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

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


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.


Glaciology Sea ice Turbulent heat transfer Mathematical Modelling 



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).


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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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