# A coupled model of episodic warming, oxidation and geochemical transitions
on early Mars

Robin Wordsworth,1,2 Andrew H. Knoll,3 Joel Hurowitz,4
Mark Baum,2 Bethany L. Ehlmann,5,6 James W. Head,7 Kathryn Steakley,8
1School of Engineering and Applied Sciences, Harvard University, Cambridge MA
02137, USA
2Department of Earth and Planetary Sciences, Harvard University, Cambridge MA
02137, USA
3Department of Organismic and Evolutionary Biology,
Harvard University, Cambridge MA 02137, USA
4Department of Geosciences, Stony Brook University, Stony Brook NY 11794-2100,
USA
5Division of Geological and Planetary Sciences,
California Institute of Technology, Pasadena CA 91125, USA
6NASA Jet Propulsion Laboratory, Pasadena CA 91109, USA
7Department of Earth, Environmental and Planetary Sciences,
Brown University, Providence, RI 02912, USA
8NASA Ames Research Center, Moffett Blvd, Mountain View, CA 94035, USA

Reconciling the geology of Mars with models of atmospheric evolution remains a
major challenge. Martian geology is characterized by past evidence for
episodic surface liquid water, and geochemistry indicating a slow and
intermittent transition from wetter to drier and more oxidizing surface
conditions. Here we present a new model incorporating randomized injection of
reducing greenhouse gases and oxidation due to hydrogen escape, to investigate
the conditions responsible for these diverse observations. We find that Mars
could have transitioned repeatedly from reducing (H2-rich) to oxidizing
(O2-rich) atmospheric conditions in its early history. Our model predicts a
generally cold early Mars, with mean annual temperatures below 240 K. If peak
reducing gas release rates and background CO2 levels are high enough, it
nonetheless exhibits episodic warm intervals sufficient to degrade crater
walls, form valley networks and create other fluvial/lacustrine features. Our
model also predicts transient buildup of atmospheric O2, which can help
explain the occurrence of oxidized mineral species such as manganese oxides at
Gale Crater. We suggest that the apparent Noachian–Hesperian transition from
phyllosilicate deposition to sulfate deposition around 3.5 billion years ago
can be explained as a combined outcome of increasing planetary oxidation,
decreasing groundwater availability and a waning bolide impactor flux, which
dramatically slowed the remobilization and thermochemical destruction of
surface sulfates. Ultimately, rapid and repeated variations in Mars’ early
climate and surface chemistry would have presented both challenges and
opportunities for any emergent microbial life.

Today, Mars is dry, cold and volcanically quiet, with mean surface
temperatures of around 210 K and a thin ($\sim 6$ mbar) CO2-dominated
atmosphere. Extensive geomorphological and geochemical evidence indicates,
however, that in the distant past, surface conditions on Mars were
dramatically different, with enhanced fluvial erosion, aqueous geochemical
alteration and sediment deposition (?, ?). The most plausible explanation for
the aqueous alteration of Mars’ surface is strong greenhouse warming from a
thicker early atmosphere, although details of the warming mechanism continue
to be debated [e.g., (?, ?, ?, ?, ?, ?)]. Geomorphic and geochemical analyses
suggest that in total, between around $10^{4}$ and $10^{7}$ years of warm
conditions were required to erode observed valley networks, deposit sediment
in craters and form Al-/Fe- phyllosilicate weathering sequences (?, ?, ?, ?,
?). In addition, abundant ancient exposures of unaltered igneous minerals such
as olivine and the relative absence of surface carbonates on Mars indicate
that large bodies of surface liquid water were likely not present over periods
much longer than a few million years (?, ?, ?).

The chemistry of the martian surface has also varied over time. Orbital and
rover observations of surface mineralogy indicate extensive phyllosilicate
formation at the Noachian surface and/or in the crust (?) and an increase in
the deposition of sulfates in the Hesperian (?). Martian meteorite data
suggest that much of Mars’ mantle is more reducing than Earth’s (?), and hence
that its early atmosphere was also at least intermittently reducing (?, ?).
Some Mars meteorites also preserve non-zero sulfur mass-independent
fractionation (MIF) signatures, suggesting sulfur deposition during anoxic
atmospheric intervals (?). Today, however, Mars’ surface is highly oxidized,
with abundant ferric iron lending the planet its reddish appearance and
species such as hydrogen peroxide and perchlorates present in the atmosphere
and regolith. Rover observations at both Meridiani Planum and Gale Crater have
also shown strong variability in mineral redox chemistry (?), with oxidizing
surface conditions around the Noachian-Hesperian boundary ca. 3.5 Gya (Figure
1) suggested by the presence of concentrated hematite and manganese oxide (?,
?, ?). The manganese deposits in particular appear to require the simultaneous
presence of liquid water and strong oxidants such as O2 or ultraviolet
radiation (?). Formation of manganese oxide from manganese carbonate via
ultraviolet photo-oxidation may be possible in certain circumstances (?), but
it requires the prior presence of rhodochrosite deposits and has difficulty
explaining manganese oxide formation in sub-surface fracture fills (?).

### A coupled atmospheric evolution and climate model

To investigate how these diverse, apparently contradictory strands of geologic
evidence can be reconciled, we have constructed an integrated atmospheric
evolution and climate model. A key feature of our model is that it is
stochastically forced in a way that captures the episodic nature of the key
processes that altered Mars’ atmosphere in its early history. We represent the
release of reducing gases to the atmosphere due to meteorite impacts (?),
volcanism (?) and crustal alteration (?, ?, ?, ?) in a generalized way by
randomly sampling from a power law distribution, which has probability density
function

$p(x)=Cx^{\gamma},$ (1)

where $x$ is the reducing gas input rate in mol/s defined on the interval
$[x_{0},x_{1}]$ and $\gamma$ is a power-law coefficient (?). We assume a
default value of $\gamma=-1.95$ based on observed meteorite impact and
volcanic outgassing distributions from crater-counting and terrestrial
occurrence data, respectively, but tested the sensitivity of the results to
variations in this parameter (?). $C$ is a normalization constant defined such
that

$\int_{x_{0}}^{x_{1}}p(x)dx=1.$ (2)

In our model, the distribution mean $\mu$ and the maximum input value $x_{1}$
are used to determine the minimum input value $x_{0}$, which in turn
determines $C$ and hence the probability density function $p(x)$ (?). We allow
$\mu$ to decrease slowly with time to represent the secular decay in all input
processes over martian history. Escape of hydrogen and oxygen to space via
diffusion-limited and non-thermal escape processes (?) is also included (Fig.
S1), as is oxidative weathering of the crust. Changes in surface temperature
over time due to greenhouse warming by CO2, H2O and reducing gases are
calculated using a line-by-line radiative-convective model that includes
collision-induced absorption (CIA) effects (?). CO2 evolution through time is
represented by an empirical function constrained by observations and modeling,
although we study model sensitivity to variations in total CO2. To remain
conservative, we take CO2-H2 collision-induced absorption into account using
recent experimental results (?) rather than slightly stronger previous
theoretical estimates (?).

Figure 1 shows the model output for an example run with time mean reducing gas
input $\overline{\mu}=1.5\times 10^{4}$ mol/s and variability ratio
$\beta\equiv x_{1}/\overline{\mu}=10^{3}$. As can be seen, both the
atmospheric redox state (Fig. 1B) and the surface temperature (Fig. 1C) are
highly variable in time, showing rapid and repeated fluctuations between
warmer, more reducing and colder, more oxidizing conditions during Mars’ early
history. The bulk oxidation state of the planet increases monotonically with
time due to non-stochiometric hydrogen escape to space (?), but the atmosphere
undergoes multiple reducing episodes in both the Noachian (reducing around 13%
of the time) and the Hesperian / Amazonian (reducing around 6% of the time)
(see also Figs. S2 and S3). The time-mean temperature is far below the melting
point of liquid water, but the total integrated duration of warm periods is
consistent with the timescale required from geological constraints (Fig. 1D).

Figure 2 summarizes the results of varying both $\overline{\mu}$ and $\beta$,
with additional runs varying other parameters shown in Fig. S4. For each case,
we show the mean and standard deviation of an ensemble of 256 stochastic
simulations. When variability is high, our model produces integrated warm
periods sufficient to match geomorphic observations for mean rates of $4\times
10^{3}$ to about $1\times 10^{5}$ mol/s of hydrogen input. These mean rates
are in the range of upper limits from volcanism ($1.2\times 10^{4}$ mol/s),
although obtaining the extreme levels of episodicity in volcanic activity
required is challenging (?). They are also within the range of bolide impact
upper limits. The impact basins large enough to drive extended warming
episodes alone (e.g. Hellas, Argyre and Isidis) can plausibly explain much of
the Noachian-era fluvial crater degradation (?, ?), although they appear 100
to 500 My older than many valley networks based on crater statistics (?).
Finally, upper limits on H release from crustal alteration ($1.5\times 10^{4}$
mol/s) also match the required constraints, and crustal alteration processes
may have exhibited substantial episodicity via nonlinear aqueous feedbacks and
coupling to impact thermal forcing (?, ?). Additional effects such as warming
from C_nH_n hydrocarbons or cirrus clouds produced following CH4 photolysis
(?), and a higher solar flux due to uncertainties in reported terrain ages and
early solar mass loss are neglected here but would allow the model to match
observations at lower $\beta$ and $\overline{\mu}$ values (?). When the
average model H input flux is low, build-up of O2 in Mars’ atmosphere
continues to the present day, in conflict with observations. Average H input
fluxes above $2\times 10^{6}$ mol/s, which are required for permanently ‘warm
and wet’ early conditions, are not plausible by any known mechanism and
produce permanently reducing surface conditions that are hard to reconcile
with the observed geochemical record.

