# 3D climate simulations of the Archean find that methane has a strong cooling
effect at high concentrations

###### Abstract

Methane is thought to have been an important greenhouse gas during the
Archean, although its potential warming has been found to be limited at high
concentrations due to its high shortwave absorption. We use the Met Office
Unified Model, a general circulation model, to further explore the climatic
effect of different Archean methane concentrations. Surface warming peaks at a
pressure ratio pCH4:pCO2 of approximately 0.1, reaching a maximum of up to 7 K
before significant cooling above this ratio. Equator-to-pole temperature
differences also tend to increase up to pCH4 $\leq 300$ Pa, which is driven by
a difference in radiative forcing at the equator and poles by methane and a
reduction in the latitudinal extend of the Hadley circulation. 3D models are
important to fully capture the cooling effect of methane, due to these impacts
of the circulation.

JGR: Atmospheres

Department of Physics and Astronomy, University of Exeter, Exeter, EX4 4QL, UK
Kapteyn Astronomical Institute, University of Groningen, Landleven 12, 9747 AD
Groningen, The Netherlands Global Systems Institute, University of Exeter,
Exeter, EX4 4QE, UK Department of Mathematics and Statistics, University of
Exeter, Exeter, EX4 4QF, UK Met Office, FitzRoy Road, Exeter, EX1 3PB, UK
Laboratory for Atmospheric and Space Physics, University of Colorado Boulder,
Boulder, CO, USA NASA NExSS Virtual Planetary Laboratory, Seattle, WA, 98195,
USA NASA GSFC Sellers Exoplanet Environments Collaboration

Jake<EMAIL_ADDRESS>
Methane warming peaks at a pCH4:pCO2 ratio of 0.1, with global-mean surface
warming $<$7 K.

Uneven meridional methane radiative forcing and changes to atmospheric
circulation determine the equator-to-pole temperature difference.

3D modelling is important to fully capture methane’s cooling effect for
pCH4:pCO2 ratios greater than 0.1

## Plain Language Summary

The Archean is a period in Earth history spanning approximately 4 to 2.5
billion years ago. During this period oxygen concentrations were much lower
than today, which in turn allowed methane concentrations to be much higher
during the Archean. Methane would have been produced by microbes, and
depending on the exact nature of the ecosystem could have led to a wide range
of atmospheric concentrations. Using a three-dimensional climate model and
with various methane concentrations in the atmosphere we show that the warming
effect of methane first increases and then, at high concentrations, decreases.
This decrease is stronger than those found in previous studies using one-
dimensional (single column) atmosphere models. We find that methane can only
warm the Archean by up to 7 K.

##  1 Introduction

Methane (CH4) is thought to have played an important role as a greenhouse gas
in warming the Archean Earth [Haqq-Misra . (2008), Catling Zahnle (2020)]. The
Archean is the geological eon spanning 4.0–2.5 billion years ago (Ga). The
Archean was believed to be oxygen poor, with oxygen concentrations less than
$3\times 10^{-6}$ of the present atmospheric level (PAL) [BS. Gregory .
(2021)], which allowed reduced gases, such as methane, to accumulate in the
atmosphere [Catling . (2001)]. Here, we look to understand the potential role
of methane, and to a lesser extent carbon dioxide (CO2), on the Archean
climate using a three-dimensional general circulation model (GCM), at various
carbon dioxide concentrations. The use of a GCM further allows an
understanding to be gained of the effect of methane on the global mean climate
and the meridional temperature structure.

The Archean could have supported high methane concentrations at various points
in its history [<]e.g Fig. 5 in¿catling20. A primitive pre-photosynthetic
biosphere would effectively turn reductant (electron donors) from mantle
inputs or oxidation of the crust into reduced organic carbon and ultimately
methane [<]e.g.¿nicholson22. As methane will be photolysed to hydrogen at high
altitude, atmospheric methane levels are then determined by the balance
between surface net reductant (hence methane) input, and hydrogen escape
[Kharecha . (2005), Goldblatt . (2006), Claire . (2006)]. kharecha05 used a
coupled ecosystem-atmosphere model to suggest that the early Archean biosphere
could have sustained methane concentrations between 100 to 35,000 ppm
(equivalent to 10–3,500 Pa in surface partial pressure for a $10^{5}$ Pa
atmosphere). Subsequent evolution of increasingly productive photosynthetic
biospheres and ultimately oxygenic photosynthesis could increase methane
concentrations as they increase the net reductant input via oxidation of
crustal material [<]primarily Fe,¿walker87. This is supported by a depletion
in organic carbon-13 in deep water sediments at 2.7 Ga [Eigenbrode Freeman
(2006)]. After the great oxidation event, the concentration of methane as a
minority gas in an oxic atmosphere will be controlled by the balance between
primarily biological production and photochemistry, where the net biological
flux to the atmosphere will be controlled by ecosystem structure and
biogeochemical cycling hence methane oxidation within the surface environment
[Daines Lenton (2016)].

Updates to the high-resolution transmission molecular absorption database
(HITRAN) have led to work finding that earlier studies have overestimated
methane’s potential to warm the Archean [Byrne Goldblatt (2015)]. Previously,
haqq-misra08 found that methane, ethane and the subsequent formation of longer
chain hydrocarbons can provide significant warming. However, updates to HITRAN
[L. Brown . (2013), Rothman . (2013)] show an increase in the shortwave
absorption by methane that was previously underestimated, leading to a
decrease in tropopause radiative forcing by methane at high concentrations
[<]see discussion in¿byrne14. This was found to lead to the greenhouse effect
of CH4 becoming offset by strong shortwave absorption by methane in the
atmosphere [Byrne Goldblatt (2015)]. Using a 1D radiative convective model
(RCM) byrne15 found that surface warming due to methane is diminished at 100
Pa (0.1% by volume), with shortwave cooling dominating longwave heating above
this. Methane shortwave radiative forcing has also been investigated for the
modern Earth [Etminan . (2016), Collins . (2018), Byrom Shine (2022)]. byrom22
found that methane’s warming of the stratosphere by absorption of shortwave
radiation can enhance methane longwave radiative forcing.

During the Archean, the Sun’s luminosity was 75% to 80% of the present day
value [Gough (1981)]. As discussed in charnay20, as the Sun fuses hydrogen
into helium the mean molecular weight of the Sun’s core increases. The core
then contracts and warms to maintain the balance between the pressure gradient
and gravitational forces. This increases the rate of fusion, which causes the
Solar flux to increase with time. Under present atmospheric conditions the
Earth is predicted to have been globally ice covered (known as a snowball
state) prior to $\sim$2.0 Ga [Kasting Catling (2003)]. However, there is ample
evidence that the Earth was not in a snowball state [<]for example
see¿feulner12,charnay20. This was termed the faint young Sun (FYS) paradox
[Sagan Mullen (1972)], with uncertainty over what kept the early Earth warm.
The resolution of the FYS paradox is likely to be due to increased greenhouse
gas concentrations during the Archean, particularly carbon dioxide [Charnay .
(2020)] as well as methane.

Geological evidence has been used to predict CO2 concentrations through the
Archean. Mass balance calculations from CO2 dissolved in rainwater give
estimates of CO2 10–50 PAL (340–1,700 Pa) at 2.7 Ga [Sheldon (2006), Driese .
(2011)], although this may be a lower limit [Catling Zahnle (2020)]. Another
method using chemical compositions of paleosols predicts CO2 85-510 PAL
(3,000–15,000 Pa) at 2.77 Ga and 78-2500 PAL (2,000–75,000 bar) at 2.75 Ga
[Kanzaki Murakami (2015)]. A more recent approach using oxidation of
fossilised micrometeorites from 2.7 Ga [Tomkins . (2016)] suggests a lower
limit for atmospheric CO2 of 32$\%$ (32,000 Pa) [Huang . (2021)], although
debate remains over these estimates, with a lower surface pressure offering an
alternative solution to explain the micrometeorite oxidation [Rimmer .
(2019)].

General Circulation Models (GCMs), which are three-dimensional models
attempting to capture the main processes determining the planetary climate,
have played an important role in understanding the climate of the Archean
[Charnay . (2013), Wolf Toon (2013), Kunze . (2014), Le Hir . (2014), Charnay
. (2020)]. GCMs have been used to show that compared to 1D models, lower
amounts of CO2 are required to maintain global surface temperatures of
15$\degree$C, and more importantly, avoid a full glaciation [Charnay . (2013),
Wolf Toon (2013)]. Furthermore, the use of GCMs has found that potential
reductions in land fraction and albedo during the Archean, as well as a
reduction in cloud condensation nuclei may have helped to keep the early Earth
warm [Wolf Toon (2014), Goldblatt . (2021)]. GCMs have also been used to
explore the potential for glaciations at the end of the Archean [Teitler .
(2014)], alongside being combined with models of carbon cycling to investigate
the plausibility of hot Archean climates [Charnay . (2017)].

In this work we extend the 1D work of byrne15 by exploring the 3D effects of
changing the methane concentration using the Met Office Unified Model (UM)
GCM. First we outline the model configurations used for our Archean-like Earth
simulations using the UM in Section 2. The results are presented in Section 3
where we demonstrate that methane has a maximum potential global warming of up
to 7 K. We then go on to show that methane changes the equator-to-pole
temperature differences by changing the meridional circulation and the
radiative forcing at the poles. In Section 4 we discuss the importance of 3D
modelling in understanding the meridional circulation, and the possible impact
haze may have on the results. Finally, we draw conclusions in Section 5 and
highlight future avenues for improving on this study.

##  2 Modelling framework

The UM has been used extensively to study the modern Earth
[<]e.g.¿walters19,sellar19,andrews20,maher22, and has been adapted to simulate
a range of idealised Earth-like planets
[<]e.g.¿mayne14b,boutle17,lewis18,yates20,boutle20,sergeev20,eager20,sergeev22.
Here, we apply this model to the Archean, deep in the Earth’s past. We use the
Global Atmosphere (GA) 7.0 configuration [Walters . (2019)]. Dynamics are
calculated using the ENDGame dynamical core [Wood . (2014)], while convection
is treated using a mass-flux approach based on gregory90. Water clouds are
treated using the prognostic cloud fraction and prognostic condensate scheme
(PC2) [Wilson . (2008)], which incorporates mixed phase microphysics based on
wilson99. Turbulent mixing is based on lock00 and brown08. These schemes are
combined and shown as a schematic in Figure 1. Simulations have a horizontal
resolution of 2.5$\degree$ in longitude by 2$\degree$ in latitude, with 38
vertical levels between the surface ($z=0$ km) and the top-of-atmosphere
($z=40$ km) the same as that of eager20. The vertical levels are quadratically
stretched to enhance the resolution at the surface.

Figure 1: Schematic of the different components of the the model. The GA 7.0
atmospheric configuration consists of the ENDGame dynamical core [Wood .
(2014)], the PC2 scheme to treat clouds [Wilson Ballard (1999), Wilson .
(2008)], microphysics is based on wilson99, SOCRATES to treat radiative
transfer, the Gregory-Rowntree Convection Scheme (GRCS) [D. Gregory Rowntree
(1990)], with turbulent mixing in the planetary boundary layer (PBL) based on
lock00 and brown08. The ocean is treated as a single layer slab of 50m depth
with no horizontal heat transport. Sea ice albedo is treated using Equation 1.

The Suite of Community Radiative Transfer codes based on Edwards and Slingo
(SOCRATES) scheme treats the radiative transfer in the UM, employing the
correlated-k method (included in schematic in Figure 1). Thermal radiation is
treated via 17 bands (between 3.3 $\mu$m-10 mm), while solar radiation is
treated by 43 bands (0.20-20 $\mu$m) using the sp_lw_17_etw_arcc10bar and
sp_sw_43_etw_arcc10bar_sun_2.9gya spectral files respectively. These are
suitable for atmospheres dominated by a mixture of N2 and CO2 (from 1% to
20%), with up to 3.5% CH4 (tested in B), supporting surface pressures up to
106 Pa. These include CO2 sub-Lorentzian line wings and CO2 self-broadening.
Collision induced absorption is included for: N2–CH4, N2–N2 and CO2–CO2 from
HITRAN [Karman . (2019)], and CH4–CO2 from turbet20. Line data are from HITRAN
2012 [Rothman . (2013)], the same as used in byrne15. The solar spectrum is
taken for a 2.9 Ga Sun spectrum from claire12. Testing of our radiative
transfer against higher resolutions for the gas mixtures used here can be
found in B and Figure 16, focusing on the CH4 tropopause radiative forcing.

