New Momentum, Stress, and Transport Schemes for the CICE Sea Ice Model on a C-Grid
The CICE model solves equations that describe the dynamics and the growth and melt of sea ice. To do so, the domain is divided into grid cells and variables are positioned at specific locations in the cells. A new implementation (C-grid) is presented, with the velocity components located on cell edges. Earlier versions of CICE used the Arakawa B-grid, in which the horizontal velocity components are co-located at cell corners, for the spatial discretization. Discretizing the sea ice dynamical core for a different grid is challenging because conserved quantities and boundary conditions (physical and parallelization) must be properly accounted for, and because the fundamental equations are susceptible to nonphysical solutions associated with a singularity in the continuous equations and a null space in their discrete form. The null space solution is a checkerboard pattern that is excited only when coupling the discretized sea ice momentum and advection equations. The implementation described in this paper overcomes all of these challenges, including a small modification to the existing incremental remapping transport scheme that allows its direct use for C-grid configurations.
The new C-grid dynamics implementation allows flow in narrow channels, more accurate physical response to the dynamical forcing of sea ice (inertial-plastic compressive waves in the sea ice), and straightforward coupling of sea ice dynamics quantities with C-grid ocean and atmospheric models.
This article presents the C-grid discretization of the momentum equation, the boundary conditions, and modifications to the CICE sea ice model required to use the incremental remapping transport scheme. To validate the new C-grid implementation, many numerical experiments were conducted and compared to the B-grid solutions. In idealized experiments, the standard advection method (incremental remapping with C-grid velocities interpolated to the cell corners) leads to a checkerboard pattern. A modal analysis demonstrates that this computational noise originates from the spatial averaging of C-grid velocities at corners. The checkerboard pattern can be eliminated by adjusting the departure regions to match the divergence obtained from the solution of the momentum equation. We refer to this approach as the edge flux adjustment method. The C-grid discretization with edge flux adjustment allows transport in channels that are one grid cell wide—a capability that is not possible with the B-grid discretization nor with the C-grid and standard remapping advection. Simulation results match the predicted values of a novel analytical solution for one-grid-cell-wide channels.