### Implications for Mars’ sedimentary geochemistry

As well as providing a way to explain many features of Noachian to early
Hesperian fluvial and lacustrine geomorphology, intermittent warming by
reducing gases on a planet whose surface oxidizes over time can help account
for key features of Mars’ aqueous mineralogy. Warming of up to a few million
years total duration is consistent with the formation timescales of
Noachian/Early Hesperian Al/Fe phyllosilicate weathering sequences (?) and the
lack of evidence for open-system, weathering-driven chemical fractionation of
ancient terrains (?). Assuming cold-trapping of H2O on the southern highlands
due to adiabatic cooling (?), episodic warming (with subsequent localized
hydrological activity and evaporation) is also consistent with the formation
of chloride deposits on the Noachian southern highlands (?, ?).

One particularly visible and puzzling feature of martian aqueous mineralogy is
the broad trend from phyllosilicate formation in the Noachian to mainly
evaporite formation, including regional sulfate deposition, in the subsequent
Hesperian (?, ?, ?, ?). Previously, this transition has been interpreted in
terms of a change in the rate or style of volcanic outgassing at the Noachian-
Hesperian boundary (?, ?, ?). While this may have been a contributing factor,
overall there was more volcanic outgassing in the Noachian than in the
Hesperian, and changes in the quantity of S outgassed as a function of
atmospheric pressure and melt composition are relatively modest over plausible
ranges (?). The detected sulfates on Mars probably represent only a fraction
of the sulfur outgassed throughout martian history (?), which suggests that a
larger inventory of S may currently be present near the surface or deeper in
the crust, given Mars’ modest degree of crustal recycling.

We hypothesize that the increase in sulfate deposition from the Noachian into
the Hesperian was directly linked to the secular changes in the planet’s redox
state through time, for three reasons. First, oxidation of the upper martian
mantle due to metamorphism of hydrated crust (?) could potentially have
moderately increased the fraction of S outgassed per unit volume of melt by
the Hesperian (?). Second, under the fluctuating wet-dry climate conditions
driven by intermittent reducing gas fluxes, evaporite formation would have
been ongoing, along with clay formation, throughout the Noachian. However, the
preservation of such deposits against later remobilization would have only
been favored toward the waning stages, from 3.5 Ga onward (?, ?), which is
consistent with the geologic record of chlorides and sulfates (?). Third,
sulfate minerals can be converted to minerals like pyrite when dissolved under
reducing conditions.

As can be seen from Figure 3a, for O2 fugacities below around $10^{-38}$ atm,
pyrite and pyrrhotite are predicted to be the primary precipitating minerals
from an S-rich solution across a wide range of pH conditions. While most
outgassed SO2 and H2S is converted efficiently to atmospheric H2SO4 aerosols
and hence ultimately to surface sulfate deposits even in an H2-rich atmosphere
(?), aqueous thermochemical sulfate reduction (TSR) can proceed slowly in warm
environments and becomes rapid once temperatures exceed $\sim 150^{\circ}$C.
The frequency of large bolide impacts, high geothermal heat flux and relative
abundance of water during the pre- to mid-Noachian means that moderate to high
temperature aqueous environments may have occurred repeatedly in combination
with reducing atmospheric conditions early in martian history (?, ?, ?),
resulting in the repeated dissolution and reduction of early surface sulfate
deposits. Interestingly, TSR of surface-derived sulfates has very recently
been proposed as an explanation for non-zero S-MIF values in the pyrite of
martian meteorite NWA 7533 (?).

In the short-term aftermath of a large impact (timescales of months to years),
hot ejecta causes a thermal wave to propagate downwards into the regolith and
widespread rainfall occurs (?, ?), leading to high-temperature aqueous
chemical alteration on regional to global scales (?, ?, ?, ?, ?). Figure 3b
shows the amount of sulfate minerals on the surface that would have been
thermochemically reduced due to this effect as a function of ejecta layer
depth. Following the largest impactors such as Isidis and Hellas, up to
several hundred meters of the crust over wide regions of the surface could
have undergone rapid sulfate reduction via this effect. Longer term sub-
surface alteration at more moderate temperatures, while hard to quantify in
the Noachian, could have contributed to TSR further. Hydrological and
thermochemical suppression of sulfate preservation until the late Noachian can
therefore help to explain the paucity of evaporite preservation in the
Noachian record.

Finally, redox fluctuations can also help explain the appearance of hematite
and manganese oxide deposits in sediments at Meridiani Planum, and at Gale
Crater, where they are frequently found in combination with more reducing
species (?). Our model predicts intervals of elevated atmospheric oxygen (O2
levels up to around 0.05 bar in our nominal simulations; Fig. 1B) throughout
the Noachian and Hesperian. In these intervals, upper layers of the regolith
would slowly oxidize via dissolution of O2 into lava, dry weathering
reactions, formation of oxychlorine species (?), and adsorption of volatile
species like H2O2. During warming intervals, some of this regolith would have
been transported as sediment to standing bodies of water. The extremely slow
rate of reaction of H2_(aq) with oxidized species like Fe^3+, combined with
photo-oxidation and other processes that produce H2_(aq) by oxidizing Fe^2+ to
Fe^3+ (?, ?), mean these sediments would have remained out of chemical
equilibrium with the atmosphere, plausibly leading to the local formation
within the sediments of oxidized minerals such as hematite over time.

Warming of early Mars on $10^{4}-10^{7}$ year timescales under O2-rich
atmospheric conditions is not currently predicted in state-of-the-art climate
models (?), but if it did occur, it could also have led to the formation of
diagenetic hematite and manganese in Hesperian sediments. In any case, shorter
periods of warming (up to a few years) would still have occurred episodically
when the atmosphere was O2-rich, via the mobilization of surface ice deposits
by redox-neutral bolide impacts (?, ?). This would have provided additional
routes for the formation, transport and deposition of highly oxidizing
minerals. Manganese takes several years to be oxidized by O2 at moderate
($\sim 280-300$ K) temperatures (?); at higher temperatures, however, the rate
increases. Our thermal and kinetic chemical modeling indicates that a few
relatively short episodes of elevated surface temperatures in an oxidizing
atmosphere with $\sim 10^{-2}$ bar O2 are sufficient to cause the oxidation of
manganese, particularly if the aqueous chemistry occurs under conditions where
the water-to-rock ratio is low and the pH is relatively high (Fig. 4). Short
intervals of this kind provide a plausible explanation for the Mn-rich
fracture-filling materials in the Kimberley Formation at Gale Crater (?).

### Model Predictions and Wider Implications

An episodically fluctuating scenario for Mars’ chemical and climate evolution
appears consistent with several key features of the planet’s geological
record. It also predicts formation scenarios for various aqueous minerals that
can be tested further by NASA’s _Perseverance_ rover, by the upcoming European
and Chinese rover missions and, eventually, by investigation of returned
samples on Earth. First, intermittent warming and redox fluctuations imply
multiple erosion episodes of fluvial features like valley networks, rather
than formation during a single long warm interval. Second, if TSR was an
important early sulfate removal process, reduced sulfur minerals with a
petrology consistent with formation at moderate to high temperatures should be
present in some Noachian crustal samples. Third, any model in which long-term
warming requires reducing atmospheric conditions predicts specific formation
pathways for hematites and manganese oxide, which may also be testable via
detailed in-situ analysis of samples. Investigation of the oxidation state and
MIF of sulfur species in terrains of various ages would allow a direct test of
the prediction that O2-rich atmospheric conditions occurred intermittently in
the Hesperian and Amazonian. Finally, because high levels of CO2 and H input
are required in our stochastic model to produce even episodically warm
conditions, continued investigation of additional atmospheric warming effects
by minor species and aerosols and refined constraints on the change in solar
flux over geological time will be valuable.

In the present-day Solar System, the only planet with an oxygen-rich
atmosphere is Earth, which has led to suggestions that oxygen could serve as a
biomarker gas in the hunt for life on exoplanets. However, our model predicts
long-lived (up to $>$100 My), relatively oxygen-rich atmospheres for Mars in
the middle period of its history without requiring the presence of life,
indicating that O2 detection alone can be a ‘false positive’ for life in some
circumstances. Because prebiotic chemistry does not occur in highly oxidizing
environments, this work places constraints on the time periods and locations
in which life could have originated and persisted on early Mars (i.e. either
during the relatively short warm reducing intervals, or in the subsurface).
This proposed scenario places Mars intermediate to other bodies in the solar
system. For example, Venus has undergone extensive water loss to space and
likely also oxidation of its surface and mantle, based on its enhanced
atmospheric D/H ratio and the limited surface geochemistry constraints that
exist (?, ?). At the other end of the spectrum, Saturn’s moon Titan has a
strongly reducing atmosphere rich in CH4 and H2 (?), despite its low mass. The
dynamic history of martian environments proposed here suggests opportunities
for the emergence of life during warm, wet intervals when reducing conditions
would have favored prebiotic chemistry, but also challenges for the
persistence of surface life in the face of frequent and, through time,
lengthening intervals of mainly cold and dry oxidizing environments.

