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The Cryosphere An interactive open-access journal of the European Geosciences Union
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Volume 10, issue 4
The Cryosphere, 10, 1753–1769, 2016
https://doi.org/10.5194/tc-10-1753-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
The Cryosphere, 10, 1753–1769, 2016
https://doi.org/10.5194/tc-10-1753-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 17 Aug 2016

Research article | 17 Aug 2016

Similitude of ice dynamics against scaling of geometry and physical parameters

Johannes Feldmann1,2 and Anders Levermann1,2,3 Johannes Feldmann and Anders Levermann
  • 1Potsdam Institute for Climate Impact Research (PIK), Potsdam, Germany
  • 2Institute of Physics, University of Potsdam, Potsdam, Germany
  • 3LDEO, Columbia University, New York, USA

Abstract. The concept of similitude is commonly employed in the fields of fluid dynamics and engineering but rarely used in cryospheric research. Here we apply this method to the problem of ice flow to examine the dynamic similitude of isothermal ice sheets in shallow-shelf approximation against the scaling of their geometry and physical parameters. Carrying out a dimensional analysis of the stress balance we obtain dimensionless numbers that characterize the flow. Requiring that these numbers remain the same under scaling we obtain conditions that relate the geometric scaling factors, the parameters for the ice softness, surface mass balance and basal friction as well as the ice-sheet intrinsic response time to each other. We demonstrate that these scaling laws are the same for both the (two-dimensional) flow-line case and the three-dimensional case. The theoretically predicted ice-sheet scaling behavior agrees with results from numerical simulations that we conduct in flow-line and three-dimensional conceptual setups. We further investigate analytically the implications of geometric scaling of ice sheets for their response time. With this study we provide a framework which, under several assumptions, allows for a fundamental comparison of the ice-dynamic behavior across different scales. It proves to be useful in the design of conceptual numerical model setups and could also be helpful for designing laboratory glacier experiments. The concept might also be applied to real-world systems, e.g., to examine the response times of glaciers, ice streams or ice sheets to climatic perturbations.

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