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Modelling Sea Ice and Melt Ponds Evolution: Sensitivity to Microscale Heat Transfer Mechanisms

  • Andrea ScagliariniEmail author
  • Enrico Calzavarini
  • Daniela Mansutti
  • Federico Toschi
Chapter
  • 32 Downloads
Part of the Springer INdAM Series book series (SINDAMS, volume 38)

Abstract

We present a mathematical model describing the evolution of sea ice and meltwater during summer. The system is described by two coupled partial differential equations for the ice thickness h and pond depth w fields. We test the sensitivity of the model to variations of parameters controlling fluid-dynamic processes at the pond level, namely the variation of turbulent heat flux with pond depth and the lateral melting of ice enclosing a pond. We observe that different heat flux scalings determine different rates of total surface ablations, while the system is relatively robust in terms of probability distributions of pond surface areas. Finally, we study pond morphology in terms of fractal dimensions, showing that the role of lateral melting is minor, whereas there is evidence of an impact from the initial sea ice topography.

Keywords

Glaciology Sea ice Turbulent heat transfer Mathematical Modelling 

Notes

Acknowledgements

AS and DM acknowledge financial support from the National Group of Mathematical Physics of the Italian National Institute of High Mathematics (GNFM-INdAM). EC acknowledge supports form the French National Agency for Research (ANR) under the grant SEAS (ANR-13-JS09-0010).

