC000526

Høyland, K. V. (2007). Morphology and small-scale strength of ridges in the North- western Barents Sea. Cold Regions Science and Technology, 48, 169-187.

Høyland, K. V., & Løset, S. (1999). Measurements of temperature distribution, consolidation and morphology of a first-year sea ice ridge. Cold Regions Science and Technology, 29, 59-74.

Hughes, B. A. (1991). On the Use of Lognormal Statistics to Simulate One- and Two- Dimensional Under-Ice Draft Profiles. Journal of Geophysical Research, 96(C12), 22,101-22,111.

International Organization for Standardization. (2010). Petroleum and natural gas industries - Arctic offshore structures.

Jefferies, M., Kärnä, T., & Løset, S. (2008). Field data on the magnification of ice loads on vertical structures. 19th IAHR International Symposium on Ice. Vancouver.

Jones, S. J. (1997). High Strain-Rate Compression Tests on Ice. Journal of Physical Chemistry B, 6099-6101.

Kärnä, T., & Nykänen, E. (2004). An Approach for Ridge Load Determination in Probabilistic Design. Proc. 17th International Symposium on Ice. Int. Ass. Hydr. Eng. Res., (pp. 42-50). St. Petersburg.

Kärnä, T., Qu, Y., & Yue, Q. (2006). Extended Baltic Model of Global Ice Forces. 18th IAHR International Symposium on Ice, (pp. 261 - 268).

155 Key, J. R., & McLaren, A. S. (1989). Periodicities and Keel Spacings in the Under-Ice Draft Distribtuion of the Canada Basin. Cold Regions Science and Technology, 16, 1-10.

Key, J. R., & McLaren, A. S. (1991). Fractal Nature of the Sea Ice Draft Profile. Geophysical Research Letters, 18(8), 1437-1440.

Kim, H., & Keune, J. N. (2007, January 13). Compressive strength of ice at impact strain rates. Journal of Materials Science, 2802 - 2806. doi:10.1007/s10853-006-1376-x

Kovacs, A. (1970). On the Structure of Pressure Sea Ice.

Kovacs, A. (1977). Sea Ice Thickness Profiling and Under-Ice Oil Entrapment. Offshore Technology Conference.

Kovacs, A. (1983). Characteristics of Multi-Year Pressure Ridges. USA Cold Regions Research and Engineering Laboratory.

Kovacs, A. (1997, April 15). Estimating the full-scale flexural and compressive strength of first-year sea ice. Journal of Geophysical Research, Vol. 102(C4), 8681-8689.

Kovacs, A., Weeks, W. F., Ackley, S., & Hibler III, W. D. (1973). Structure of a Multi- Year Pressure Ridge.

Krishfield, R. A., Proshutinsky, A., Tateyama, K., Williams, W. J., Carmack, E. C., McLaughlin, F. A., & Timmermans, M. L. (2014, Februrary 22). Deterioration of perennial sea ice in the Beaufort Gyre from 2003 to 2012 and its impact on the oceanic freshwater cycle. Journal of Geophysical Research: Oceans, 1,271 - 1,305. doi:10.1002/2013Jc008999

Kuehn, G. A., & Schulson, E. M. (1993). The Mechanical Properties of Saline Ice Under Uniaxial Compression. IGS International Symposium on Applied Ice and Snow Research. Rovaniemi.

Kvadsheim, S. (2014). Ice ridge keel size distributions.

156 Laxon, S. W., Giles, K. A., Ridout, A. L., Wingham, D. J., Willatt, R., Cullen, R., . . . Davidson, M. (2013). CryoSat-2 estimates of Arctic sea ice thickness and volume. Geophysical Research Letters, 40, 732-737. doi:10.1002/grl.50193

Leijnse, S. (2010). Friction Coefficient Measurements of Casing While Drilling with Steel and Composite Tubulars. AES.

Leppäranta, M., Lensu, M., Kosloff, P., & Veitch, B. (1995). The life story of a first-year sea ice ridge. Cold Regions Science and Technology, 23, 279-290.

Lowry, R. T., & Wadhams, P. (1979). On the Statistical Distribution of Pressure Ridges in Sea Ice. 84(C5), 2487-2494.

Lyon, W. (1961, June). Ocean and Sea-Ice Research in the Arctic Ocean via Submarine. Transactions of the New York Academy of Sciences, 23(8 series ii), 662-674.

Lyon, W. (1967). Under Surface Profiles of Sea Ice Observed by Submarine. Eleventh Pacific Science Congress, (pp. 707 - 711). Tokyo.

Mahoney, A. R. (2012). Sea Ice Conditions in the Chukchi and Beaufort Seas. University of Alaska Fairbanks, Geophysical Institute, Fairbanks.

Mahoney, A. R., Eicken, H., Fukamachi, Y., Ohshima, K. I., Simizu, D., Kambhamettu, C., . . . Jones, J. (2015). Taking a look at both sides of the ice: comparison of ice thickness and drift speed as observed from moored, airborne and shore-based instruments near Barrow, Alaska. Annals of Glaciology, 363 - 372. doi:10.3189/2015AoG69A565

Mahoney, A. R., Eicken, H., Gaylord, A. G., & Gens, R. (2014). Landfast sea ice extent in the Chukchi and Beaufort Seas: The annual cycle and decadal variability. Cold Regions Science and Technology, 41 - 56.

