The Cryosphere Discussions www.the-cryosphere-discuss.net 1994-0432 1994-0440 4 3 2010 10.5194/tcd-4-1277-2010 http://www.the-cryosphere-discuss.net/4/1277/2010/ http://www.the-cryosphere-discuss.net/4/1277/2010/tcd-4-1277-2010.html http://www.the-cryosphere-discuss.net/4/1277/2010/tcd-4-1277-2010.pdf 1277 1306 2010-08-18 The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 1: Model description R. Winkelmann M. A. Martin M. Haseloff T. Albrecht E. Bueler C. Khroulev A. Levermann anders.levermann@pik-potsdam.de Earth System Analysis, Potsdam Institute for Climate Impact Research, Potsdam, Germany Institute of Physics, Potsdam University, Potsdam, Germany Dept. of Physics, Humboldt-University, Berlin, Germany Dept. of Mathematics and Statistics, University of Alaska, Fairbanks, USA Geophysical Institute, University of Alaska, Fairbanks, USA We present the Potsdam Parallel Ice Sheet Model (PISM-PIK), developed at the Potsdam Institute for Climate Impact Research to be used for simulations of large-scale ice sheet-shelf systems. It is derived from the Parallel Ice Sheet Model (Bueler and Brown, 2009). Velocities are calculated by superposition of two shallow stress balance approximations within the entire ice covered region: the shallow ice approximation (SIA) is dominant in grounded regions and accounts for shear deformation parallel to the geoid. The plug-flow type shallow shelf approximation (SSA) dominates the velocity field in ice shelf regions and serves as a basal sliding velocity in grounded regions. Ice streams naturally emerge through this approach and can be identified diagnostically as regions with a significant contribution of membrane stresses to the local momentum balance. All lateral boundaries in PISM-PIK are free to evolve, including the grounding line and ice fronts. Ice shelf margins in particular are modeled using Neumann boundary conditions for the SSA equations, reflecting a hydrostatic stress imbalance along the vertical calving face. The ice front position is modeled using a subgrid scale representation of calving front motion (Albrecht et al., 2010) and a physically motivated dynamic calving law based on horizontal spreading rates. The model is validated within the Marine Ice Sheet Model Intercomparison Project (MISMIP) and is used for a dynamic equilibrium simulation of Antarctica under present-day conditions in the second part of this paper (Martin et al., 2010). Albrecht,~T., Martin,~M A., Winkelmann,~R., Haseloff,~M., and Levermann,~A.: Parametrization for subgrid-scale motion of ice-shelf calving-fronts, The Cryosphere Discuss., submitted, 2010. Alley,~R B., Horgan,~H J., Joughin,~I., Cuffey,~K M., Dupont,~T K., Parizek,~B R., Anandakrishnan,~S., and Bassis,~J.: A simple law for ice-shelf calving, Science, 322, p 1344, 2008. Bamber,~J L., Alley,~R B., and Joughin,~I.: Rapid response of modern day ice sheets to external forcing, Earth Planet. Sc. Lett., 257, 1–13, 2007. Blatter,~H.: Velocity and stress fields in grounded glaciers: a~simple algorithm for including deviatoric stress gradients, J. Glaciol., 41, 333–344, 1995. Bueler,~E. and Brown,~J.: The shallow shelf approximation as a~sliding law in a~thermomechanically coupled ice sheet model, J. Geophys. Res., 114, F03008, doi:10.1029/2008JF001179, 2009. Bueler,~E., Khroulev,~C., Aschwanden,~A.: Parallel Ice Sheet Model – open source website, 2008. Bueler,~E., Lingle,~C., Kallen-Brown,~J., Covey,~D., and