U. of Delaware College of Earth, Ocean, and Environment

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Helga S. Huntley's Research

Sea Ice

Sea Ice in Nares Strait

(In collaboration with Andreas Münchow.)

Sea ice plays an important role in the climate system. It critically controls the albedo (reflectance) of high latitude oceans. The presence of ice changes the dynamic and thermodynamic interactions between the atmosphere and ocean. As a key component in fresh water transport in the Arctic, it also contributes to the ocean circulation. Despite its significance, however, sea ice dynamics is still not entirely understood, and some phenomena are not well captured in state-of-the-art models. Ice bridge formation in the straits of the Canadian Archipelago, for example, is a notoriously difficult problem, although there have been recent successes (Dumont et al., 2009). The physics behind the formation and disintegration of these ice arches is the topic of one of my current projects. The extent of the impact of such blockages on local circulation patterns and on freshwater exchange between the Arctic and the Atlantic is also an open question.


An Optimization Approach to Sea Ice Dynamics

(In collaboration with Esteban Tabak and David Holland.)

Given the limitations on model resolution, scientists are tasked with describing the larger scale motion of ice fields without relying on the first physical principles for the solid bodies that make up sea ice. Most models today are based on one of two analogies to capture the nature of the dynamics: ice as a fluid or ice as a granular material. Models following the first of these almost uniformly relate back in some way to the ice rheology first proposed by Hibler, 1979, based on the postulate that ice behaves like a nonlinear viscous-plastic compressible fluid. Improvements have been made on the original model over the years, including an extension with an elastic component to the constitutive law (cf. Hunke and Dukowicz, 1997), but the essential character has been maintained. Some have attempted to lessen the computational cost by treating ice as a cavitating fluid (cf., for example, Flato and Hibler, 1992), although in this formulation shear strength is not naturally included. Models treating ice as a granular material (for example, Tremblay and Mysak, 1997) are less common, but are better equipped to take into account some consequences of imperfect packing of ice floes. Model intercomparison studies have shown that there is still significant disagreement between ice models currently in use, as well as some discrepancy between models and available observations. Ice bridge formation in the straits of the Canadian Archipelago, for example, is notoriously difficult to reproduce. This, along with the fact that some aspects of the current models are somewhat ad hoc (such as the use of an elliptic yield curve more for calculational rather than physical reasons), motivated the development of a novel approach.

For my model, I began with the analogy of ice on a large scale behaving like a fluid with some special properties. In particular, sea ice is semi-incompressible: It allows divergence without much resistance, due to the many cracks and leads within the ice pack, but strongly resists convergence when its fractional area coverage (or concentration) is high. This resistance is limited by the ice strength, which depends on ice thickness (and possibly other parameters). The question is how to derive the internal pressure arising from and enforcing this semi-incompressibility in a mathematically elegant and computationally acceptable manner. I proposed to take the pressure as the solution to the constrained optimization problem minimizing the deviation from the path without the pressure term. The mass and momentum conservation laws, along with the limit on the concentration (c <= 1), act as constraints. Results of one-dimensional models using this formulation, both in Lagrangian and Eulerian coordinates, have exhibited good agreement with exact solutions (where possible) and physical intuition. We have also shown that a finite ice strength can be incorporated into this framework. (See Huntley et al., 2007, Huntley and Tabak, 2007.)

Early results from the extension of this model to two dimensions show promise. The complexity of the problem increases, as in addition to the normal stress, shear stress has to be considered and determined. We are attempting to fold this step into the optimization structure. An alternative would be to rely on a Mohr-Coulomb law, as used in soil dynamics, to relate shear stress to normal stress. It remains to be seen which of these methods will be computationally advantageous and better reflect the actual behavior of sea ice, such as blockages in channel flows under the appropriate forcing.

In the future, I would also like to investigate how to adapt the model to allow for resistance to compression at concentrations slightly less than 100%. Observations indicate that resistance to compression begins at concentrations around 90%, with a steep increase as concentration increases. Introducing a penalty or barrier function may be one way to allow such behavior in the optimization-based model. Ultimately, this sea ice dynamics model should be coupled with existing thermodynamic components and subjected to variable forcing, in order to compare its performance to that of other sea ice models and evaluate its ability to reproduce observed phenomena and features of the ice cover. A separate but related avenue of interest is a combined empirical and modeling study of the factors determining the timing of the formation and break-up of the ice bridges and how the presence or absence of them affects the throughflow of ice and water.


Dumont, D., Y. Gratton, and T.E. Arbetter, Modeling the dynamics of the North Water polynya ice bridge, J. Phys. Oceanogr., 39, 1448-1461, 2009.

Flato, G.M. and W.D. Hibler, III, Modeling pack ice as a cavitating fluid, J. Phys. Oceanogr., 22, 626-651, 1992.

Hibler, W.D., III, A dynamic thermodynamic sea ice model, J. Phys. Oceanogr., 9, 817-846, 1979.

Hunke, E.C. and J.K. Dukowicz, An elastic-viscous-plastic model for sea ice dynamics, J. Phys. Oceanogr., 27, 1849-1867, 1997.

Huntley, H.S., E.G. Tabak, and E.H. Suh, An optimization approach to modeling sea ice dynamics; part 1: Lagrangian framework, SIAM J. Appl. Math., 67, 543-560, 2007.

Huntley, H.S. and E.G. Tabak, An optimization approach to modeling sea ice dynamics; part 2: finite ice strength effects, SIAM J. Appl. Math., 67, 561-581, 2007.

Tremblay, L.-B. and L.A. Mysak, Modeling sea ice as a granular material, including the dilatancy effect, J. Phys. Oceanogr., 27, 2342-2360, 1997.

Related publication

Huntley, H.S. and E.G. Tabak, 2007: An optimization approach to modeling sea ice dynamics; part 2: finite ice strength effects, SIAM J. Appl. Math., 67, 561-581.

Huntley, H.S., E.G. Tabak, and E.H. Suh, 2007: An optimization approach to modeling sea ice dynamics; part 1: Lagrangian framework, SIAM J. Appl. Math., 67, 543-560.

Schaffrin, H., 2005: An Optimization Approach to Sea Ice Dynamics, Ph.D. Thesis, New York University.

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