Illustration of model parameterization. a) Model I parameters are core radius r_core, mantle composition c comprising the oxides Na₂O-CaO-FeO-MgO-Al₂O₃-SiO₂, mantle radius r_mantle, mass of water m_water, mass of envelope m_env, envelope Luminosity L, and envelope metallicity Z_env. b) Model II parameters are as for a), with atmosphere parameterized by pressure at the bottom of the atmosphere p_batm, number of scale-heights of opaque layers N, mean molecular weight μ, and a temperature-related parameter α. See Sect. 2.2 and Table 1 for more details.