Methane radiative forcing is calculated at the tropopause. It is the net
downward total “all-sky” radiative flux subtracted by the all-sky flux with
methane switched off radiatively, which is calculated for the present model
configuration without altering the climate state. Similar to the definition
from the wmo57, the tropopause is defined as the region above 500 hPa where
the lapse rate is less than or equal to 2 K/km for at least two consecutive
vertical model levels.

The simulations were configured as an aquaplanet, using a single layer slab
homogeneous flat surface as the inner boundary (planet’s surface), which is
based on frierson06. It represents an ocean surface with a 50 m mixed layer
with a heat capacity of 2.08$\times 10^{8}$ J/K/m2, with no horizontal heat
transport. The emissivity of the surface is fixed at 0.985 [Snyder . (1998)]
and the liquid water surface albedo ($\alpha_{sea}$) is fixed at 0.07 [Jin .
(2004)]. The assumption of an aquaplanet was made with predictions that the
ocean water content may have been larger than today [Dong . (2021)], and
continental coverage was likely lower [Cawood . (2013)]. Although excluding
horizontal heat transport in the ocean is inherently inaccurate, the
uncertainty in continental coverage and location means that the inclusion of a
dynamic ocean will also lead to further inaccuracies that may obfuscate the
effects we are exploring in this work.

Sea ice albedo effect is represented by a change in albedo at 271.35 K
($T_{threshold}$) using the HIRHAM parametrization from liu07, which
calculates a temperature dependent sea ice albedo ($\alpha_{ice}$) as

$\boldsymbol{\alpha_{ice}=\alpha_{max}-\exp{\bigg{(}-\frac{T_{threshold}-T_{surf}}{2}}\bigg{)}\times(\alpha_{max}-\alpha_{sea}),}$
(1)

where $T_{surf}$ is the surface temperature and $\alpha_{max}$ is the maximum
sea ice albedo. A spectrally dependent $\alpha_{max}$ is used following
joshi12, which is independent of the spectral type of the host star. For
spectral bands below 0.5$\mu$m $\alpha_{max}=0.8$, while bands above 0.5$\mu$m
$\alpha_{max}=0.05$. If a bands range contains 0.5$\mu$m the albedo of the
band is a linear weighting of the two components. When convolved with the
solar flux, in practice, our simplified scheme leads to a maximum ice albedo
of approximately 0.2. Although this value is somewhat lower than expected, the
simulations reproduced reasonable ice coverage for the modern Earth (not shown
here). In reality, the scheme setup is compensating for missing heat transport
via the ocean and the lack of a more sophisticated thermodynamic ice scheme,
alongside sea ice transport. Simple non-thermodynamic ice schemes like the
ones used here have been shown to result in larger climate fluctuations and
generally less ice coverage than their thermodynamic counterparts [Poulsen
Jacob (2004)]. Therefore, in our simulations we expect our approach to result
in a smaller ice albedo feedback impact, subsequently making our simulations
more resistant to entering a snowball state. In the future we will continue to
develop the complexity and completeness of our model, but this often comes at
a price of increased difficulty in understanding specific processes.
Therefore, for this work, focused on the radiative impact of methane, we
elected to use the simplified scheme described.

We focus our study on 2.7 Ga as at this time methane concentrations could have
been high, as the evolution of oxygenic photosynthesis may have supported a
widespread productive biosphere [<]indicated by depletion of organic carbon-13
in marine sediments,¿eigenbrode06,daines16. This increase in biotic oxygen
production is prevented from oxidising the atmosphere by burial of oxidants in
the highly insoluble form of iron oxides whilst reductant was added to the
atmosphere as methane through recycling of organic carbon [Walker (1987)].
Hence, there is a net oxidation of the Earth’s surface and net reductant input
into the atmosphere. Planetary parameters used in our simulations are
presented in Table 1. The fainter Sun at 2.7 Ga meant that the solar constant
was less than the present day. From gough81 (their Equation 1), we can
estimate this to be 81$\%$ of the modern solar constant, $S_{0}$, of 1361 W/m2
[Kopp . (2016)].

At 2.7 Ga the Earth’s rotation rate was believed to be faster than the present
Earth. williams00 predict that the rotational period at 2.45 Ga could have
been between 16.0 and 19.4 hrs, while bartlett16 (from their Figure 5) suggest
a range of between approximately 16.0 to 19.5 hrs at 2.7 Ga depending on the
magnitude of the lunar torque at the time. In this study we use the value of
17 hrs, although the exact value over this range has a minimal impact on the
overall results presented here. For simplicity, the modern obliquity (see
Table 1) is used as it is unclear how obliquity could be significantly
different to the present day, however, following the choices made by
charnay13,wolf14, we set the eccentricity to zero.

In these simulations, we vary the methane partial pressures from 1 to 3,500 Pa
to cover the range predicted by kharecha05, as well as extending the lower
limit in line with byrne15, to include potential methane concentrations from
only abiotic sources, pCH4$\approx$1 Pa [Kasting (2005)]. We also include a
baseline case, without methane, as a comparison for our simulations with
varying atmospheric methane concentrations. We vary the initialised CO2
surface partial pressure from 100 to 3,000 Pa covering some of the large
variation in paleosol constraints (340–75,000 Pa) and use the lower value of
100 Pa to match byrne15. We vary pCO2 to cover a range of predicted CO2
abundances at the time, from 100–3,000 Pa. For pCO2=10,000 Pa our simulations
were significantly warmer than the modern day Earth and the UM becomes
unstable for the higher methane concentrations. Therefore, we omitted these
cases from our study and used pCO2$\leq$3,000 Pa as the upper limit.

These surface partial pressures are the values initialised in the model, while
the total surface pressure, and thus individual partial pressures, can evolve
from the initialised value. However, the equivalent volume mixing ratios have
no spatial or temporal variation. The reason for the choice in using partial
pressures is to ensure that the mass of N2 and CO2 is kept constant with
variations in CH4 abundance. This is to replicate methane production by the
biosphere, adding methane to the atmosphere. Surface pressures range from
1-1.035$\times 10^{5}$ Pa, which aligns with the upper limit of surface
pressures from som12, as well as using similar conditions to byrne15.

Fixed gas mixing profiles are used in these simulations, with no chemistry
included. This assumption is validated by 1D photochemical models, which show
that the volume mixing ratio remains relatively constant up to 40 km (top of
model in our simulations) for carbon dioxide [<]e.g.¿huang21 and methane
[<]e.g.¿kharecha05,gregory21 at low oxygen concentrations.

Table 1: The planetary and orbital parameters used for all planetary configurations, based on a 2.7 Ga Earth. Stellar irradiance is calculated using gough81, based on a modern day solar constant $S_{0}=1361$ W/m2 [Kopp . (2016)]. Rotation rate is based on estimates from williams00 and bartlett16. Partial pressures represent the values initialised in the model at the surface.  Parameter | 2.7 Ga Archean Earth
---|---
Stellar irradiance (W/m2) | 1100.8 (0.809$S_{0}$)
Day length (hours) | 17.0
Eccentricity | 0
Obliquity ($\degree$) | 23.44
pCO2 (Pa) | 100, 300, 1000, 3,000
pCH4 (Pa) | 0, 1, 3, 10, 30, 100, 300, 1000, 3,500
pN2+pCO2 (Pa) | 100,000
Surface pressure | pN2+pCO2+pCH4

Initial simulations with no CH4 ran for 60 years to allow for atmospheric
equilibrium to be reached. Subsequent runs with CH4 present were initialised
from these simulations and ran for another 50 years to reach a new steady
state. All the simulations were in steady state by the final 15 years, so we
use this period for our analysis. Steady state was deemed to have been reached
when the top of atmosphere radiative flux was in balance and the mean global
surface temperature was near constant. In this work, we refer to equatorial
and polar regions. The equatorial region is considered as spanning latitudes
of 10° S to 10° N, while the polar regions are 70° S/N to the pole, which are
averaged over these regions in figures henceforth. UM output was processed and
plotted using Python’s iris [Met Office (2010-2020)], aelous [Sergeev
Zamyatina (2022)] and Matplotlib [Hunter (2007)] packages.

##  3 Results

In this section we demonstrate that methane has a maximum potential warming of
up to 7 K globally in our Archean-like simulations. Furthermore, we find that
the equator-to-pole temperature difference generally increases with pCH4,
which is driven by the difference in methane radiative forcing at the equator
and poles and also the decrease in circulation strength driven by upper
troposphere heating by methane shortwave absorption.

Figure 2: (a) shows the global average net down radiative forcing at the
tropopause for methane for shortwave (dashed), longwave (dotted) and their sum
(solid). (b) and (c) show the same as (a) averaged over 10$\degree$S to
10$\degree$N as the equator in (b), and poleward of 70$\degree$N/S for the
polar regions in (c).

Methane radiative forcing plays an important role in driving the climate. This
is shown for all of our simulations in Figure 2. Figure 2a shows the global
tropopause radiative forcing by methane. As pCH4 is increased, initially total
radiative forcing increases due to an increase in longwave radiative forcing
(dotted lines in Figure 2a) causing surface temperature to increase. As pCH4
continues to increase, shortwave radiative forcing becomes more negative
(dashed lines in Figure 2a) caused by absorption of shortwave radiation, which
becomes comparable to the magnitude of longwave radiative forcing and causes
methane’s total radiative forcing to decrease again, driving a cooling of the
surface. Similar to the results found in byrne14, the shortwave absorption
becomes significant for pCH4$>$10 Pa, with the total (longwave plus shortwave)
methane radiative forcing similarly having a maximum of approximately 8.5
W/m2, compared to 9 W/m2 in byrne14.

Figure 2b,c show the methane radiative forcing for equatorial and polar
regions respectively. Equatorial forcing exhibits similar trends to the global
average, while polar radiative forcing is of a lower magnitude, with total
radiative forcing peaking at smaller pCH4 compared to the equatorial and
global regions. Shortwave forcing is weaker at the poles for pCO2$=$3000 Pa
compared to the other pCO2 values, while longwave forcing is stronger, leading
to methane radiaitve forcing at the poles plateauing at pCH4$\geq$1000 Pa.

The effects of this change in radiative forcing by methane are now explored
for these different cases by examining the difference in climate between these
configurations.

###  3.1 Meridional air temperature variation and the Hadley circulation

Figure 3: Zonal averaged air temperature (colour scale), for increasing
surface partial pressures of carbon dioxide from left to right, and methane
from top to bottom. The right hand column shows the difference in air
temperature between pCO2$=$100 Pa and pCO2$=$3,000 Pa (the left and middle
columns). The bottom row shows the change in air temperature between the
pCH4$=$1 Pa and pCH4$=$3,500 Pa case for a given pCO2. In both of these cases
a positive increase represents an increase in air temperature for the
simulation with higher pCH4/pCO2. Plotted as latitude vs $\sigma$, where
$\sigma$ is the pressure divided by the surface pressure. This is for a subset
of the simulations, with the full grid available in A (Figure 11). The same
colour scale is used for the left and middle columns, with maximum and minimum
temperatures for each simulation displayed in the top right of each sub
figure. The right column and bottom row use a another colour scale that is
constant between the subplots. These subplots also displays the
maximum/minimum temperature differences in the top right of each sub figure.

Increasing pCO2 in our Archean-like configuration leads to a familiar result
in increasing temperatures globally [<]e.g.¿charnay13. Figure 3 shows a subset
of our simulations and reveals that increasing pCO2 from 100 Pa to 3,000 Pa
(comparing left and middle columns) at any pCH4 leads to the zonal mean air
temperatures rising globally in the troposphere, with the polar regions
warming more than equatorial regions, shown by the right hand column of Figure
3, which shows the increase in air temperature from pCO2$=$100 Pa to
pCO2$=$3,000 Pa. Minimum temperatures decrease due to the stratosphere cooling
with increasing pCO2 due to more efficient cooling of the atmosphere.