##  1 Methods

###  1.1 Stochastic atmospheric evolution model

Our atmospheric evolution model is designed to capture the key processes
governing atmospheric compositional changes on Mars throughout its geologic
history. The model includes terms for supply of reducing species from the
subsurface and interior, atmospheric escape and weathering. The key prognostic
variable for the model is the oxidizing power of the atmosphere. This is
expressed in terms of a single quantity $N$, which we define as the global
number of moles of electron acceptors or total oxidizing power present, as in
(?). The oxidizing power of a given element is defined under typical planetary
conditions, such that O is defined as accepting 2 electrons and H as providing
1, leading to an $N$ contribution of +4 for O2, –2 for H2, and 0 for H2O. We
assume $N=0$ at the beginning of each simulation. We work with $N$ in moles,
although sometimes it is also convenient to express it in terms of the number
of electrons accepted by the oxygen in 1 m global equivalent layer (GEL) of
H2O ice on the martian surface ($1.5\times 10^{19}$ mol). The model solves an
ordinary differential equation for the evolution of $N$ with time

$\frac{dN}{dt}=-\left.\frac{dN}{dt}\right|_{s}+\left.\frac{dN}{dt}\right|_{e}-\left.\frac{dN}{dt}\right|_{w}$
(3)

where the three terms on the right-hand side represent tendencies due to
supply of reducing power from the planet’s interior and/or bolide impacts,
oxidation via hydrogen loss to space and loss of oxidizing power to the
surface via weathering, respectively.

#### Supply of reducing gases to the atmosphere

All the main processes that supplied volatiles to the atmosphere of early Mars
were highly episodic in nature. To capture this episodicity in a general way,
we developed a stochastic representation of the injection of reducing gases to
the atmosphere, with the value of ${dN}/{dt}|_{s}$ sampled at every timestep
from a power law distribution. A power law distribution is a physically
realistic choice, because similar statistics are observed in a wide range of
geophysical settings, including specifically both bolide impacts and volcanism
on planetary bodies [e.g., (?, ?, ?, ?)]. Keeping the representation of the
reducing gas supply general also has the advantage of allowing systematic
study of the behaviour of the model when the governing parameters are varied.
To avoid unnecessary complexity in the model, we assume zero autocorrelation
in the forcing.

The power law distribution over some interval $x\in[x_{0},x_{1}]$ is defined
as

$p(x)=Cx^{\gamma},$ (1)

with the normalization requirement

$\int_{x_{0}}^{x_{1}}p(x)dx=1$ (2)

allowing us to define

$C=\frac{\gamma+1}{x_{1}^{\gamma+1}-x_{0}^{\gamma+1}}.$ (4)

The expectation value of this distribution, $\mu$, is

$\mu\equiv
E[x]=\frac{\gamma+1}{\gamma+2}\frac{x_{1}^{\gamma+2}-x_{0}^{\gamma+2}}{x_{1}^{\gamma+1}-x_{0}^{\gamma+1}}$
(5)

and the variance $\sigma^{2}$ is

$\sigma^{2}\equiv
E[(x-\mu)^{2}]=\frac{\gamma+1}{x_{1}^{\gamma+1}-x_{0}^{\gamma+1}}\left(\frac{x_{1}^{\gamma+3}-x_{0}^{\gamma+3}}{\gamma+3}-2\mu\frac{x_{1}^{\gamma+2}-x_{0}^{\gamma+2}}{\gamma+2}+\mu^{2}\frac{x_{1}^{\gamma+1}-x_{0}^{\gamma+1}}{\gamma+1}\right).$
(6)

Both of these quantities remain finite-valued as long as $x_{0}$ and $x_{1}$
are finite and $\gamma$ is not exactly equal to -1, -2 or -3.

In our model, $x$ is the supply rate of reducing power to the atmosphere in
mol/s. Hence $\mu$ is the mean supply rate, which we allow to vary slowly over
geological time to account for the secular decline in all reducing gas supply
processes (see below). $x_{1}$ is taken to be the largest possible flux of
reducing power in a single timestep, which we also estimate below. Given $\mu$
and $x_{1}$, $x_{0}$ is then calculated from equation (5) via a root-finding
algorithm.

The distribution is sampled in the model by first selecting a random number
from the uniform distribution on the domain $x\in[0,1]$. Then the sampled
value from the power law distribution is

$x_{s}=[(x_{1}^{\gamma+1}-x_{0}^{\gamma+1})x+x_{0}^{\gamma+1}]^{1/(\gamma+1)}$
(7)

The supply tendency is then simply

$\left.\frac{dN}{dt}\right|_{s}=x_{s}.$ (8)

or

$\left.\Delta N\right|_{s}=x_{s}\Delta t.$ (9)

in the discretized model with timestep $\Delta t$.

Along with their short-term variability, all the major mechanisms for supply
of reducing gases to the martian atmosphere also underwent secular decay with
time, because the interior and crust cooled from the early Noachian onwards
and the bolide impactor flux declined after the main period of planetary
accretion. We represent this decline in our model via a simple exponential
decay law

$\mu(t)=\mu_{0}\mbox{e}^{-t/\tau}.$ (10)

Here $\mu_{0}$ and $\tau$ are model parameters that we allow to vary within
physically constrained ranges. The absolute time mean is then defined as

$\overline{\mu}=\frac{1}{t_{n}}\int_{0}^{t_{n}}\mu(t)dt=\mu_{0}(1-\mbox{e}^{-t_{n}/\tau})(\tau/t_{n})$
(11)

and the total integrated gas injection value as $N_{s}=\overline{\mu}t_{n}$,
where $t_{n}=4.5$ Gy is taken as the current age of Mars.

To build a comprehensive picture of the range of plausible climate scenarios
on early Mars, we tested the effects of varying $\overline{\mu}$ and $x_{1}$
and other parameters over a range of values (Table S1). For Figure 2, an
ensemble of 256 simulations with identical initial and boundary conditions was
created for each $\overline{\mu}$ and $\beta\equiv x_{1}/\overline{\mu}$ value
studied. The colored lines in the plot correspond to the ensemble mean values
for each case. We also tested the effect of varying $\gamma$ and $\tau$ (Fig.
S4). The range for $\tau$ was determined based on timescales in volcanic and
impactor flux models [e.g., (?, ?)]. The range for $\gamma$ was determined
based on values in standard impactor flux models (?, ?, ?) and scalings for
volcanism on present-day Earth (?, ?, ?). For bolide impacts, the data
suggests $\gamma$ is between $-1.5$ and $-2$ in the solar system (?). For
volcanism, (?) argue for a power law distribution with $\gamma=-1.95$, (?)
argue for $\gamma=-2.16$, while comparison with the distribution proposed in
(?) with equivalent power law distributions suggests $\gamma\approx-3.1$. Here
we use $\gamma=-1.95$ as our nominal value but also study sensitivity to both
lower and higher values (Fig. S3). For crustal alteration and clathrate
release, $\gamma$ is difficult to constrain, but a similar range is expected
if release events are triggered by bolide impacts or volcanism.

### Constraints on reducing gas release

We produced the generalized constraints on reducing gas release in Figure 2
and accompanying discussion in the main text as follows.

Volcanism: Grott et al. (?) estimated a total volcanic outgassing of 17.5-61 m
GEL of H2O throughout martian history assuming a mantle H2O concentration of
100 ppm, depending on whether a global melt channel or localized mantle plume
melting is assumed. Later, (?) estimated a martian mantle H2O content range
from 73 to 290 ppmw based on a geochemical analysis of apatites in shergottite
meteorites. Finally, oxygen fugacity ($f_{\ce{O2}}$) values in martian
meteorites range from around the iron-wüstite (IW) buffer to the quartz-
fayalite-magnetite (QFM) buffer, which translates to outgassed molar ratios of
H2 to H2O from around 0.65 to 0.025 (?, ?, ?, ?). Taken together, these limits
imply a range of 12.25 to 176.9 m total H2O outgassed and an average H2
outgassing rate over 4.5 Gy from $33.2$ to $1.2\times 10^{4}$ mol H/s. These
latter two values correspond to the lower and upper limits for
$\overline{\mu}$ for volcanism given in Figure 2. For comparison, the hydrogen
outgassing rate required for steady-state warming via an atmospheric H2 molar
concentration of 5%, assuming escape at the diffusion limit, is $2.2\times
10^{6}$ mol H/s. Even assuming all volcanism occurred over the 700 My period
from 4.2 to 3.5 Gya, this value is over an order of magnitude higher than the
upper limit given above.

