1 Introduction and Background
1.1 The Faint Young Sun Problem
 The Archean is the geological era following the Hadean (starting with Earth formation 4.56 Ga) and preceding the Proterozoic. It starts at 3.8 Ga, after the Late Heavy Bombardment (LHB), and ends at 2.5 Ga with the Great Oxidation Event. The first reported fossils of bacteria date back 3.5 Ga [Schopf, 2006] and there is possibly evidence for life from carbon isotopes up to 3.8 Ga [Mojzsis et al., 1996; Rosing, 1999]. The emergence of life is believed to have occurred before 3.5 Ga and maybe even before the LHB [Nisbet and Sleep, 2001]. Thus, studying the climates of the Archean Earth is of prime interest to understand the environment in which life emerged and evolved.
 According to the standard model of stellar evolution, the Sun was 20 to 25% weaker during the Archean [Gough, 1981]. With such a weaker Sun, the Earth with the present-day atmospheric composition would fall into a full glaciation, hardly reconcilable with the evidence of liquid water and life during the whole Archean [Sagan and Mullen, 1972; Feulner, 2012]. This has been named the “faint young Sun problem” or the “faint young Sun paradox.”
 While the Earth was unfrozen during most of the Archean, there is geological evidence for glaciations at the end of the Archean (the Huronian glaciations), between 2.45 and 2.22 Ga [Evans et al., 1997]. These have been linked to the rise of oxygen in the atmosphere [Kasting and Howard, 2006; Kasting and Ono, 2006] and the destruction of atmospheric methane. There was also a possible glaciation at 2.9 Ga [Young et al., 1998] but it would have been regional, not global, and its origin remains unknown [Kasting and Ono, 2006]. The Archean Earth therefore seems to have experienced very few glaciations, implying that there were temperate or hot climates during most of the Archean. However, the Archean rock record is extremely sparse and the latitudes of these geological data are unknown. Sea ice and continental ices could have existed at high latitudes, and other glaciations may have occurred.
 Paleotemperatures were estimated from the isotopic composition of marine cherts [Knauth and Lowe, 2003; Robert and Chaussidon, 2006] and indicate hot oceans (between 60°C and 80°C) during the Archean. This makes the faint young Sun problem even more challenging. The validity of these measurements has been questioned, however, because of the possible variation of the isotopic composition of oceans during the time [Kasting and Howard, 2006; Kasting et al., 2006; Jaffrés et al., 2007] and because of the impact of hot hydrothermal circulation on chert formation [van den Boorn et al., 2007]. The most recent analyses obtained an upper limit at 40°C [Hren et al., 2009; Blake et al., 2010].
 Estimating the temperature of the oceans is also controversial as far as biological evidence is concerned. Genetic evolution models suggest that the ancestors of bacteria, eukaryota, and archaea were thermophylic during the Archean [Gaucher et al., 2008; Bousseau et al., 2008] consistent with the oceans at 60°C to 80°C. The environment of the last universal common ancestor has been estimated to be more temperate (around 20°C), suggesting an adaptation to high temperatures [Bousseau et al., 2008] possibly in response either to a change in the climate of the early Earth, or to the strong impacts during the LHB. Yet these trends do not necessarily correspond to the climate of the Archean Earth, but maybe just reflect the environment where life was thriving. To avoid glaciation and allow such temperate or hot climates, the early Earth must have experienced warming processes.
1.2 Solutions to the Faint Young Sun Problem
 A different atmospheric composition with a larger amount of greenhouse gases was first proposed as the key to get a habitable Earth under a fainter Sun. The first studies examined ammonia (NH3) [Sagan and Mullen, 1972], a strong greenhouse gas. However, ammonia would have had a short lifetime (less than 40 years) due to photolysis in the high atmosphere. It would therefore not have been present in sufficient amounts unless there was a large, permanent surface source [Kuhn and Atreya, 1979]. Yet such a permanent source would have produced so much N2 (compared to present inventory) by photolysis of ammonia that it could not happen.
