A number of potentially habitable exoplanets located within the habitable zone of their host star have been detected. The habitable zone, which is defined as the region around a star where liquid water on a planetary surface remains stable, is the most widely used concept in exoplanetary science, as it helps narrow the search for oceans beyond Earth (e.g., Kasting et al., 1993;Kopparapu et al., 2013Kopparapu et al., , 2014. In the next decade, planets within the habitable zone will be primary candidates for observation of their biosignature.The edges of the classical habitable zone have been estimated for an aqua planet that is globally covered with ocean using a one-dimensional radiative-convective model. Recently, one can address the climate for terrestrial potential habitable planets and their habitability using three-dimensional general circulation models (GCMs). GCM studies have produced examples of climates for potentially habitable planets -for example, Proxima Centauri b and the Trappist-1 planets (Turbet et al., 2016(Turbet et al., , 2018(Turbet et al., , 2020.There are two definitions of the inner edge of the habitable zone: the runaway greenhouse limit and the moist greenhouse limit (e.g., Kasting et al., 1993;Kopparapu et al., 2013). From 1D radiative-convective equilibrium models, we know that a planet with a wet atmosphere has a limit on planetary radiation, called the Simpson-Nakajima limit, due to an atmospheric structure whereby the temperature profile asymptotically approaches the saturated vapor pressure curve for water vapor, leading to constant planetary radiation at the position where the optical depth equals unity (Ingersoll, 1969;Nakajima, Hayashi & Abe, 1992). When such a planet receives insolation