Constraining the upper limit for $\beta$ from volcanism is challenging given
the uncertainties in martian geodynamics and eruptive processes, but an order-
of-magnitude estimate can be gained by considering the Tharsis Rise, which was
formed during the Noachian. The total volume of Tharsis has been estimated as
around 2000 m GEL of basalt (?). Given a basalt density of 3000 kg/m3 and
upper limit melt H2O specific concentration of 2870 ppmw (?), this implies
release of $1.4\times 10^{20}$ mol of H2O, or $3.6\times 10^{18}$ mol to
$9.4\times 10^{19}$ mol of H2 for $f_{\ce{O2}}$ at IW to QFM. Achieving
$\beta=10^{2}$ to $10^{3}$ requires a maximum of $1.2\times 10^{6}$ to
$1.2\times 10^{7}$ mol H release in a 100,000 y interval, which translates to
a few to tens of percent of the volume of Tharsis created in this time period.
This is challenging, but might not be impossible during a period of
particularly intense volcanic activity.

Bolide impacts: To derive the upper limit on H input from bolide impacts in
Fig. 2, we used the methodology of (?). We used the full set of impact crater
radii listed in their Supplementary Information and calculate the impactor
radius as $r=0.022D_{c}^{1.076}$ m, where $D_{c}$ is the crater radius in
metres, based on their eqns. S1 and S3. We assume that the impactors were
composed of H-chondrite material with a metallic iron mass fraction of 27% and
use an iron–water reaction to form H2 as Fe + H2O →FeO + H2. The contribution
of shocked crustal material to H release is neglected in this calculation. The
calculation gives an average H input over 4.5 Gy from impacts of $2.47\times
10^{4}$ mol H/s. Regarding episodicity, a sense of the numbers can be gained
by considering Antoniadi Crater, which is a ‘typical’ moderate-sized Noachian
crater with diameter 381 km, yielding an estimated bolide impactor radius of
34.8 km. Using the above assumptions on H release gives $8.9\times 10^{17}$
mol H, equivalent to $2.8\times 10^{5}$ mol H/s in a 100,000 year model
timestep or $\beta\approx 11.4$. In contrast, for the biggest impactor craters
such as Argyre (1315 km) and Hellas (2070 km), which are dated to the early to
mid Noachian (?), we find $\beta\approx 620$ and $2680$, respectively. Hence
we conclude that direct bolide impact H creation can explain the formation of
fluvial features and crater degradation in the early to mid Noachian, but
probably not in the late Noachian / early Hesperian.

Crustal alteration: Processes such as serpentinization and radiolytic H2
production likely caused extensive episodic outgassing of H2 and related
species like CH4 (?, ?, ?, ?). Globally, it has previously been estimated that
up to 300-1000 m GEL of water could have been consumed by serpentinization of
Mars’ Noachian crust (?). Assuming that the ratio of H2O consumed to H2
emitted is around 7, this implies 42.9 to 142.9 m H2O equiv. of H2, or
$4.5\times 10^{3}$ to $1.48\times 10^{4}$ mol H/s averaged over 4.5 Gy.
Emission rates peaking at up to $5\times 10^{14}$ to $5\times 10^{16}$
molecules/m2/s via serpentinization of mafic and ultramafic minerals could
have occurred locally (?), based on observations of emissions from terrestrial
ophiolites (?). Formation of CH4 clathrates could lead to instantaneous
reduced gas release rates that are even higher than this, depending on the
efficiency of methane formation during serpentinization and other factors (?,
?, ?). Finally, positive crustal feedbacks on H release may occur once warming
begins due to authigenic magnetite formation and associated hydrogen release
in surface aqueous environments (?). The effect of this process is hard to
quantify, but it would likely strongly increase the peak hydrogen flux
following short-term thermal perturbations by bolide impacts.

#### Atmospheric escape

The second term in equation (3) describes net change in atmospheric oxidizing
power via escape of hydrogen and (to a lesser extent) oxygen to space. We
include a number of processes to determine the variation of this term with
time.

Molecular and atomic hydrogen escape: We assume that when H2 is present in the
atmosphere ($N<0$ in our model), its loss is diffusion-limited following the
formula for a general diffusing species $i$

$\Phi_{diff-lim}=b_{i}x_{i}\left(\overline{H}^{-1}-H_{i}^{-1}\right).$ (12)

Here $\overline{H}$ is the scale height of the background atmosphere, $H_{i}$
is the scale height of H2, $x_{i}$ is the H2 molar concentration and $b_{i}$
is the binary diffusion coefficient for H2 and CO2, which we take from (?).

When H2 is present in the atmosphere, equation (12) determines the oxidation
rate. However, oxidation still occurs even in the absence of atmospheric H2 if
photodissociation of H2O can lead to non-stoichiometric hydrogen escape. On
present-day Mars, convective lofting during global dust storms is a key
contributor to non-stoichiometric H loss today (?). Propagation of volatile
species to the upper atmosphere of any planet is a strong function of orbital
obliquity, the dust cycle, surface ice distribution and surface pressure, so
during periods in the past where these parameters varied, transport of H2O to
the high atmosphere could have been increased by many orders of magnitude.
This is consistent with Mars’ high degree of water loss based on the observed
deuterium to hydrogen (D/H) ratio through time.

Here we incorporate an average transport rate of H2O to the high atmosphere
during cold periods that permits the model to match D/H values through time.
Mars’ D/H ratio today is about $6$ times standard mean ocean water (SMOW) (?,
?, ?). The D/H value around 3.5 Gya was $3\pm 0.2$ times SMOW, based on
analysis of sedimentary rocks at Gale crater (?), while Mars’ formation D/H
value was likely 1.2 to 1.6 times SMOW (?). The H2O inventory in moles at time
$t$ from initial delivery is derived from the D/H ratio as

$N_{\ce{H2O}}(t)=N_{\ce{H2O}}(t_{n})\left(\frac{r_{D-H}(t_{n})}{r_{D-H}(t)}\right)^{1/(1-f)}$
(13)

(?, ?), where $t_{n}$ is the time today (4.5 Gy), $r_{D-H}(t)$ is the D/H
ratio at time $t$, and $f$ is the fractionation parameter. Here we take
$f=0.016$, which leads to an estimate of an initial 130-170 m GEL H2O
inventory on Mars (?, ?, ?, ?). We assume that the time-dependence of
$N_{\ce{H2O}}(t)$ is

$N_{\ce{H2O}}(t)=\frac{1}{2}\alpha
L_{\ce{H},n}\tau_{\ce{H2O}}(\mbox{e}^{-(t-t_{n})/\tau_{\ce{H2O}}}-1)+N_{\ce{H2O}}(t_{n}).$
(14)

Here $N_{\ce{H2O}}(t_{n})$ is the estimated present-day surface H2O inventory
($2.5\times 10^{20}$ mol or 34 m GEL H2O) (?) and $L_{\ce{H},n}=1.7\times
10^{3}$ mol/s (3.6 m H2O equiv./Gy) is the present-day loss rate of H to
space. $\tau_{\ce{H2O}}$ and $\alpha$ are free parameters that we determined
to be $1.11$ Gy and $0.48$, respectively, using an L2 norm error minimization
procedure vs. observational D/H data. This parametrization correctly
reproduces the initial, 3.5 Gya and present-day martian D/H ratios, within
error bounds (Fig. S1).

The change in overall oxidizing power vs. time from the associated H loss in
our model is then

$\left.\frac{dN}{dt}\right|_{e,\ce{H2O}}=-2\frac{dN_{\ce{H2O}}}{dt}=+\alpha
L_{\ce{H},n}\mbox{e}^{-(t-t_{n})/\tau_{\ce{H2O}}}.$ (15)

For simplicity, we neglect the effects of deep crustal interaction with H2O on
D/H variations here [e.g., (?)]. The importance of this process remains
unclear, although if early Mars was mainly cold, the subsurface cryosphere
would have placed strong constraints on the rate of isotopic exchange between
deep groundwater and the surface H2O inventory.

Non-thermal O escape: We also include non-thermal escape of O to space in our
model. The escape flux of all O species observed from Mars today by MAVEN is
around $6\times 10^{25}$ atom/s (?, ?, ?). Past escape rates of O (from both
H2O and CO2) were likely larger via a combination of enhanced dissociative
recombination, ion escape, and ion sputtering (?, ?, ?, ?). Here we include
the effect of non-thermal loss on redox balance in our model by assuming the
dominant loss channel is dissociative recombination and using the formula from
(?) with power law coefficient of $1.7$ (?). Before 3.5 Gya, we fix the
maximum loss rate at $1\times 10^{27}$, based on (?). We also calculated the
drag of oxygen with escaping hydrogen when the extreme ultraviolet
(XUV)-driven escape flux was high, but found that it was small from the early
Noachian onwards and therefore neglected it.

Finally, all escape fluxes $\Phi$ are converted to a global rate of change in
mol/s as

$\left.\frac{dN}{dt}\right|_{e}=4\pi r^{2}\Phi/N_{A}$ (16)

where $r$ is the radius of Mars and $N_{A}$ is Avogadro’s constant. Because
the input of reducing gas in the model is stochastic, the percentage of time
the atmosphere is oxic is a function of both $\overline{\mu}$ and $\beta$.
Figure S2 shows the effect of varying $\beta$ on the model output, while Fig.
S3 shows the total percentage of time the atmosphere is oxic for Noachian and
for Hesperian + Amazonian time periods as a function of $\overline{\mu}$ and
$\beta$.