 Current thinking is that the early Earth had a CO2- and CH4-rich atmosphere. The amount of CO2 in the atmosphere is controlled by the carbonate-silicate cycle [Walker et al., 1981], which acts as a thermostat on the climate, preserving Earth from a full glaciation by injecting CO2 from volcanoes in the atmosphere. CO2 may have reached large amounts during the early Earth, although the maximum is not well known (between 0.1 and 10 bars [Walker, 1985; Sleep and Zahnle, 2001]). According to 1-D models [von Paris et al., 2008; Pavlov et al., 2000], with a 20% weaker Sun, ∼0.03 bar of CO2 is required to raise the temperature above the frost point and ∼0.2 bar to get present-day temperatures. However, geochemical data from paleosols constrain the maximum partial pressure of CO2 to around 0.02 bar for the end of the Archean [Rye et al., 1995; Sheldon, 2006; Driese et al., 2011; Feulner, 2012], 10 times lower than what is required to get a temperate climate. A stronger constraint of 0.9 mbar of CO2 has been obtained [Rosing et al., 2010] based on the coexistence of siderite and magnetite in Archean-banded iron formations. However, this contradicts other measurements [Hessler et al., 2004; Sheldon, 2006; Driese et al., 2011] and is currently debated [Reinhard and Planavsky, 2011].
 Methane has been suggested as an important complement to CO2 to warm the early Earth [Kiehl and Dickinson, 1987]. It can absorb thermal radiation at 7–8 μm, thus at the edge of the atmospheric window (8–12 μm), where CO2 cannot. It can therefore produce an efficient warming. In an anoxic atmosphere, the lifetime of methane is 1000 times higher than today [Zahnle, 1986; Kasting and Howard, 2006]. During the Archean, methane would have been released by methanogenic bacteria through the reaction:
where H2 comes from hydrothermal sources and volcanoes, or from the primitive atmosphere [Tian et al., 2005].
 With the present-day biological flux, the Archean atmosphere would contain around 3 mbar of methane [Kasting and Howard, 2006]. Based on the biological flux and the escape rate of hydrogen, the amount of methane is estimated to be on the order of 1 mbar during the Archean, with a plausible range between 0.1 mbar and 35 mbar [Kharecha et al., 2005]. However, the time when methanogens appeared and diversified is still highly uncertain. Attempts to determine this time have been made using genomic evolution models [Battistuzzi et al., 2004; House et al., 2003] but the resulting times range from the beginning to the end of the Archean.
 Before methanogens appeared or when they were confined to hydrothermal vents, methane was present in the atmosphere but in lower amounts. Tian et al.  estimate around 0.5–5×10−3 mbar of methane for the prebiotic atmosphere, based on emanations from the Lost City hydrothermal vent field studied by Kelley et al. .
 If the mixing ratio of methane is large, an organic haze forms. This is expected to happen when the CH4/CO2 ratio becomes higher than 0.1–0.3 according to photochemical models and experimental data [Zerkle et al., 2012; Trainer et al., 2006]. In addition to limiting the amount of methane, the formation of haze could produce an anti-greenhouse effect [McKay et al., 1991; Haqq-Misra et al., 2008; Kasting and Ono, 2006], and hence cool the Earth. The impact of this anti-greenhouse effect on surface temperature is unknown, mostly because the fractal nature of haze particles is unconstrained. Fractal particles produce a limited anti-greenhouse effect, compared to spherical particles. Moreover, they act as a UV shield, like the ozone layer, protecting both life and photolytically unstable reduced gases [Wolf and Toon, 2010]. Under this shielding, ammonia may have been maintained in sufficient amount to solve the faint young Sun problem.
 In any event, measurements of carbon isotopes appear consistent with a methane-rich atmosphere at the end of the Archean with possible episodic formation of haze [Zerkle et al., 2012]. According to the 1-D model of Haqq-Misra et al. , which includes haze formation, 1 mbar of methane in an atmosphere containing 20 mbar of CO2 allows to reach present-day temperatures at the end of the Archean. However, an ice-free Earth cannot be maintained with only a CO2-CH4 greenhouse warming consistent with the geological constraints for CO2.
