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The runaway greenhouse effect [1-4] is a very interesting process for terrestrial planets, studied in particular to determine the inner limit of the Habitable Zone (HZ). This is also important to understand a possible evolution of terrestrial planets from temperate Earth-like planets to magma-ocean planets. This runway greenhouse transition is usually defined via the calculation of the asymptotic limit of thermal emission of the planet (OLR = Outgoing Longwave Radiation), also called Simpson-Nakajima limit. We have recently shown, using a 1D radiative-convective model, that a radiatively inactive gas such as nitrogen (N2) strongly modifies the OLR of the atmosphere [5] and can extend the inner edge of the HZ towards the host star [6]. We have also highlighted the importance of some physical processes sometimes considered as second order processes (e.g., collisional broadening of water lines). In continuation of this work, we use a 3D global climate model, LMD-Generic, to study the runaway greenhouse for similar atmospheres. First, we explore the runaway evaporation in a temperature range that goes beyond every previous work which only studied up to the tipping point [7,8]. We aim to understand the contribution of the inherently three-dimensional processes (e.g. clouds and dynamics) to the evolution of the atmosphere. We find strong differences with 1D simulations but also with the usual climate pattern of temperate stable states. Second, we also explore the evolution of the atmosphere when the entire water ocean is evaporated, and the convergence on a post-runaway state. This allow us to have a complete overview of the runway transition by linking our results to previous studies of hot Earth-like planets [9]. References [1] Komabayasi, M. 1967, Journal of the Meteorological Society of Japan. Ser. II [2] Ingersoll, A. 1969, Journal of the Atmospheric Sciences [3] Nakajima, S., Hayashi, Y.-Y., & Abe, Y. 1992, Journal of the Atmospheric Sciences [4] Goldblatt, C. & Watson, A. J. 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences [5] Chaverot G., Bolmont, E., Turbet, M., Leconte, J. 2021, Astronomy & Astrophysics [6] Goldblatt, C., Robinson, T. D., Zahnle, K. J., & Crisp, D. 2013, Nature Geoscience [7] Pop, M., Schmidt, H., Marotzke, J. 2016, Nature Communications [8] Leconte, J., Forget, F., Charnay, B. et al., 2013, Nature [9] Turbet, M., Bolmont, E., Chaverot, G., et al. 2021, Nature

The runaway greenhouse effect [1-4] is a very interesting process for terrestrial planets, studied in particular to determine the inner limit of the Habitable Zone (HZ). This limit is usually defined via the calculation of the asymptotic limit of thermal emission of the planet (OLR = Outgoing Longwave Radiation), also called Simpson-Nakajima limit. We have recently shown, using a 1D radiative-convective model, that a radiatively inactive gas such as nitrogen (N2) strongly modifies the OLR of the atmosphere [5] and can extend the inner edge of the HZ towards the host star [6]. We have also highlighted the importance of some physical processes sometimes considered as second order processes (e.g., collisional broadening of water lines).In continuation of this work, we use a 3D global climate model, LMD-Generic, to study the onset of the runaway greenhouse for similar atmospheres. Some studies have shown that evaporation can lead to a moist stable state [7, 8], while others suggest an inevitable runaway greenhouse effect [9].Here, we re-explore these possible moist stable states to better understand the key physical processes that potentially lead an Earth-like planet to a surface warming of several thousand degrees. We compare the results from 3D and 1D simulations, based on the conclusions of our previous study [5], in order to better understand the contribution of each process with a focus on clouds and dynamics, which are inherently three-dimensional processes. References[1] Komabayasi, M. 1967, Journal of the Meteorological Society of Japan. Ser. II[2] Ingersoll, A. 1969, Journal of the Atmospheric Sciences[3] Nakajima, S., Hayashi, Y.-Y., & Abe, Y. 1992, Journal of the Atmospheric Sciences[4] Goldblatt, C. & Watson, A. J. 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences[5] Chaverot G., Bolmont, E., Turbet, M., Leconte, J. 2021, Astronomy & Astrophysics[6] Goldblatt, C., Robinson, T. D., Zahnle, K. J., & Crisp, D. 2013, Nature Geoscience[7] Wolf, E. T., Toon, O. B. 2015, Journal of Geophysical Research[8] Pop, M., Schmidt, H., Marotzke, J. 2016, Nature Communications[9] Leconte, J., Forget, F., Charnay, B. et al., 2013, Nature