#### Evolution of CO2 with time

The evolution of CO2 in Mars’ atmosphere is taken into account using
constraints from spacecraft atmospheric escape observations, and models of
impact ejection, carbon isotopic evolution and crustal sequestration (?). We
use the following empirical function for the variation of $p_{\ce{CO2}}$ with
time:

$p_{\ce{CO2}}=A(1-\tanh[a(t-0.8~{}\mbox{Gy})]).$ (17)

Here $t$ is in Gy. In our standard scenario, $a=1.5$ Gy-1 and $A=2.1$ bar,
which leads to 0.46 bar 3.0 Gya, 1.5 bar 3.5 Gya and 2.99 bar 4.0 Gya. This is
consistent with the review of (?), which estimates $\sim 1.5$ to $>3$ bar of
CO2 has been lost from the martian atmosphere since 4.3 Gya, primarily due to
a combination of impact erosion, stripping to space and deep crustal carbonate
formation. It is also consistent with paleo-atmosphere modeling constraints
based on observed crater size distributions (?), which yield an upper limit
for atmospheric pressure of 1-2 bar 3.6 Gya. Finally, it is within the range
of upper limits for Noachian $p_{\ce{CO2}}$ from C isotope fractionation
modeling, as long as the bulk of subsurface carbonate formation is not driven
by evaporative processes (?). Sensitivity tests assuming lower and higher
values of $A$ are presented in Figure S4.

#### Removal of atmospheric O2 via surface processes

Because the martian crust and mantle contain large quantities of reduced
species (particularly iron in the Fe^2+ oxidation state), interaction of any
liberated O2 in the martian atmosphere with the surface is a potentially
important sink of oxidizing power (decrease in $N$ towards zero). Sinks of O2
due to aqueous processes during brief ($\sim$a few years) warming events are
likely to be small (see Supporting Information). When Mars is in a cold
climate state, the rate of iron oxidation is orders of magnitude lower than
during warm periods, but probably still non-zero (?). Processes such as
oxidation during local transient melting events at the surface (?, ?),
alteration of hydrothermal fluids in intermittent contact with the atmosphere
and possibly dry photo-oxidation (?) may all have contributed to slow removal
of O2 and related oxidants from the atmosphere. We included a small constant
flux of oxidizing power out of the atmosphere during periods where $N>0$,
although we found it had little effect on the duration of warm periods in the
model. The default value we use in the simulations is $dN/dt|_{w}=1.6\times
10^{3}$ mol/s (equivalent to the H in 15 m GEL of H2O over 4.5 Gya), although
a wider range of values was studied in sensitivity tests (see Table S1).

#### Climate parametrization

We use the PCM_LBL line-by-line radiative-convective code (?) to calculate
equilibrium surface temperature as a function of reducing gas concentration in
the model. For simplicity, we assume that CO2 and H2 are the primary warming
agents, although other gases such as CH4 and longer chain hydrocarbons may
also have made important contributions that we neglect here. Surface
temperatures are calculated as a function of solar flux, total surface
pressure and hydrogen molar concentration. All other parameters were set as in
(?). Simulations were run for 500 steps, which was sufficient to achieve
equilibrium in all cases. The resulting array was then used to produce surface
temperature values during operation of the stochastic climate model via linear
interpolation. We tested the effect of using CO2-H2 collision-induced
absorption values from both (?) and (?). The latter values are slightly lower,
so to remain conservative in our predictions of surface warming we used them
for the results reported here. Our results closely match those of (?), which
found surface temperature $T_{s}=273$ K at 2 bar CO2 and 6% H2 using the
correlated-$k$ model described in (?). Our calculated surface temperatures at
0% H2 are warmer by a few Kelvins than previous correlated-$k$ calculations
because our line-by-line model produces a slightly cooler upper atmosphere [an
effect seen already in other intercomparisons, e.g. (?)]. Solar luminosity
through time was calculated using the formula from (?). We also tested the
effect of assuming constant solar luminosity at the present-day value in some
runs as an upper limit implementation of the ‘massive young Sun hypothesis’
(?) (Fig. S4).

###  1.2 Short-term regolith heating from bolide impacts

The initial effect of large impacts is to cause a short intense pulse of
regional to global surface heating by mobilizing ice and rock as liquid and
vapor ejecta that is subsequently deposited on the surface (see Supporting
Information). To calculate the sub-surface warming due to emplacement of a hot
surface layer, we used a regolith thermal evolution model, with the upper
boundary condition either Stefan-Boltzmann cooling or surface temperatures
from the results of 3D global climate modeling in the aftermath of a giant
impact (?). The regolith thermal evolution model solves the heat equation

$c_{h}\rho\frac{\partial T}{\partial t}=\frac{\partial}{\partial
z}\left(\kappa_{r}\frac{\partial}{\partial z}T\right)$ (18)

where $T$ is temperature, $t$ time, $z$ depth, $\kappa_{r}$ the regolith
thermal conductivity, $c_{h}$ heat capacity (840 J/K/kg here) and $\rho$
density (3000 kg/m3 here). Each simulation is initialized with a hot upper
layer overlying a colder layer representing pre-impact regolith in geothermal
equilibrium. The hot upper layer is between 1 and 500 m deep and is assigned a
uniform temperature of 800 to 1600 K. The cold lower layer is initialized at
220 K at its shallowest level, with higher initial values with depth according
to the geothermal gradient. We use a geothermal gradient of 32.5 K/km based on
an assumed Noachian geothermal heat flux of $F_{geo}=65$ mW/m2 and a thermal
conductivity of 2 W/m/K (?). Latent heat was incorporated via the apparent
heat capacity method (?), using a saturated regolith with 20 % porosity. The
bottom boundary condition is set by $F_{geo}$. For the upper boundary
condition, Stefan-Boltzmann cooling was used to give a conservative upper
limit on the cooling rate.

###  1.3 Sulfur chemistry modeling

We produced the pH–$f_{\ce{O2}}$ equilibrium plot for sulfur minerals in Fig.
3A using _The Geochemist’s Workbench_ software package. The magnetite-hematite
and quartz-fayalite-magnetite mineral redox buffers were calculated using the
same approach as in (?). The thermochemical sulfate reduction calculation for
Fig. 3B was performed by coupling the one-dimensional thermal diffusion model
discussed above to a chemical solver. We used existing experimental data on
thermochemical sulfate reduction obtained at H2 partial pressures of 4-16 bar
(?) to parameterize this process. We express the removal rate of sulfate as

$k(T)=k_{0}\mbox{e}^{-\frac{E_{a}}{R}(1/T-1/T_{ref})}\quad\mbox{s}^{-1}$ (19)

where $k_{0}=7\times 10^{-8}$ s-1, $R$ is the ideal gas constant,
$T_{ref}=280$ ∘C and $E_{a}=131$ kJ/mol. The dependence of the reaction rate
on H2 pressure is relatively weak (?) and was therefore neglected here.

The decrease in the local concentration of sulfate $C_{\ce{SO4}}$ as a
function of time is expressed as

$\frac{dC_{\ce{SO4}}}{dt}=-k(T)C_{\ce{SO4}}$ (20)

The fraction of sulfate that becomes reduced as a function of depth $f_{Sred}$
is then calculated by integrating equation (20) to get

$f_{Sred}(z,t_{f})\equiv C_{\ce{SO4},t_{f}}/C_{\ce{SO4},0}=\mbox{
exp}\left[-\int_{0}^{t_{f}}k[T(z,t)]dt\right].$ (21)

We use the subsurface thermal evolution data described in the last section to
obtain temperature and hence $k$ as a function of depth and time at the end of
the simulation $t_{f}$. As discussed above, $t_{f}$ is pre-determined in the
thermal simulations as a function of impactor size. The effective depth to
which sulfate is reduced is then calculated for a given hot layer depth by
integrating $f_{Sred}$ in depth $z$

$d_{Sred}=\int_{0}^{z_{m}}f_{Sred}(z,t_{f})dz.$ (22)

where $z_{m}$ is the lowest layer depth in the model. We neglected the
dissolution of sulfate minerals in the calculation on the basis that it should
proceed much faster than the thermochemical reduction itself.

Aqueous solutions of sulfate in open-water systems near the surface can be
reduced by dissolved H2 or other reducing gas species from the atmosphere
itself. For sulfates that percolate deeper into the regolith, the transport
rate of gas species from the atmosphere will eventually become limited, but
TSR can also be driven by ferrous iron from crustal minerals (?). As is clear
from Fig. 3A, pyrite and pyrrhotite are the stable forms of sulfur when the
oxygen fugacity of the surrounding fluid is at the magnetite-hematite buffer
value or lower. Most early martian regolith would have been much more
reducing, probably at oxygen fugacity between QFM and IW+1. H2_(aq) reduces
minerals such as hematite slowly compared to other reductants, which suggests
that the TSR reaction is likely to proceed faster in the deeper regolith than
(19) suggests, but further experimental constraints on TSR in this regime
would be useful. Finally, we do not consider sulfate reduction in the sub-
surface over long time periods at more moderate temperatures in our TSR
calculation, although this process may also have been important, particularly
in the early to mid-Noachian.

