Citation: C. Heining, M. Sellier. Direct Reconstruction of Three-dimensional Glacier Bedrock and Surface Elevation from Free Surface Velocity[J]. AIMS Geosciences, 2016, 2(1): 45-63. doi: 10.3934/geosci.2016.1.45
[1] | Lythe, MB, Vaughan, DG (2001) BEDMAP: a new ice-thickness and and subglacial topographic model of Antarctica. J Geophys Res-Earth 106: 11335-11351. doi: 10.1029/2000JB900449 |
[2] | Le Brocq, AM, Payne, AJ, Vieli, A (2010) An improved Antarctic dataset for high resolution numerical ice sheet models (ALBMAP v1). Earth Syst Sci Data 2: 247–260. doi: 10.5194/essd-2-247-2010 |
[3] | Pattyn, F, Schoof, C, Perichon, L, et al. (2012) Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP. The Cryosphere 6: 573-588. doi: 10.5194/tc-6-573-2012 |
[4] | Huss, M, Farinotti, D (2014) A high-resolution bedrock map for the Antarctic peninsula. The Crysophere 8: 1261-1273. doi: 10.5194/tc-8-1261-2014 |
[5] | Huybrechts, P, Payne, T (1996) The EISMINT benchmarks for testing ice-sheet models. Annals Glaciol 23: 1-12. |
[6] | Le Meur, E, Gagliardini, O, Zwinger, T, et al. (2004) Glacier flow modelling: a comparison of the Shallow Ice Approximation and the full-Stokes solution. CR Phys 5: 709-722. doi: 10.1016/j.crhy.2004.10.001 |
[7] | Kirchner, N, Hutter, K, Jakobsson, M, et al. (2011) Capabilities and limitations of numerical ice sheet models: a discussion for Earth-scientists and modelers. Quaternary Sci Rev 30(25-26): 3691-3704. |
[8] | Ahlkrona, J, Kirchner, N, Lötstedt, P (2013) Accuracy of the zeroth- and second-order shallow-ice approximation - numerical and theoretical results. Geosci Model Dev 6(6): 2135-2152. |
[9] | Engl, HW, Hanke, M, Neubauer, A (2000) Regularization of inverse problems. Kluwer. |
[10] | Sellier, M, Gessese, A, Heining, C (2012) Analytical and numerical bedrock reconstruction in glacier flows from free surface elevation data. Proceedings of the 23rd International Congress of Theoretical and Applied Mechanics (ICTAM2012), Beijing, China. |
[11] | Gessese, A, Heining, C, Sellier, M, et al. (2015) Direct reconstruction of glacier bedrock from known free surface data using the one-dimensional shallow ice approximation. Geomorphology 228: 356-371. doi: 10.1016/j.geomorph.2014.09.015 |
[12] | Gudmundsson, GH (2003) Transmission of basal variability to a glacier surface. J Geophys Res 108: No. B5. |
[13] | Thorsteinsson, T, Raymond, CF, Gudmundsson, GH, et al. (2003) Bed topography and lubrication inferred from surface measurements on fast-flowing ice streams. J Glaciol 49(167): 481-490. |
[14] | Rasmussen, LA (1988) Bed topography and mass-balance distribution of Columbia glacier, Alaska, USA, determined from sequential aerial-photography. J Glaciol 34(117): 208-216. |
[15] | McNabb, RW, Hock, R, O'Neel, S, et al. (2012) Using surface velocities to calculate ice thickness and bed topography: a case study at Columbia Glacier, Alaska, USA. J Glaciol 58(212): 1151-1164. |
[16] | Fastook, JL, Henry, HB, Terence JH (1995) Derived bedrock elevations, strain rates and stresses from measured surface elevations and velocities-Jakobshavns-Isbrae, Greenland. J Glaciol 41(137): 161-173. |
[17] | Warner, RC, Budd, WF (2000) Derivation of ice thickness and bedrock topography in data-gap regions over Antarctica. Ann Glaciol 31(1): 191-197. |