Mahoney, A., & Eicken, H. (n.d.).

Mahoney, A., Eicken, H., Gaylord, A. G., & Shapiro, L. (2007). Alaska landfast sea ice: Links with bathymetry and atmospheric circulation. Journal of Geophysical Research, 112(C02001). doi:10.1029/2006JC003559 157 Matlab©. (n.d.).

Melling, H. (2002). Sea ice of the northern Canadian Arctic Archipelago. Journal of Geophysical Research, 107(C11), (2-1)-(2-21). doi:10.1029/2001JC001102

Melling, H., & Riedel, D. A. (1995). The underside topography of sea ice over the continental shelf of the Beaufort Sea in the winter of 1990. Journal of Geophysical Research, 100(C7), 13,641-13,653.

Melling, H., & Riedel, D. A. (1996). Development of seasonal pack ice in the Beaufort Sea during the winter of 1991-1992: A view from below. Journal of Geophysical Research, 101(C5), 11,975-11,991.

Melling, H., & Riedel, D. A. (2004). Draft and Movement of Pack Ice in the Beaufort Sea: A Time-Series Presentation April 1990-August 1999. Fisheries and Oceans Canada. Canadian Technical Report of Hydrography and Ocean Sciences.

Melling, H., Johnston, P. H., & Riedel, D. A. (1995). Measurements of the Underside Topography of Sea Ice by Moored Subsea Sonar. Journal of Atmospheric and Oceanic Technology, 12, 589-602.

Melling, H., Riedel, D. A., & Gedalof, Z. (2005). Trends in the draft and extent of seasonal pack ice, Canadian Beaufort Sea. 32. doi:10.1029/2005GL024483

Mock, S. J., Hartwell, A. D., & Hibler III, W. D. (1972). Spatial Aspects of Pressure Ridge Statistics. Journal of Geophysical Research, 77(30), 5945-5953.

Moslet, P. O. (2007). Field testing of uniaxial compression strength of columnar sea ice. Cold Regions Science and Technology, 1-14.

Mudge, T., Borg, K., Sadowy, D., Jackson, J., Fissel, D., & Ross, E. (2014). Varying Ice Conditions as Observed in the Chukchi and Beaufort Seas 2008-2013. Canada.

National Oceanic and Atmospheric Administration. (n.d.). Arctic theme page. Retrieved from http://www.arctic.noaa.gov/ice-rubble-pressure.html

158 Norton, D. W., & Gaylord, A. G. (2004). Drift Velocities of Ice Floes in Alaska's Northern Chukchi Sea Flaw Zone: Determinants of Success by Spring Subsistence Whalers in 2000 and 2001. ARCTIC, 57(4), 347-362.

Nuber, A., Rabenstein, L., Lehmann-Horn, J. A., Hertrich, M., Hendricks, S., Mahoney, A., & Eicken, H. (2013). Water content estimates of a first-year sea-ice pressure ridge keel from surface-nuclear magnetic resonance tomography. Annals of Glaciology, 54(No. 64), 33 - 43. doi:10.3189/2013AoG64A205

Obert, K. M., & Brown, T. G. (2011). Ice ridge keel characteristics and distribution in the Northumberland Strait. Cold Regions Science and Technology, 66, 53-64.

Oikkonen, A., & Haapala, J. (2011). Variability and changes of Arctic sea ice draft distribution - submarine sonar measurements revisited. The Cryosphere, 5, 917- 929. doi:10.5194/tc-5-917-2011

Palmer, A., & Croasdale, K. (2013). Arctic Offshore Engineering. World Scientific Publishing Co. Pte. Ltd.

Parmerter, R. R. (1975, May 20). A Model of Simple Rafting in Sea Ice. Journal of Geophysical Research, 80(No. 15), 1,948 - 1,952.

Parmerter, R. R., & Coon, M. D. (1972). Model of Pressure Ridge Formation in Sea Ice. Journal of Geophysical Research, 77(NO. 33), 6565-6575.

Peterson, I. K., Prinsenberg, S. J., & Holladay, J. S. (2008). Observations of sea ice thickness, surface roughness and ice motion in the Amundsen Gulf. Journal of Geophysical Research, 113. doi:10.1029/2007JC004456

Pilkington, G. R., & Wright, B. D. (1991). Beaufort Sea Ice Thickness Measurements From an Acoustic, Under Ice, Upward Looking Ice Keel Profiler. Proceedings of the First (1991) International Offshore and Polar Engineering Conference.

Prodanovic, A. (1981). Upper Bounds of Ridge Pressure on Structures.

159 Reimnitz, E., & Barnes, P. (1974). Sea ice as a geologic agent on the Beaufort Sea shelf of Alaska. (J. C. Reed, & J. E. Sater, Eds.) Arlington: Arctic Institute of North America.

Ren, J.-J. (1995). Generalized Cramer-von Mises Tests of Goodness of fit for Doubly Censored Data. Annals of the Institute of Statistical Mathematcis, 47(No. 3), 525 - 549.

Ross, E., Fissel, D., Mudge, T., Kanwar, A., & Sadowy, D. (2014). The Sensitivity of Ice Keel Statistics to Upward Looking Sonar Ice Draft Processing Methods.

Ross, S. (2002). A First Course in Probability (Sixth Edition ed.). Upper Saddle River, New Jersey, United States: Prentice-Hall, Inc.

