The Cryosphere Discussions www.the-cryosphere-discuss.net 1994-0432 1994-0440 3 1 2009 10.5194/tcd-3-77-2009 http://www.the-cryosphere-discuss.net/3/77/2009/ http://www.the-cryosphere-discuss.net/3/77/2009/tcd-3-77-2009.html http://www.the-cryosphere-discuss.net/3/77/2009/tcd-3-77-2009.pdf 77 115 2009-01-22 The Gregoriev Ice Cap evolution according to the 2-D ice flowline model for various climatic scenarios in the future Y. V. Konovalov yu-v-k@yandex.ru O. V. Nagornov Moscow Engineering Physics Institute (State University), Kashirskoe shosse, 31, 115409 Moscow, Russia Different flowline thickness distributions and flowline length changes of the Gregoriev Ice Cap were obtained for some surface mass balance histories which can be considered as possible surface mass balances in the future. The ice cap modeling was performed by solving full Stokes equations in the form of one mechanical equilibrium equation in terms of stress deviator components in couple with continuity equation for incompressible substance. The numerical solution was obtained by the finite-difference method. The problem of diagnostic equations stability was overcome by a~compound approximation of the ice surface boundary condition based on the extending of the mechanical equilibrium equation to ice surface points. The problem of stability in the prognostic equation can arise at relatively small grid size in horizontal direction in the case of steep velocity decreasing closely to the ice front and was overcome by introducing the artificial viscosity into the prognostic equation. The basal sliding can arise in the glacier tongue at certain climatic conditions and was introduced through the linear friction law. The correlations between glacier length changes and annual air temperature histories were investigated within the simplified equation in the form of linear dependence of annual air temperature versus the glacier length and time derivation of the length. Arkhipov, S M., Mikhalenko,~V N., Kunakhovich,~M G., Dikikh,~A N., and Nagornov,~O V.: Termicheskii rezhim, usloviia l'doobrazovaniia i akkumulyatsiia na ladnike Grigor'eva (Tyan'-Shan') v 1962–2001 gg. [Thermal regime, ice types and accumulation in Grigoriev Glacier, Tien Shan, 1962–2001], Data of Glaciological Studies, 96, 77–83, 2004. Hindmarsh, R C A.: A~numerical comparison of approximations to the Stokes equations used in ice sheet and glacier modeling, J. Geophys. Res., 109, F01012, doi:10.1029/2003JF000065, 2004. Hindmarsh, R C A. and Payne,~A J.: Time-step limits for stable solutions of the ice sheet equation, Ann. Glaciol., 23, 74–85, 1996. Hutter, K.: Theoretical Glaciology, Dordrecht, Kluwer Academic Publishers, 1983. MacAyeal, D. R.: Large-scale ice flow over a~viscous basal sediment: theory and application to ice stream B, Antarctica, J. Geophys. Res., 94(B4), 4071–4088, 1989. MacAyeal, D R.: The basal stress-distribution of Ice Stream-E, Antarctica, inferred by control methods, J. Geophys. Res.-Solid Ea., 97(B1), 595–603, 1992. MacAyeal, D., Rommelaere, V., Huybrechts, P., Hulbe, C., Determann, J., and Ritz, C.: An ice-shelf model test based on the Ross Ice Shelf, Ann. Glaciol., 23, 46–51, 1996. Makarevich, K G., Palgov,~N N., Tokmagambetov,~G A., Vilesov,~E N., Sudakov,~P A., Golovkova,~B G., Denisova,~T Y., and Yegorova,~N D.: Glaciation of Zailiysky Alatau, Results of researches of International Geohysical Projects, IX section of IGY program, 23, 228 pp., 1969. Mikhalenko, V N.: Features of mass-exchange of plane-top glaciers of internal Tien-Shan, Data of Glaciological Studies, 65, 86–91, 1989. Nagornov, O., Konovalov,~Y., and Mikhalenko.,~V.: Prediction of thermodynamic state of the Gregoriev Ice Cap, Tien Shan, Central Asia, in the future, Ann. Glaciol. 43, 307–312, 2006. Pattyn, F.: Ice-sheet modeling at different spatial resolutions: focus on the grounding zone, Ann. Glaciol. 31, 211–216, 2000. Pattyn, F.: A~new three-dimensional higher-order thermomechnical ice sheet model: basic sensitivity, ice stream development, and ice flow across subglacial lakes, J. Geophys. Res., 108(B8), 2382, doi:10.1029/2002JB002329, 2003. Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de Smedt, B., Gagliardini, O., Gudmundsson, G. H., Hindmarsh, R. C. A., Hubbard, A., Johnson, J. V., Kleiner, T., Konovalov, Y., Martin, C., Payne, A. J., Pollard, D., Price, S., R�ckamp, M., Saito, F., Souček, O., Sugiyama, S., and Zwinger, T.: Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP–HOM), The Cryosphere, 2, 95–108, 2008. Oerlemans, J.: Quantifying global warming from the retreat of glaciers, Science, 264, 243–245, 1994. Van der Veen, C J. and Whillans,~I M.: Force budget: I. Theory and numerical methods, J. Glaciol., 35, 53–60, 1989. Vinogradov, O N.: Surface ice flow velocities of the plane-top glaciers in the Tien-Shan, Data of Glaciological Studies, 6, 138–139, 1962 (in Russian).