  A sufficient amount of water is required at the surface to develop water
oceans. A significant fraction of water, however, remains in the mantle during
magma ocean solidification, and thus the existence of water oceans is not
guaranteed even for exoplanets located in the habitable zone. To discuss the
likelihood of ocean formation, we built two models to predict the rate of
mantle degassing during the magma ocean stage and the subsequent solid-state
convection stage. We find that planets with low H$_2$O/CO$_2$ ratios would not
have a sufficient amount of surface water to develop water oceans immediately
after magma ocean solidification, and the majority of the water inventory would
be retained in the mantle during their subsequent evolution regardless of
planetary size. This is because oceanless planets are likely to operate under
stagnant lid convection, and for such planets, dehydration stiffening of the
depleted lithospheric mantle would limit the rate of mantle degassing. In
contrast, a significant fraction of CO$_2$ would already be degassed during
magma ocean solidification. With a strong greenhouse effect, all surface water
would exist as vapor, and water oceans may be absent throughout planetary
evolution. Volatile concentrations in the bulk silicate Earth are close to the
threshold amount for ocean formation, so if Venus shared similar
concentrations, small differences in solar radiation may explain the divergent
evolutionary paths of Earth and Venus.