Rothrock, D. A., & Thorndike, A. S. (1980). Geometric Properties of the Underside of Sea Ice. Journal of Geophysical Research, 85(C7), 3955-3963.

Samuelson, T., Hoisington, D., Bronga, J., Halcomb, R., Hearn, P., & Wiehe, C. (2012). Chukchi Sea Weather Station.

Sayed, M., & Frederking, R. (1986). On Modelling of Ice Ridge Formation. Proceedings of IAHR Ice Symposium.

Sayed, M., & Frederking, R. M. (1988). Measurements of ridge sails in the Beaufort Sea. Canadian Journal of Civil Engineering, 16, 16-21.

Schulson, E. M., Renshaw, C. E., & Snyder, S. A. (2013). The Effect of Deformation Damage on the Mechanical Behavior of Sea Ice: Ductile-to-Brittle Transition, Elastic Modulus, and Brittle Compressive Strength. Thayer School of Engineering, Dartmouth College.

Schwarz, J., Frederking, R., Gavrillo, V., Petrov, I. G., Hirayama, K. I., Mellor, M., . . . Vaudrey, K. D. (1981). Standardized Testing Methods for Measuring Mechanical Properties of Ice. Cold Regions Science and Technology, 4, 245-253.

Sear, C. B., & Wadhams, P. (1992). Statistical properties of Arctic sea ice morphology derived from sidescan sonar images. Progress in Oceanography, 29, 133-160. 160 Shafrova, S. (2007). First-year sea ice features: Investigation of ice field strength heterogeneity and modelling of ice rubble behaviour. The University Centre in Svalbard Department of Arctic Technology.

Shazly, M., Prakash, V., & Lerch, B. A. (2009). High strain-rate behavior of ice under uniaxial compression. International Journal of Solids and Structures, 1499-1515.

Shestov, A. (2011). Morphology and PHysical Properties of Old Sea Ice in the Fram Strait. Proceedings of the 21st International Conference on Port and Ocean Engineering under Arctic Conditions.

Sinha, N. K. (1983). Uniaxial compressive strength of first-year and multi-year sea ice. Canadian Journal of Civil Engineering, 82 - 91.

Spencer, P., & Morrison, T. (2014). Quantile Regression as a Tool for Investigating Local and Global Ice Pressures. Offshore Technology Conference. Houston.

Strass, V. H. (1997). Measuring sea ice draft and coverage with moored upward looking sonars. Deep-Sea Research I, 45, 795-818.

Strub-Klein, L., & Sudom, D. (2012). A comprehensive analysis of the morphology of first-year sea ice ridges. Cold Regions Science and Technology, 82, 94-109.

Sudom, D., & Timco, G. (2013). Knowledge Gaps in Sea Ice Ridge Properties. Port and Ocean Engineering under Arctic Conditions. Espoo.

Sudom, D., Timco, G., Sand, B., & Fransson, L. (2011). Analysis of First-Year and Old Ice Ridge Characteristics. Proceedings of the 21st International Conference on Port and Ocean Engineering under Arctic Conditions.

Tassoulas, J. L. (2009). Seabed Scour and Buried-Pipeline Deformation Due to Ice Ridges.

Timco, G. W., & Burden, R. P. (1997). An analysis of the shapes of sea ice ridges. Cold Regions Science and Technology, 25, 65-77.

161 Timco, G. W., & Frederking. (1985). Confined Compression Tests: Outlining the Failure Envelope of Columnar Sea Ice\. Cold Regions Science and Technology, 13-28.

Timco, G. W., & Frederking, R. (1989, July 5). Compressive Strength of Sea Ice Sheets. Cold Regions Science and Technology, 227 - 240.

Timco, G. W., & Frederking, R. (2009). Overview of Historical Canadian Beaufort Sea Information. Canadian Hydraulics Centre.

Timco, G. W., & Johnston, M. (2004). Ice loads on caisson structures in the Canadian Beaufort Sea. Cold Regions Science and Technology, 180-209.

Timco, G. W., & Johnston, M. E. (2002). Caisson Structures in the Beaufort Sea 1982- 1990: Characteristics, Instrumentation and Ice Loads.

Timco, G. W., & Weeks, W. F. (2010). A review of the engineering properties of sea ice. Cold Regions Science and Technology, 60, 107-129.

Timco, G. W., Wright, B. D., Barker, A., & Poplin, J. P. (2005). Ice damage zone around the Molikpaq: Implications for evacuation systems. Cold Regions Science and Technology, 67-85.

Timco, G., & Johnston, M. (2002). Ice Strength During the Melt Season. 16th IAHR International Symposium, (pp. 187 - 193). Dunedin.

Timco, G., Croasdale, K., & Wright, B. (2000). An Overview of First-Year Sea Ice Ridges.

Timco, G., Frederking, R., Kamesaki, K., & Tada, H. (1999). Comparison of Ice Load Calculation Algorithms for First-Year Ridges. Proceedings International Workshop on Rational Evaluation of Ice Forces on Structures, (pp. 88-102).

Tucker III, W. B., & Govoni, J. W. (1981). Morphological Investigations of First-Year Sea Ice Pressure Ridge Sails. Cold Regions Science and Technology, 5, 1-12.