References

  1. 1.
    Hunke, E.C., Lipscomb, W.H., Turner, A.K.: Sea-ice models for climate study: retrospective and new directions. J. Glaciol. 56, 1162–1172 (2010)CrossRefGoogle Scholar
  2. 2.
    Notz, D.: Challenges in simulating sea ice in Earth System Models. WIREs Clim. Change 3, 509–526 (2012)CrossRefGoogle Scholar
  3. 3.
    Cattle, H., Crossley, J.: Modelling Arctic climate change. Philos. Trans. R. Soc. A 352, 1699 (1995)Google Scholar
  4. 4.
    Ebert, E.E., Schramm, J.L., Curry, J.A.: Disposition of solar radiation in sea ice and the upper ocean. J. Geophys. Res. 100(C8), 965–975 (1995)CrossRefGoogle Scholar
  5. 5.
    Maykut, G.A., McPhee, M.G.: Solar heating of the arctic mixed layer. J. Geophys. Res. 100(C12), 24691–24703 (1995)CrossRefGoogle Scholar
  6. 6.
    Tsamados, M., Feltham, D.L., Schröder, D., Flocco, D., Farrell, S.L., Kurtz, N., Laxon, S.W., Bacon, S.: Impact of variable atmospheric and oceanic form drag on simulations of arctic sea ice. J. Phys. Oceanogr. 44, 1329–1353 (2014)CrossRefGoogle Scholar
  7. 7.
    Vancoppenolle, M., Fichefet, T., Goosse, H., Bouillon, S., Madec, G., Morales Maqueda, M.A.: Simulating the mass balance and salinity of Arctic and Antarctic sea ice. 1. Model description and validation. Ocean Model. 27, 33–53 (2009)Google Scholar
  8. 8.
    Vancoppenolle, M., Fichefet, T., Goosse, H.: Simulating the mass balance and salinity of Arctic and Antarctic sea ice. 2. Importance of sea ice salinity variations. Ocean Model. 27, 54–69 (2009)Google Scholar
  9. 9.
    Mauritzen, C., Häkkinen, S.: Influence of sea ice on the thermohaline circulation in the Arctic-North Atlantic Ocean. Geophys. Res. Lett. 24, 3257–3260 (1997)CrossRefGoogle Scholar
  10. 10.
    Kwok, R., Cunningham, G.F., Wensnahan, M., Rigor, I., Zwally, H.J., Yi, D.: Thinning and volume loss of the Arctic Ocean sea ice cover: 2003–2008. J. Geophys. Res. 114, C07005 (2009)CrossRefGoogle Scholar
  11. 11.
    Stroeve, J.C., Kattsov, V., Barrett, A., Serreze, M., Pavlova, T., Holland, M., Meier, W.N.: Trends in Arctic sea ice extent from CMIP5, CMIP3 and observations. Geophys. Res. Lett. 39, L16502 (2012)CrossRefGoogle Scholar
  12. 12.
    Laxon, S.W., Giles, K.A., Ridout, A.L., Wingham, D.J., Willatt, R., Cullen, R., Kwok, R., Schweiger, A., Zhang, J., Haas, C., Hendricks, S., Krishfield, R., Kurtz, N., Farrell, S., Davidson, M.: CryoSat-2 estimates of Arctic sea ice thickness and volume, Geophys. Res. Lett. 40, 732–737 (2013)CrossRefGoogle Scholar
  13. 13.
    Maykut, G.A., Untersteiner, N.: Some results from a time-dependent thermodynamic model of sea ice. J. Geophys. Res. 76(6), 1550–1575 (1971)CrossRefGoogle Scholar
  14. 14.
    Ebert, E.E., Curry, J.A.: An intermediate one-dimensional thermodynamic sea ice model for investigating ice–atmosphere interactions, J. Geophys. Res. 98(C6), 10085–10109 (1993)CrossRefGoogle Scholar
  15. 15.
    Eisenman, I., Wettlaufer, J.S.: Nonlinear threshold behavior during the loss of Arctic sea ice. Proc. Natl. Acad. Sci. 106, 28–32 (2009)CrossRefzbMATHGoogle Scholar
  16. 16.
    Steele, M.: Sea ice melting and floe geometry in a simple ice-ocean model. J. Geophys. Res. 97(C11), 17729–17738 (1992)CrossRefGoogle Scholar
  17. 17.
    Bitz, C.M., Lipscomb, W.H.: An energy-conserving thermodynamic model of sea ice. J. Geophys. Res. 104(C7), 15669–15677 (1999)CrossRefGoogle Scholar
  18. 18.
    Freitag, J., Eicken, H.: Melt water circulation and permeability of Arctic summer sea ice derived from hydrological field experiments. J. Glaciol. 49, 349–358 (2003)CrossRefGoogle Scholar
  19. 19.
    Feltham, D.L., Untersteiner, N., Wettlaufer, J.S., Worster, M.G.: Sea ice is a mushy layer. Geophys. Res. Lett. 33, L14501 (2006)CrossRefGoogle Scholar