###  1.4 Manganese oxidation modeling

The pH–$f_{\ce{O2}}$ equilibrium plot for manganese minerals in Fig. 4A was
produced using _The Geochemist’s Workbench_. For Fig. 4B, we modeled the
kinetics of manganese oxide formation as follows. In the presence of dissolved
oxygen (O2), manganese in aqueous solution oxidizes slowly via reactions such
as

$\ce{4Mn^{2+}_{(aq)}+O2_{(aq)}+6H2O\to}\ce{4MnOOH_{(s)}+8H^{+}}$ (23)

and

$\ce{3Mn^{2+}_{(aq)}+\frac{1}{2}O2_{(aq)}+3H2O\to
Mn_{3}O_{4}{}_{(s)}+6H^{+}}.$ (24)

The oxidized forms of Mn produced in these reactions are relatively insoluble
and subsequently fall out of the solution to form minerals such as
hausmannite. We modeled the oxidation of manganese during oxidizing
atmospheric intervals in the short-term aftermath of a bolide impact using
reaction rates from the experimental literature (?, ?). Surface temperature
values vs. time for impactors of radius 30 km and atmospheric CO2
concentrations from 0.15 to 1 bar were taken from 3D global climate model
output, using simulations performed as described in (?).

We assume that oxidation of aqueous Mn is the rate-limiting step for Mn oxide
formation, and model it via the representative equation

$\frac{d\ce{[Mn^{2+}_{(aq)}]}}{dt}=-k_{app}(T)K_{H}(T)p_{\ce{O2}}\ce{[Mn^{2+}_{(aq)}]}=-\frac{\ce{[Mn^{2+}_{(aq)}]}}{\tau_{MnOx}}$
(25)

where [Mn^2+_(aq)] is dissolved manganese concentration, $p_{\ce{O2}}$ is the
atmospheric O2 partial pressure, $K_{H}$ is the Henry’s law coefficient for O2
and $k_{app}$ is an effective reaction rate. Here we take
$K_{H}=K^{o}_{H}\mbox{e}^{\alpha(T^{-1}-T_{0}^{-1})}$, where
$K^{o}_{H}=1.3\times 10^{-8}$ mol/kg/Pa, $\alpha=1700$ K and $T_{0}=298.15$ K
(?). We assume a room-temperature value for $k_{app}$ of $1\times 10^{-4}$
kg/mol/s, based on experiments carried out at a pH of 8 and assuming 1 kg/L of
H2O (?). Manganese oxidation proceeds faster at higher pH values, but pH = 8
was judged to be a reasonable value for reactions occurring in the presence of
basaltic crust at relatively low water to rock ratios. Manganese oxidation
also proceeds faster when self-catalysis can occur. We do not model this
process explicitly, but we note that the high temperatures immediately
following a bolide impact would allow rapid oxidation of small quantities of
Mn, likely driving effective subsequent self-catalysis. The temperature
dependence of $k_{app}$ is taken into account by assuming Arrhenius rate
dependence and calculating the activation energy from experimental data at a
fixed pH of 8 [specifically, we use experiments K13 and K17 from (?)]. Using
this data, we derive an effective activation energy of $E_{a}=182.6$ kJ/mol.