Increasing surface pCH4 from 1 Pa to 3,500 Pa, leads to a smaller change in
troposphere air temperatures compared to changing pCO2, but large increases in
stratospheric temperature. Figure 3 shows that increasing pCH4 initially leads
to troposphere warming, which peaks between pCH4 values of 30–300 Pa and
increasing pCH4 further leads to cooling of the troposphere at lower pCO2 and
plateauing at higher pCO2 (see bottom row of Figure 3), which is driven by
changes the methane radiative forcing (Figure 2a). Increasing pCH4 also leads
to a warming of the stratosphere, and the formation of a stratospheric
temperature inversion, visible at pCH4$\geq$300 Pa at pCO2$=$100 Pa and
pCH4$=$3,500 Pa at pCO2$=$3,000 Pa in Figure 3. The magnitude of the warming
can by seen in bottom row of Figure 3, which shows the change in air
temperature between pCH4$=$1 Pa and pCH4$=$3,500 Pa with the stratosphere
warmer by up to 87 K at pCH4$=$3,500 Pa and pCO2$=$100 Pa. This warming of the
stratosphere is caused by the increase in shortwave heating of the upper
atmosphere caused by methane (shown by the contours in Figure 4). These
changes in air temperature show similar trends to those presented in byrne15.
Horizontally averaged pressure-temperature plots for the equator and poles are
shown in Figure 14.

The Hadley circulation strength is shown in Figure 4 in the form of meridional
stream functions. The shorter rotational period of the planet used here (17
hour day compared to 24 hour) leads to the Hadley circulation having a reduced
latitudinal depth, however there remains only three circulating cells.
Additional cells are only expected to form at shorter rotational periods
[Kaspi Showman (2015)].

The latitudinal and vertical extent of the Hadley circulation increases when
increasing pCO2 as shown in Figure 4 (see Figure 12 for full grid of
simulations). Increasing pCO2 (left to right) leads to a stronger and deeper
Hadley circulation, due to more efficient cooling of the upper tropopause and
increasing surface temperatures increasing specific humidity. This is shown by
the Hadley cells highlighted by the stream function intensifying, extending in
latitudinal breadth and increasing the range of pressures they cover as pCO2
is increased.

Increasing pCH4 leads to a decrease in the latitudinal and vertical extent of
the Hadley circulation, due to methane’s shortwave heating of the upper
troposphere for pCO2 $<$ 3000 Pa, while at pCO2 $=$ 3000 Pa the Hadley cell
extent remains similar. For pCO2 $=$ 100 Pa, Figure 4 shows that at lower
values of pCH4 shortwave heating (black contour lines) predominantly takes
place in the lower troposphere, while at higher pCH4 the shortwave heating is
largest in the upper troposphere. This is caused by high pCH4 values
increasing the shortwave absorption of the atmosphere. This results in the
upper troposphere being more stable against convection at higher pCH4, and
reduces the tropopause height and subsequently the depth and strength of the
Hadley circulation (also see lapse rates for a low pCO2 and high pCH4 case and
a high pCO2 and low pCH4 in Figure 15). For pCO2 $=$ 3000 Pa, efficient
cooling of the upper troposphere by CO2 counteracts methane heating in the
stratosphere and upper troposphere (compare warming due to methane in the
bottom two panels of Figure 3), allowing the vertical extent of the Hadley
circulation to remain similar for all pCH4 values.

Figure 4: Zonal averaged meridional stream functions (colour scale), for
increasing surface partial pressures of carbon dioxide from left to right, and
methane from top to bottom, in the same format as Figure 3, with the full grid
available in A (Figure 12). Positive and negative values represent clockwise
and anticlockwise circulation respectively. Contours show the heating of the
atmosphere due to shortwave radiation in K/day. The same colour scale is used
for each plot, with maximum values for the stream function (SF) and shortwave
heating rate (SW) are shown for each simulation in the bottom right of each
sub figure.

###  3.2 The global effect of methane on climate

Figure 5: (a) shows the global mean surface temperature with respect to the
carbon dioxide concentration and assuming pCH4 is zero, with (b) showing the
subsequent change in global mean surface temperature due to the addition of
pCH4 (positive indicates warming). Colours of markers in (a) correspond to the
same pCO2 in (b). Similar plots for near surface specific humidity are shown
in Figure 13. (c) show the global average atmospheric absorption of shortwave
radiation by methane (dashed) and water vapour (dotted) and their sum (solid).
(d) shows the specific humidity in the stratosphere at $\sigma=0.1$. (e) and
(f) shows the fractional contribution of atmospheric (dashed), surface
(dotted) and total (atmospheric plus surface) to the shortwave radiation
budget global mean for shortwave absorption (e) and solar-weighted albedo (f).
These were calculated using donohoe11, which accounted for atmospheric
attenuation of shortwave radiation reflected by the surface.

We now focus on the global effects of changing pCH4 and pCO2. In this section
we demonstrate that methane has a maximum warming potential on the global mean
surface temperature of less than 7 K for pCO2$\leq$3,000 Pa for our 2.7 Ga
Archean-like aquaplanet configuration (see Figure 5b). We compare these
results to those of byrne15 who used a 1D RCM and find that our GCM
simulations predict a stronger cooling effect at high methane concentrations.

The global mean surface temperature increase, caused by the addition of
methane, is less than 7 K. Figure 5a shows the mean surface temperature for
our simulated atmospheres without methane, i.e. N2 and CO2 only with pCH4=0,
to act as a baseline for simulations where pCH4$>$0\. The subsequent
temperature change from increasing pCH4 is shown in Figure 5b. For our
simulations the contribution of methane to the greenhouse effect peaks between
pCH4 values of 30 to 300 Pa, with peak global mean warming ranging from
approximately 3.5 K to nearly 7 K as shown in Figure 5b. The location and
magnitude of the peak in global mean surface temperature is dependent on pCO2,
with the peak occurring at higher pCH4 and a larger maximum temperature as
pCO2 is increased. Past the peak, increasing pCH4 leads to the global mean
surface temperature decreasing, for which the decrease is largest for the
lowest pCO2, with some simulations for pCO2 $\leq$ 1000 Pa globally cooler
than the simulation with no methane at all (below grey dotted line in Figure
5b), with global mean surface temperature dropping by up to approximately 8 K
at pCH4$=3500$ Pa compared to the maximum methane warming at constant pCO2
(Figure 5b). This peaked response is caused by the balance between methane’s
longwave warming effect and its shortwave cooling effect, as discussed in
byrne15 and presented here in Figure 2a.

Conversely, at the higher pCO2 amount of 3,000 Pa, the decrease in surface
temperature caused by pCH4=3,500 Pa is minimal. From Figure 5c, it can be seen
that the total water vapour and methane shortwave absorption increases less as
pCH4 increases for pCO2$=$3,000 Pa compared to lower values of pCO2. This is
because the warmer climate at pCO2$=$3,000 Pa allows for more water vapour in
the atmosphere, which reduces the methane shortwave absorption due to overlap
in their absorption cross sections in the shortwave. At higher pCO2, the
stratosphere becomes more resistant to the emergence of a stratospheric
temperature inversion (see byrne15, Figure 3 and Figure 14), and at
pCO2$=$3,000 Pa, a cold trap only forms much deeper in the atmosphere (see
Figure 14). This allows water vapour to reach higher abundances higher in the
atmosphere, with stratospheric water vapour increasing significantly with pCH4
for the pCO2$=$3,000 Pa case only, shown in Figure 5d. This increase in
stratospheric water vapour also acts to enhance the greenhouse effect, and
leads to only a marginal drop in the global mean surface temperature for
pCO2$=$3,000 Pa in Figure 5b.

Use of a 3D GCM leads to a more significant global cooling at high pCH4 (see
Figure 5b) compared to results from a 1D RCM. pCO2=100 Pa and pCO2=1000 Pa
offer the most comparable configurations to byrne15, who used CO2 abundances
of 10-3 and 10-2. For a CO2 abundance of 10-2, byrne15 found a plateau in
methane’s greenhouse warming with surface temperature remaining constant up to
a CH4 abundance of 10-2 from 10-3, compared to a $\approx$3 K drop in average
surface temperature from the peak at pCH4=100 Pa for pCO2=1000 Pa at pCH4=1000
Pa (temperature difference for green line between pCH4=100 Pa to pCH4=1000 Pa
in Figure 5b). Similarly for a CO2 abundance of 10-3, there is a cooling from
the peak of $\approx$1 K in the 1D model compared to $\approx$5.5 K for
pCO2=100 Pa in our 3D model (temperature difference for orange line between
pCH4=30 Pa to pCH4=1000 Pa in Figure 5b). This increases to $\approx$8 K when
pCH4=3500 Pa, however methane was not investigated at such levels in byrne15.
These are caused, in part, by the presence of a 3D atmospheric circulation in
the GCM, with methane affecting the meridional temperature gradient and Hadley
circulation (see Section 3.3).

The addition of methane increases atmospheric shortwave absorption (Figure 5c)
in the upper atmosphere and leads to a reduction in planetary albedo. Figure
5e shows this increase in atmospheric absorption of shortwave radiation with
pCH4. This leads to a decrease in surface shortwave absorption and a reduction
in total albedo, shown in Figure 5f. As discussed in Section 3.1 as pCH4
increases, shortwave heating transitions from predominantly heating the lower
troposphere to heating the stratosphere and upper troposphere. This is caused
by the increase in shortwave absorption higher in the atmosphere. This is
summarised in the schematic in Figure 6.

The increase in shortwave absorption by methane higher in the atmosphere leads
to a reduction in the water vapour shortwave absorption, shown in Figure 5c.
This is due to spectral overlap between the absorption cross-sections of water
vapour and methane in the shortwave [<]see Figure 6 in¿byrne14. Increasing
pCH4 leads to an increase in shortwave radiation absorption high in the
atmosphere by methane, where specific humidity is lower in concentration
compared to lower in the troposphere (see Figure 14). However, the relative
contributions to shortwave absorption by methane and water vapour also depends
on the temperature, with warmer simulations having a higher specific humidity,
leading to shortwave absorption higher in the atmosphere. This explains the
greater rates of shortwave heating in the troposphere in Figure 4 for
pCO2=3,000 Pa (compared to pCO2=100 Pa), which is significantly warmer than
the other simulations. As a result, these simulations have less shortwave
heating by methane at a given pCH4 (compare magenta and orange dashed lines in
Figure 5c).

Figure 6: Schematic showing how methane affects the vertical distribution of
shortwave radiation in the atmosphere for a low (left) and high (right)
methane case. Shortwave radiation is represented by yellow arrows. A thinning
of the arrow represents a loss of shortwave radiation through absorption in
the atmosphere. Upward shortwave radiation represents reflected shortwave
radiation from the surface and atmosphere. The tropopause is marked by a
dashed line, and for simplicity is placed at the same level in these diagrams.

###  3.3 The effect of methane on equator-to-pole temperature gradients

Although the global impacts of methane within our 3D GCM simulations
qualitatively match the trends identified in byrne15, differences are apparent
between the 1D and 3D results. In this section we describe the impacts of
changing meridional transport across our simulations, which cannot be captured
in 1D models. We find that the equator-to-pole temperature difference tends to
increase with pCH4 initially due to an increase in methane radiative forcing
at the equator relative to the poles. As pCH4 increases further, equator-to-
pole temperature differences plateau due to an increase in radiative forcing
at the poles and a decrease in efficiency in meridional heat transport.

Figure 7: (a) shows the average equator-to-pole temperature difference with
only carbon dioxide (pCH4=0), with (b) showing the subsequent increase in
equator-to-pole temperature difference due to the addition of methane
(positive indicates an increase in the equator-to-pole temperature
difference). (c) shows the atmospheric heat flux out of the equatorial region
for different pCO2 with pCH4=0 (referred to as baseline cases), while (d)
shows the increase in the equatorial heat flux from the subsequent addition of
methane to (c). (e) shows the atmospheric heat flux into the polar regions for
different pCO2 (with pCH4=0), while (f) shows the increase in the polar heat
flux from the subsequent addition of methane to (e). Calculations for (c)-(f)
use methods from lambert11 to calculate atmospheric heat fluxes (see C for
more detail). The equatorial region is considered as spanning latitudes of 10°
S to 10° N, while the polar regions are 70° S/N to the pole. Colours of data
points in (a), (c) and (d) correspond to the same pCO2 in (b), (d) and (f).

