Numerical simulations of the quiet chromosphere

Numerical simulations of the solar chromosphere have become increasingly realistic over the past 5 years. However, many observed chromospheric structures and their behavior are not reproduced. Current models do not show fibrils in Ca ii 8542 Å, and neither reproduce the Ca ii 8542 Å bisector. The emergent H line core intensity computed from the models show granulation instead of chromospheric shocks or fibrils. I discuss these deficiencies and speculate about what physics should be included to alleviate these shortcomings.