Implications of Numerical Error Growth in the Maxwell Elasto-Brittle Rheology for Sea Ice Fracturing and Spatial Heterogeneity

The accurate simulation of sea ice deformation and fracturing remains a significant challenge, driving the development of advanced continuum rheologies. In particular, brittle (elasto-brittle or EB, Maxwell elasto-brittle or MEB, brittle Bingham-Maxwell or BBM) rheologies are a promising advancement, introducing a damage parameter that accounts for sub-grid scale fractures and material degradation under high stresses without requiring large deformations. They simulate realistic large scale fields with adequate heterogeneity and intermittency even at coarser resolution.

However, the conventional MEB implementation, which relies on correcting super-critical stresses to bind the simulated stress to the yield criterion, inadvertently introduces a growth of numerical errors in the stress field. These errors can be reduced by introducing the Plante and Tremblay (2021) generalized stress correction scheme.

Here, the generalized stress correction scheme is added to the implemenation of the MEB rheology in the sea ice component of the Massachussetts Institute of Technology general circulation model (MITgcm), a community model that also includes a viscous-plastic (VP) rheology.

The results of pan-Arctic simulations with different levels of numerical errors in the stress field are compared against simulations using the VP rheology to identify the effect of numerical errors on the deformation behaviour. Our findings reveal three critical insights. First, we find that the generalized correction scheme successfully reduces numerical errors in the stress field in the complex Arctic simulations. Second, we show that reducing the numerical errors effectively reduce the number of simulated Linear Kinematic Features (LKFs). This confirms that numerical errors are partly responsible for the generated spatial heterogeneity in the MEB rheology. Third, we introduce artificial numerical errors to the yield curve of both MEB and VP to find that the MEB rheology is a lot more sensitive to it than the VP rheology. Additionally, we use idealized scenarios to isolate the problem from the complexitiy of an Arctic simulation. In the idealized experiments we can reproduce our results and find that the fracture angle seems to be dependent on the generalized correction scheme, as well.

Our work leads to more understanding of the MEB rheology with the goal of finding the source of heterogeneity and the seeding of LKFs in sea ice models.