A Variational Method for Sea Ice Ridging in Earth System Models

The first analytic solution for the evolution of sea ice thickness with macro-porosity of pack ice in the Arctic and Southern Ocean.

The Science

This work provides the first analytic solution to the redistribution of sea ice thickness that accounts for evolution of the macro-porosity in the ridged mélange of pack ice.  Ridges account for most thick ice in the Arctic and Southern Ocean, and the voids within them typically cause deformed ice keels and sails. A better accounting for ridging in sea-ice will provide better estimates of sea ice thickness and extent. Current Earth system models do not account for this aspect of ridging, i.e., reduction in bulk density in deformed ice relative to thinner and undeformed ice, and therefore overestimate total sea ice mass. This work therefore has implications for simulating ice loss or gain in the Arctic and Southern Ocean.

The Impact

This paper has a wide range for implications for model development, analysis, and evaluation at a wide range of scales. This work is important for improving simulations of the coupled cryosphere and water cycle in the Arctic for Global and Regional Earth system models (e.g., Energy Exascale Earth System Model and Regional Arctic System Model). At a more localized scale, it helps in better representing ice deformation in the sea ice models, in particular, in the Icepack software which is part of the CICE Consortium. Theory within this paper also provides a mechanism for simulating scale-aware ridging in a new Discrete Element Model of Sea ice (DEMSI).  The mathematical derivations within this manuscript also facilitate sophisticated evaluation of sea ice thickness in models using space-borne altimeter measurements, and for improving estimates of sea ice mass from submarine sonar.


Improvements to sea ice models evolving from this paper will result in improvements to the state space of simulated sea ice, affecting representations of form drag and therefore the primary mechanical forcing on the pack:  wind and ocean stress. The mathematical methods derived in this manuscript will allow sea ice models to explicitly track distributions of the spacing, shape and size of ridges, affecting land-fast ice simulation, important for modeling coastal change in the Arctic, as well as biogeochemistry, important for modeling biological productivity in the Southern Ocean and in a warming Arctic Ocean.  As part of this paper, a new software package called Ridgepack was released for analyzing coupled sea ice models and sea ice thickness evolution. A short movie is provided demonstrating sea ridging in the Beaufort Sea.

Principal Investigator(s)

Andrew Roberts
Los Alamos National Laboratory

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This work was supported by United States Department of Energy (DOE) grants DESC0005522 and DESC0005783, Office of Naval Research grant N0001417WX00563 and National Science Foundation grants 0612527, 1108542, and 1603602. We are also grateful for support from the DOE Office of Biological and Environmental Research’s High-Latitude Application and Testing of Global and Regional Climate Models (HiLAT) project and the Scientific Discovery through Advanced Computing (SciDAC) program.  The National Center for Atmospheric Research is sponsored by the National Science Foundation. Andrew Roberts and Elizabeth Hunke thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the Mathematics of Sea Ice Phenomena programme where part of this research was undertaken (EPSRC grant EP/K032208/1).


Roberts, A. F., E. C. Hunke, S. M. Kamal, W. H. Lipscomb, C. Horvat, W. Maslowski. “A Variational Method for Sea Ice Ridging in Earth System Models.” J. Adv. Model. Earth Sy.  (2019). DOI:10.1029/2018MS001395