A Variational Method for Sea Ice Ridging in Earth System Models

Abstract

We have derived an analytic form of the thickness redistribution function, Ψ, and compressive strength of sea ice using variational principles. By using the technique of coarse‐graining vertical sea ice deformation, or ridging, in the momentum equation of the pack, we isolate frictional energy loss from potential energy gain in the collision of floes. The method accounts for macroporosity of ridge rubble, ϕR, and by including this in the state space of the pack, we expand the sea ice thickness distribution, g(h), to a bivariate distribution, g(h,ϕR). The effect of macroporosity is for the first time included in the large‐scale mass conservation and momentum equations of frozen oceans. We make assumptions that have simplified the problem, such as treating sea ice as a granular material in ridges, and assuming that bending moments associated with ridging are perturbations around an isostatic state. Regardless of these simplifications, the coarse‐grained ridge model is highly predictive of macroporosity and ridge shape. By ensuring that vertical sea ice deformation observes a variational principle both at the scale of individual ridges and over the pack as a whole, we can predict distributions of ridge shapes using equations that can be solved in Earth system models. Our method also offers the possibility of more accurate derivations of sea ice thickness from ice freeboard measured by space‐borne altimeters over polar oceans.

Comparing Observations and Parameterizations of Ice‐Ocean Drag Through an Annual Cycle Across the Beaufort Sea

“…Despite mismatches in predictions of ice geometry statistics which are used as inputs, the general success of the parameterization schemes described here gives greater confidence in our ability to use modeled results to learn about the "new Arctic", provided that methods can be developed to account for those mismatches. New sea-ice modeling schemes may be able to directly represent floe size distributions (Roach et al, 2018) or keel statistics (Roberts et al, 2019), reducing the need to redefine parameterizations of sea ice geometry.…”

Estimating the sea ice floe size distribution using satellite altimetry: theory, climatology, and model comparison

“…Modeled MIZ representative radii have a similar magnitude compared to the MIZ observations, though these regions have smaller floes than the interior. To address the scale mismatch between the too-high modeled floe sizes and observed representative radii in the interior Arctic, as well as the strong and different seasonal cycle in representative radius in both regions, modeling efforts must include additional mechanisms for reducing floe size in the Arctic interior away from waves, such as mechanical fragmentation (Toyota et al, 2006;Rynders et al, 2016) or ridge dynamics (Roberts et al, 2019), to obtain realistic representative radii across the entire Arctic, as these processes are not present in the model used to make this comparison.…”

Estimating The Sea Ice Floe Size Distribution Using Satellite Altimetry: Theory, Climatology, and Model Comparison

“…Modeled MIZ representative radii have a similar magnitude compared to the MIZ observations, though these regions have smaller floes than the interior. To address the scale mismatch between the too-high modeled floe sizes and observed representative radii in the interior Arctic, as well as the strong and different seasonal cycle in representative radius in both regions, modeling efforts must include additional mechanisms for reducing floe size in the Arctic interior away from waves, such as mechanical fragmentation (Toyota et al, 2006;Rynders et al, 2016) or ridge dynamics (Roberts et al, 2019), to obtain realistic representative radii across the entire Arctic, as these processes are not present in the model used to make this comparison.…”