Environmental Controls on Calving in Grounded Tidewater Glaciers Susan Jennifer Cook Submitted to Swansea University in fulfilment of the requirements for the Degree of Doctor of Philosophy Swansea University 2012 Abstract The calving of icebergs is an important mass loss process in many glaciers worldwide, including the Antarctic and Greenland Ice Sheets. Despite its importance, calving is still relatively poorly reproduced in ice sheet models, largely due to the complexity of the processes involved. In this thesis a new grounded tidewater glacier model is presented using a physically realistic calving criterion, based on the penetration of crevasses in the ice, applied in a two-dimensional, vertically-resolved ice flow model using the finite element software Elmer. This is the only tidewater glacier model so far developed which can been used to model individual calving events, allowing a detailed analysis of calving at the terminus of the glacier. The model is tested with four environmental variables which have been thought to a↵ect calving rates: water depth in crevasses, basal water pressure, undercutting of the calving face by subaqueous melt and backstress from ice m´elange. Of the four variables, only crevasse water depth and basal water pressure were found to have a significant e↵ect on terminus behaviour when applied at a realistic magnitude. This is in contrast to previous modelling and observational studies, which had suggested that ocean temperatures could strongly influence the calving front. The apparent contradiction in results is likely to be caused by either the feedback processes linking air and ocean temperatures, or by the fact that floating ice is likely to respond more strongly to subaqueous melt and backstress than grounded ice. The lack of basal elevation data makes it difficult to distinguish grounded and floating ice in many regions. The results presented highlight the importance of good basal elevation data in interpreting glacier behaviour. They also raise the possibility that Greenland outlet glaciers could respond more strongly than previously thought to the recent trend of increased surface melt observed in Greenland, as surface ablation can strongly a↵ect calving dynamics through both the pooling of water in crevasses and changing water pressure at the glacier bed. Declaration This work has not previously been accepted in substance for any degree and is not being concurrently submitted in candidature for any degree. Signed ...................................................................... (candidate) Date ........................................................................ Statement 1 This thesis is the result of my own investigations, except where otherwise stated. Where correction services have been used, the extent and nature of the correction is clearly marked in a footnote(s). Other sources are acknowledged by footnotes giving explicit references. A bibliog- raphy is appended. Signed ..................................................................... (candidate) Date ........................................................................ Statement 2 Iherebygiveconsentformythesis,ifaccepted,tobeavailableforphotocopying and for inter-library loan, and for the title and summary to be made available to outside organisations. Signed ..................................................................... (candidate) Date ........................................................................ Contents Acknowledgements ............................... viii ListofFigures.................................. ix List of Tables . xv ListofNotation................................. xvii 1 Introduction 1 1.1 Calving Processes . 2 1.2 Tidewater Glacier Behaviour . 4 1.2.1 Calving and glacier dynamics . 4 1.2.2 Ocean forcing . 6 1.2.3 E↵ects of air temperature . 7 1.2.4 Role of modelling . 8 1.3 Summary . 9 1.4 ThesisAimsandOutline. 10 1.5 Publication from this thesis . 12 2 Calving Models 13 i CONTENTS ii 2.1 IceFlowModelling ............................ 14 2.1.1 Mathematical basis . 14 2.1.2 Numericalsolutions. 16 2.2 Calving Models . 17 2.2.1 Empirically derived models . 18 2.2.2 Physicallyderivedmodels . 21 2.2.3 Statistical calving models . 25 2.2.4 Summary . 26 2.3 Previous Tidewater Glacier Models . 26 2.3.1 Minimal calving model . 27 2.3.2 Vertically averaged models . 28 2.3.3 Full-Stokes models . 30 2.4 CalvingModelUsedinThisThesis . 32 3 Methodology 33 3.1 NumericalModel ............................. 34 3.1.1 Mathematical basis . 34 3.1.2 Numericalsolution . 36 3.1.3 Upperboundaryconditions . 37 3.1.4 Basal boundary conditions . 37 3.1.5 Other boundary conditions . 44 CONTENTS iii 3.1.6 Mesh update . 45 3.2 Calving Model . 45 3.2.1 Crevasse-depth model . 46 3.2.2 Python wrapper . 47 4 Columbia Glacier Experiments 50 4.1 Introduction . 50 4.2 Data . 51 4.3 Model Set-up . 53 4.3.1 Mass balance . 54 4.3.2 Basal sliding . 55 4.3.3 Lateral e↵ects . 56 4.3.4 Bed sensitivity . 59 4.4 Model Experiments . 60 4.5 Results . 60 4.5.1 Sensitivity tests . 60 4.5.2 Calving behaviour . 62 4.5.3 Response to water in crevasses . 64 4.6 Discussion . 66 4.7 Chapter Summary . 69 5 Helheim Glacier: Sensitivity Analysis 71 CONTENTS iv 5.1 Introduction . 71 5.2 Study Location . 72 5.3 Data . 72 5.4 Model Set-up . 75 5.4.1 Geometry . 75 5.4.2 Englacial temperatures . 76 5.4.3 Lateral drag . 79 5.4.4 Influx boundary condition . 80 5.4.5 Mass balance . 80 5.4.6 Surface relaxation . 81 5.4.7 Basal sliding . 83 5.5 Results: SensitivityAnalysis . 85 5.5.1 Mesh sensitivity . 86 5.5.2 Timestep sensitivity . 88 5.5.3 Surface relaxation sensitivity . 90 5.5.4 Englacial temperature sensitivity . 90 5.5.5 Lateral drag sensitivity . 95 5.5.6 Inflow velocity sensitivity . 96 5.5.7 Basal water pressure sensitivity . 98 5.5.8 Surface mass balance sensitivity . 100 5.5.9 Bed DEM sensitivity . 102 CONTENTS v 5.6 Chapter Summary . 103 6 Helheim Glacier: Environmental forcing 105 6.1 Introduction . 105 6.2 Model Experiment Set-up . 106 6.2.1 Crevasse water depth . 106 6.2.2 Basal water pressure . 107 6.2.3 Subaqueous melt . 108 6.2.4 Ice m´elange . 111 6.3 Results: Response to Climatic Forcing . 113 6.3.1 Crevasse water depth . 113 6.3.2 Basal water pressure . 116 6.3.3 Subaqueous melt . 121 6.3.4 Ice m´elange . 127 6.4 Discussion . 133 6.4.1 Crevasse water depth . 133 6.4.2 Basal water pressure . 135 6.4.3 Subaqueous melt . 136 6.4.4 Ice m´elange . 138 6.5 Chapter Summary . 140 7 Helheim Glacier: Seasonal forcing 142 CONTENTS vi 7.1 Introduction . 142 7.2 Model Experiment Set-up . 142 7.2.1 Crevasse water depth . 145 7.2.2 Basal water pressure . 145 7.2.3 Subaqueous melt . 146 7.2.4 Ice m´elange . 147 7.3 Results: Seasonal Experiments . 148 7.3.1 Crevasse water depth . 148 7.3.2 Basal water pressure . 151 7.3.3 Subaqueous melt . 153 7.3.4 Ice m´elange . 156 7.3.5 Checking the e↵ect of ice temperature . 158 7.4 Discussion . 164 7.4.1 Crevasse water depth . 164 7.4.2 Basal water pressure . 165 7.4.3 Subaqueous melt . 166 7.4.4 Ice m´elange . 167 7.4.5 E↵ect of ice temperature . 167 7.4.6 Calving statistics . 168 7.5 Chapter Summary . 169 CONTENTS vii 8 Discussion 171 8.1 Comparison to Previous Modelling Approaches. ..