 Given the difficulties in reconciling the warm temperatures estimated for the Archean with geological constraints for CO2, other mechanisms of warming than greenhouse gases have been explored. Clouds both warm the surface by absorbing and reemitting infrared radiation and cool it by reflecting sunlight in the visible. Through these mechanisms, lower clouds tend to globally cool the Earth, while higher clouds tend to warm it. A negative feedback, increasing the amount of cirrus (higher clouds), was considered to keep the climate clement, the “Iris hypothesis” [Lindzen et al., 2001; Rondanelli and Lindzen, 2010], but remains controversial [Lin et al., 2002; Goldblatt and Zahnle, 2011b]. A more plausible hypothesis is that lower clouds were optically thinner during the Archean, owing to the lack of cloud condensation nuclei from biological sources, which yields a decrease of the planetary albedo, and hence a warming (∼+10°C) [Rosing et al., 2010].
 The planetary albedo has been suggested to be lower in the Archean because of the reduced surface of emerged continents [Rosing et al., 2010]. It has also been proposed that the pressure was higher in the past, because the equivalent of around 2 bars of nitrogen is present in the Earth's mantle [Goldblatt et al., 2009]. That nitrogen, initially in the atmosphere, should have been incorporated by subduction (probably by biological fixation). Therefore, it is plausible that the partial pressure of nitrogen reached 2 to 3 bars during the Archean. According to 1-D modeling, doubling the amount of present-day atmospheric nitrogen would cause a warming of 4–5°C [Goldblatt et al., 2009]. Besides, hydrogen could have been abundant in the early Earth's atmosphere. The lack of O2 would have led to a cooler exosphere limiting the hydrogen escape. Thus, the balance between hydrogen escape and volcanic outgassing could have maintained a hydrogen mixing ratio of more than 30% [Tian et al., 2005].
 The combination of a hydrogen-rich atmosphere with a higher atmospheric pressure (2 to 3 bars) would produce an important greenhouse effect by collision absorption of H2-N2, sufficient to get present-day temperatures with a limited amount of CO2 [Wordsworth and Pierrehumbert, 2013]. These mechanisms remain to be further explored. They might not be sufficient to solve the faint young Sun problem alone, although they probably played a role in maintaining a clement climate, complementing the greenhouse effect by CO2 and methane.
1.3 Previous Modeling Studies
 Given the paucity of available data for the early Earth, climate modeling is particularly useful to explore and understand the evolution of the atmosphere and the climate. One-dimensional radiative-convective models allow different hypotheses to solve the faint young Sun problem to be tested [Owen et al., 1979; Kasting et al., 1984; Kiehl and Dickinson, 1987; Kasting and Ackerman, 1986; Haqq-Misra et al., 2008; von Paris et al., 2008; Domagal-Goldman et al., 2008; Goldblatt et al., 2009; Rosing et al., 2010]. However, such models calculate the mean surface temperature below a single atmospheric column with averaged solar flux. Clouds are often omitted, or widely fixed (altitude, optical depth, and covering). Furthermore, the transport of energy by the atmosphere and the ocean is not taken into account in 1-D modeling. The continental and oceanic ice formation is not accounted for either. Thus, 1-D radiative-convective models fail to capture both cloud and ice-albedo feedbacks and transport processes, which are fundamental to determine the climate sensitivity under different conditions. Moreover, the lack of clouds in 1-D radiative-convective models can lead to overestimates of the radiative forcing of greenhouse gases [Goldblatt and Zahnle, 2011b].
 The most accurate way to simulate the climate is to use 3-D global climate models (GCMs), including more of the fundamental processes which control climate sensitivity (e.g., clouds, oceanic transport, continental and oceanic sea ice). Studies of the Archean Earth using GCMs are rare. However, preliminary GCM studies showed that the absence of an ozone layer, continent, and a faster rotation rate could modify cloud coverage and hence the surface temperature [Jenkins, 1993; Jenkins et al., 1993; Jenkins, 1995, 1999]. Using a 3-D oceanic model coupled to a parameterized atmospheric model, Kienert et al.  explored the key role of the ice-albedo feedback and found that 0.4 bar of CO2 is required to avoid full glaciation. This illustrates the key role of ice-albedo feedback.
 We describe below the application of a new generic GCM recently developed by our team to Archean climates. The versatility of this model allowed us to explore the climates of the Archean Earth under many conditions discussed in the literature (such as greenhouse gases, atmospheric pressure, and rotation rate). Our goal is to test different warming processes suggested by 1-D models to better constrain the Archean climate and address key questions left unresolved by 1-D models.