The equator-to-pole temperature gradient reduces with increasing pCO2,
demonstrated in Figure 7a. This is due to an increase in the atmospheric
temperature which increases the moist static energy transport [Kaspi Showman
(2015)]. The meridional stream functions also increases in latitudinal and
vertical extent, as shown in Figure 4. However, the meridional temperature
gradient’s response to methane is more complex.

Figure 7b shows the increase in equator-to-pole temperature difference as a
result of the addition of methane to the simulations. From Figure 7b we find
that increasing pCH4 generally causes an increase in equator-to-pole
temperature differences for pCH4$\leq$300 Pa, above this the equator-to-pole
temperature difference either begins to plateau or decreases. The exact change
is dependent on the pCO2, with the behaviour more extreme for lower pCO2, but
the general trends remain. As well as this the main drivers for the meridional
temperature gradients are methane’s varying meridional radiative forcing
(Figure 2b,c) and the effect on the meridional heat transport.

Figure 8a shows that for pCO2$\leq$1000 Pa increasing pCH4 initially leads to
an increase in the relative CH4 tropopause forcing at the equator compared to
the pole, which drives an increase in the equator to pole temperature
difference. This suggests, that for pCH4$\leq$300 Pa, the equator-to-pole
temperature difference in Figure 7b is driven by the differences in CH4
radiative forcing.

The plateau that emerges in the equator-to-pole temerature differences in
Figure 7b as pCH4 increases above 300 Pa, can be explained by a balance
between a weakening of the meridional heat transport and an increase in
methane radiative forcing at the poles relative to the equator. For
pCO2$\leq$1000 Pa, as pCH4 increases above 100 Pa, the difference in the
equator-to-pole radiative forcing decreases in Figure 8a, with polar forcing
approaching equality to the equatorial radiative forcing and eventually
exceeding it at pCH4$=$3500 Pa. However the change in equator-to-pole
temperature differences over this period shows only a small (order of 2 K
between 300-3500 Pa) generally increasing trend compared to the large increase
in the relative methane radiative forcing between the equator and pole (Figure
8a), which would work to decrease the equator-to-pole temperature difference.
The minimal change in the equator-to-pole temperature difference is caused by
a reduction in the meridional heat transport, which offsets the increase in
methane radiative forcing at the poles relative to the equator. Meridional
heat transport weakens due to a reduction in the latitudinal extent of the
Hadley circulation (Figure 4) and a reduction in global mean surface
temperature compared to the peak in Figure 5b, which would act to increase
equator-to-pole temperature differences (see Figure 8b). This balance
maintains a relatively small change in equator-to-pole temperature differences
for pCH4$\geq$300 Pa in Figure 7b.

At pCO2=3,000 Pa, the equator-to-pole temperature difference change is smaller
compared to the other case, changing by $\approx$6 K in total from pCH4$=$1 Pa
to pCH4$=$3,500 Pa. This is partly due to the latitudinal extent of the Hadley
circulation in Figure 4 remaining similar at pCO2=3,000 Pa, which may be more
important in controlling equator-to-pole temperature difference compared to
the change in radiative forcing between the equator and poles. For
pCH4$\leq$30 Pa and pCO2=3,000 Pa relative radiative forcing between the
equator and poles remains constant (Figure 8a). At pCO2=3,000 Pa for pCH4$>$30
Pa equatorial forcing increases relative to the poles, with the equator-to-
pole temperature difference increasing. The reduction in temperature
difference between pCH4=1,000 Pa and pCH4=3,500 Pa may be partially driven by
larger methane radiative forcing at the poles compared to the equator at
pCH4$=$3,500 Pa.

Figure 8: (a) Shows the equator-to-pole temperature difference against the
difference in equatorial and polar net downward pCH4 tropopause radiative
forcing (positive indicates an increase in radiative forcing at the equator
relative to the poles). (b) shows the global mean surface temperature against
the equator-to-pole temperature difference. The equatorial region is
considered as spanning latitudes of 10° S to 10° N, while the polar regions
are 70° S/N to the pole. pCH4 is represented through the size of the marker
(larger maker equivalent to a higher pCH4) for pCH4 values of
$\\{1,3,10,30,100,300,1000,3500\\}$ Pa.

A reduction in the meridional heat transport with increasing pCH4 above 30 Pa
contributes towards an increase in the equator-to-pole temperature gradient.
As discussed in Section 3.1 the Hadley circulation reduces in vertical and
latitudinal extent when increasing pCH4 (see Figure 4). The effect this has on
the atmospheric heat transport for the equatorial and polar regions is shown
in Figures 7c-f. We used the net flux difference between the surface and top
of atmosphere to estimate the flux transported horizontally into a region, as
described in lambert11 (see C for more detail), and shown for our simulations
in Figures 7c-f. The change in heat flux out of the equator is relatively
small compared to the poles, with changes on order of less than 5$\%$ due to
changes in methane (by comparing Figure 7c and Figure 7d). Figure 7f shows
that as pCH4 increases, there is an initial increase in heat flux into the
poles, which peaks at pCH4$\approx$30 Pa, potentially a result of the warmer
global temperatures increasing the energy transported into the poles through
moisture. Above pCH4$\approx$30 Pa heat flux into poles reduces again, which
is expected from the weakening circulation in Figure 4, and a corresponding
sharp decrease in polar heat flux can be seen with a corresponding sharp rise
in the equator-to-pole temperature difference (shown in Figure 7b). The
equator-to-pole temperature difference’s response to increasing pCH4 is also
dependent on pCO2, as shown in Figure 7b.

Figure 9: Shows the temperature contrast between the surface and atmosphere at
$\sigma$=0.2 horizontally averaged over the polar regions. The poles span from
70° N/S to the pole. $\sigma$=0.2 is used to approximate the tropopause
height.

The enhanced longwave forcing by methane at higher pCO2 values in Figure 2 is
due to an increasing temperature contrast between the surface and upper
troposphere. Figure 9 shows this change in temperature contrast for the polar
regions. The temperature contrast increases with pCO2, leading to the
increased longwave forcing seen in Figure 2a-c. In contrast, methane acts to
warm the stratosphere and upper troposphere by absorbing solar radiation and
thus increasing methane decreases the temperature contrast, shown in Figure 9.

Figure 10: (a) shows the global average net down cloud radiative effect at
$\sigma$=0.2 (approximate location of the tropopause) where $\sigma$ is the
pressure divided by the global mean surface pressure. Cloud radiative effect
is shown for shortwave (dashed), longwave (dotted) and their sum (solid). (b)
and (c) show the same as (a) averaged over 10$\degree$S to 10$\degree$N as the
equator in (b), and poleward of 70$\degree$N/S for the polar regions in (c).

For this study clouds play only a secondary effect, and are not, therefore,
discussed in detail. Figure 10 shows the cloud radiative effect at the
tropopause, and although the magnitude of the change in longwave and shortwave
cloud radiative effect vary the total cloud radiative effect remains nearly
constant. Cloud fractions horizontally averaged pressure-temperature plots for
the equator and poles are shown in Figure 14. We are currently working on a
more in-depth study of the impacts of clouds over this parameter space.

##  4 Discussion

GCMs provide useful insight into the role of methane in the Archean climate,
both validating effects found in RCMs and also finding important differences
that come from 3D modelling. The initial global warming due to methane is
similar between both models, with the models diverging when predicting
temperatures for pCH4:pCO2 $>$ 0.1. In this range GCMs predict large
temperature drops, particularly for cooler, lower CO2 configurations, with
temperatures dropping by up to 8 K from the peak temperature.

GCMs are also useful in their ability to investigate the meridional heat
distribution, where methane plays three important roles. 1) Differences in
equator-to-pole methane radiative forcing: equator dominated for pCH4:pCO2 $<$
0.1, and transitioning to polar dominated above this. 2) Hadley circulation
weakens when increasing pCH4, which reduces meridional heat transport. 3)
Atmospheric temperatures affect the moisture held in the atmosphere, so the
peaking in temperature at pCH4:pCO2 $=$ 0.1 leads to increases in meridional
heat transport below this and decreasing heat transport above this when
increasing pCH4. It may be possible to replicate this in a 2 column model
(equatorial and polar column) by parameterising these three factors.

Our study supports that the FYS paradox can be resolved based on pCO2
constraints around 2.7 Ga. Global mean surface temperatures close to the pre-
industrial Earth, can be achieved with pCO2$=$3000 Pa and pCH4$=$0 Pa and
pCO2$=$1000 Pa and pCH4$\approx$100 Pa (Figure 5a,b). The first of these falls
within the range of pCO2 values constrained by kanzaki15 from 2.75 Ga, while
the latter composition falls within the constraint of driese11 at 2.7 Ga. The
addition of methane to pCO2$=$3000 Pa up to pCH4$=$3500 Pa would lead to
global mean surface temperatures up to 7 K warmer than the pre-industrial
Earth, while increasing or decreasing methane from the pCO2$=$1000 Pa and
pCH4$\approx$100 Pa configuration would lead to global mean temperatures
decreasing. For pCO2$=$300 Pa and pCO2$=$100 Pa, global mean temperatures
could reach up to 278 and 274 K respectively, with optimal methane abundances.
In our simulations, these remain ice free, with wolf13 finding that these
concentrations of CO2 with some CH4 also avoid being fully glaciated, with at
least 50% of the surface remaining ice free. Higher pCO2 values than 3000 Pa
are not necessary for surface pressures around 105 Pa, but could be important
to warm the Archean Earth if the total surface pressure was lower.

Some studies have suggested that surface pressures may have been lower than
the present day. Fossil raindrops have been used to approximate surface
pressure at 2.7 Ga to between 5$\times 10^{4}$ to 1.1$\times 10^{5}$ Pa [Som .
(2012)], although debate remains over the upper limit of this constraint
[Kavanagh Goldblatt (2015)]. Furthermore, fossilised gas bubbles in lava flows
at 2.74 Ga predict a surface pressure of 2.3$\pm$2.3$\times 10^{4}$ Pa [Som .
(2016)]. The understanding of the effect of methane on the climate at
different pressures is thus very important for the Archean, to be considered
in future studies.

Methane has a secondary impact on the climate through its importance in the
formation of hydrocarbon hazes, and it is suggested that there may have been
periods during the Archean where a haze layer was present [Domagal-Goldman .
(2008), Izon . (2015)]. Haze forms when the CH4:CO2 ratio exceeds
approximately 0.1 [Trainer . (2006)], and potentially has a cooling effect on
climate by up to 20 K [Arney . (2016)]. arney16 found that a thick haze was
produced for pCH4:pCO2$>$0.2. For 0.1$<$pCH4:pCO2$<$0.2 a thin haze is
produced that is spectrally indistinguishable from an atmosphere with no haze
[Arney . (2016)]. The peak surface temperature in our experiments were found
to occur around pCH4/pCO2$>$0.1 so we expect this peak to remain with the
presence of haze, and for pCH4/pCO2$>$0.2 hazes form and accelerate cooling
further. Although we intend to study hazes in future work, with global mean
surface temperatures for a given pCO2 tending to peak around
pCH4=0.1$\times$pCO2, higher methane concentrations are not able to increases
global mean surface temperatures further, even without considering the effects
of haze.

byrom22 and collins18 found that surface albedo can affect the shortwave
radiative forcing, with higher albedos at wavelengths where methane absorbs
strongly leading to an increase in absorption of upward radiation leading to a
positive radiative forcing, which can arise from high albedo on land surfaces
such as deserts [Byrom Shine (2022)]. Land fraction remains uncertain for the
Archean [<]see discussion in¿charnay20, with a general consensus that the
fraction of continental crust was less than present day [Hawkesworth .
(2019)], as well as the potential for a larger ocean volume [Dong . (2021)],
with suggestions land fraction could have been as low as 2-3% until 2.5 Ga
[Flament . (2008)]. We test the sensitivity of the tropopause radiative
forcing by increasing global ocean albedo to 0.533 (value for albedo of quartz
sand in near infrared, used in byrom22) and run the model for one time step
and compare the radiative forcings, shown in D. Using this extreme value for
albedo, we find that the shortwave radiative forcing becomes less negative.
However the general trend for radiative forcing remains the same. Thus, for a
surface with higher albedo, we would expect the decline in global mean surface
temperatures to be less at higher methane values. Further exploration is
required to explore the effect of different continent configurations on the
methane radiative forcing and the overall effect on climate, with a spectrally
dependent surface albedo.

