@article{PattynPerichonDurandetal.2013,
  author    = {Pattyn, Frank and Perichon, Laura and Durand, Gael and Favier, Lionel and Gagliardini, Olivier and Hindmarsh, Richard C. A. and Zwinger, Thomas and Albrecht, Torsten and Cornford, Stephen and Docquier, David and Furst, Johannes J. and Goldberg, Daniel and Gudmundsson, Gudmundur Hilmar and Humbert, Angelika and Huetten, Moritz and Huybrechts, Philippe and Jouvet, Guillaume and Kleiner, Thomas and Larour, Eric and Martin, Daniel and Morlighem, Mathieu and Payne, Anthony J. and Pollard, David and Rueckamp, Martin and Rybak, Oleg and Seroussi, Helene and Thoma, Malte and Wilkens, Nina},
  title     = {Grounding-line migration in plan-view marine ice-sheet models: results of the ice2sea MISMIP3d intercomparison},
  series = {Journal of glaciology},
  volume    = {59},
  journal   = {Journal of glaciology},
  number    = {215},
  publisher = {International Glaciological Society},
  address   = {Cambridge},
  issn      = {0022-1430},
  doi       = {10.3189/2013JoG12J129},
  pages     = {410 -- 422},
  year      = {2013},
  abstract  = {Predictions of marine ice-sheet behaviour require models able to simulate grounding-line migration. We present results of an intercomparison experiment for plan-view marine ice-sheet models. Verification is effected by comparison with approximate analytical solutions for flux across the grounding line using simplified geometrical configurations (no lateral variations, no buttressing effects from lateral drag). Perturbation experiments specifying spatial variation in basal sliding parameters permitted the evolution of curved grounding lines, generating buttressing effects. The experiments showed regions of compression and extensional flow across the grounding line, thereby invalidating the boundary layer theory. Steady-state grounding-line positions were found to be dependent on the level of physical model approximation. Resolving grounding lines requires inclusion of membrane stresses, a sufficiently small grid size (<500 m), or subgrid interpolation of the grounding line. The latter still requires nominal grid sizes of <5 km. For larger grid spacings, appropriate parameterizations for ice flux may be imposed at the grounding line, but the short-time transient behaviour is then incorrect and different from models that do not incorporate grounding-line parameterizations. The numerical error associated with predicting grounding-line motion can be reduced significantly below the errors associated with parameter ignorance and uncertainties in future scenarios.},
  language  = {en}
}
@article{FuerstLevermann2012,
  author    = {F{\"u}rst, Johannes J. and Levermann, Anders},
  title     = {A minimal model for wind- and mixing-driven overturning threshold behavior for both driving mechanisms},
  series = {Climate dynamics : observational, theoretical and computational research on the climate system},
  volume    = {38},
  journal   = {Climate dynamics : observational, theoretical and computational research on the climate system},
  number    = {1-2},
  publisher = {Springer},
  address   = {New York},
  issn      = {0930-7575},
  doi       = {10.1007/s00382-011-1003-7},
  pages     = {239 -- 260},
  year      = {2012},
  abstract  = {We present a minimal conceptual model for the Atlantic meridional overturning circulation which incorporates the advection of salinity and the basic dynamics of the oceanic pycnocline. Four tracer transport processes following Gnanadesikan in Science 283(5410):2077-2079, (1999) allow for a dynamical adjustment of the oceanic pycnocline which defines the vertical extent of a mid-latitudinal box. At the same time the model captures the salt-advection feedback (Stommel in Tellus 13(2):224-230, (1961)). Due to its simplicity the model can be solved analytically in the purely wind- and purely mixing-driven cases. We find the possibility of abrupt transition in response to surface freshwater forcing in both cases even though the circulations are very different in physics and geometry. This analytical approach also provides expressions for the critical freshwater input marking the change in the dynamics of the system. Our analysis shows that including the pycnocline dynamics in a salt-advection model causes a decrease in the freshwater sensitivity of its northern sinking up to a threshold at which the circulation breaks down. Compared to previous studies the model is restricted to the essential ingredients. Still, it exhibits a rich behavior which reaches beyond the scope of this study and might be used as a paradigm for the qualitative behaviour of the Atlantic overturning in the discussion of driving mechanisms.},
  language  = {en}
}