  20. 20.
    Wells, A.J., Wettlaufer, J.S., Orszag, S.A.: Nonlinear mushy-layer convection with chimneys: stability and optimal solute fluxes. J. Fluid Mech. 716, 203–227 (2013)CrossRefMathSciNetzbMATHGoogle Scholar
  21. 21.
    Turner, A.K., Hunke, E.C.: Impacts of a mushy-layer thermodynamic approach in global sea-ice simulations using the CICE sea-ice model. J. Geophys. Res. Oceans 120(2), 1253–1275 (2015)CrossRefGoogle Scholar
  22. 22.
    Feltham, D.L.: Sea ice rheology. Annu. Rev. Fluid Mech. 40, 91–112 (2008)CrossRefMathSciNetzbMATHGoogle Scholar
  23. 23.
    Hunke, E.C., Dukowicz, J.K.: An elastic-viscous-plastic model for sea ice dynamics. J. Phys. Oceanogr. 27(9), 1849–1867 (1997)CrossRefGoogle Scholar
  24. 24.
    Tsamados, M., Feltham, D.L., Wilchinsky, A.: Impact of a new anisotropic rheology on simulations of Arctic sea ice. J. Geophys. Res. Oceans 118(1), 91–107 (2013)CrossRefGoogle Scholar
  25. 25.
    Rabatel, M., Rampal, P., Carrassi, A., Bertino, L., Jones, C.K.R.T.: Impact of rheology on probabilistic forecasts of sea ice trajectories: application for search and rescue operations in the Arctic. Cryosphere 12, 935–953 (2018)CrossRefGoogle Scholar
  26. 26.
    Steele, M., Zhang, J., Rothrock, D., Stern, H.: The force balance of sea ice in a numerical model of the Arctic Ocean. J. Geophys. Res. Oceans 102(C9), 21061–21079 (1997)CrossRefGoogle Scholar
  27. 27.
    Schröder, D., Vihma, T., Kerber, A., Brümmer, B.: On the parameterization of turbulent surface fluxes over heterogeneous sea ice surfaces. J. Geophys. Res. 108(C6), 3195 (2003)CrossRefGoogle Scholar
  28. 28.
    Rampal, P., Weiss, J., Marsan, D.: Positive trend in Arctic sea ice mean speed and deformation 1979–2007. J. Geophys. Res. Oceans 114, C05013 (2009)Google Scholar
  29. 29.
    Rampal, P., Weiss, J., Dubois, C., Campin, J.-M.: IPCC climate models do not capture the Arctic sea ice drift acceleration: consequences in terms of projected sea ice thinning and decline. J. Geophys. Res. Oceans 116, C00D07 (2011)Google Scholar
  30. 30.
    Petty, A.A., Feltham, D.L., Holland, P.R.: Impact of atmospheric forcing on Antarctic continental shelf water masses. J. Phys. Oceanogr. 43(5), 920–940 (2013)CrossRefGoogle Scholar
  31. 31.
    Heorton, H.D.B.S., Feltham, D.L., Tsamados, M.: Stress and deformation characteristics of sea ice in a high-resolution, anisotropic sea ice model. Philos. Trans. A Math. Phys. Eng. Sci. 376(2129), 20170349 (2018)CrossRefGoogle Scholar
  32. 32.
    Hunke, E.C., Notz, D., Turner, A.K., Vancoppenolle, M.: The multiphase physics of sea ice: a review for model developers. Cryosphere 5, 989–1009 (2011)CrossRefGoogle Scholar
  33. 33.
    Massonnet, F., Vancoppenolle, M., Goosse, H., Docquier, D., Fichfet, T., Blanchard-Wrigglesworth, E.: Arctic sea-ice change tied to its mean state through thermodynamic processes. Nat. Clim. Change 8, 599–603 (2018)CrossRefGoogle Scholar
  34. 34.
    Fetterer, F., Untersteiner, N.: Observations of melt ponds on Arctic sea ice. J. Geophys. Res. 103(C11), 24821–24835 (1998)CrossRefGoogle Scholar
  35. 35.
    Perovich, D.K., Tucker III, W.B., Ligett, K.A.: Aerial observations of the evolution of ice surface conditions during summer. J. Geophys. Res. 107(C10), 8048 (2002)CrossRefGoogle Scholar
  36. 36.
    Hanesiak, J.M., Barber, D.G., De Abreu, R.A., Yackel, J.J.: Local and regional albedo observations of arctic first-year sea ice during melt ponding. J. Geophys. Res. 106(C1), 1005–1016 (2001)CrossRefGoogle Scholar
  37. 37.
    Perovich, D.K., Grenfell, T.C., Light, B., Hobbs, P.V.: Seasonal evolution of the albedo of multiyear Arctic sea ice. J. Geophys. Res. 107(C10), 8044 (2002)CrossRefGoogle Scholar
  38. 38.