Bowman,~L.: Exact solutions and verification of numerical models for isothermal ice sheets, J. Glaciol., 51, 291–306, 2005. Bueler,~E., Brown,~J., and Lingle,~C.: Exact solutions to the thermomechanically coupled shallow-ice approximation: effective tools for verification, J. Glaciol., 53, 499–516, 2007. De Angelis,~H. and Skvarca,~P.: Glacier surge after ice shelf collapse, Science, 299, 1560–1563, 2003. Doake,~C S M., Corr,~H F J., Skvarca,~P., and Young,~N W.: Breakup and conditions for stability of the Northern Larsen ice shelf, Antarctica, Nature, 391, 778–780, 1998. Dupont,~T K. and Alley,~R B.: Assessment of the importance of ice-shelf buttressing to ice-sheet flow, Geophys. Res. Lett., 32, L04503, doi:10.1029/2004GL022024, 2005. Fowler,~A C.: Modelling the Flow of Glaciers and Ice Sheets, Continuum Mechanics and Applications in Geophysics and the Environment, Springer, 201–221, 2001. Glasser,~N F. and Scambos,~T A.: A~structural glaciological analysis of the 2002 Larsen B ice shelf collapse, J. Glaciol., 54, 3–16, 2008. Goldberg,~D., Holland,~D M., and Schoof,~C.: Grounding line movement and ice shelf buttressing in marine ice sheets, J. Geophys. Res., 114, F04026, doi:10.1029/2008JF001227, 2009. Greve,~R.: Application of a~polythermal three-dimensional ice sheet model to the Greenland ice sheet: response to steady-state and transient climate scenarios, J. Climate, 10, 901–918, 1997b. Greve,~R. and Blatter,~H. (Eds.): Dynamics of Ice Sheets and Glaciers, Springer, 2009. Hutter,~K. (Ed.): Theoretical Glaciology, D. Reidel Publishing Company/Terra Scientific Publishing Company, 1983. Huybrechts,~P.: A~3-D model for the Antarctic ice-sheet: a~sensitivity study on the glacial-interglacial contrast, Clim. Dynam., 5, 79–92, 1990. Jarosch,~A H. and Gudmundsson,~M T.: Numerical studies of ice flow over subglacial geothermal heat sources at Grímsvötn, Iceland, using Full Stokes equations, J. Geophys. Res., 112, F02008, doi:10.1029/2006JF000540, 2007. Le Brocq,~A M., Payne,~A J., and Vieli,~A.: Antarctic dataset in netCDF format, \doi10.1594/PANGAEA.734145, available at: http://doi.pangaea.de/10.1594/PANGAEA.734145, 2010. Levermann,~A., Albrecht,~T., Winkelmann,~R., Martin,~M A., and Haseloff,~M.: Universal dynamic calving law implies potential for abrupt ice-shelf retreat, submitted, 2010. Lythe,~M B., Vaughan,~D G., and BEDMAP Consortium: BEDMAP: A~new ice thickness and subglacial topographic model of Antarctica, J. Geophys. Res., 106, 11335–11351, 2001. MacAyeal,~D R.: Large-scale ice flow over a~viscous basal sediment – Theory and application to ice stream B, Antarctica, J. Geophys. Res., 94, 4071–4087, 1989. MacAyeal,~D R., Rommelaere,~V., Huybrechts,~P., Hulbe,~C L., Determann,~J., and Ritz,~C.: An ice-shelf model test based on the Ross Ice Shelf, Ann. Glaciol., 23, 46–51, 1996. Marshall,~S J., Tarasov,~L., Clarke,~G K C., and Peltier,~W R.: Glaciological reconstruction of the Laurentide Ice Sheet: physical processes and modelling challenges, Canad. J. Earth Sci., 37, 769–793, 2000. Martín,~C., Navarro,~F., Otero,~J., Cuadrado,~M L., and Corcuera,~M I.: Three-dimensional modelling of the dynamics of Johnsons Glacier, Livingston Island, Antarctica, Ann. Glaciol., 39, 1–8, 2004. Martin,~M A., Winkelmann,~R., Haseloff,~M., Albrecht,~T., Bueler,~E., Khroulev,~C., and Levermann,~A.: The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part~2: Dynamic equilibrium simulation of the Antarctic ice sheet, The Cryosphere Discuss.,\blackbox\bfwill be updated. 