Sea ice is an important component of the climate system. The thermodynamic processes of freezing and melting are generally straightforward to parameterize in a sea ice model on climate scales, but the internal dynamics in a sea ice model still rely on crude assumptions. The sea ice cover is treated as a quasi-continuous non-Newtonian fluid with a rheology describing its behavior under compression and shear. With model grid spacings of 10 to 100km, these assumptions have been used successfully to simulate the large scale properties of sea ice, but they may need to be reevaluated as numerical climate models are operated at increasingly high resolution. Still, simulations with conventional sea ice models with a viscous-plastic rheology improve with increasing resolution. Here we show two examples: fractal scaling properties of simulated sea ice at high resolution agree with satellite observations and the distribution and formation of fast ice in the Arctic Ocean improves with increasing resolution.