[18] | Farinotti, D, Huss, M, Bauder, A, et al. (2009) A method to estimate ice volume and ice-thickness distribution of alpine glaciers. J Glaciol 55(191): 422-430. |
[19] | Huss, M, Farinotti, D (2012) Distributed ice thickness and volume of all glaciers around the globe. J Geophys Res-Earth 2003-2012: 117.F4. |
[20] | Glen, JW (1955) The creep of polycrystalline ice. P Roy Soc A-Math Phys 228(1175): 519-538. |
[21] | Gantayat, P, Kulkarni, AV, Srinivasan, J (2014) Estimation of ice thickness using surface velocities and slope: case study at Gangotri Glacier. India, J Glaciol 60(220): 277-282. |
[22] | Michel, L, Picasso, M, Farinotti, D, et al. (2013) Estimating the ice thickness of mountain glaciers with an inverse approach using surface topography and mass-balance. Inverse Probl 29(3): 035002. |
[23] | Michel, L, Picasso, M, Farinotti, D, et al. (2014) Estimating the ice thickness of shallow glaciers from surface topography and mass-balance data with a shape optimization algorithm. Comput Geosci 66: 182-199. doi: 10.1016/j.cageo.2014.01.012 |
[24] | Michel-Griesser, L, Picasso, M, Farinotti, D, et al. (2014) Bedrock topography reconstruction of glaciers from surface topography and mass–balance data. Comput Geosci 18(6): 969-988. |
[25] | Morlighem, M, Rignot, E, Seroussi, H, et al. (2011) A mass conservation approach for mapping glacier ice thickness, Geophys Res Lett 38.19. |
[26] | Habermann, M, Maxwell, D, Truffer, M (2012) Reconstruction of basal properties in ice sheets using iterative inverse methods. J Glaciol 58(210): 795-807. |
[27] | Goldberg, DN, Heimbach, P (2013) Parameter and state estimation with a time-dependent adjoint marine ice sheet model. The Cryosphere 7(6): 1659-1678. |
[28] | van Pelt, WJJ, Oelermans, J, Reijmer, CH, et al. (2013) An iterative inverse method to estimate basal topography and initialize ice flow models. The Cryosphere Discussions 7: 987-1006. doi: 10.5194/tc-7-987-2013 |
[29] | Bueler, E, Brown, J (2009) Shallow shelf approximation as a “sliding law” in a thermomechanically coupled ice sheet model. J Geophys Res: Res-Earth (2003–2012) 114(F3). |
[30] | Winkelmann, R, Martin, MA, Haseloff, M, et al. (2011) The Potsdam Parallel Ice Sheet Model (PISM-PIK)–Part 1: Model description. The Cryosphere 5(3): 715-726. |
[31] | Martin, N, Monnier, J (2015) Inverse rheometry and basal properties inference for pseudoplastic geophysical flows. Eur J Mech B - Fluids 50: 110-126. doi: 10.1016/j.euromechflu.2014.11.011 |
[32] | Golledge, NR, Marsh, OJ, Rack, W, et al. (2014) Basal conditions of two transantarctic maountain outlet glaciers from observation-constrained diagnostic modelling. J Glaciol 60(223): 855-866. |
[33] | Sellier, M (2016) Inverse problems in free surface flows: a review. Acta Mech 227: 913-935. doi: 10.1007/s00707-015-1477-1 |
[34] | Hutter, K. (1983) Theoretical Glacieology. D. Reidel Publishing Company, Dordrecht. |
[35] | Gessese, A. (2013) Algorithm for bed topography reconstruction in geophysical flows, PhD Thesis, University of Canterbury, 2013. url: http://www.ir.canterbury.ac.nz/bitstream/handle/10092/8673/Thesis_fulltext.pdf?sequence=1&isAllowed=y |