2010. Morland,~L W.: Unconfined ice-shelf flow, in: Dynamics of the West Antarctic ice sheet, edited by: der Veen,~C J V. and Oerlemans,~J., Cambridge University Press, Cambridge, UK and New York, NY, USA, 1987. Morland,~L W. and Johnson,~I R.: Steady motion of ice sheets, J. Glaciol., 25, 229–246, 1980. Morland,~L W. and Zainuddin,~R.: Plane and radial ice-shelf flow with prescribed temperature profile, in: Dynamics of the West Antarctic Ice Sheet, edited by: Van der Veen,~C J. and Oerlemans,~J., Reidel Publ., Dordrecht, the Netherlands, 99–116, 1987. Paterson,~W.: The Physics of Glaciers, Elsevier, Oxford, 1994. Paterson,~W S B. and Budd,~W F.: Flow parameters for ice sheet modelling, Cold. Reg. Sci. Technol., 6, 175–177, 1982. Pattyn,~F.: A~new three-dimensional higher-order thermomechanical ice sheet model: Basic sensitivity, ice stream development, and ice flow across subglacial lakes, J. Geophys. Res., 108, 2382–2397, 2003. Pattyn,~F.: Investigating the stability of subglacial lakes with a~full Stokes ice sheet model, J. Glaciol.,54, 353–361, 2008. Pattyn,~F., Huyghe,~A., De Brabander,~S., and De Smedt,~B.: Role of transition zones in marine ice sheet dynamics, J. Geophys. Res., 111, 2004–2014, 2006. Payne,~A J.: A~thermomechanical model of ice flow in West Antarctica, Clim. Dynam., 15, 115–125, 1999. Pollard,~D. and Deconto,~R M.: Modelling West Antarctic ice sheet growth and collapse through the past five million years, Nature, 458, 329–332, 2009. Rignot,~E., Bamber,~J L., den Broeke,~M R V., Li,~Y., Davis,~C., de~Berg,~W J V., and Meijgaard,~E.: Recent Antarctic ice mass loss from radar interferometry and regional climate modelling, Nat. Geosci., 1, 106–110, 2008. Ritz,~C., Rommelaere,~V., and Dumas,~C.: Modeling the evolution of Antarctic ice sheet over the last 420 000 years: Implications for altitude changes in the Vostok region, J. Geophys. Res., 106, 31943–31964, 2001. Rott,~H., Rack,~W., and Nagler,~T.: Increased export of grounded ice after the collapse of northern Larsen ice shelf, Antarctic Peninsula, observed by Envisat ASAR, Geoscience and Remote Sensing Symposium, IEEE International, 1174–1176, 2007. Schoof,~C.: Variational methods for glacier flow over plastic till, J. Fluid Mech., 555, 299–320, 2006a. Schoof,~C.: A~variational approach to ice stream flow, J. Fluid Mech., 556, 227–251, 2006b. Schoof,~C.: Marine ice-sheet dynamics. Part 1. The case of rapid sliding, J. Fluid Mech., 573, 27–55, 2007a. Schoof,~C.: Ice sheet grounding line dynamics: Steady states, stability, and hysteresis, J. Geophys. Res., 112, F03S28, doi:10.1029/2006JF000664, 2007b. Schoof,~C. and Hindmarsh,~R C A.: Thin-film flows with wall slip: An asymptotic analysis of higher order glacier flow models, Q. J. Mech. Appl. Math., 63, 73-114, doi:10.1093/qjmam/hbp025, 2010. Schoof,~C., Hindmarsh,~R C A., and Pattyn,~F.: MISMIP: Marine ice sheet model intercomparison project, available at: http://homepages.ulb.ac.be/~fpattyn/mismip/, 2009. Van der Veen,~C J.: A~note on the equilibrium porfile of a~free floating ice shelf, IMAU Report V83-15. State University Utrecht, 1983. Weertman,~J.: Deformation of floating ice shelves, J. Glaciol., 3, 38–42, 1957. Weis,~M., Greve,~R., and Hutter,~K.: Theory of shallow ice shelves, Continuum Mech. Therm., 11, 15–50, 1999.