Toward next generation sea ice models: taking the rough with the smooth?

Existing sea ice models, such as those that appear in environmental and climate models, are built on continuum local balances of heat, momentum, and mass. State variables such as ice thickness and concentration are smooth and continuously differentiable. While there are important rheological differences, these models are mathematically similar in type to standard continuum models such as the Navier-Stokes (NS) equations for Newtonian fluid flow. Unlike these latter models, however, the continuum assumption is often invalidated in sea ice simulations because the sea ice floe, the analogue of a molecule in the NS equations, is of comparable size to the grid cell used for numerical simulation. In this case, the grid cell cannot be taken to contain a statistically representative sample of sea ice floes (or other features such as leads). Continuity violation has led to suggestions that the next generation of sea ice models should be built on a discrete architecture, where individual floe interactions can be represented. This project will examine the issues of continuity violation in continuum models. In particular, if it can be shown that a continuum model represents an average of the discrete behaviour then this would provide much needed confidence in the interpretation of these models, particularly in climate simulations. The limitations of existing continuum models and the possibilities of discrete approaches will be explored, with a view to the needs of future model development.
Sea ice models were largely built in the 1970s, where fundamental assumptions were made concerning continuity, isotropy, and rheology. The models were designed to be valid over length scales where the sea ice could be treated as continuous by averaging over many floes (~50-100km) and the ice cover assumed isotropic (now known to be an invalid at all length scales). These are the same sea ice models being used in climate and weather models now, where there is a push to increasingly high resolutions (down to ~1km), invalidating the continuity assumption. Since the models were not built for such high resolutions, and contain assumptions now known to be wrong, there are fundamental concerns over whether such sea ice models are valid and can be trusted. This is an issue well appreciated within the sea ice modeling community, but is less well known in the broader climate community.

In this project we will take the first steps towards a climate model-capable discrete representation of sea ice by addressing the feasibility of blending discrete and continuum modelling approaches. Building on previous approaches and code, the student will develop a discrete element sea ice model (DEM), where the discrete elements are the actual floes, and use this to examine sea ice breakup and flow for a range of idealised geometries and imposed boundary forcing. These simulations will be compared with equivalent continuum simulations. The DEM will be used to examine sea ice breakup and flow in narrow straits, such as are typical of the Canadian Archipelago using boundary conditions from a simulation using a continuum sea ice model. The nested DEM simulations would be compared with the direct simulations from the continuum model for the study region and observations.