  For the first time we introduce an error estimator for the numerical
approximation of the equations describing the dynamics of sea ice. The idea of
the estimator is to identify different error contributions coming from spatial
and temporal discretization as well as from the splitting in time of the ice
momentum equations from further parts of the coupled system. The novelty of the
error estimator lies in the consideration of the splitting error, which turns
out to be dominant with increasing mesh resolution. Errors are measured in user
specified functional outputs like the total sea ice extent. The error estimator
is based on the dual weighted residual method that asks for the solution of an
additional dual problem for obtaining sensitivity information. Estimated errors
can be used to validate the accuracy of the solution and, more relevant, to
reduce the discretization error by guiding an adaptive algorithm that optimally
balances the mesh size and the time step size to increase the efficiency of the
simulation.