    Flocco, D., Schroeder, D., Feltham, D.L., Hunke, E.C.: Impact of melt ponds on Arctic sea ice simulations from 1990 to 2007. J. Geophys. Res. 117, C09032 (2012)CrossRefGoogle Scholar
  39. 39.
    Schröder, D., Feltham, D.L., Flocco, D., Tsamados, M.: September Arctic sea-ice minimum predicted by spring melt-pond fraction. Nat. Clim. Change 4(5), 353–357 (2014)CrossRefGoogle Scholar
  40. 40.
    Taylor, P.D., Feltham, D.L.: A model of melt pond evolution on sea ice. J. Geophys. Res. 109, C12007 (2004)CrossRefGoogle Scholar
  41. 41.
    Skyllingstad, E.D., Paulson, C.A.: A numerical simulations of melt ponds. J. Geophys. Res. 112, C08015 (2007)CrossRefGoogle Scholar
  42. 42.
    Rabbanipour Esfahani, B., Hirata, S.C., Berti, S., Calzavarini, E.: Basal melting driven by turbulent thermal convection. Phys. Rev. Fluids 3, 053501 (2018)CrossRefGoogle Scholar
  43. 43.
    Lüthje, M., Feltham, D.L., Taylor, P.D., Worster, M.G.: Modeling the summertime evolution of sea–ice melt ponds. J. Geophys. Res. 111, C02001 (2006)CrossRefGoogle Scholar
  44. 44.
    Lüthje, M., Pedersen, L.T., Reeh, N., Greuell, W.: Modelling the evolution of supraglacial lakes on the West Greenland ice-sheet margin. J. Glaciol. 52(179), 608–618 (2006)CrossRefGoogle Scholar
  45. 45.
    Skyllingstad, E.D., Paulson, C.A., Perovich, D.K.: Simulation of melt pond evolution on level ice. J. Geophys. Res. 114, C12019 (2009)CrossRefGoogle Scholar
  46. 46.
    Scott, F., Feltham, D.L.: A model of the three-dimensional evolution of Arctic melt ponds on first-year and multiyear sea ice. J. Geophys. Res. 115, C12064 (2010)CrossRefGoogle Scholar
  47. 47.
    Thorndike, A.S., Rothrock, D.A., Maykut, G.A., Colony, R.: The thickness distribution of sea ice. J. Geophys. Res. 80(33), 4501–4513 (1975)CrossRefGoogle Scholar
  48. 48.
    Hunke, E.C., Lipscomb, W.H.: CICE: The Los Alamos Sea Ice Model. Documentation and software user’s manual version 4.0. Tech. Rep. LA-CC-06-012. T-3 Fluid Dyn. Group, Los Alamos Natl. Lab., Los Alamos, NM (2008)Google Scholar
  49. 49.
    Vancoppenolle, M., Bouillon, S., Fichefet, T., Goosse, H., Lecomte, O., Morales Maqueda, M.A., Madec, G.: The Louvain-la-Neuve sea ice model. Notes du pole de modélisation, Institut Pierre-Simon Laplace (IPSL), Paris (2012)Google Scholar
  50. 50.
    Flocco, D., Feltham, D.L.: A continuum model of melt pond evolution on Arctic sea ice. J. Geophys. Res. 112, C08016 (2007)CrossRefGoogle Scholar
  51. 51.
    Flocco, D., Feltham, D.L., Turner, A.K.: Incorporation of a physically based melt pond scheme into the sea ice component of a climate model. J. Geophys. Res. 114, C08012 (2010)Google Scholar
  52. 52.
    Ahlers, G., Grossmann, S., Lohse, D.: Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection. Rev. Mod. Phys. 81, 503 (2009)CrossRefGoogle Scholar
  53. 53.
    Kim, J.-H., Moon, W., Wells, A.J., Wilkinson, J.P., Langton, T., Hwang, B., Granskog, M.A., Rees Jones, D.W.: Salinity control of thermal evolution of late summer melt ponds on Arctic sea ice. Geophys. Res. Lett. 45 (2018). https://doi.org/10.1029/2018GL078077
  54. 54.
    Grossmann, S., Lohse, D.: Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56 (2000)CrossRefMathSciNetzbMATHGoogle Scholar
  55. 55.
    Malkus, M.V.R.: The heat transport and spectrum of thermal turbulence. Proc. R. Soc. Lond. A 225, 196 (1954)CrossRefMathSciNetzbMATHGoogle Scholar
  56. 56.
    Rallabandi, B., Zheng, Z., Winton, M., Stone, H.A.: Formation of sea ice bridges in narrow straits in response to wind and water stresses. J. Geophys. Res. Oceans 122(7), 5588–5610 (2017)CrossRefGoogle Scholar
  57. 57.
    Domaradzki, J.A., Metcalfe, R.W.: Direct numerical simulations of the effects of shear on turbulent Rayleigh-Bénard convection. J. Fluid Mech. 193, 499 (1988)CrossRefGoogle Scholar
