the average optical depth at 5000 Å is unity in a patch of the model atmosphere without strong vertical field strength. Due to the Wilson depression, there are columns where the height of optical depth unity at 5000 Å is below the zero point of our height scale. The largest offset is $-$0.9 Mm located in the upper sunspot in Fig. \[fig:atmos\_photosphere\].

For our non-LTE calculations with hydrogen we resampled the vertical resolution of the model from 32 km to 16 km around the transition region to better resolve large gradients. This resulted in a grid size of $1024 \times 512 \times 499$ points. For magnesium and calcium, we kept the original grid spacing because the spectra of these atoms are formed below the transition region.

In the MURaM simulation there exist locations where the temperature is as low as 1100 K. Our background opacities are not correct at such low temperatures, and therefore we set the minimum temperature to 3250 K in the model atmosphere. This has a minimal effect on the resulting spectra.

The simulation used a LTE equation of state. The electron densities in the real chromosphere are however far from LTE, and should ideally be computed 