Schematic depicting the setup of the volatile exchange during initialization (t=0) and run time. For initialization, a surface temperature of 4000 K and a completely molten magma ocean was assumed, where the dissolved volatiles are in balance with the outgassed volatile content, set by the volatile melt fraction, F_i. As the magma ocean solidifies, part of the volatile budget is deposited in the solid mantle. Furthermore, atmospheric escape can remove H₂O. These two sink terms thus reduce the amount of a volatile available in the fully coupled MOA system, $M_i^{moa}$. The full overview of all included processes, including radiogenic heating, is shown in Barth et al. (2021, Fig. 1).