Rocky planets with temperate conditions provide the best chance for discovering habitable worlds and life outside the Solar System. In the last decades, new instrumental facilities and large observational campaigns have been driven by the quest for habitable worlds. Climate models aimed at studying the habitability of rocky planets are essential tools to pay off these technological and observational endeavours. In this context, we present EOS-ESTM, a fast and flexible model aimed at exploring the impact on habitability of multiple climate factors, including those unconstrained by observations. EOS-ESTM is built on ESTM, a seasonal-latitudinal energy balance model featuring an advanced treatment of the meridional and vertical transport. The novel features of EOS-ESTM include: (1) parameterizations for simulating the climate impact of oceans, land, ice, and clouds as a function of temperature and stellar zenith distance; (2) a procedure (EOS) for calculating the radiative transfer in atmospheres with terrestrial and non-terrestrial compositions illuminated by solar- and non-solar-type stars. By feeding EOS-ESTM with Earth’s stellar, orbital and planetary parameters we derive a reference model that satisfies a large number of observational constraints of the Earth’s climate system. Validation tests of non-terrestrial conditions yield predictions that are in line with comparable results obtained with a hierarchy of climate models. The application of EOS-ESTM to planetary atmospheres in maximum greenhouse conditions demonstrates the possibility of tracking the snowball transition at the outer edge of the HZ for a variety of planetary parameters, paving the road for multi-parametric studies of the HZ.

We present EOS, a procedure for determining the outgoing longwave radiation (OLR) and top-of-atmosphere (TOA) albedo for a wide range of conditions expected to be present in the atmospheres of rocky planets with temperate conditions. EOS is based on HELIOS and HELIOS-K, which are novel and publicly available atmospheric radiative transfer (RT) codes optimized for fast calculations with GPU processors. These codes were originally developed for the study of giant planets. In this paper we present an adaptation for applications to terrestrial-type, habitable planets, adding specific physical recipes for the gas opacity and vertical structure of the atmosphere. To test the reliability of the procedure, we assessed the impact of changing line opacity profile, continuum opacity model, atmospheric lapse rate, and tropopause position prescriptions on the OLR and the TOA albedo. The results obtained with EOS are in line with those of other RT codes running on traditional CPU processors, while being at least one order of magnitude faster. The adoption of OLR and TOA albedo data generated with EOS in a zonal and seasonal climate model correctly reproduces the fluxes of the present-day Earth measured by the CERES spacecraft. The results of this study disclose the possibility to incorporate fast RT calculations in climate models aimed at characterizing the atmospheres of habitable exoplanets.

<p>The next generation of astronomical facilities will be able to retrieve exoplanetary atmospheric spectra in increasing quantity and of increasing quality. Radiative transfer (RT) models of these atmospheres is essential both for interpreting observational data and for linking these data to the planetary physical state with the aid of dedicated climate models. So far, a large effort has been placed in modelling the atmospheres of giant planets, which are the most easily accessible to observations. Now times are ripe to extend these studies to treat the relatively thin atmospheres of terrestrial-type exoplanets, which are the most likely targets for the search of atmospheric biomarkers.</p> <p><br />Here we present a procedure to perform radiative transfer calculations for terrestrial-type exoplanets with temperate physical conditions (Simonetti et al. in preparation). The procedure is based on HELIOS and HELIOS-K, which are novel, flexible and publicly available codes developed by the University of Bern (Grimm & Heng, 2015; Malik et al., 2017, 2019; Grimm et al., 2021) as a part of the Exoclime Simulation Platform (ESP) repository. These codes make full use of the computing power of Graphics Processing Units (GPUs, colloquially known as graphics cards) being therefore much faster (up to one order of magnitude, see Grimm et al. 2021) than other similar codes and are integrated with a variety of molecular and atomic line repositories such as HITRAN (Gordon et al., 2017), HITEMP (Rothman et al., 2010) and Kurucz. Until now, HELIOS has been mostly applied to study Jupiter-like planets. The main features of the procedure that we have implemented for the treatment of rocky, habitable planets can be summarized as follows.</p> <p><br />First, we added the treatment of the continuum absorption features of a variety of gases, in particular H2O (Clough et al., 1989; Mlawer et al., 2012) and CO2 (Gruszka & Borysow, 1997; Baranov et al., 2004; Baranov, 2018). These continua strongly contribute to the overall opacity of Earth-like atmospheres and cannot be neglected. Second, we paid special attention to the sub-Lorentzian profile of CO2 absorption lines, testing the effects of different recipes (Perrin & Hartmann, 1989; Tonkov et al., 1996). Third, we considered different hypotheses regarding the convective lapse rate of the troposphere. On these basis we: (i) tested the robustness of HELIOS and HELIOS-K against changes in model variables and (ii) compared them with other codes already published and used in the same context (e.g. LBLRTM Clough et al., 2005), as done by Yang et al. (2016).</p> <p><br />One of the main goals of this work is to provide a new and fast radiative transfer treatment for the ESTM, an energy balance climate model with upgraded treatment of the vertical and horizontal energy transport Vladilo et al. (2015). The ESTM is extremely flexible and allows for a rapid exploration of the planetary and atmospheric parameter space, providing us the ability to map quantitative indices of habitability on these parameters (Silva et al., 2017). The flexibility of both HELIOS and ESTM will allow us to test a wide variety of atmospheric compositions, which have applications in the study both of exoplanets and of ancient Earth and Mars. Moreover, the HELIOS procedure adapted to terrestrial-type atmospheres can be used to generate synthetic TOA fluxes useful to link the conditions at the planet's surface with quantities that will become observable with future generations of instruments, such as secondary eclipse spectra and direct IR emission spectra from terrestrial-type exoplanets (see e.g. Quanz et al., 2021). Finally, the output of the same procedure can be applied to other codes in the ESP repository, such as the THOR GCM (Mendonca et al., 2016; Deitrick et al., 2020).</p> <p><img src="data:image/png;base64, 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