162 Tucker III, W. B., Weeks, W. F., & Frank, M. (1979). Sea Ice Ridging Over the Alaskan Continental Shelf. 84(C8), 4885-4897.

U.S. Department of the Interior. (1988). SEA ICE FORCES AND MECHANICS. Anchorage.

Wadhams, P. (1981). Sea-Ice Topography of the Arctic Ocean in the Region 70° W to 25° E. Philosophical Transactions of The Royal Society, 302(A 1464). doi:10.1098/rsta.1981.0157

Wadhams, P. (1983). THE PREDICTION OF EXTREME KEEL DEPTHS FROM SEA ICE PROFILES. Cold Regions Science and Technology, 6, 257-266.

Wadhams, P. (1992). Sea Ice Thickness Distribution in the Greenland Sea and Eurasian Basin, May 1987. Journal of Geophysical Research, 97(C4), 5331-5348.

Wadhams, P. (2000). Ice in the Ocean. (1, Ed.) CRC Press.

Wadhams, P. (2011). New predictions of extreme keel depths and scour frequencies for the Beaufort Sea using ice thickness statistics. Cold Regions Science and Technology, 76-77, 77-82. doi:10.1016/j.coldregions.2011.12.002

Wadhams, P. (2012). Arctic Ice Cover, Ice Thickness and Tipping Points. AMBIO, 41, 23-33. doi:10.1007/s13280-011-0222-9

Wadhams, P., & Davis, N. R. (2001). Arctic sea-ice morphological characteristics in summer 1996. Annals of Glaciology, 33, 165-170.

Wadhams, P., & Davy, T. (1986). On the Spacing and Draft Distributions for Pressure Ridge Keels. Journal of Geophysical Research, 91(C9), 10,697-10,708.

Wadhams, P., & Doble, M. (2014). D1.26-Report on ridge shapes and distributions for extreme value analyses in WP2, WP4 and under-ice ecosystems in WP3.

163 Wadhams, P., & Doble, M. J. (2008). Digital terrain mapping of the underside of sea ice from a small AUV. Geophysical Research Letters, 35. doi:10.1029/2007GL031921

Wadhams, P., & Horne, R. J. (1980). An Analysis of Ice Profiles Obtained by Submarine Sonar in the Beaufort Sea. Journal of Glaciology, 25(93), 401-424.

Wadhams, P., & Toberg, N. (2012). Changing characteristics of arctic pressure ridges. Polar Science, 6, 71-77. doi:10.1016/j.polar.2012.03.002

Wadhams, P., Hughes, N., & Rodrigues, J. (2011). Arctic sea ice thickness characteristics in winter 2004 and 2007 from submarine sonar transects. Journal of Geophysical Research, 116(C00E02). doi:10.1029/2011JC006982

Wadhams, P., McLaren, A. S., & Weintraub, R. (1985). Ice Thickness Distribution in Davis Strait in February From Submarine Sonar Profiles. Journal of Geophysical Research, 90(C1), 1069-1077.

Wadhams, P., Wilkinson, J. P., & McPhail, S. D. (2006). A new view of the underside of Arctic sea ice. Geophysical Research Letters, 33. doi:10.1029/2005GL025131

Walker, E. R., & Wadhams, P. (1979). Thick Sea-ice Floes. ARCTIC, 32(2), 140-147.

Wang, M., & Overland, J. E. (2009). A sea ice free summer Arctic within 30 years? Geophysical Research Letters, 36(L07502). doi:10.1029/2009GL037820

Williams, E., Swithinbank, C., & Robin, G. (1975). A Submarine Sonar Study of Arctic Pack Ice. Journal of Glaciology, 13(No. 73), 349 - 362.

Wolfram. (n.d.). Wolfram Language & System | Documentation Center.

Woodgate, R. A., Weingartner, T., & Lindsay, R. (2010, January 07). The 2007 Bering Strait oceanic heat flux and anomalous Arctic sea-ice retreat. Geophysical Research Letters, 37(L01602). doi:10.1029/2009GL041621

164 Wright, B. D., & Timco, G. W. (2001). First-year interaction with the Molikpaq in the Beaufort Sea. Cold Regions Science and Technology, 27-44.

Yu, Y., Maykut, G. A., & Rothrock, D. A. (2004). Changes in the thickness distrbution of Arctic sea ice between 1958-1970 and 1993-1997. Journal of Geophysical Research, 109(C08004). doi:10.1029/2003JC001982

165

166 Appendix A:

Pressure Ridge Keel Draft

Beaufort Sea Keel Draft 0.35

0.3

0.25

0.2

0.15 Fraction (-)

0.1

0.05

0 6 10 15 20 25 30 35 Keel Depth (m)

Figure A.1: Beaufort Sea Keel Draft Histogram

167 Appendix A (Continued)

Chukchi Sea Keel Draft 0.4

0.35

0.3

0.25

0.2

Fraction (-) 0.15

0.1

0.05

0 6 10 15 20 25 30 35 Keel Depth (m)

Figure A.2: Chukchi Sea Keel Draft Histogram

Beaufort Keel Draft Exponential Probability Plot

0.9999

0.9995 0.999

0.995

Probability 0.99

0.95 0.9 0.75 0.5 0.25 0 5 10 15 20 25 [Keel Draft - 6] (m)