1) Introduction If an Earth-like planet with a large amount of water is drifted towards its host star, the surface temperature increases, which leads the atmosphere to enter a catastrophic runaway greenhouse state [1-4]. Studying this runaway greenhouse effect allows to better determine the runaway greenhouse insolation threshold and therefore the inner edge of the habitable zone (HZ). Some studies [5-7] have shown that radiatively inactive background gases - such as N2 - can increase the Outgoing Longwave Radiation (OLR) and delay the onset of the runaway greenhouse. In other words, the OLR may “overshoot” the Simpson-Nakajima limit [4]. Consequently the inner edge of the HZ is moved closer to the star [8-11] and the planet is further from a catastrophic runaway greenhouse feedback. Explanations for this overshoot include the modification of the scale height of the atmosphere [7] or the coupled effect of the pressure broadening and a lapse rate close to a dry lapse rate [12]. However, there is still no consensus so far in the literature on whether an OLR overshoot is expected or not and what are the responsible mechanisms. 2) Method First, we did multiple sensitivity tests to constrain the most important physical processes and parameterizations involved in 1D climate models by using a suite of models available in the literature [13-16]. This allows us to build a new hybrid 1D radiative-convective model named PyRADS-Conv1D to produce reference curves of the OLR relative to the surface temperature for H2O+N2 atmospheres (Fig. 1) to solve the question of the potential overshoot. This sensitivity study, and particularly the understanding of the relevant processes involved in such atmospheres, are useful knowledge to produce accurate 3D simulations using a Global Climate Model (GCM). Therefore we are doing simulations with the LMD-Generic model for different theoretical study cases: a waterworld and a planet with Earth’s continents. Unique features of the LMD-Generic allow to explore the onset of the runaway greenhouse, even in situations where water is not a trace gas. 3) Results By using the PyRADS-Conv1D model [17], we propose reference OLR curves relative to the surface temperature for different nitrogen pressures (Fig. 1). We confirm the occurrence of an overshoot of the OLR regarding the Simpson-Nakajima limit. We explain also that the non usual transition between a nitrogen dominated and a water dominated atmosphere challenges the modeling by making important usually second order processes. For example, neglecting the transition from the foreign to the self pressure broadening of the center of the water absorption lines leads to the suppression the overshoot [17]. PyRADS-Conv1D is based on the line-by-line radiative transfer method from PyRADS [7] but we built an accurate correlated-k table able to reproduce line-by-line results (exo_k curves on Fig. 1). This table is suitable for 3D GCM studies. Finally we show through preliminary results from the LMD-Generic model (Fig. 2) that a GCM provides the same tendency than 1D models with a strong decrease of the OLR when the surface temperature increases, even without the radiative effect of the clouds. These results may be helpful to better understand the runaway greenhouse effect and thus the possible future of the Earth. We will explain in details during the presentation our results from 3D simulations for the different considered study cases assuming an H2O-dominated atmosphere. Figure 1: OLR relative to the surface temperature for different nitrogen pressures. PyRADS-Conv1D is our reference 1D model. Exo_k [15] is an accurate 1D model used to test the correlated-k table built for this work. Figure 2: OLR relative to the surface temperature with (blue curve) or without (green curve) the radiative effect of the clouds, using the 3D LMD-Generic model. Here we assume 1 bar of nitrogen. References [1] Komabayasi, M. 1967, Journal of the Meteorological Society of Japan. Ser. II [2] Ingersoll, A. 1969 [3] Nakajima, S., Hayashi, Y.-Y., & Abe, Y. 1992, Journal of the Atmospheric Sciences [4] Goldblatt, C. & Watson, A. J. 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences [5] Goldblatt, C., Claire, M. W., Lenton, T. M., et al. 2009, Nature Geoscience [6] Goldblatt, C., Robinson, T. D., Zahnle, K. J. et al., 2013, Nature Geoscience [7] Koll, D. D. B. & Cronin, T. W. 2019, The Astrophysical Journal [8] Leconte, J., Forget, F., Charnay, B. et al., 2013, Nature [9] Kopparapu, R. k., Ramirez, R., Kasting, J. F., et al. 2013, The Astrophysical Journal [10] Ramirez, R. M. 2020, Monthly Notices of the Royal Astronomical Society [11] Zhang, Y. & Yang, J. 2020, The Astrophysical Journal [12] Pierrehumbert, R. T. 2010, Principles of planetary climate (Cambridge ; New York: Cambridge University Press) [13] Koll, D. D. B. & Cronin, T. W. 2018, Proceedings of the National Academy of Sciences [14] Turbet, M., Ehrenreich, D., Lovis, C. et al. 2019, Astronomy & Astrophysics [15] Leconte, J. 2021, Astronomy & Astrophysics [16] Marcq, E., Salvador, A., Massol, H. et al. 2017, Journal of Geophysical Research [17] Chaverot et al. 2021, In prep.