Although methane, across the range we have studied, has a relatively small
effect on global mean surface temperatures of –6 to +7 K, its abundance has a
more significant impact on the meridional heat transport, which could affect
the likelihood of the planet entering a snowball state. High methane levels
generally increase the equator-to-pole difference by up to 8 K, which combined
with a realistic ice-albedo feedback could affect the stability of the
temperate state – which in this case refers to a state that is not fully
glaciated. However full understanding of this would require consideration of
ocean heat transport, continental configuration and a thermodynamic treatment
of sea-ice, all of which are beyond the scope of this study, which focuses on
the climate differences stemming from methane’s radiative effect.

Theoretical opacity data that further fill in missing regions of methane’s
shortwave absorption up to 833 nm [Yurchenko Tennyson (2014)] and 746 nm
[Hargreaves . (2020)] have also become available that allows for further
investigation into the significance of methane’s shortwave absorption.
However, line lists for methane covering much of the wavelength region covered
by the Sun’s emission are not yet available, motivating the extension of work
generating line lists to cover this missing absorption data.

Potentially habitable planets have now been detected orbiting M-dwarf stars,
which are cooler than the Sun. For these exoplanets the shortwave absorption
would be stronger due to a larger fraction of the stellar emission coming from
the near infrared, for M-dwarfs compared to G-dwarfs like the Sun, where
methane has strong absorption. The impacts of missing absorption data, as
discussed above, become even more important due to the host star emitting more
radiation at longer wavelengths where absorption from greenhouse gases is
higher [Eager-Nash . (2020)]. If these planets host life, their early
environment may have resembled that of the Archean Earth, given that a
significant fraction of Earth’s own ‘inhabited’ history is represented by this
period [Catling Zahnle (2020)]. Therefore, these planets could have high
concentrations of methane and an even stronger temperature sensitivity to
methane abundance due to the interaction of the host star spectrum and the
methane rich atmosphere.

##  5 Conclusions

We used the Met Office Unified Model to understand the potential effect of
atmospheric CH4 and CO2 on the climate of the Archean at 2.7 Ga. A productive
biosphere could have led to an atmosphere with pCH4 ranging from 10–3,500 Pa
[Kharecha . (2005)]. We found that the greenhouse effect of methane does not
exceed a global average of 7 K for pCO2$\leq$3,000 Pa, with the peak
temperature occurring for pCH4 between 30–300 Pa. This peak in temperature
shifts to higher pCH4 for higher values of pCO2. The peaked effect is due to
methane’s absorption of shortwave radiation in the stratosphere that reduces
heating of the surface, which dominates over the greenhouse effect of methane
at higher pCH4. We confirm results from byrne15 and extend them to 3D
simulations, but also demonstrate that use of a 3D GCM is important to fully
capture cooling of the climate at high methane concentrations, due to changes
in meridional circulation and methane radiative forcing. Maximum temperatures
are reached when the CH4:CO2 is approximately 0.1, below the ratio where
significant cooling occurs due to the presence of haze [Arney . (2016)]. More
work is required to understand the interaction of biogeochemical cycles with
the atmospheric composition and potential haze formation.

## Open Research

The research data supporting this publication are openly available from the
University of Exeter’s institutional repository at:
https://doi.org/10.24378/exe.4347 with CC BY 4.0 [Eager-Nash . (2022)].

##  Appendix A Additional figures

Here, we present results from all of our simulations for cases matching
figures in the main paper, as well as additional figures relating to specific
humidity, clouds and lapse rate. Figure 11 and Figure 12 shows the same
information as Figure 3 and Figure 4 respectively, but for the full grid of
simulations. Figure 13 shows the global mean near surface specific humidity
change for different pCO2 and pCH4 values, similar to Figure 5a,b. Figure 14
show air temperature, specific humidity and cloud area fractions to supplement
data presented in Figure 5, Figure 2 and Figure 9. Figure 15 shows the lapse
rate for a low CO2 and high CH4 case (pCO2=100 Pa, pCH4=3500 Pa) and a high
CO2 and low CH4 case (pCO2=3000 Pa, pCH4=1 Pa).

Figure 11: Zonal averaged air temperature (colour scale), for increasing
surface partial pressures of carbon dioxide from left to right, and methane
from top to bottom. Plotted as latitude vs $\sigma$, where $\sigma$ is the
pressure divided by the global mean surface pressure. The same colour scale is
used for each plot, with maximum and minimum temperatures for each simulation
displayed in the top right of each sub figure.

Figure 12: Zonal averaged meridional stream functions (colour scale), for
increasing surface partial pressures of carbon dioxide from left to right, and
methane from top to bottom. Positive and negative values represent clockwise
and anticlockwise circulation respectively. Contours show the heating of the
atmosphere due to shortwave radiation in K/day. The same colour scale is used
for each plot, with maximum values for the stream function (SF) and shortwave
heating rate (SW) are shown for each simulation in the bottom right of each
sub figure.  Figure 13: Similar to Figure 5 (a) shows the global mean near
surface ($\sigma=1.0$) specific humidity with respect to the carbon dioxide
concentration and assuming pCH4 is zero, with (b) showing the subsequent
change in global mean near surface specific humidity due to the addition of
pCH4 (positive indicates warming). Colours of markers in (a) correspond to the
same pCO2 in (b).

Figure 14: Shows horizontally averaged air temperature (left column), specific
humidity (middle column) and cloud area fraction (right column) for the
equator (solid lines) and poles (dotted lines), for increasing surface partial
pressures of methane from top to bottom. The equator is considered as spanning
latitudes of 10° S to 10° N, while the poles are 70° S/N to the pole.

Figure 15: Shows lapse rate for the global (solid lines), equatorial (dashed
lines) and polar (dotted lines) averages, for pCO2=100 Pa and pCH4=3500 Pa
(purple) and pCO2=3000 Pa and pCH4=1 Pa (green). The equator is considered as
spanning latitudes of 10° S to 10° N, while the poles are 70° S/N to the pole.

##  Appendix B Spectral resolution sensitivity analysis

Figure 16: (a) shows the high resolution minus the low resolution spectral
file global average net down radiative forcing at the tropopause for methane
for shortwave (dashed), longwave (dotted) and their sum (solid). (b) and (c)
show the same as (a) averaged over 10$\degree$S to 10$\degree$N as the equator
in (b), and poleward of 70$\degree$N/S for the polar regions in (c). The high
resolution spectral files for thermal and solar radiation are
sp_lw_350_etw_arcc10bar and sp_sw_280_etw_arcc10bar_sun_2.9gya respectively,
while the low resolution spectral files are sp_lw_17_etw_arcc10bar and
sp_sw_43_etw_arcc10bar_sun_2.9gya for thermal and solar radiation
respectively.

Here, we make comparisons between spectral resolutions used in this study and
a higher resolution spectral file treatment with 280 solar radiation bands
(sp_sw_280_etw_arcc10bar_sun_2.9gya) and 350 thermal radiation bands
(sp_lw_350_etw_arcc10bar) to assess the accuracy of our radiative transfer
calculation. The results of this are shown in Figure 16. Errors in both the
shortwave and longwave forcing remain small compared to the trends observed in
Figure 2, and thus will not affect the overall results.

##  Appendix C Calculations of heat fluxes in polar and equatorial regions

Here, we outline the method used by lambert11 to understand the net heat
transport in and out of regions of the atmosphere. This method was initially
designed for use in understanding heat transport by the atmosphere between
regions of the atmosphere covering land and ocean. Here, we apply this to heat
transport out of equatorial regions and into polar regions, with the heat flux
out of the equatorial region, $\frac{\Delta A_{E}}{f_{E}}$, given as:

$-\frac{\Delta A_{E}}{f_{E}}=\Delta N_{E}-\Delta U_{E}-\Delta U_{EA},$ (2)

where $\Delta A_{E}$ is the heat transport anomaly between the equatorial
region and the rest of the planet. $f_{E}$ is the equatorial fraction of the
global surface (spanning latitudes of 10° S to 10° N, $f_{E}=$17.4%). $\Delta
N_{E}$ is the net incoming radiation at the top-of-atmosphere, while $\Delta
U_{E}$ is the net upward flux at the surface including both turbulent and
radiative fluxes. $\Delta U_{EA}$ is the rate of heat storage by the
atmosphere over the equatorial region, which is approximated by the globally
averaged heat uptake by the atmosphere, $\Delta U_{GA}$:

$\Delta U_{GA}=\Delta N_{G}-\Delta U_{G},$ (3)

where the subscript $G$ refers to the global averaged quantities discussed
above.

Equivalent expressions can be written for heat flux into the rest of the
planet from the equatorial region, as well as the heat flux into the poles and
the heat flux from the rest of the atmosphere into the poles:

$\frac{\Delta A_{E}}{1-f_{E}}=\Delta N_{E^{\prime}}-\Delta
U_{E^{\prime}}-\Delta U_{E^{\prime}A},$ (4)

$\frac{\Delta A_{P}}{f_{P}}=\Delta N_{P}-\Delta U_{P}-\Delta U_{PA},$ (5)

$\frac{\Delta A_{P}}{1-f_{P}}=\Delta N_{P^{\prime}}-\Delta
U_{P^{\prime}}-\Delta U_{P^{\prime}A},$ (6)

where subscript $P$ represents the polar regions, while $E^{\prime}$ and
$P^{\prime}$ are the rest of the world excluding the equatorial and polar
regions respectively.

Figure 17: (a) shows the difference between the heat flux leaving the
equatorial region and the heat flux into the rest of the atmosphere from the
equator from Equation 2 and Equation 4. Similarly (b) shows the difference
between the heat flux entering the polar regions and the heat flux from the
rest of the atmosphere from Equation 5 and Equation 6. The equatorial region
is considered as spanning latitudes of 10° S to 10° N, while the polar regions
are 70° S/N to the pole.

This method can be validated by calculating the difference of the heat flux
between the equatorial/polar regions and the rest of the atmosphere. These are
shown in Figure 17, with the differences more than 1000 times smaller than 1
W/m2, showing the self consistency of the method and that it is suitable for
applying to understanding heat transport between regions of the atmosphere
other than just those over land and sea.

##  Appendix D Methane radiative forcing: albedo dependence

Figure 18: (a) shows the global average net down radiative forcing at the
tropopause for methane for shortwave (dashed), longwave (dotted) and their sum
(solid), for an ocean surface with an albedo of 0.07. (b) and (c) show the
same as (a) averaged over 10$\degree$S to 10$\degree$N as the equator in (b),
and poleward of 70$\degree$N/S for the polar regions in (c). These are
calculated for just one model time step. (d), (e) and (f) shows the same as
(a), (b) and (c) respectively, but for an ocean surface albedo of 0.533. (g),
(h) and (i) show the difference between a), (b) and (c), and (d), (e) and (f),
with a positive value indicating an increase in radiative forcing with the
higher albedo of 0.533.

To compare the effect of surface albedo on methane radiaitve forcing, Figure
18 shows a sensitivity test for two surface albedos of 0.07 (case used in this
study) and 0.533, which represents a high value for albedo produced by sand in
the near infrared. Figure 18 shows methane radiative forcing after running the
model for one additional timestep from the configurations discussed in the
main body of text, hence the slight differences between Figure 2 and Figure
18a-c. As these are calculated with no evolution of the climate state, there
is no change in the longwave radiative forcing between the two cases Figure
18g-i, and the change in shortwave methane radiative forcing is zero at the
pole due to this region being ice and ice albedo remains unchanged.

Increasing ocean albedo causes the shortwave methane radiative forcing to
decrease, however, general trends in radiative forcings discussed in Section 3
remain the same. At high pCH4 global temperatures may increase, leading to a
less pronounced decline in temperatures compared to those found in Figure 5.

