A second-order accurate in time IMplicit-EXplicit (IMEX) integration scheme for sea ice dynamics

11 Current sea ice models use numerical schemes based on a splitting in time 12 between the momentum and continuity equations. Because the ice strength 13 is explicit when solving the momentum equation, this can create unrealis14 tic ice stress gradients when using a large time step. As a consequence, 15 noise develops in the numerical solution and these models can even become 16 numerically unstable at high resolution. To resolve this issue, we have imple17 mented an iterated IMplicit-EXplicit (IMEX) time integration method. This 18 IMEX method was developed in the framework of an already implemented 19 Jacobian-free Newton-Krylov solver. The basic idea of this IMEX approach 20 is to move the explicit calculation of the sea ice thickness and concentration 21 inside the Newton loop such that these tracers evolve during the implicit 22 integration. To obtain second-order accuracy in time, we have also modified 23 the explicit time integration to a second-order Runge-Kutta approach and 24 by introducing a second-order backward di↵erence method for the implicit 25 integration of the momentum equation. These modifications to the code are 26 minor and straightforward. By comparing results with a reference solution 27 obtained with a very small time step, it is shown that the approximate so28 lution is second-order accurate in time. The new method permits to obtain 29 the same accuracy as the splitting in time but by using a time step that is 30 10 times larger. Results show that the second-order scheme is more than five 31 times more computationally e cient than the splitting in time approach for 32 an equivalent level of error. 33