There is a strong interest to study the runaway greenhouse effect [1-4] to better determine the runaway greenhouse insolation threshold and therefore the inner edge of the habitable zone (HZ). Some studies [5-7] have shown that the onset of the runaway greenhouse may be delayed due to an increase of the Outgoing Longwave Radiation (OLR) by adding radiatively inactive gas (e.g. N2 or O2, as in the Earth's atmosphere). For such atmosphere the OLR may “overshoot” the Simpson-Nakajima limit [4], i.e. the moist greenhouse limit of a pure vapor atmopshere. This has direct consequences on the position of the inner edge of the HZ [8-11] and thus on how close the Earth is from a catastrophic runaway greenhouse feedback. The OLR overshoot has previously been interpreted as a modification of the atmospheric profile due to the background gas [7,12]. However there is still no consensus so far in the literature on whether an OLR overshoot is really expected or not.The first aim of our work is to determine, through sensitivity tests, the main important physical processes and parametrizations involved in the OLR computation with a suite of 1D radiative-convective models. By doing multiple sensitivity experiments we are able to explain the origin of the differences in the results of the literature for a H2O+N2 atmosphere. We showed that physical processes usually assumed as second order effects are actually key to explain the shape of the OLR (e.g., line shape parameters). This work can also be useful to guide future 3D GCM simulations. We propose also preliminary results from the LMD-Generic model to study how these effects may be understand in a 3D simulation.Secondly we propose a reference OLR curve, done with a 1D model built according to the sensitivity tests, for a H2O+N2 atmosphere, to solve the question of the potential overshoot. References[1] Komabayasi, M. 1967, Journal of the Meteorological Society of Japan. Ser. II[2] Ingersoll, A. 1969[3] Nakajima, S., Hayashi, Y.-Y., & Abe, Y. 1992, Journal of the Atmospheric Sciences[4] Goldblatt, C. & Watson, A. J. 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences[5] Goldblatt, C., Claire, M. W., Lenton, T. M., et al. 2009, Nature Geoscience[6] Goldblatt, C., Robinson, T. D., Zahnle, K. J. et al., 2013, Nature Geoscience[7] Koll, D. D. B. & Cronin, T. W. 2019, The Astrophysical Journal[8] Leconte, J., Forget, F., Charnay, B. et al., 2013, Nature[9] Kopparapu, R. k., Ramirez, R., Kasting, J. F., et al. 2013, The Astrophysical Journal[10] Ramirez, R. M. 2020, Monthly Notices of the Royal Astronomical Society[11] Zhang, Y. & Yang, J. 2020, The Astrophysical Journal[12] Pierrehumbert, R. T. 2010, Principles of planetary climate

As the insolation of an Earth-like (exo)planet with a large amount of water increases, its surface and atmospheric temperatures also increase, eventually leading to a catastrophic runaway greenhouse transition. While some studies have shown that the onset of the runaway greenhouse may be delayed due to an overshoot of the outgoing longwave radiation (OLR) – compared to the Simpson-Nakajima threshold – by radiatively inactive gases, there is still no consensus on whether this is occurring and why. Here, we used a suite of 1D radiative-convective models to study the runaway greenhouse transition, with particular emphasis on taking into account the radical change in the amount of water vapour (from trace gas to dominant gas). The aim of this work is twofold: first, to determine the most important physical processes and parametrisations affecting the OLR; and second, to propose reference OLR curves for N2+H2O atmospheres. Through multiple sensitivity tests, we list and select the main important physical processes and parametrisations that need to be accounted for in 1D radiative-convective models to compute an accurate estimate of the OLR for N2+H2O atmospheres. The reference OLR curve is computed with a 1D model built according to the sensitivity tests. These tests also allow us to interpret the diversity of results already published in the literature. Moreover, we provide a correlated-k table able to reproduce line-by-line calculations with high accuracy. We find that the transition between an N2-dominated atmosphere and an H2O-dominated atmosphere induces an overshoot of the OLR compared to the (pure H2O) Simpson–Nakajima asymptotic limit. This overshoot is first due to a transition between foreign and self-broadening of the water absorption lines, and second to a transition between dry and moist adiabatic lapse rates.