Inferring Histories of Accumulation Rate, Ice Thickness, and Ice Flow from Internal Layers in Glaciers and Ice Sheets Michelle R. Koutnik A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2009 Program authorized to offer degree: Earth and Space Sciences University of Washington Graduate School This is to certify that I have examined this copy of a doctoral dissertation by Michelle R. Koutnik and have found that it is complete and satisfactory in all respects, and that any and all revisions required by the final examining committee have been made. Chair of the Supervisory Committee: ___________________ _____________________________ Edwin D. Waddington Reading Committee: ___________________ _____________________________ Edwin D. Waddington ___________________ _____________________________ Howard B. Conway __________________ _____________________________ Dale P. Winebrenner Date: ______________________ In presenting this dissertation in partial fulfillment of the requirements for the doctoral degree at the University of Washington, I agree that the Library shall make its copies freely available for inspection. I further agree that extensive copying of this dissertation is allowable for scholarly purposes, consistent with “fair use” as prescribed in the U.S. Copyright Law. Request for copying or reproduction of this dissertation may be referred to ProQuest Information and Learning, 300 North Zeeb Road, Ann Arbor, MI 48106-1346, 1-800-521-0600, to whom the author has granted “the right to reproduce and sell (a) copies of the manuscript in microform and/or (b) printed copies of the manuscript made from microform.” Signature _______________________________________ Date _______________________________________ University of Washington Abstract Inferring Histories of Accumulation Rate, Ice Thickness, and Ice Flow from Internal Layers in Glaciers and Ice Sheets Michelle R. Koutnik Chair of Supervisory Committee: Professor Edwin D. Waddington Earth and Space Sciences Spatial and temporal variations in past accumulation, ice thickness, and ice flow of polar ice sheets are weakly constrained on Earth, and are fundamental unknowns on Mars. On Earth, the spatial and temporal histories of accumulation and ice-sheet flow are necessary to recreate ice- volume and sea-level histories, and are important to properly interpret ice- core chemistry. On Mars, accumulation and ice-flow histories are necessary to decipher the connection between climate and ice-mass formation, evolution, and observable structure. Internal layers in ice sheets on Earth and on Mars have been observed with ice-penetrating radar. These layers preserve information about how the ice sheet responded to past spatial and/or temporal changes in accumulation rate and ice flow, and present-day internal-layer shapes observed by radar are the most accessible remaining record of this past information. Deeper layers contain information from further in the past, making them highly valuable, but they are more difficult to decipher. In this work, an inverse problem is solved to infer transients in accumulation rate, ice-sheet thickness, and ice flow from the shapes of deep internal layers. While some details of these histories can be recovered from ice cores, ice cores represent conditions at only a single point. However, the approach presented here is more robust in combination with ice-core data. If internal layers are dated, for example by an intersecting ice core, then radar-observed internal layers provide both spatial and temporal information. Each layer represents a past surface of a particular age that has been subsequently buried by accumulation and also modified by ice flow. In this work, the goal of solving this inverse problem is to find a set of model parameters (e.g. accumulation-rate history) that have the minimum variation required to explain the data (e.g. internal-layer shapes). The process of internal-layer formation is described with a 2.5-D thermomechanical ice-flow flowband model. Estimates of the data are matched to measured values within their uncertainties, and to an expected tolerance. We seek an accumulation pattern that is spatially smooth, and a parameter set that is consistent with characteristic values of the parameters. This dissertation presents this inverse approach, and discusses applications to data from Antarctica and from Mars. Table of Contents List of Figures .............................................................................................................. v List of Tables .............................................................................................................. vii Acknowledgements ..................................................................................................... ix Chapter 1: Introduction ..................................................................................... 1 1.1. Motivation and goals ........................................................................................ 1 1.2. Background ....................................................................................................... 5 1.3. Structure and synopsis of the dissertation ................................................. 8 Chapter 2: A Method to Infer Past Surface Mass Balance and Topography from Internal Layers in Martian Polar Layered Deposits ........ 13 2.1. Introduction ...................................................................................................... 14 2.2. Methods ............................................................................................................ 18 2.3. Results .............................................................................................................. 21 2.4. Discussion ........................................................................................................ 46 2.5. Conclusions ..................................................................................................... 48 A2.1. Forward algorithm ................................................................................ 50 A2.2. Inverse algorithm ................................................................................... 54 A2.3. Modified flow law ................................................................................... 57 Chapter 3: Response Timescales for Martian Ice Masses and Implications for Past Ice Flow and Climate ........................................................ 59 3.1. Introduction ...................................................................................................... 60 3.2. Background and theory ................................................................................ 61 3.3. Results .............................................................................................................. 64 i 3.4. Discussion ....................................................................................................... 72 3.5. Conclusions ..................................................................................................... 74 A3.1. Values for a typical flowband on Gemina Lingula, NPLD ........... 75 A3.2. Present-day PLD .................................................................................... 75 A3.3. Ice temperature ....................................................................................... 79 A3.4. Ice rheology .............................................................................................. 82 Chapter 4: An Efficient Model for Transient Ice Flow Using a Spatially Limited Domain ......................................................................................................... 87 4.1. Introduction ..................................................................................................... 88 4.2. Boundary Conditions for a limited-domain model ................................ 92 4.3. Results ............................................................................................................ 106 4.4. Discussion ..................................................................................................... 117 4.5. Conclusions ................................................................................................... 119 A4.1. Ice-sheet flowband model ................................................................... 121 A4.2. Numerical solution using the Finite Volume Method .................. 124 A4.3. Full-domain model .............................................................................. 126 Chapter 5: A Method to Infer Transients in Accumulation Rate, Ice Thickness, and Ice Flow from Internal Layers .................................................. 135 5.1. Introduction ................................................................................................... 136 5.2. Forward algorithm ...................................................................................... 143 5.3. Inverse algorithm ......................................................................................... 151 5.4. Results with synthetic data ....................................................................... 160 5.5. Results with data from Taylor Mouth, Antarctica ............................... 169 5.6. Discussion ..................................................................................................... 173 5.7. Conclusions ..................................................................................................