## References

  * 1. Carr, M. H. & Head, J. W.  Geologic history of Mars  Earth and Planetary Science Letters, 294, 185–203 (2010).
  * 2. Grotzinger, J. P. et al.  A habitable fluvio-lacustrine environment at Yellowknife Bay, Gale Crater, Mars.  Science, 343, 1242777 (2014).
  * 3. Halevy, I., Zuber, M. T., & Schrag, D. P.  A sulfur dioxide climate feedback on early Mars.  Science, 318, 1903–1907 (2007).
  * 4. Tian, F. et al.  Photochemical and climate consequences of sulfur outgassing on early Mars.  Earth and Planetary Science Letters, 295, 412-418 (2010).
  * 5. Toon, O. B., Segura, T. and Zahnle, K.  The formation of martian river valleys by impacts.  Annual Review of Earth and Planetary Sciences, 38, 303–322 (2010).
  * 6. Forget, F. et al.  3D modelling of the early martian climate under a denser CO2 atmosphere: Temperatures and CO2 ice clouds.  Icarus, 222, 81-99 (2013).
  * 7. Haberle, R. M. Catling, D. C. Carr, M. H. & Zahnle, K. J.  The Atmosphere and Climate of Mars, Chapter 17: The Early Mars Climate System.  Cambridge University Press, Cambridge, 2017.
  * 8. Ramirez, R. M. & Craddock, R. A.  The geological and climatological case for a warmer and wetter early Mars.  Nature Geoscience, 11, 230–237 (2018).
  * 9. Hoke, M. R. T., Hynek, B. M. & Tucker, G. E.  Formation timescales of large martian valley networks.  Earth and Planetary Science Letters, 312, 1–12 (2011).
  * 10. Bishop, J. L. et al.  Surface clay formation during short-term warmer and wetter conditions on a largely cold ancient Mars.  Nature Astronomy, 2, 206 (2018).
  * 11. Lapotre, M. G. & Ielpi, A.  The pace of fluvial meanders on Mars and implications for the western delta deposits of Jezero crater.  AGU Advances, 1, 206, e2019AV000141 (2020).
  * 12. Olsen, A. A. & Rimstidt, J. D.  Using a mineral lifetime diagram to evaluate the persistence of olivine on Mars.  American Mineralogist, 92, 598–602 (2007).
  * 13. Ehlmann, B. L. & Edwards, C. S.  Mineralogy of the martian surface.  Annual Review of Earth and Planetary Sciences, 42, 291–315 (2014).
  * 14. Niles, P. B. et al.  Geochemistry of carbonates on Mars: Implications for climate history and nature of aqueous environments.  Space Science Reviews, 174, 301–328 (2013).
  * 15. Ehlmann, B. L. et al.  Subsurface water and clay mineral formation during the early history of Mars  Nature, 479, 53–60 (2011).
  * 16. Bibring, J.-P. et al.  Global Mineralogical and Aqueous Mars History Derived from OMEGA/Mars Express Data.  Science, 312, 400–404 (2006).
  * 17. Wadhwa, M.  Redox state of Mars’ upper mantle and crust from Eu anomalies in shergottite pyroxenes.  Science, 291, 1527–1530 (2001).
  * 18. Ramirez, R. M. et al.  Warming early Mars with CO2 and H2.  Nature Geoscience, 7, 59–63 (2014).
  * 19. Wordsworth, R. et al.  Transient reducing greenhouse warming on early Mars.  Geophysical Research Letters, 44, 665-671 (2017).
  * 20. Lorand, J.-P. et al.  The sulfur budget and sulfur isotopic composition of Martian regolith breccia NWA 7533.  Meteoritics and Planetary Science, 55, 2097–2116 (2020).
  * 21. Hurowitz, J. A. et al.  Redox stratification of an ancient lake in Gale Crater, Mars.  Science, 356, eaah6849 (2017).
  * 22. Lanza, N. L. et al.  Oxidation of manganese in an ancient aquifer, Kimberley formation, Gale Crater, Mars.  Geophysical Research Letters, 43, 7398–7407 (2016).
  * 23. Hurowitz, J. A. Fischer, W. W., Tosca, N. J., & Milliken, R. E.  Origin of acidic surface waters and the evolution of atmospheric chemistry on early Mars.  Nature Geoscience, 3, 323 (2010).
  * 24. Liu, W. et al.  Anoxic photogeochemical oxidation of manganese carbonate yields manganese oxide.  Proceedings of the National Academy of Sciences, 117, 22698-22704 (2020).
  * 25. Haberle, R. M., Zahnle, K. J., Barlow, N. G., & Steakley, K.  Impact degassing of H2 on early Mars and its effect on the climate system.  Geophysical Research Letters, 46, 13355-13362 (2019).
  * 26. Chassefière, E. Lasue, J. Langlais, B. & Quesnel, Y.  Early Mars serpentinization-derived CH4 reservoirs, H2-induced warming and paleopressure evolution.  Meteoritics & Planetary Science, 51, 2234–2245 (2016).
  * 27. Tosca, N. J., Ahmed, I. A. M., Tutolo, B. M., Ashpitel, A. & Hurowitz, J. A.  Magnetite authigenesis and the warming of early Mars.  Nature Geoscience, 11, 635–639 (2018).
  * 28. See Methods for further details.
  * 29. Jakosky, B. M. et al.  Loss of the martian atmosphere to space: Present-day loss rates determined from MAVEN observations and integrated loss through time.  Icarus, 351, 146–157 (2018).
  * 30. Turbet, M., Boulet, C. & Karman, T.  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.  Icarus, 346, 113762 (2020).
  * 31. Mangold, N., Adeli, S., Conway, S., Ansan, V. & Langlais, B..  A chronology of early Mars climatic evolution from impact crater degradation.  Journal of Geophysical Research: Planets, 117, (2012).
  * 32. Fassett, C. I. & Head, J. W.  Sequence and timing of conditions on early Mars.  Icarus, 211, 1204–1214 (2008).
  * 33. Wordsworth, R. et al.  Global modelling of the early martian climate under a denser CO2 atmosphere: Water cycle and ice evolution.  Icarus, 222, 1–19 (2013).
  * 34. Osterloo, M. M., Anderson, F. S., Hamilton, V. E., and Hynek, B. M.  Geologic context of proposed chloride-bearing materials on Mars.  Journal of Geophysical Research: Planets, 115, E10012 (2010).
  * 35. Hynek, B. M., Osterloo, M. K. & Kierein-Young, K. S.  Late-stage formation of martian chloride salts through ponding and evaporation.  Geology, 43, 787–790 (2015).
  * 36. McLennan, S. M. et al.  Provenance and diagenesis of the evaporite-bearing Burns formation, Meridiani Planum, Mars.  Earth and Planetary Science Letters, 240, 95–121 (2005).
  * 37. Gaillard, F., Michalski, J., Berger, G., McLennan, S. M. & Scaillet, B.  Geochemical reservoirs and timing of sulfur cycling on Mars.  Space Science Reviews, 174, 251–300 (2013).
  * 38. Halevy, I. & Head, J. W.  Episodic warming of early Mars by punctuated volcanism.  Nature Geoscience, 7, 865-868 (2014).
  * 39. Wade, J., Dyck, B., Palin, R. M., Moore, J. D. P., & Smye, A. J.  The divergent fates of primitive hydrospheric water on Earth and Mars.  Nature, 552, 391 (2017).
  * 40. Milliken, R. E., Fischer, W. W. & Hurowitz, J. A.  Missing salts on early Mars.  Geophysical Research Letters, 36, L11202 (2009).
  * 41. Zolotov, M. Y., & Mironenko, M. V.  Chemical models for martian weathering profiles: Insights into formation of layered phyllosilicate and sulfate deposits.  Icarus, 275, 203–220 (2016).
  * 42. Sholes, S. F., Smith, M. L., Claire, M. W., Zahnle, K. J., & Catling, D. C.  Anoxic atmospheres on Mars driven by volcanism: Implications for past environments and life.  Icarus, 290, 46–62 (2017).
  * 43. Segura, T. L., Toon, O. B., Colaprete, A. & Zahnle, K..  Environmental effects of large impacts on Mars.  Science, 298, 1977–1980 (2002).
  * 44. Steakley, K., Murphy, J., Kahre, M., Haberle, R., & Kling, A.  Testing the impact heating hypothesis for early Mars with a 3-D global climate model.  Icarus, 330, 169–188 (2019).
  * 45. Palumbo, A. M. & Head, J. W.  Impact cratering as a cause of climate change, surface alteration, and resurfacing during the early history of Mars.  Meteoritics & Planetary Science, 54, 687–725 (2018).
  * 46. Turbet, M. et al.  The environmental effects of very large bolide impacts on early Mars explored with a hierarchy of numerical models.  Meteoritics & Planetary Science, 54, 687–725 (2018).
  * 47. Mitra, K., Moreland, E. L. & Catalano, J.G.  Capacity of chlorate to oxidize ferrous iron: Implications for iron oxide formation on Mars.  Minerals, 10, 729 (2020).
  * 48. Fegley, B., Zolotov, M. Y., & Lodders, K.  The oxidation state of the lower atmosphere and surface of Venus.  Icarus, 125, 416–439 (1997).
  * 49. R. D. Wordsworth.  Atmospheric nitrogen evolution on Earth and Venus.  Earth and Planetary Science Letters, 447:103–111, 2016.
  * 50. Niemann, H. B. et al.  The abundances of constituents of Titan’s atmosphere from the GCMS instrument on the Huygens probe.  Nature, 438, 779–784 (2005).
  * 51. Wordsworth, R., Schaefer, L., & Fischer, R.  Redox evolution via gravitational differentiation on low-mass planets: implications for abiotic oxygen, water loss, and habitability.  The Astronomical Journal, 155, 195 (2018).
  * 52. Tremaine, S. & Dones, L.  On the statistical distribution of massive impactors.  Icarus, 106, 335–341 (1993).
  * 53. Werner, S. C. & Tanaka, K. L.  Redefinition of the crater-density and absolute-age boundaries for the chronostratigraphic system of Mars.  Icarus, 215, 603–607 (2011).
  * 54. Mason, B. G., Pyle, D. M. & Oppenheimer, C.  The size and frequency of the largest explosive eruptions on Earth.  Bulletin of Volcanology, 66, 735–748 (2004).
  * 55. Cannavò, F. & Nunnari, G.  On a possible unified scaling law for volcanic eruption durations.  Scientific Reports, 6, 22289 (2016).
  * 56. Grott, M., Morschhauser, A., Breuer, D., & Hauber, E.  Volcanic outgassing of CO2 and H2O on Mars.  Earth and Planetary Science Letters, 308, 391–400 (2011).
  * 57. Sleep, N. H. & Zahnle, K.  Carbon dioxide cycling and implications for climate on ancient Earth.  Journal of Geophysical Research, 106, 1373–1400 (2001).
  * 58. Papale, P.  Global time-size distribution of volcanic eruptions on Earth.  Scientific Reports, 8, 1-11 (2018).
  * 59. Zahnle, K., Pollack, J. B., Grinspoon, D. & Dones, L.  Impact-generated atmospheres over Titan, Ganymede, and Callisto.  Icarus, 95, 1-23 (1992).
  * 60. McCubbin, F. M. et al.  Hydrous melting of the martian mantle produced both depleted and enriched shergottites.  Geology, 40, 683–6865 (2012).
  * 61. Herd, C. D.  The oxygen fugacity of olivine-phyric martian basalts and the components within the mantle and crust of Mars.  Meteoritics & Planetary Science, 38, 1793–1805 (2003).
  * 62. Phillips, R. J. et al.  Ancient geodynamics and global-scale hydrology on Mars.  Science, 291, 2587–2591 (2001).
  * 63. Chassefière, E., Langlais, B., Quesnel, Y., & Leblanc, F.  The fate of early Mars’ lost water: The role of serpentinization.  Journal of Geophysical Research: Planets, 118, 1123–1134 (2013).
  * 64. Batalha, N., Domagal-Goldman, S. D., Ramirez, R., & Kasting, J. F.  Testing the early Mars H2–CO2 greenhouse hypothesis with a 1-D photochemical model.  Icarus, 258, 337–349 (2015).
  * 65. Tarnas, J. D. et al.  Radiolytic H2 production on Noachian Mars: Implications for habitability and atmospheric warming.  Earth and Planetary Science Letters, 502, 133–145 (2018).
  * 66. Etiope, G., Ehlmann, B. L. & Schoell, M.  Low temperature production and exhalation of methane from serpentinized rocks on Earth: A potential analog for methane production on Mars.  Icarus, 224, 276–285 (2013).
  * 67. Lasue, J., Quesnel, Y., Langlais, B. & Chassefière, E.  Methane storage capacity of the early martian cryosphere.  Icarus, 260, 205–214 (2015).
  * 68. Chamberlain, J. W. & Hunten, D. M.  Theory of Planetary Atmospheres. An Introduction to Their Physics and Chemistry (Academic Press, Orlando, 1987).
  * 69. Heavens, N. et al.  Hydrogen escape from Mars enhanced by deep convection in dust storms.  Nature Astronomy, 2, 126 (2018).
  * 70. Donahue, T. M.  Evolution of water reservoirs on Mars from D/H ratios in the atmosphere and crust.  Nature, 374, 432 (1995).
  * 71. Villanueva, G. L. et al.  Strong water isotopic anomalies in the martian atmosphere: Probing current and ancient reservoirs.  Science, 348, 218–221 (2015).
  * 72. Heard, A. & Kite, E. S.  A probabilistic case for a large missing carbon sink on Mars after 3.5 billion years ago.  Earth and Planetary Science Letters, 531, 116001 (2020).
  * 73. Mahaffy, P. R. et al.  The imprint of atmospheric evolution in the D/H of Hesperian clay minerals on Mars.  Science, 347, 412–414 (2015).
  * 74. Lunine, J. I., Chambers, J., Morbidelli, A., & Leshin, L. A.  The origin of water on Mars.  Icarus, 165, 1–8 (2003).
  * 75. Kurokawa, H. et al.  Evolution of water reservoirs on Mars: Constraints from hydrogen isotopes in martian meteorites.  Earth and Planetary Science Letters, 394, 179–185 (2014).
  * 76. Yung, Y. L. et al.  HDO in the martian atmosphere: Implications for the abundance of crustal water.  Icarus, 76, 146–159 (1988).
  * 77. Krasnopolsky, V. A., Mumma, M. J. & Gladstone, G. R.  Detection of atomic deuterium in the upper atmosphere of Mars.  Science, 280, 1576–1580 (1998).
  * 78. Carr, M. H. & Head, J. W.  Martian surface/near-surface water inventory: Sources, sinks, and changes with time.  Geophysical Research Letters, 42, 726–732 (2015).
  * 79. Brain, D. A. et al.  The spatial distribution of planetary ion fluxes near Mars observed by MAVEN.  Geophysical Research Letters, 42, 9142–9148 (2015).
  * 80. Lillis, R. J. et al.  Characterizing atmospheric escape from Mars today and through time, with MAVEN.  Space Science Reviews, 195, 357–422 (2015).
  * 81. Jakosky, B. M., Pepin, R. O., Johnson, R. E. & Fox, J. L.  Mars atmospheric loss and isotopic fractionation by solar-wind-induced sputtering and photochemical escape.  Icarus, 111, 271–288 (1994).
  * 82. Chassefière, E. & Leblanc, F.  Mars atmospheric escape and evolution; interaction with the solar wind.  Planetary and Space Science, 52, 1039–1058 (2004).
  * 83. Lammer, H. et al.  Outgassing history and escape of the martian atmosphere and water inventory.  Space Science Reviews, 174, 113–154 (2013).
  * 84. Lillis, R. J. et al.  Photochemical escape of oxygen from Mars: First results from MAVEN in situ data.  Journal of Geophysical Research: Space Physics, 122, 3815-3836 (2017).
  * 85. Jakosky, B. M.  The CO2 inventory on Mars.  Planetary and Space Science, 175, 52–59 (2019).
  * 86. Kite, E. S., Williams, J.-P., Lucas, A.& Aharonson, O.  Low palaeopressure of the martian atmosphere estimated from the size distribution of ancient craters.  Nature Geoscience, 7, 335–339 (2014).
  * 87. Hu, R., Kass, D. M., Ehlmann, B. L. & Yung, Y. L.  Tracing the fate of carbon and the atmospheric evolution of Mars.  Nature Communications, 6, 10003 (2015).
  * 88. Burns, R. G. & Fisher, D. S.  Rates of oxidative weathering on the surface of Mars.  Journal of Geophysical Research: Planets, 98, 3365–3372 (1993).
  * 89. Haberle, R. M. et al.  On the possibility of liquid water on present-day Mars.  Journal of Geophysical Research: Planets, 106, 23317–23326 (2001).
  * 90. McEwen, A. S. et al.  Recurring slope lineae in equatorial regions of Mars.  Nature Geoscience, 7, 53 (2014).
  * 91. Huguenin, R. L.  Photostimulated oxidation of magnetite: 1. Kinetics and alteration phase identification.  Journal of Geophysical Research, 78, 8481–8493 (1973).
  * 92. Wordsworth, R., Forget, F. & Eymet, V.  Infrared collision-induced and far-line absorption in dense CO2 atmospheres.  Icarus, 210, 992–997 (2010).
  * 93. Ding, F. & Wordsworth, R. D.  A New Line-by-line General Circulation Model for Simulations of Diverse Planetary Atmospheres: Initial Validation and Application to the Exoplanet GJ 1132b.  The Astrophysical Journal, 878, 117 (2019).
  * 94. Gough, D. O.  Solar Interior Structure and Luminosity Variations.  Physics of Solar Variations 21–34, (Springer, Dordrecht, 1981).
  * 95. Minton, D. A. & Malhotra, R.  Assessing the massive young Sun hypothesis to solve the warm young Earth puzzle.  The Astrophysical Journal, 660, 1700–1706 (2007).
  * 96. Clifford, S. M.  A model for the hydrologic and climatic behavior of water on Mars.  Journal of Geophysical Research, 98, 10–973 (1993).
  * 97. Hu, H. & Argyropoulos, S. A.  Mathematical modelling of solidification and melting: A review.  Modelling and Simulation in Materials Science and Engineering, 4, 371–396 (1996).
  * 98. Truche, L. et al.  Experimental reduction of aqueous sulphate by hydrogen under hydrothermal conditions: Implication for the nuclear waste storage.  Geochimica et Cosmochimica Acta, 73, 4824–4835 (2009).
  * 99. Hem, J. D.  Rates of manganese oxidation in aqueous systems.  Geochimica et Cosmochimica Acta, 45, 1369–1374 (1981).
  * 100. Linstrom, P. J. & Mallard, W. G.  The NIST Chemistry WebBook: A chemical data resource on the internet.  Journal of Chemical & Engineering Data, 46, 1059–1063 (2001).
  * 101. Morgan, J. J.  Kinetics of reaction between O2 and Mn(II) species in aqueous solutions.  Geochimica et Cosmochimica Acta, 69, 35–48 (2005).

