Numerical modeling of ridging of sea ice: Towards linking scales in ice dynamics

Abstract

Convergent motion of sea ice, caused by wind and ocean currents, creates ice ridges. These ridges consist of broken ice pieces piled above and below the waterline, thereby significantly increasing the local ice thickness relative to the surrounding ice cover. In turn, ridges influence ice motion by affecting air and ocean drag and by limiting large-scale ice strength. Despite their importance, several open questions remain regarding ridging processes and their representation in large-scale sea-ice dynamics models. In conventional continuum models, the influence of ridging on ice thickness is either represented by an increase in the mean ice thickness or by changes in the ice thickness distribution (ITD), which requires sub-grid parametrization of ridging. The research in this thesis contributes to an understanding of ridging by conducting detailed simulations on ridge formation. The main modelling method used is the discrete element method (DEM), which allows for an explicit description of ridge formation, including ice failure and ice accumulation within the ridge.

First, the three-dimensional DEM model A3D-DEM is used to simulate the formation process of an individual ridge. The simulations are validated against ridging forces and ridge geometries resulting from laboratory-scale experiments. Additional simulations at full scale are conducted to show, for the first time, that Cauchy-Froude scaling applies when translating ridging results from laboratory scale to full scale. Based on these simulations, a linear relationship between the ridging forces and ice thickness is found, which differs from earlier results from two-dimensional simulations. This difference is likely due to non-simultaneous failure, meaning the ice floe fails at different locations and at different times along the length of the ridge. Non-simultaneous failure cannot be described by two-dimensional simulations, indicating that three-dimensional simulations are needed for accurate modeling of ridging processes.

Then, another three-dimensional DEM model, HiDEM, is used to simulate ridging across a significantly larger sea-ice domain. These simulations lead to a deformed ice cover composed of multiple ridges of varying shapes. The ridge shapes include triangular and trapezoidal ridges, with the latter significantly affecting the ITD of the deformed ice cover by creating a bump in the ITD towards thicker ice. Further, the ITD resulting from the DEM simulations is compared with ITDs derived from a continuum model using only the mean thickness and from two commonly used ridging functions used as sub-grid parametrizations within redistribution schemes. The shape of the ITDs from conventional continuum models differs from that of the ITD from the DEM simulations. The thesis demonstrates how to derive an analytical redistribution function that accounts for the effects of triangular and trapezoidal ridges.

Overall, the suitability of DEM models contributing to an understanding of larger-scale sea-ice dynamics is also demonstrated in this research. The results from the DEM models are set in the context of current understanding of ridge properties and ridging processes and discussed with respect to their application in large-scale continuum models.