Figure A.3: Beaufort Sea Keel Draft Exponential Plot

168 Appendix A (Continued)

Beaufort Keel Draft Weibull Probability Plot

0.9999 0.9990.99 0.9 0.75 0.5 0.25 0.1 0.05 0.01 0.005 Probability 0.001 0.0005 0.0001

-4 -2 0 2 10 10 10 10 [Keel Draft - 6] (m)

Figure A.4: Beaufort Sea Keel Draft Weibull Plot

Chukchi Keel Draft Exponential Probability Plot

0.9999

0.9995 0.999

0.995

Probability 0.99

0.95 0.9 0.75 0.5 0.25 0 5 10 15 20 25 [Keel Draft - 6] (m)

Figure A.5: Chukchi Sea Keel Draft Exponential Plot

169 Appendix A (Continued)

Chukchi Keel Draft Weibull Probability Plot

0.9999 0.9990.99 0.9 0.75 0.5 0.25 0.1 0.05 0.01 0.005 Probability 0.001 0.0005 0.0001

-4 -2 0 2 10 10 10 10 [Keel Draft - 6] (m)

Figure A.6: Chukchi Sea Keel Draft Weibull Plot

2005-06 Site A Keels By Month 1400

1200

1000

800

600 # of Keels

400

200

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.7: 2005-06 Site A Keel Totals by Month

170 Appendix A (Continued)

2005-06 Site B Keels By Month 2500

2000

1500

# of Keels 1000

500

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.8: 2005-06 Site B Keel Totals by Month

2006-07 Site A Keels By Month 1200

1000

800

600 # of Keels 400

200

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.9: 2006-07 Site A Keel Totals by Month

171 Appendix A (Continued)

2006-07 Site B Keels By Month 900

800

700

600

eels 500

400 # of K 300

200

100

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.10: 2006-07 Site B Keel Totals by Month

2007-08 Site A Keels By Month 1400

1200

1000

800

600 # of Keels

400

200

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.11: 2007-08 Site A Keel Totals by Month

172 Appendix A (Continued)

2007-08 Site K Keels By Month 1000

800

600 eels

# of K 400

200

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.12: 2007-08 Site K Keel Totals by Month

2007-08 Site V Keels By Month 2000

1500

1000 # of Keels

500

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.13: 2007-08 Site V Keel Totals by Month

173 Appendix A (Continued)

2009-10 Site A Keels By Month 1500

1000 # of Keels 500

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.14: 2009-10 Site A Keel Totals by Month

2009-10 Site V Keels By Month 1600

1400

1200

1000

800

# of Keels 600

400

200

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.15: 2009-10 Site V Keel Totals by Month

174 Appendix A (Continued)

2009-10 Burger Keels By Month 1200

1000

800

600 # of Keels 400

200

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.16: 2009-10 Burger Keel Totals by Month

2009-10 Crackerjack Keels By Month 1400

1200

1000

800

600 # of Keels

400

200

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.17: 2009-10 Crackerjack Keel Totals by Month

175 Appendix A (Continued)

2010-11 Site A Keels By Month 900

800

700

600

500

400 # of Keels 300

200

100

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.18: 2010-11 Site A Keel Totals by Month

2010-11 Site V Keels By Month 900

800

700

600

500

400 # of Keels 300

200

100

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.19: 2010-11 Site V Keel Totals by Month

176 Appendix A (Continued)

2010-11 Burger Keels By Month 1600

1400

1200

1000

800

# of Keels 600

400

200

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.20: 2010-11 Burger Keel Totals by Month

2010-11 Crackerjack Keels By Month 1500

1000 eels # of K 500

0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Figure A.21: 2010-11 Crackerjack Keel Totals by Month

177

178 Appendix B:

Pressure Ridge Keel Width

Figure B.1: Beaufort Sea Diagrammatic Keel Width/Angle

Figure B.2: Chukchi Sea Diagrammatic Keel Width/Angle

179

180 Appendix C:

Ice Velocity

2005-06 Site A Ice Velocity Rose

Ice Speeds (cm/s) 25% I  120 S 20% 100  I < 120 S 15% 80  I < 100 S 10% 60  IS < 80 5% 40  IS < 60 20  I < 40 S W 0% E 0  IS < 20

Figure C.1: 2005-06 Site A Ice Velocity Rose

181 Appendix C (Continued)

2005-06 Site B Ice Velocity Rose

Ice Speeds (cm/s) 35% I  160 S 28% 140  I < 160 S 21% 120  IS < 140 14% 100  IS < 120 7% 80  IS < 100 60  I < 80 S W 0% E 40  IS < 60

20  IS < 40

0  IS < 20

Figure C.2: 2005-06 Site B Ice Velocity Rose

2006-07 Site A Ice Velocity Rose

Ice Speeds (cm/s) 45% I  120 S 36% 100  I < 120 S 27% 80  IS < 100 18% 60  IS < 80 9% 40  IS < 60 20  I < 40 S W 0% E 0  IS < 20

Figure C.3: 2006-07 Site A Ice Velocity Rose

182 Appendix C (Continued)

2006-07 Site B Ice Velocity Rose

Ice Speeds (cm/s) 45% I  120 S 36% 100  I < 120 S 27% 80  IS < 100 18% 60  IS < 80 9% 40  IS < 60 20  I < 40 S W 0% E 0  IS < 20