<p>INTRODUCTION</p> <p>Over the past two decades, ground- and space-based observations have unveiled thousands exoplanets and planetary systems around other stars in our Galaxy. About 5000 exoplanets are currently confirmed, in large part detected as transits by the Kepler and TESS missions. Launched in 2019, PLATO mission represents the first-step characterisation towards the understanding of the structural properties of these planets. Nevertheless, a significant boost for the detection of transiting Earth-analogues around bright stars is expected from the PLATO mission. <br />However, it's only through remote atmospheric spectroscopy of potentially habitable rocky planets, that one of the main goals of exoplanetary science, the quest for life outside the Solar System, can be tackled. This observational challenge should be partly within reach of the recently launched JWST and the next ground-based astronomical observatory, E-ELT.</p> <p>To accomplish the demanding task of searching for and  deciphering spectral signatures, a thorough and holistic observational and theoretical characterization of carefully selected rocky exoplanets is required.<br />The selection, among the observationally reachable targets for high-resolution spectroscopy of thin atmospheres, requires habitability studies with climate models. <br />These simulations will enable the identification of those exoplanets with the largest chance of potentially hosting a surface diffuse life, i.e. with the largest habitability, that must be evaluated over a wide range of mostly unknown conditions. <br />A considerable effort of modelization that exploits all available observations will be needed in order to assess the global physical characterization of the selected exoplanets, and in particular precisely of their potential surface climate and habitability.</p> <p> </p> <p>THE MODEL</p> <p>Here we present EOS-ESTM, a flexible climate model aimed at simulating the surface and atmospheric conditions that characterize habitable planets. The model allows one to perform a fast exploration of the parameter space representative of planetary quantities, including those currently not measurable in rocky exoplanets. EOS-ESTM has been built up starting from ESTM (Vladilo et al. 2013, 2015), a seasonal-latitudinal EBM featuring an advanced treatment of surface and cloud components and a 2D (vertical and latitudinal) treatment of the energy transport.</p> <p>The main features of the model that we have implemented can be summarised as follows.</p> <p>Firstly, we have calculated the atmospheric radiative transfer using EOS (Simonetti et al. 2022), a procedure tailored for atmospheres of terrestrial-type planets, based on the opacity calculator HELIOS-K (Grimm & Heng 2015; Grimm et al. 2021) and the radiative transfer code HELIOS (Malik et al. 2017, 2019). Thanks to EOS, the ESTM radiative transfer can be now calculated for a variety of atmospheres with different bulk and greenhouse compositions, illuminated by stars with different SEDs.</p> <p>Then, we have upgraded the parameterizations that describe the clouds properties. New equations have been introduced for the albedo of the clouds and its dependence on the albedo of the underlying surface. The clouds coverage over ice is now a function of the global planetary ice coverage. A specific treatment for the transmittance and OLR forcing of clouds at very low temperature has been introduced.</p> <p>Lastly, we have introduced a generalized logistic function to estimate the ice coverage as a function of mean zonal surface temperature. Based on a detailed study of the ice distribution on Earth, the adopted algorithm discriminates between ice over lands and oceans. The albedo and thermal capacity of transitional ice is now estimated using the fractional ice coverage. </p> <p><br />RESULTS</p> <p>With the aim of providing a reference model for studies of habitable planets, we calibrated EOS-ESTM using a large set of Earth satellite and reanalysis data.  <br />The reference Earth model satisfies a variety of diagnostic tests, including mean latitudinal profiles of surface temperature (Figure 1), TOA albedo, OLR and ice coverage.</p> <p><img src="" alt="" width="849" height="636" /></p> <p>Fig. 1. Mean annual latitude profile of surface temperature predicted by the reference Earth model The temperature profile is compared with ERA5 temperatures averaged in the period 2005-2015 (blue dots).</p> <p>To test the consistency of EOS-ESTM with previous studies of non-terrestrial climate conditions we performed a series of comparisons with a hierarchy of climate models, varying the levels of insolation (Figure 2), the stellar spectrum and planetary parameters (radius and rotation rate).</p> <p><img src="" alt="" width="851" height="638" /></p> <p>Fig. 2. Comparison of global and annual  mean surface temperature obtained from different climate Earth's models by increasing the solar constant. Red, solid line: EOS-ESTM (this work). Black, solid line: 3D model CAM4 (Wolf & Toon, 2015). Cyan, solid line: 3D model CAM3 (Wolf & Toon, 2014). Green, solid line: 3D model by Leconte et al. (2013).</p> <p>The application of EOS-ESTM to the case of a CO<sub>2</sub>-dominated atmosphere in maximum greenhouse conditions (Kasting et al. 1993) yields a detailed description of the transition to a snowball state that takes place when the insolation decreases in the proximity of the outer edge of the HZ. Thanks to the flexibility of our model we can explore how this transition develops in different planetary conditions (e.g. rotation rate, Figure 3).</p> <p><img src="" alt="" width="852" height="639" /></p> <p>Fig. 3. Dependence on planetary rotation period rotation period, P<sub>rot</sub>, of the fractional ice coverage calculated at the outer edge of the HZ. The results were obtained for an Earth-like planet with a CO<sub>2</sub>-dominated, maximum greenhouse atmosphere, the remaining parameters being fixed to Earth values.</p> <p> </p> <p>REFERENCES</p> <p>Grimm S. L., Heng K., 2015, HELIOS-K: Opacity Calculator for Radiative Transfer (ascl:1503.004)</p> <p>Grimm S. 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