## Corresponding Author

Correspondence and requests for materials should be addressed to R.
Wordsworth:
<EMAIL_ADDRESS>
## Acknowledgments

RW thanks D. Johnston, K. Loftus, Y. Sekine and K. Zahnle for discussions. We
thank N. Lanza, E. Kite, D. Catling and N. Mangold for their helpful comments
during peer review. Funding: RW and MB acknowledge funding from NSF CAREER
award AST-1847120 and NASA/VPL grant UWSC10439. JAH acknowledges support from
the Simons Collaboration on the Origin of Life. Author contributions: RW, AK
and JH conceived the paper. MB performed the 1D regolith heating calculations.
KS performed the post-impact 3D climate simulations. RW performed the rest of
the modeling and wrote most of the manuscript. BE provided ideas and text on
surface geochemical evolution, timing, and the role of evaporitic vs.
thermochemical processes. JWH provided input and background on planetary
volcanism, impactor and fluvial/lacustrine processes, and geological
evolution. All authors discussed the results and provided input on multiple
draft versions of the manuscript. Code availability: The stochastic
atmospheric evolution model, along with other scripts to reproduce plots in
the paper, is available open-source at
_https://github.com/wordsworthgroup/mars_redox_2021_. The line-by-line
radiative-convective model used to produce the climate parametrization
(PCM_LBL) is available open-source at
_https://github.com/wordsworthgroup/mars_redox_2021/tree/main/PCM_LBL_. The
regolith thermal evolution model is available open-source at
_https://github.com/wordsworthgroup/crustal-heat_. _The Geochemist’s
Workbench_ is proprietary software available at _https://www.gwb.com/_. Data
availability: The input data to the model used to produce the plots in this
paper is contained within the _github_ repositories listed above, with the
exception of the HITRAN data used by PCM_LBL and the 1D regolith heating data,
which are available at _10.5281/zenodo.4458673_.

Figure 1: Observations vs. atmospheric evolution model predictions over Mars’
history.  A) Timeline of major events on the martian surface from geologic
observations (here Gya means gigayears ago). B) Changes in the net redox state
of the atmosphere vs. time due to the competing effects of episodic release of
reducing gases, atmospheric escape and surface weathering. C) Corresponding
surface temperature evolution and D) cumulative integral of time spent with
surface temperature $>273$ K ($t_{warm}$), for three assumed CO2 evolutionary
tracks (nominal value of $p_{\ce{CO2}}$ 3.5 Gya $=1.5$ bar). In the nominal
run, the time-mean surface temperature is 222 K, and the integrated period of
warm conditions from the Noachian onwards is a little over 1 My.  Figure 2:
Integrated duration of warm intervals as a function of H fluxes into the
martian atmosphere. Colored lines show the integrated warm period from 4.1 Gya
onwards (ensemble mean of 256 runs at each point) as a function of the average
rate of reducing gas (H2) input to the atmosphere over the entire 4.5 Gy
simulation interval. Colors indicate the assumed variability ratio $\beta$
[specifically, the maximum possible input rate in a 0.1 My interval relative
to the time-varying mean value $\overline{\mu}(t)$]. The central bright lines
show mean values, while the lighter shading indicates 1-$\sigma$ deviation
from the ensemble mean. Results show that when source variability is high
(cyan, blue and green lines), this strongly increases the total warm duration
for physically reasonable average H input rates (see black vertical lines).
Figure 3: Thermochemical sulfate reduction on Mars in the Noachian period. A)
Equilibrium aqueous chemistry of sulfur as a function of pH and oxygen
fugacity, assuming a temperature of $473$ K (200 ∘C) and [SO_4^2-] = [Fe^2+] =
[Ca^2+] = $10^{-3}$. Locations of the magnetite-hematite and quartz-fayalite-
magnetite buffers are shown in red and blue, respectively. B) Depth of surface
layer in which sulfate can be reduced to pyrite or pyrrhotite following
emplacement of a hot surface layer. Results are shown as a function of the hot
layer depth and initial temperature. The estimated global mean ejecta depths
from (?) due to a few known impactors are also shown. Figure 4: Manganese
oxidation on Mars during a late-stage brief warming event. A) Equilibrium
aqueous chemistry of manganese as a function of pH and oxygen fugacity,
assuming a temperature of $348$ K (75 ∘C) and [Mn^2+] = $10^{-3}$. B)
Temperature required for a given reaction time [inverse rate constant; (?)]
for manganese oxidation at a pH of 8 and various values of atmospheric partial
O2 pressure (colored lines). For comparison, the surface temperature on Mars
vs. time following a 30 km diameter bolide impact at three different
atmospheric pressures, based on 3D climate model results, is also shown. The
blue dot indicates the time at which the manganese reaction timescale equals
the time passed since impact; before this point manganese oxidation is rapid,
while after it the reaction becomes quenched.