Figure C.4: 2006-07 Site B Ice Velocity Rose

2006-07 Site K Ice Velocity Rose

Ice Speeds (cm/s) 35% I  150 S 28% 100  I < 150 S 21% 50  IS < 100 14% 0  IS < 50 7%

W 0% E

Figure C.5: 2006-07 Site K Ice Velocity Rose

183 Appendix C (Continued)

2007-08 Site A Ice Velocity Rose

Ice Speeds (cm/s) 40% I  140 S 32% 120  I < 140 S 24% 100  IS < 120 16% 80  IS < 100 8% 60  IS < 80 40  I < 60 S W 0% E 20  IS < 40

0  IS < 20

Figure C.6: 2007-08 Site A Ice Velocity Rose

2007-08 Site K Ice Velocity Rose

Ice Speeds (cm/s) 30% I  150 S 24% 100  I < 150 S 18% 50  IS < 100 12% 0  IS < 50 6%

W 0% E

Figure C.7: 2007-08 Site K Ice Velocity Rose

184 Appendix C (Continued)

2007-08 Site V Ice Velocity Rose

Ice Speeds (cm/s) 35% I  120 S 28% 100  I < 120 S 21% 80  IS < 100 14% 60  IS < 80 7% 40  IS < 60 20  I < 40 S W 0% E 0  IS < 20

Figure C.8: 2007-08 Site V Ice Velocity Rose

2009-10 Site A Ice Velocity Rose

N Ice Speeds (cm/s) 30% I  140 S 24% 120  I < 140 S 18% 100  IS < 120 12% 80  IS < 100 6% 60  IS < 80 40  I < 60 S W 0% E 20  IS < 40

0  IS < 20

Figure C.9: 2009-10 Site A Ice Velocity Rose

185 Appendix C (Continued)

2009-10 Site V Ice Velocity Rose

N Ice Speeds (cm/s) 30% I  120 S 24% 100  I < 120 S 18% 80  IS < 100 12% 60  IS < 80 6% 40  IS < 60 20  I < 40 S W 0% E 0  IS < 20

Figure C.10: 2009-10 Site V Ice Velocity Rose

2009-10 Burger Ice Velocity Rose

Ice Speeds (cm/s) 20% I  90 S 16% 80  I < 90 S 12% 70  IS < 80 8% 60  IS < 70 4% 50  IS < 60 40  I < 50 S W 0% E 30  IS < 40

20  IS < 30

10  IS < 20

0  IS < 10

Figure C.11: 2009-10 Burger Ice Velocity Rose

186 Appendix C (Continued)

2009-10 Crackerjack Ice Velocity Rose

Ice Speeds (cm/s) 20% I  70 S 16% 60  I < 70 S 12% 50  IS < 60 8% 40  IS < 50 4% 30  IS < 40 20  I < 30 S W 0% E 10  IS < 20

0  IS < 10

Figure C.12: 2009-10 Crackerjack Ice Velocity Rose

2010-11 Site A Ice Velocity Rose

Ice Speeds (cm/s) 25% I  120 S 20% 100  I < 120 S 15% 80  IS < 100 10% 60  IS < 80 5% 40  IS < 60 20  I < 40 S W 0% E 0  IS < 20

Figure C.13: 2010-11 Site A Ice Velocity Rose

187 Appendix C (Continued)

2010-11 Site V Ice Velocity Rose

N Ice Speeds (cm/s) 30% I  100 S 24% 90  I < 100 S 18% 80  IS < 90 12% 70  IS < 80 6% 60  IS < 70 50  I < 60 S W 0% E 40  IS < 50

30  IS < 40

20  IS < 30

10  IS < 20

0  IS < 10

Figure C.14: 2010-11 Site V Ice Velocity Rose

2010-11 Burger Ice Velocity Rose

Ice Speeds (cm/s) 15% I  120 S 12% 100  I < 120 S 9% 80  IS < 100 6% 60  IS < 80 3% 40  IS < 60 20  I < 40 S W 0% E 0  IS < 20

Figure C.15: 2010-11 Burger Ice Velocity Rose

188 Appendix C (Continued)

2010-11 Crackerjack Ice Velocity Rose

Ice Speeds (cm/s) 15% I  100 S 12% 90  I < 100 S 9% 80  IS < 90 6% 70  IS < 80 3% 60  IS < 70 50  I < 60 S W 0% E 40  IS < 50

30  IS < 40

20  IS < 30

10  IS < 20

0  IS < 10

Figure C.16: 2010-11 Crackerjack Ice Velocity Rose

189

190 Appendix D:

Level Ice

2005-06 Site A Level Ice Distribution 3 400 Mean Median 350 2.5 Lower 5% Upper 5% 300 2 250

1.5 200

33.3% 150 1 56.1%

100 Ice Drift Distance (km) Level Ice Thickness (m) 32.0% 0.5 54.6% 15.3% 50 16.4% 0.0% 7.8% 3.2% 1.7% 0.7% 1.9% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.1: 2005-06 Site A Level Ice Distribution

191 Appendix D (Continued)

2005-06 Site B Level Ice Distribution 3 500 Mean Median 2.5 Lower 5% 400 Upper 5% 2 300 1.5 200 48.3% 37.8% 1 39.7% Ice Drift Distance (km) Level Ice Thickness (m) 100 0.5 25.3% 65.2% 25.3% 0.0% 46.3% 6.8% 2.1% 1.0% 0.5% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.2: 2005-06 Site B Level Ice Distribution

