@misc{FeldmannLevermann2016,
  author    = {Feldmann, Johannes and Levermann, Anders},
  title     = {Similitude of ice dynamics against scaling of geometry and physical parameters},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {564},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41244},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-412441},
  pages     = {1753 -- 1769},
  year      = {2016},
  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.},
  language  = {en}
}
@misc{FeldmannLevermann2015,
  author    = {Feldmann, Johannes and Levermann, Anders},
  title     = {Interaction of marine ice-sheet instabilities in two drainage basins},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Universit{\"a}t},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Universit{\"a}t},
  number    = {511},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-40890},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-408903},
  pages     = {15},
  year      = {2015},
  abstract  = {The initiation of a marine ice-sheet instability (MISI) is generally discussed from the ocean side of the ice sheet. It has been shown that the reduction in ice-shelf buttressing and softening of the coastal ice can destabilize a marine ice sheet if the bedrock is sloping upward towards the ocean. Using a conceptional flow-line geometry, we investigate the possibility of whether a MISI can be triggered from the direction of the ice divide as opposed to coastal forcing and explore the interaction between connected basins. We find that the initiation of a MISI in one basin can induce a destabilization in the other. The underlying mechanism of basin interaction is based on dynamic thinning and a consecutive motion of the ice divide which induces a thinning in the adjacent basin and a successive initiation of the instability. Our simplified and symmetric topographic setup allows scaling both the geometry and the transition time between both instabilities. We find that the ice profile follows a universal shape that is scaled with the horizontal extent of the ice sheet and that the same exponent of 1/2 applies for the scaling relation between central surface elevation and horizontal extent as in the pure shallow ice approximation (Vialov profile). Altering the central bed elevation, we find that the extent of grounding-line retreat in one basin determines the degree of interaction with the other. Different scenarios of basin interaction are discussed based on our modeling results as well as on a conceptual flux-balance analysis. We conclude that for the three-dimensional case, the possibility of drainage basin interaction on timescales on the order of 1 kyr or larger cannot be excluded and hence needs further investigation.},
  language  = {en}
}