###### Acknowledgements.

We would like to thank the three reviewers for their very helpful reviews that
improved the manuscript. We would also like to thank Colin Goldblatt for
providing helpful comments on the manuscript. JE-N would like to thank the
Hill Family Scholarship. The Hill Family Scholarship has been generously
supported by University of Exeter alumnus, and president of the University’s
US Foundation Graham Hill (Economic & Political Development, 1992) and other
donors to the US Foundation. Material produced using Met Office Software. AN,
NM and TL gratefully acknowledge funding from a Leverhulme Trust Research
Project Grant [RPG-2020-82]. SD and TL would to thank the John Templeton
Foundation Grant [62220]. JM and IB acknowledge the support of a Met Office
Academic Partnership secondment. We acknowledge use of the Monsoon2 system, a
collaborative facility supplied under the Joint Weather and Climate Research
Programme, a strategic partnership between the Met Office and the Natural
Environment Research Council. This research made use of the ISCA High
Performance Computing Service at the University of Exeter. This work was
partly supported by a Science and Technology Facilities Council Consolidated
Grant [ST/R000395/1]. This work was also supported by a UKRI Future Leaders
Fellowship [grant number MR/T040866/1]. For the purpose of open access, the
author(s) has applied a Creative Commons Attribution (CC BY) licence to any
Author Accepted Manuscript version arising. We would also like to note the
energy intensive nature of super-computing. We estimate the final production
runs needed for this paper resulted in roughly 4 tCO2e emitted into the
atmosphere.