  58. 58.
    Scagliarini, A., Gylfason A., Toschi, F.: Heat-flux scaling in turbulent Rayleigh-Bénard convection with an imposed longitudinal wind. Phys. Rev. E 89, 043012 (2014)CrossRefGoogle Scholar
  59. 59.
    Prandtl, L.: Bericht über die Entstehung der Turbulenz. Z. Angew. Math. Mech. 5, 136–139 (1925)CrossRefzbMATHGoogle Scholar
  60. 60.
    Tsamados, M., Feltham, D.L., Petty, A.A., Schröder D., Flocco, D.: Processes controlling surface, bottom and lateral melt of Arctic sea ice in a state of the art sea ice model. Philos. Trans. R. Soc. A 373, 20140167 (2015)CrossRefGoogle Scholar
  61. 61.
    Eicken, H., Krouse, H.R., Kadko, D., Perovich, D.K.: Tracer studies of pathways and rates of meltwater transport through Arctic summer sea ice. J. Geophys. Res. 107(C10), 8046 (2002)CrossRefGoogle Scholar
  62. 62.
    Landau, L.D., Lifshitz, E.M.: Fluid Mechanics, 2nd edn. Pergamon Press, Oxford (1987)Google Scholar
  63. 63.
    Marche, F.: Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects. Eur. J. Mech. B Fluids 26, 49–63 (2007)CrossRefMathSciNetzbMATHGoogle Scholar
  64. 64.
    Oron, A., Davis, S.H., Bankoff, S.G.: Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69(3), 931–980 (1997)CrossRefGoogle Scholar
  65. 65.
    Hvidegaard, S.M., Forsberg, R.: Sea-ice thickness from airborne laser altimetry over the Arctic Ocean north of Greenland. Geophys. Res. Lett. 29(20), 1952 (2002)CrossRefGoogle Scholar
  66. 66.
    Hoshen, J., Kopelman, R.: Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm. Phys. Rev. B. 14, 3438–3445 (1976)Google Scholar
  67. 67.
    Moritz, R.E., Curry, J.A., Thorndike, A.S., Untersteiner, N.: SHEBA a Research Program on the Surface Heat Budget of the Arctic Ocean. Rep. 3, 34 pp., Arctic Syst. Sci.: Ocean-Atmos.-Ice Interact. (1993)Google Scholar
  68. 68.
    Moritz, R.E., Perovich, D.K. (eds.): Surface Heat Budget of the Arctic Ocean, Science Plan, ARCSS/OAII. Rep. 5, 64 pp., Univ. of Wash., Seattle (1996)Google Scholar
  69. 69.
    Perovich, D.K., Grenfell, T.C., Light, B., Elder, B.C., Harbeck, J., Polashenski, C., Tucker III, W.B., Stelmach, C.: Transpolar observations of the morphological properties of Arctic sea ice. J. Geophys. Res. 114, C00A04 (2009)Google Scholar
  70. 70.
    Ma, Y.-P., Sudakov, I., Strong, C., Golden, K.M.: Ising model for melt ponds on Arctic sea ice (2014). arXiv:1408.2487Google Scholar
  71. 71.
    Popović, P., Cael, B.B., Silber, M., Abbot, D.S.: Simple rules govern the patterns of arctic sea ice melt ponds. Phys. Rev. Lett. 120, 148701 (2018)CrossRefGoogle Scholar
  72. 72.
    Hohengger, C., Alali, B., Steffen, K.R., Perovich, D.K., Golden, K.M.: Transition in the fractal geometry of Arctic melt ponds. Cryosphere 6, 1157–1162 (2012)CrossRefGoogle Scholar
  73. 73.
    Mandelbrot, B.B.: The Fractal Geometry of Nature. Freeman, New York (1982)zbMATHGoogle Scholar
  74. 74.
    Cheng, Q.: The perimeter-area fractal model and its application to geology. Math. Geol. 27, 69–84 (1995)CrossRefGoogle Scholar
  75. 75.
    Grassberger, P.: Generalized dimensions of strange attractors. Phys. Lett. 97A(6), 227–230 (1993)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Andrea Scagliarini
    • 1
    Email author
  • Enrico Calzavarini
    • 2
  • Daniela Mansutti
    • 1
  • Federico Toschi
    • 3
    • 4
  1. 1.Istituto per le Applicazioni del Calcolo ‘M. Picone’, CNRRomeItaly
  2. 2.Université de LilleUnité de Mécanique de Lille, UML EA 7512LilleFrance
  3. 3.Eindhoven University of TechnologyEindhovenThe Netherlands
  4. 4.Istituto per le Applicazioni del Calcolo ‘M. Picone’CNRRomeItaly

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