192 Appendix D (Continued)

2006-07 Site A Level Ice Distribution 3 500 Mean Median 2.5 Lower 5% 400 Upper 5% 2 57.9% 300 1.5

88.4% 200 1 36.8% Ice Drift Distance (km) Level Ice Thickness (m) 100 0.5 12.7% 20.1% 14.7% NaN% 24.0% 1.5% 6.1% NaN% NaN% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.3: 2006-07 Site A Level Ice Distribution

193 Appendix D (Continued)

2006-07 Site B Level Ice Distribution 3 600 Mean Median 2.5 Lower 5% 500 Upper 5% 2 400 57.1% 1.5 300

37.6% 1 87.8% 200 31.1% Ice Drift Distance (km) Level Ice Thickness (m) 0.5 100 30.4% NaN% 18.8% 6.9% 16.4%13.1% NaN% NaN% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.4: 2006-07 Site B Level Ice Distribution

194 Appendix D (Continued)

2006-07 Site K Level Ice Distribution 3 600 Mean Median 2.5 Lower 5% 500 Upper 5% 2 400 62.8%

1.5 300

1 95.8% 200 Ice Drift Distance (km) Level Ice Thickness (m) 30.6% 0.5 100 21.3% 33.3%

NaN% 15.6% 3.5% 14.4% 3.2% 0.0% NaN% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.5: 2006-07 Site K Level Ice Distribution

195 Appendix D (Continued)

2007-08 Site A Level Ice Distribution 3 600 Mean Median 2.5 Lower 5% 500 Upper 5% 2 400 57.9% 65.4% 1.5 300

1 45.4% 200 Ice Drift Distance (km)

Level Ice Thickness (m) 49.5% 0.5 100 15.7% 25.1% NaN% 22.2% 0.0% 14.9% 0.8% NaN% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.6: 2007-08 Site A Level Ice Distribution

196 Appendix D (Continued)

2007-08 Site K Level Ice Distribution 3 600 Mean Median 2.5 Lower 5% 500 Upper 5% 2 69.7% 400

61.0% 1.5 300

65.2% 1 46.4% 200 Ice Drift Distance (km) Level Ice Thickness (m) 0.5 24.8% 100 35.3% 15.5% NaN% 48.0% 23.7% 52.4% NaN% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.7: 2007-08 Site K Level Ice Distribution

197 Appendix D (Continued)

2007-08 Site V Level Ice Distribution 3 600 Mean Median 2.5 Lower 5% 500 Upper 5% 2 400

69.4%67.2% 1.5 300

1 97.2% 33.7% 200 Ice Drift Distance (km) Level Ice Thickness (m) 31.1% 0.5 100 25.7% 16.0%32.4% NaN% 22.4% 4.9% NaN% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.8: 2007-08 Site V Level Ice Distribution

198 Appendix D (Continued)

2009-10 Site A Level Ice Distribution 3 400 Mean Median 350 2.5 Lower 5% Upper 5% 300 2 67.2% 250

1.5 200

150 1

100 Ice Drift Distance (km) Level Ice Thickness (m) 19.2% 0.5 39.1% 17.8% 50 16.3% 99.6% NaN% 22.3%11.5%34.0%34.3% 0.0% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.9: 2009-10 Site A Level Ice Distribution

199 Appendix D (Continued)

2009-10 Site V Level Ice Distribution 3 600 Mean Median 2.5 Lower 5% 500 Upper 5% 72.3% 2 400

1.5 300

1 200

35.8% Ice Drift Distance (km) Level Ice Thickness (m) 32.1% 0.5 100 98.3% 16.3% NaN% 8.7% 9.5%11.2% 2.6% 2.6%12.2% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.10: 2009-10 Site V Level Ice Distribution

200 Appendix D (Continued)

2009-10 Burger Level Ice Distribution 3 500 Mean Median 2.5 Lower 5% 400 70.8% Upper 5% 2 300 1.5 49.0% 200 1 79.5% Ice Drift Distance (km) Level Ice Thickness (m) 25.2% 30.7% 100 0.5 21.3% 21.3% NaN% NaN% 33.0% NaN% NaN% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.11: 2009-10 Burger Level Ice Distribution

201 Appendix D (Continued)

2009-10 Crackerjack Level Ice Distribution 10 600 Mean Median 500 8 Lower 5% Upper 5% 75.4% 400 6 300 63.2% 4 93.0% 200 Ice Drift Distance (km) Level Ice Thickness (m) 2 36.3% 100 17.6% 14.7% 13.6% 19.0% NaN% NaN% NaN% NaN% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.12: 2009-10 Crackerjack Level Ice Distribution

202 Appendix D (Continued)

2010-11 Site A Level Ice Distribution 3 600 Mean Median 2.5 Lower 5% 500 Upper 5% 2 400

1.5 47.5% 300

1 47.2% 200 37.5% Ice Drift Distance (km) Level Ice Thickness (m) 0.5 100 21.1% 16.8% NaN% NaN% 7.7% 0.0% 0.0% NaN% NaN% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.13: 2010-11 Site A Level Ice Distribution

203 Appendix D (Continued)

2010-11 Site V Level Ice Distribution 3 500 Mean Median 2.5 Lower 5% 400 Upper 5% 2 300 1.5 48.9% 200 1 34.9% Level Ice Thickness (m)