## References

  * Andrews . (2020) andrews20Andrews, MB., Ridley, JK., Wood, RA., Andrews, T., Blockley, EW., Booth, B.Sutton, RT.  2020\.  Historical Simulations With HadGEM3-GC3.1 for CMIP6 Historical simulations with hadgem3-gc3.1 for cmip6.  Journal of Advances in Modeling Earth Systems126e2019MS001995.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2019MS001995 e2019MS001995 10.1029/2019MS001995  https://doi.org/10.1029/2019MS001995
  * Arney . (2016) arney16Arney, G., Domagal-Goldman, SD., Meadows, VS., Wolf, ET., Schwieterman, E., Charnay, B.Trainer, MG.  2016\.  The Pale Orange Dot: The Spectrum and Habitability of Hazy Archean Earth The pale orange dot: The spectrum and habitability of hazy archean earth.  Astrobiology1611873.
  * Bartlett Stevenson (2016) bartlett16Bartlett, BC. Stevenson, DJ.  2016\.  Analysis of a Precambrian resonance-stabilized day length Analysis of a precambrian resonance-stabilized day length.  Geophysical Research Letters43115716-5724.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2016GL068912 https://doi.org/10.1002/2016GL068912
  * Boutle . (2020) boutle20Boutle, IA., Joshi, M., Lambert, FH., Lyster, D., Manners, J., Mayne, N.others  2020\.  Airborne dust increases the habitability of terrestrial exoplanets. Airborne dust increases the habitability of terrestrial exoplanets.  Accepted for publication in Nature Communications  10.1038/s41467-020-16543-8
  * Boutle . (2017) boutle17Boutle, IA., Mayne, NJ., Drummond, B., Manners, J., Goyal, J., Hugo Lambert, F.Earnshaw, PD.  201705\.  Exploring the climate of Proxima B with the Met Office Unified Model Exploring the climate of Proxima B with the Met Office Unified Model.  Astronomy & Astrophysics601A120.  10.1051/0004-6361/201630020
  * AR. Brown . (2008) brown08Brown, AR., Beare, RJ., Edwards, JM., Lock, AP., Keogh, SJ., Milton, SF. Walters, DN.  2008Jul01.  Upgrades to the Boundary-Layer Scheme in the Met Office Numerical Weather Prediction Model Upgrades to the boundary-layer scheme in the met office numerical weather prediction model.  Boundary-Layer Meteorology1281117–132.  https://doi.org/10.1007/s10546-008-9275-0 10.1007/s10546-008-9275-0
  * L. Brown . (2013) brown13Brown, L., Sung, K., Benner, D., Devi, V., Boudon, V., Gabard, T.Spickler, P.  2013\.  Methane line parameters in the HITRAN2012 database Methane line parameters in the hitran2012 database.  Journal of Quantitative Spectroscopy and Radiative Transfer130201-219.  https://www.sciencedirect.com/science/article/pii/S0022407313002744 HITRAN2012 special issue  https://doi.org/10.1016/j.jqsrt.2013.06.020
  * Byrne Goldblatt (2014) byrne14Byrne, B. Goldblatt, C.  2014\.  Radiative forcings for 28 potential Archean greenhouse gases Radiative forcings for 28 potential archean greenhouse gases.  Climate of the Past1051779–1801.  https://cp.copernicus.org/articles/10/1779/2014/ 10.5194/cp-10-1779-2014
  * Byrne Goldblatt (2015) byrne15Byrne, B. Goldblatt, C.  2015\.  Diminished greenhouse warming from Archean methane due to solar absorption lines Diminished greenhouse warming from archean methane due to solar absorption lines.  Climate of the Past113559–570.  https://cp.copernicus.org/articles/11/559/2015/ 10.5194/cp-11-559-2015
  * Byrom Shine (2022) byrom22Byrom, RE. Shine, KP.  2022\.  Methane’s Solar Radiative Forcing Methane’s solar radiative forcing.  Geophysical Research Lettersn/an/ae2022GL098270.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2022GL098270 e2022GL098270 2022GL098270  https://doi.org/10.1029/2022GL098270
  * Catling Zahnle (2020) catling20Catling, DC. Zahnle, KJ.  2020\.  The Archean atmosphere The archean atmosphere.  Science Advances69.  https://advances.sciencemag.org/content/6/9/eaax1420 10.1126/sciadv.aax1420
  * Catling . (2001) catling01Catling, DC., Zahnle, KJ. McKay, CP.  2001\.  Biogenic Methane, Hydrogen Escape, and the Irreversible Oxidation of Early Earth Biogenic methane, hydrogen escape, and the irreversible oxidation of early earth.  Science2935531839-843.  https://www.science.org/doi/abs/10.1126/science.1061976 10.1126/science.1061976
  * Cawood . (2013) cawood13Cawood, P., Hawkesworth, C. Dhuime, B.  201301\.  The continental record and the generation of continental crust The continental record and the generation of continental crust.  GSA Bulletin1251-214-32.  https://doi.org/10.1130/B30722.1 10.1130/B30722.1
  * Charnay . (2013) charnay13Charnay, B., Forget, F., Wordsworth, R., Leconte, J., Millour, E., Codron, F. Spiga, A.  2013\.  Exploring the faint young Sun problem and the possible climates of the Archean Earth with a 3-D GCM Exploring the faint young sun problem and the possible climates of the archean earth with a 3-d gcm.  Journal of Geophysical Research: Atmospheres1181810,414-10,431.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/jgrd.50808 https://doi.org/10.1002/jgrd.50808
  * Charnay . (2017) charnay17Charnay, B., Le Hir, G., Fluteau, F., Forget, F. Catling, DC.  2017\.  A warm or a cold early Earth? New insights from a 3-D climate-carbon model A warm or a cold early earth? new insights from a 3-d climate-carbon model.  Earth and Planetary Science Letters47497 - 109.  http://www.sciencedirect.com/science/article/pii/S0012821X17303394 https://doi.org/10.1016/j.epsl.2017.06.029
  * Charnay . (2020) charnay20Charnay, B., Wolf, ET., Marty, B. Forget, F.  2020\.  Is the Faint Young Sun Problem for Earth Solved? Is the faint young sun problem for earth solved?  Space Science Reviews216590.  https://doi.org/10.1007/s11214-020-00711-9 10.1007/s11214-020-00711-9
  * Claire . (2006) claire06Claire, MW., Catling, DC. Zanhle, KJ.  2006\.  Biogeochemical modelling of the rise in atmospheric oxygen Biogeochemical modelling of the rise in atmospheric oxygen.  Geobiology44239-269.  https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1472-4669.2006.00084.x https://doi.org/10.1111/j.1472-4669.2006.00084.x
  * Claire . (2012) claire12Claire, MW., Sheets, J., Cohen, M., Ribas, I., Meadows, VS. Catling, DC.  2012sep.  THE EVOLUTION OF SOLAR FLUX FROM 0.1 nm TO 160 $\mu$m: QUANTITATIVE ESTIMATES FOR PLANETARY STUDIES THE EVOLUTION OF SOLAR FLUX FROM 0.1 nm TO 160 $\mu$m: QUANTITATIVE ESTIMATES FOR PLANETARY STUDIES.  The Astrophysical Journal757195.  https://doi.org/10.1088/0004-637x/757/1/95 10.1088/0004-637x/757/1/95
  * Collins . (2018) collins18Collins, WD., Feldman, DR., Kuo, C. Nguyen, NH.  2018\.  Large regional shortwave forcing by anthropogenic methane informed by Jovian observations Large regional shortwave forcing by anthropogenic methane informed by jovian observations.  Science Advances49eaas9593.  https://www.science.org/doi/abs/10.1126/sciadv.aas9593 10.1126/sciadv.aas9593
  * Daines Lenton (2016) daines16Daines, SJ. Lenton, TM.  2016\.  The effect of widespread early aerobic marine ecosystems on methane cycling and the Great Oxidation The effect of widespread early aerobic marine ecosystems on methane cycling and the great oxidation.  Earth and Planetary Science Letters43442-51.  https://www.sciencedirect.com/science/article/pii/S0012821X15007256 https://doi.org/10.1016/j.epsl.2015.11.021
  * Domagal-Goldman . (2008) domagalgoldman08Domagal-Goldman, SD., Kasting, JF., Johnston, DT. Farquhar, J.  2008\.  Organic haze, glaciations and multiple sulfur isotopes in the Mid-Archean Era Organic haze, glaciations and multiple sulfur isotopes in the mid-archean era.  Earth and Planetary Science Letters269129-40.  https://www.sciencedirect.com/science/article/pii/S0012821X08000630 https://doi.org/10.1016/j.epsl.2008.01.040
  * Dong . (2021) dong21Dong, J., Fischer, RA., Stixrude, LP. Lithgow-Bertelloni, CR.  2021\.  Constraining the Volume of Earth’s Early Oceans With a Temperature-Dependent Mantle Water Storage Capacity Model Constraining the volume of earth’s early oceans with a temperature-dependent mantle water storage capacity model.  AGU Advances21e2020AV000323.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2020AV000323 e2020AV000323 2020AV000323  https://doi.org/10.1029/2020AV000323
  * Donohoe Battisti (2011) donohoe11Donohoe, A. Battisti, DS.  201108\.  Atmospheric and Surface Contributions to Planetary Albedo Atmospheric and Surface Contributions to Planetary Albedo.  Journal of Climate24164402-4418.  10.1175/2011JCLI3946.1
  * Driese . (2011) driese11Driese, S., Jirsa, M., Ren, M., Brantley, S., Sheldon, N., Parker, D. Schmitz, M.  201108\.  Neoarchean paleoweathering of tonalite and metabasalt: Implications for reconstructions of 2.69Ga early terrestrial ecosystems and paleoatmospheric chemistry Neoarchean paleoweathering of tonalite and metabasalt: Implications for reconstructions of 2.69ga early terrestrial ecosystems and paleoatmospheric chemistry.  Precambrian Research1891-21–17.  10.1016/j.precamres.2011.04.003
  * Eager-Nash . (2022) eagernash22Eager-Nash, JK., Mayne, NJ., Nicholson, AE., Prins, JE., Young, OCF., Daines, SJ.Lenton, TM.  2022\.  3D climate simulations of the Archean find that methane has a strong cooling effect at high concentrations [dataset] 3d climate simulations of the archean find that methane has a strong cooling effect at high concentrations [dataset].  Open Research Exeter (ORE).  10.24378/exe.4347
  * Eager-Nash . (2020) eager20Eager-Nash, JK., Reichelt, DJ., Mayne, NJ., Hugo Lambert, F., Sergeev, DE., Ridgway, RJ.Kohary, K.  2020\.  Implications of different stellar spectra for the climate of tidally locked Earth-like exoplanets Implications of different stellar spectra for the climate of tidally locked earth-like exoplanets.  A&A639A99.  https://doi.org/10.1051/0004-6361/202038089 10.1051/0004-6361/202038089
  * Eigenbrode Freeman (2006) eigenbrode06Eigenbrode, JL. Freeman, KH.  2006\.  Late Archean rise of aerobic microbial ecosystems Late archean rise of aerobic microbial ecosystems.  Proceedings of the National Academy of Sciences1034315759–15764.  https://www.pnas.org/content/103/43/15759 10.1073/pnas.0607540103
  * Etminan . (2016) etminan16Etminan, M., Myhre, G., Highwood, EJ. Shine, KP.  2016\.  Radiative forcing of carbon dioxide, methane, and nitrous oxide: A significant revision of the methane radiative forcing Radiative forcing of carbon dioxide, methane, and nitrous oxide: A significant revision of the methane radiative forcing.  Geophysical Research Letters432412,614-12,623.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2016GL071930 https://doi.org/10.1002/2016GL071930
  * Feulner (2012) feulner12Feulner, G.  2012\.  The faint young Sun problem The faint young sun problem.  Reviews of Geophysics502.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2011RG000375 https://doi.org/10.1029/2011RG000375
  * Flament . (2008) flament08Flament, N., Coltice, N. Rey, PF.  2008\.  A case for late-Archaean continental emergence from thermal evolution models and hypsometry A case for late-archaean continental emergence from thermal evolution models and hypsometry.  Earth and Planetary Science Letters2753326-336.  https://www.sciencedirect.com/science/article/pii/S0012821X08005748 https://doi.org/10.1016/j.epsl.2008.08.029
  * Frierson . (2006) frierson06Frierson, DMW., Held, IM. Zurita-Gotor, P.  2006\.  A Gray-Radiation Aquaplanet Moist GCM. Part I: Static Stability and Eddy Scale A gray-radiation aquaplanet moist gcm. part i: Static stability and eddy scale.  Journal of the Atmospheric Sciences63102548.
  * Goldblatt . (2006) goldblatt06Goldblatt, C., Lenton, TM. Watson, AJ.  2006\.  Bistability of atmospheric oxygen and the Great Oxidation Bistability of atmospheric oxygen and the great oxidation.  Nature4437112683–686.  https://doi.org/10.1038/nature05169 10.1038/nature05169
  * Goldblatt . (2021) goldblatt20Goldblatt, C., McDonald, VL. McCusker, KE.  2021\.  Earth’s long-term climate stabilized by clouds Earth’s long-term climate stabilized by clouds.  Nature Geoscience143143–150.  https://doi.org/10.1038/s41561-021-00691-7 10.1038/s41561-021-00691-7
  * Gough (1981) gough81Gough, DO.  1981\.  Solar interior structure and luminosity variations Solar interior structure and luminosity variations.  Solar Physics74121–34.  https://doi.org/10.1007/BF00151270 10.1007/BF00151270
  * BS. Gregory . (2021) gregory21Gregory, BS., Claire, MW. Rugheimer, S.  2021\.  Photochemical modelling of atmospheric oxygen levels confirms two stable states Photochemical modelling of atmospheric oxygen levels confirms two stable states.  Earth and Planetary Science Letters561116818.  https://www.sciencedirect.com/science/article/pii/S0012821X21000777 https://doi.org/10.1016/j.epsl.2021.116818
  * D. Gregory Rowntree (1990) gregory90Gregory, D. Rowntree, PR.  1990\.  A Mass Flux Convection Scheme with Representation of Cloud Ensemble Characteristics and Stability-Dependent Closure A mass flux convection scheme with representation of cloud ensemble characteristics and stability-dependent closure.  Monthly Weather Review11871483.
  * Haqq-Misra . (2008) haqq-misra08Haqq-Misra, JD., Domagal-Goldman, SD., Kasting, PJ. Kasting, JF.  2008\.  A Revised, Hazy Methane Greenhouse for the Archean Earth A revised, hazy methane greenhouse for the archean earth.  Astrobiology861127-1137.  https://doi.org/10.1089/ast.2007.0197 PMID: 19093801  10.1089/ast.2007.0197
  * Hargreaves . (2020) hargreaves20Hargreaves, RJ., Gordon, IE., Rey, M., Nikitin, AV., Tyuterev, VG., Kochanov, RV. Rothman, LS.  2020apr.  An Accurate, Extensive, and Practical Line List of Methane for the HITEMP Database An accurate, extensive, and practical line list of methane for the HITEMP database.  The Astrophysical Journal247255.  https://doi.org/10.3847/1538-4365/ab7a1a 10.3847/1538-4365/ab7a1a
  * Hawkesworth . (2019) hawkesworth19Hawkesworth, C., Cawood, PA. Dhuime, B.  2019\.  Rates of generation and growth of the continental crust Rates of generation and growth of the continental crust.  Geoscience Frontiers101165-173.  https://www.sciencedirect.com/science/article/pii/S1674987118300501 https://doi.org/10.1016/j.gsf.2018.02.004
  * Huang . (2021) huang21Huang, G., Eager, J., Mayne, N., Cui, D., Manners, J., Hebrard, E.Lenton, T.  2021\.  CO2 and O2 oxidized 2.7 Ga micrometeorites in two stages suggesting a $>$32% CO2 atmosphere CO2 and O2 oxidized 2.7 Ga micrometeorites in two stages suggesting a $>$32% CO2 atmosphere.  Precambrian Research366106423.  https://www.sciencedirect.com/science/article/pii/S030192682100351X https://doi.org/10.1016/j.precamres.2021.106423
  * Hunter (2007) matplotlibHunter, JD.  2007\.  Matplotlib: A 2D graphics environment Matplotlib: A 2d graphics environment.  Computing in Science & Engineering9390–95.  10.1109/MCSE.2007.55
  * Izon . (2015) izon15Izon, G., Zerkle, AL., Zhelezinskaia, I., Farquhar, J., Newton, RJ., Poulton, SW.Claire, MW.  2015\.  Multiple oscillations in Neoarchaean atmospheric chemistry Multiple oscillations in neoarchaean atmospheric chemistry.  Earth and Planetary Science Letters431264-273.  https://www.sciencedirect.com/science/article/pii/S0012821X15005853 https://doi.org/10.1016/j.epsl.2015.09.018
  * Jin . (2004) jin04Jin, Z., Charlock, TP., Smith Jr., WL. Rutledge, K.  2004\.  A parameterization of ocean surface albedo A parameterization of ocean surface albedo.  Geophysical Research Letters3122.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2004GL021180 https://doi.org/10.1029/2004GL021180
  * Joshi Haberle (2012) joshi12Joshi, MM. Haberle, RM.  2012\.  Suppression of the Water Ice and Snow Albedo Feedback on Planets Orbiting Red Dwarf Stars and the Subsequent Widening of the Habitable Zone Suppression of the water ice and snow albedo feedback on planets orbiting red dwarf stars and the subsequent widening of the habitable zone.  Astrobiology1213-8.  https://doi.org/10.1089/ast.2011.0668 PMID: 22181553  10.1089/ast.2011.0668
  * Kanzaki Murakami (2015) kanzaki15Kanzaki, Y. Murakami, T.  201506\.  Estimates of atmospheric CO2 in the Neoarchean-Paleoproterozoic from paleosols Estimates of atmospheric CO2 in the Neoarchean-Paleoproterozoic from paleosols.  Geochimica et Cosmochimica Acta159190-219.  10.1016/j.gca.2015.03.011
  * Karman . (2019) karman19Karman, T., Gordon, IE., van der Avoird, A., Baranov, YI., Boulet, C., Drouin, BJ.van der Zande, WJ.  2019\.  Update of the HITRAN collision-induced absorption section Update of the hitran collision-induced absorption section.  Icarus328160-175.  https://www.sciencedirect.com/science/article/pii/S0019103518306997 https://doi.org/10.1016/j.icarus.2019.02.034
  * Kaspi Showman (2015) Kaspi15Kaspi, Y. Showman, AP.  2015\.  Atmospheric Dynamics of Terrestrial Exoplanets over a Wide Range of Orbital and Atmospheric Parameters Atmospheric dynamics of terrestrial exoplanets over a wide range of orbital and atmospheric parameters.  The Astrophysical Journal8041.
  * Kasting (2005) kasting05Kasting, JF.  2005\.  Methane and climate during the Precambrian era Methane and climate during the precambrian era.  Precambrian Research1373119-129.  https://www.sciencedirect.com/science/article/pii/S030192680500032X Stable Isotopes, Life and Early Earth History  https://doi.org/10.1016/j.precamres.2005.03.002
  * Kasting Catling (2003) kasting03Kasting, JF. Catling, D.  2003\.  Evolution of a Habitable Planet Evolution of a habitable planet.  Annual Review of Astronomy and Astrophysics411429-463.  https://doi.org/10.1146/annurev.astro.41.071601.170049 10.1146/annurev.astro.41.071601.170049
  * Kavanagh Goldblatt (2015) kavanagh15Kavanagh, L. Goldblatt, C.  2015\.  Using raindrops to constrain past atmospheric density Using raindrops to constrain past atmospheric density.  Earth and Planetary Science Letters41351-58.  https://www.sciencedirect.com/science/article/pii/S0012821X14007936 https://doi.org/10.1016/j.epsl.2014.12.032
  * Kharecha . (2005) kharecha05Kharecha, P., Kasting, J. Siefert, J.  2005\.  A coupled atmosphere–ecosystem model of the early Archean Earth A coupled atmosphere–ecosystem model of the early archean earth.  Geobiology3253-76.  https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1472-4669.2005.00049.x https://doi.org/10.1111/j.1472-4669.2005.00049.x
  * Kopp . (2016) kopp11Kopp, G., Krivova, N., Wu, CJ. Lean, J.  2016\.  The Impact of the Revised Sunspot Record on Solar Irradiance Reconstructions The impact of the revised sunspot record on solar irradiance reconstructions.  Solar Physics29192951–2965.  https://doi.org/10.1007/s11207-016-0853-x 10.1007/s11207-016-0853-x
  * Kunze . (2014) kunze14Kunze, M., Godolt, M., Langematz, U., Grenfell, J., Hamann-Reinus, A. Rauer, H.  2014\.  Investigating the early Earth faint young Sun problem with a general circulation model Investigating the early earth faint young sun problem with a general circulation model.  Planetary and Space Science9877-92.  https://www.sciencedirect.com/science/article/pii/S0032063313002389 Planetary evolution and life  https://doi.org/10.1016/j.pss.2013.09.011
  * Lambert . (2011) lambert11Lambert, FH., Webb, MJ. Joshi, MM.  2011\.  The Relationship between Land–Ocean Surface Temperature Contrast and Radiative Forcing The relationship between land–ocean surface temperature contrast and radiative forcing.  Journal of Climate24133239 - 3256.  https://journals.ametsoc.org/view/journals/clim/24/13/2011jcli3893.1.xml 10.1175/2011JCLI3893.1
  * Le Hir . (2014) lehir14Le Hir, G., Teitler, Y., Fluteau, F., Donnadieu, Y. Philippot, P.  2014\.  The faint young Sun problem revisited with a 3-D climate–carbon model – Part 1 The faint young sun problem revisited with a 3-d climate–carbon model – part 1.  Climate of the Past102697–713.  https://cp.copernicus.org/articles/10/697/2014/ 10.5194/cp-10-697-2014
  * Lewis . (2018) lewis18Lewis, NT., Lambert, FH., Boutle, IA., Mayne, NJ., Manners, J. Acreman, DM.  201802\.  The Influence of a Substellar Continent on the Climate of a Tidally Locked Exoplanet The Influence of a Substellar Continent on the Climate of a Tidally Locked Exoplanet.  Astrophysical Journal854171.  10.3847/1538-4357/aaad0a
  * Liu . (2007) liu07Liu, J., Zhang, Z., Inoue, J. Horton, RM.  2007\.  Evaluation of snow/ice albedo parameterizations and their impacts on sea ice simulations Evaluation of snow/ice albedo parameterizations and their impacts on sea ice simulations.  International Journal of Climatology27181-91.  https://rmets.onlinelibrary.wiley.com/doi/abs/10.1002/joc.1373 https://doi.org/10.1002/joc.1373
  * Lock . (2000) lock00Lock, AP., Brown, AR., Bush, MR., Martin, GM. Smith, RNB.  2000\.  A New Boundary Layer Mixing Scheme. Part I: Scheme Description and Single-Column Model Tests A new boundary layer mixing scheme. part i: Scheme description and single-column model tests.  Monthly Weather Review1289.
  * Maher Earnshaw (2022) maher22Maher, P. Earnshaw, P.  2022\.  The Flexible Modelling Framework for the Met Office Unified Model (Flex-UM, using UM 12.0 release) The flexible modelling framework for the met office unified model (flex-um, using um 12.0 release).  Geoscientific Model Development1531177–1194.  https://gmd.copernicus.org/articles/15/1177/2022/ 10.5194/gmd-15-1177-2022
  * Mayne . (2014) mayne14bMayne, NJ., Baraffe, I., Acreman, DM., Smith, C., Wood, N., Amundsen, DS.Jackson, DR.  201412\.  Using the UM dynamical cores to reproduce idealised 3-D flows Using the UM dynamical cores to reproduce idealised 3-D flows.  Geoscientific Model Development73059-3087.  10.5194/gmd-7-3059-2014
  * Met Office (2010-2020) irisMet Office.  2010-20201.  Iris: A Python library for analysing and visualising meteorological and oceanographic data sets Iris: A Python library for analysing and visualising meteorological and oceanographic data sets (v2.4 ).  Exeter, Devon.  http://scitools.org.uk/
  * Nicholson . (2022) nicholson22Nicholson, AE., Daines, SJ., Mayne, NJ., Eager-Nash, JK., Lenton, TM. Kohary, K.  202207\.  Predicting biosignatures for nutrient-limited biospheres Predicting biosignatures for nutrient-limited biospheres.  Monthly Notices of the Royal Astronomical Society5171222-239.  https://doi.org/10.1093/mnras/stac2086 10.1093/mnras/stac2086
  * Poulsen Jacob (2004) poulsen04Poulsen, CJ. Jacob, RL.  2004\.  Factors that inhibit snowball Earth simulation Factors that inhibit snowball earth simulation.  Paleoceanography194.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2004PA001056 https://doi.org/10.1029/2004PA001056
  * Rimmer . (2019) rimmer19Rimmer, PB., Shorttle, O. Rugheimer, S.  2019\.  Oxidised micrometeorites as evidence for low atmospheric pressure on the early Earth Oxidised micrometeorites as evidence for low atmospheric pressure on the early earth.  Geochemical perspectives letters938–42.  https://pubmed.ncbi.nlm.nih.gov/31187073 10.7185/geochemlet.1903
  * Rothman . (2013) rothman13Rothman, L., Gordon, I., Babikov, Y., Barbe, A., Chris Benner, D., Bernath, P.Wagner, G.  2013\.  The HITRAN2012 molecular spectroscopic database The hitran2012 molecular spectroscopic database.  Journal of Quantitative Spectroscopy and Radiative Transfer1304-50.  https://www.sciencedirect.com/science/article/pii/S0022407313002859 HITRAN2012 special issue  https://doi.org/10.1016/j.jqsrt.2013.07.002
  * Sagan Mullen (1972) sagan72Sagan, C. Mullen, G.  1972\.  Earth and Mars: Evolution of Atmospheres and Surface Temperatures Earth and Mars: Evolution of Atmospheres and Surface Temperatures.  Science177.
  * Sellar . (2019) sellar19Sellar, AA., Jones, CG., Mulcahy, JP., Tang, Y., Yool, A., Wiltshire, A.Zerroukat, M.  2019\.  UKESM1: Description and Evaluation of the U.K. Earth System Model Ukesm1: Description and evaluation of the u.k. earth system model.  Journal of Advances in Modeling Earth Systems11124513-4558.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2019MS001739 https://doi.org/10.1029/2019MS001739
  * Sergeev . (2021) sergeev22Sergeev, DE., Fauchez, TJ., Turbet, M., Boutle, IA., Tsigaridis, K., Way, MJ.Mayne, NJ.  2021\.  The TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI). Part II: Moist Cases – The Two Waterworlds. The trappist-1 habitable atmosphere intercomparison (thai). part ii: Moist cases – the two waterworlds.  arXiv.  https://arxiv.org/abs/2109.11459 10.48550/ARXIV.2109.11459
  * Sergeev . (2020) sergeev20Sergeev, DE., Lambert, FH., Mayne, NJ., Boutle, IA., Manners, J. Kohary, K.  2020may.  Atmospheric Convection Plays a Key Role in the Climate of Tidally Locked Terrestrial Exoplanets: Insights from High-resolution Simulations Atmospheric convection plays a key role in the climate of tidally locked terrestrial exoplanets: Insights from high-resolution simulations.  Astrophysical Journal894284.  https://doi.org/10.3847\%2F1538-4357\%2Fab8882 10.3847/1538-4357/ab8882
  * Sergeev Zamyatina (2022) aeolusSergeev, DE. Zamyatina, M.  202204\.  aeolus. aeolus.  Zenodo.  https://doi.org/10.5281/zenodo.6478085 10.5281/zenodo.6478085
  * Sheldon (2006) sheldon06Sheldon, ND.  2006\.  Precambrian paleosols and atmospheric CO2 levels Precambrian paleosols and atmospheric co2 levels.  Precambrian Research1471148-155.  https://www.sciencedirect.com/science/article/pii/S0301926806000581 https://doi.org/10.1016/j.precamres.2006.02.004
  * Snyder . (1998) snyder98Snyder, WC., Wan, Z., Zhang, Y. Feng, YZ.  1998\.  Classification-based emissivity for land surface temperature measurement from space Classification-based emissivity for land surface temperature measurement from space.  International Journal of Remote Sensing19142753-2774.  https://doi.org/10.1080/014311698214497 10.1080/014311698214497
  * Som . (2016) som16Som, SM., Buick, R., Hagadorn, JW., Blake, TS., Perreault, JM., Harnmeijer, JP. Catling, DC.  2016\.  Earth’s air pressure 2.7 billion years ago constrained to less than half of modern levels Earth’s air pressure 2.7 billion years ago constrained to less than half of modern levels.  Nature Geoscience96448–451.  https://doi.org/10.1038/ngeo2713 10.1038/ngeo2713
  * Som . (2012) som12Som, SM., Catling, DC., Harnmeijer, JP., Polivka, PM. Buick, R.  2012\.  Air density 2.7 billion years ago limited to less than twice modern levels by fossil raindrop imprints Air density 2.7 billion years ago limited to less than twice modern levels by fossil raindrop imprints.  Nature4847394359–362.  https://doi.org/10.1038/nature10890 10.1038/nature10890
  * Teitler . (2014) teitler14Teitler, Y., Le Hir, G., Fluteau, F., Philippot, P. Donnadieu, Y.  2014\.  Investigating the Paleoproterozoic glaciations with 3-D climate modeling Investigating the paleoproterozoic glaciations with 3-d climate modeling.  Earth and Planetary Science Letters39571-80.  https://www.sciencedirect.com/science/article/pii/S0012821X14001964 https://doi.org/10.1016/j.epsl.2014.03.044
  * Tomkins . (2016) tomkins16Tomkins, AG., Bowlt, L., Genge, M., Wilson, SA., Brand, HEA. Wykes, JL.  2016\.  Ancient micrometeorites suggestive of an oxygen-rich Archaean upper atmosphere Ancient micrometeorites suggestive of an oxygen-rich archaean upper atmosphere.  Nature5337602235–238.  https://doi.org/10.1038/nature17678 10.1038/nature17678
  * Trainer . (2006) trainer06Trainer, MG., Pavlov, AA., DeWitt, HL., Jimenez, JL., McKay, CP., Toon, OB. Tolbert, MA.  2006\.  Organic haze on Titan and the early Earth Organic haze on titan and the early earth.  Proceedings of the National Academy of Sciences1034818035-18042.  https://www.pnas.org/doi/abs/10.1073/pnas.0608561103 10.1073/pnas.0608561103
  * Turbet . (2020) turbet20Turbet, M., Boulet, C. Karman, T.  2020\.  Measurements and semi-empirical calculations of CO2+CH4 and CO2+H2 collision-induced absorption across a wide range of wavelengths and temperatures. Application for the prediction of early Mars surface temperature Measurements and semi-empirical calculations of co2+ch4 and co2+h2 collision-induced absorption across a wide range of wavelengths and temperatures. application for the prediction of early mars surface temperature.  Icarus346113762.  https://www.sciencedirect.com/science/article/pii/S0019103520301500 https://doi.org/10.1016/j.icarus.2020.113762
  * Walker (1987) walker87Walker, JCG.  1987\.  Was the Archaean biosphere upside down? Was the archaean biosphere upside down?  Nature3296141710–712.  https://doi.org/10.1038/329710a0 10.1038/329710a0
  * Walters . (2019) walters19Walters, D., Baran, AJ., Boutle, I., Brooks, M., Earnshaw, P., Edwards, J.Zerroukat, M.  2019\.  The Met Office Unified Model Global Atmosphere 7.0/7.1 and JULES Global Land 7.0 configurations The met office unified model global atmosphere 7.0/7.1 and jules global land 7.0 configurations.  Geoscientific Model Development1251909–1963.  https://www.geosci-model-dev.net/12/1909/2019/ 10.5194/gmd-12-1909-2019
  * Williams (2000) williams00Williams, GE.  2000\.  Geological constraints on the Precambrian history of Earth’s rotation and the Moon’s orbit Geological constraints on the precambrian history of earth’s rotation and the moon’s orbit.  Reviews of Geophysics38137-59.  https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/1999RG900016 https://doi.org/10.1029/1999RG900016
  * Wilson Ballard (1999) wilson99Wilson, DR. Ballard, SP.  1999\.  A microphysically based precipitation scheme for the UK meteorological office unified model A microphysically based precipitation scheme for the uk meteorological office unified model.  Quarterly Journal of the Royal Meteorological Society1255571607-1636.  https://rmets.onlinelibrary.wiley.com/doi/abs/10.1002/qj.49712555707 10.1002/qj.49712555707
  * Wilson . (2008) wilson08Wilson, DR., Bushell, AC., Kerr-Munslow, AM., Price, JD. Morcrette, CJ.  2008\.  PC2: A prognostic cloud fraction and condensation scheme. I: Scheme description Pc2: A prognostic cloud fraction and condensation scheme. i: Scheme description.  Quarterly Journal of the Royal Meteorological Society1346372093-2107.  https://rmets.onlinelibrary.wiley.com/doi/abs/10.1002/qj.333 10.1002/qj.333
  * Wolf Toon (2013) wolf13Wolf, E. Toon, O.  2013\.  Hospitable Archean Climates Simulated by a General Circulation Model Hospitable archean climates simulated by a general circulation model.  Astrobiology137656-673.  https://doi.org/10.1089/ast.2012.0936 PMID: 23808659  10.1089/ast.2012.0936
  * Wolf Toon (2014) wolf14Wolf, E. Toon, O.  2014\.  Controls on the Archean Climate System Investigated with a Global Climate Model Controls on the archean climate system investigated with a global climate model.  Astrobiology143241-253.  https://doi.org/10.1089/ast.2013.1112 PMID: 24621308  10.1089/ast.2013.1112
  * Wood . (2014) wood14Wood, N., Staniforth, A., White, A., Allen, T., Diamantakis, M., Gross, M.Thuburn, J.  2014\.  An inherently mass-conserving semi-implicit semi-Lagrangian discretization of the deep-atmosphere global non-hydrostatic equations An inherently mass-conserving semi-implicit semi-Lagrangian discretization of the deep-atmosphere global non-hydrostatic equations.  Quarterly Journal of the Royal Meteorological Society1401505.
  * World Meteorological Organisation (1957) wmo57World Meteorological Organisation.  1957\.  Meteorology: a three-dimensional science, second session of the commission for aerology Meteorology: a three-dimensional science, second session of the commission for aerology.  WMO Bulletin64134-138.
  * Yates . (2020) yates20Yates, JS., Palmer, PI., Manners, J., Boutle, I., Kohary, K., Mayne, N. Abraham, L.  202002\.  Ozone chemistry on tidally locked M dwarf planets Ozone chemistry on tidally locked M dwarf planets.  Monthly Notices of the Royal Astronomical Society49221691-1705.  10.1093/mnras/stz3520
  * Yurchenko Tennyson (2014) yurchenko14Yurchenko, SN. Tennyson, J.  201403\.  ExoMol line lists – IV. The rotation–vibration spectrum of methane up to 1500 K ExoMol line lists – IV. The rotation–vibration spectrum of methane up to 1500 K.  Monthly Notices of the Royal Astronomical Society44021649-1661.  https://doi.org/10.1093/mnras/stu326 10.1093/mnras/stu326