100 Ice Drift Distance (km) 0.5 99.2% 23.3% 16.6% NaN% NaN% 16.2% NaN% NaN% NaN% NaN% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.14: 2010-11 Site V Level Ice Distribution

204 Appendix D (Continued)

2010-11 Burger Level Ice Distribution 3 800 Mean Median 700 2.5 Lower 5% Upper 5% 600 76.0% 2 500

1.5 400 52.3% 300 1 50.4% 34.5% 200 Ice Drift Distance (km) Level Ice Thickness (m) 0.5 100 16.9%19.9% 12.5% 28.7% NaN% NaN% NaN% NaN% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.15: 2010-11 Burger Level Ice Distribution

205 Appendix D (Continued)

2010-11 Crackerjack Level Ice Distribution 3 800 Mean Median 700 2.5 Lower 5% 81.5% Upper 5% 600 2 500

1.5 400

80.5% 300 1 44.4% 51.2%

200 Ice Drift Distance (km) Level Ice Thickness (m) 0.5 100 20.7% 20.4% 14.2%19.6% NaN% NaN% NaN% NaN% 0 0 Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug

Figure D.16: 2010-11 Crackerjack Level Ice Distribution

206 Appendix E:

Other Ice

Beaufort Other Ice Draft 0.14 Other Ice Track = 11448 km 0.12

0.1

0.08

0.06 Fraction (-)

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.1: Beaufort Other Ice Draft

207 Appendix E (Continued)

Chukchi Other Ice Draft 0.16 Other Ice Track = 4796 km 0.14

0.12

0.1

0.08

Fraction (-) 0.06

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.2: Chukchi Other Ice Draft

2005-06 Site A Other Ice Draft 0.1 Other Ice Track = 1263 km

0.08

0.06

0.04 Fraction (-)

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.3: 2005-06 Site A Other Ice Draft

208 Appendix E (Continued)

2005-06 Site B Other Ice Draft 0.16 Other Ice Track = 1115 km 0.14

0.12

0.1

0.08

Fraction (-) 0.06

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.4: 2005-06 Site B Other Ice Draft

2006-07 Site A Other Ice Draft 0.14 Other Ice Track = 888 km 0.12

0.1

0.08

0.06 Fraction (-)

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.5: 2006-07 Site A Other Ice Draft

209 Appendix E (Continued)

2006-07 Site B Other Ice Draft 0.16 Other Ice Track = 1066 km 0.14

0.12

0.1

0.08

Fraction (-) 0.06

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.6: 2006-07 Site B Other Ice Draft

2006-07 Site K Other Ice Draft 0.14 Other Ice Track = 925 km 0.12

0.1

0.08

0.06 Fraction (-)

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.7: 2006-07 Site K Other Ice Draft

210 Appendix E (Continued)

2007-08 Site A Other Ice Draft 0.2 Other Ice Track = 949 km

0.15

0.1 Fraction (-)

0.05

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.8: 2007-08 Site A Other Ice Draft

2007-08 Site K Other Ice Draft 0.18 Other Ice Track = 870 km 0.16

0.14

0.12

0.1

0.08 Fraction (-) 0.06

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.9: 2007-08 Site K Other Ice Draft

211 Appendix E (Continued)

2007-08 Site V Other Ice Draft 0.14 Other Ice Track = 978 km 0.12

0.1

0.08

0.06 Fraction (-)

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.10: 2007-08 Site V Other Ice Draft

2009-10 Site A Other Ice Draft 0.12 Other Ice Track = 631 km

0.1

0.08

0.06 Fraction (-) 0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.11: 2009-10 Site A Other Ice Draft

212 Appendix E (Continued)

2009-10 Site V Other Ice Draft 0.12 Other Ice Track = 1010 km

0.1

0.08

0.06 Fraction (-) 0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.12: 2009-10 Site V Other Ice Draft

2009-10 Burger Other Ice Draft 0.12 Other Ice Track = 987 km

0.1

0.08

0.06 Fraction (-) 0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.13: 2009-10 Burger Other Ice Draft

213 Appendix E (Continued)

2009-10 Crackerjack Other Ice Draft 0.14 Other Ice Track = 952 km 0.12

0.1

0.08

0.06 Fraction (-)

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.14: 2009-10 Crackerjack Other Ice Draft

2010-11 Site A Other Ice Draft 0.16 Other Ice Track = 1015 km 0.14

0.12

0.1

0.08

Fraction (-) 0.06

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.15: 2010-11 Site A Other Ice Draft

214 Appendix E (Continued)

2010-11 Site V Other Ice Draft 0.16 Other Ice Track = 736 km 0.14

0.12

0.1

0.08

Fraction (-) 0.06

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.16: 2010-11 Site V Other Ice Draft

2010-11 Burger Other Ice Draft 0.18 Other Ice Track = 1602 km 0.16

0.14

0.12

0.1

0.08 Fraction (-) 0.06

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.17: 2010-11 Burger Other Ice Draft

215 Appendix E (Continued)

2010-11 Crackerjack Other Ice Draft 0.18 Other Ice Track = 1255 km 0.16

0.14

0.12

0.1

0.08 Fraction (-) 0.06

0.04

0.02

0 0 1 2 3 4 5 6 Other Ice Draft (m)

Figure E.18: 2010-11 Crackerjack Other Ice Draft

216