Temperatures, pressure, oxygen, and water for trees

Over the past few decades, two important observations have informed our understanding of the elevation of the treeline. First, the treeline, properly so-called, is the fundamental limit of the growth of trees [33,34]. Second, numerous observations indicate that the limit of growth of trees at high elevations is correlated with temperatures during the growing seasons, and is surprisingly independent of the speci which is linked to the fact that trees stand up above the surface boundary layer and are exposed to the atmosphere. A model organism for the first tree on Mars could be the Siberian pine (Pinus sibirica), a close relative, if not synonymous, with Pinus cembra, a widely studied species in Europe. We adopt this species as a proxy for a representative high‑elevation conifer because it is widespread, well‑characterized, and highly tolerant of harsh atmospheric conditions and low temperatures. Our intention is to use a typical coniferous tree as an illustrative example in the model, while recognizing that the results are sensitive to the chosen thermal thresholds. This choice is therefore part of a conceptual exercise aimed at highlighting the potential possibilities and limitations of transferring terrestrial life to the Martian surface. Based on [35,36], we set the temperature limits for trees on Mars to be: (i) the growing season must last at least 110 sols (Martian days) during which: (ii) the minimum temperature during the growing season must be > −6 °C, (iii) the average daily temperature must be > 6 °C, and finally (iv) the maximum temperature must be < 40°C based on observations averaged across multiple high‑elevation treeline sites (data from [37–39]).

These treeline thresholds are derived from terrestrial high‑elevation and high‑latitude sites that benefit from active hydrological cycles, well‑developed soils, and oxygen‑rich atmospheres. In this study we use them strictly as proxy thermal limits for a representative high‑elevation conifer (Pinus sibirica/ cembra) and adopt their direct application to Mars as a simplifying assumption within a conceptual framework. In Martian conditions, the effective thresholds for growth might need to be shifted due to differences in atmospheric composition, radiation environment, gravity, and soil development, and our results should therefore be interpreted as indicative rather than as precise quantitative predictions for any particular species.

The treeline‐based temperature thresholds adopted in this study should be understood as necessary but not sufficient conditions for tree growth. Our four criteria (minimum growing season length, thresholds for daily minimum and mean temperature, and an upper limit on daily maxima) specify a thermal window within which trees could, in principle, function, but they do not guarantee viability in the absence of other key environmental requirements. In particular, our model does not include explicit constraints on water availability or the hydrological cycle, the surface radiation environment, regolith properties and soil development, or the presence of a functional microbial community supporting nutrient cycling. By design, the simulations isolate thermal constraints only; satisfying the temperature thresholds identified here would therefore have to be complemented by adequate water, suitable substrates, radiation protection, and a supporting microbiome before real trees could persist on Mars.

This is also the case on Earth, the fundamental limit of the growth of trees sets the treeline elevation but tree growth on Earth often does not reach this limit due to a variety of local factors and even human activities [34].

Design studies of greenhouses on Mars and the Moon have motivated extensive experiments with growing plants, although not large trees, at reduced atmospheric pressure (as low as 100 hPa) and with a high fraction of CO₂ and reduced O₂ (e.g., [40–43]). More recent experimental and conceptual studies of controlled‑environment agriculture and bioregenerative life support for space missions further explore plant performance under reduced pressure and Martian‑analog conditions [28–30]. For plant growth at a total pressure of 100 hPa the optimal CO₂ level is ~ 1 [41–43] and levels above ~ 10 hPa would be toxic [44,45]. This optimal atmospheric composition would imply 99 hPa of N₂ in the atmosphere of Mars presumably from decomposition of the soil nitrates [46,47], which are known to be present, but the total inventory is undetermined. In our calculations of the temperature, we assume pure CO₂. This only slightly overestimates the warming effect because the greenhouse warming of 100 hPa is small and the major part of the warming is due to the artificial infrared opacity.

Plants need O₂ for growth, and hypoxia is typically reported in plants when O₂ levels fall to 1–5% (e.g., [48,49]). For example, [43] reported in radishes that O₂ as low as 70 hPa had no deleterious effects, but a significant reduction in growth was observed when the oxygen partial pressure was dropped to 20 hPa, regardless of the total pressure. However, the mitochondrial enzyme that requires oxygen has such a strong affinity that this enzyme can function with oxygen partial pressures of 0.1 hPa [50] suggesting directed adaptation to lower oxygen levels may be possible. Notwithstanding this point, we take 1 hPa as the working threshold for O₂ levels required for tree growth, based on previous conceptual analyses and physiological considerations.

Recent observations and modelling studies place strong constraints on the present and past climate of Mars, as well as on plausible atmospheric evolution pathways relevant to terraforming scenarios. In situ measurements by the Curiosity rover have refined our knowledge of the current Martian atmospheric composition and isotopic ratios, revealing a thin, CO₂ dominated atmosphere with signatures of substantial past loss [51,52]. Climate and habitability studies of early Mars highlight both the difficulty of sustaining warm, wet surface conditions and the sensitivity of the water cycle and atmospheric stability to pressure and radiative forcing [53]. In parallel, exoplanet climate–photochemistry models of dense CO₂‑rich atmospheres provide analogues for how greenhouse gases and secondary species such as O₂ might accumulate or be depleted under different stellar and climatic regimes [54,55]. Together, these lines of evidence underscore that any terraforming scale modification of the Martian atmosphere must contend with tight constraints on volatile inventories, escape processes, and the coupled radiative–chemical response of a CO₂ dominated climate system.

It is important to note that the atmospheric states used in our thermal simulations – pure CO₂ at total pressures between 10 and 1000 hPa - are not self‑consistent with the combination of plant physiological constraints discussed above, namely an optimal CO₂ partial pressure of order ~1 hPa, an upper limit of ~10 hPa for non‑toxic CO₂, and O₂ partial pressures of ~1 hPa for respiration. In our framework, these pure‑CO₂ scenarios should therefore be viewed as a parameter sweep for surface temperature as a function of total pressure and grey infrared opacity, rather than as realistic terraforming end‑states. Achieving all three requirements simultaneously (sufficient total pressure, non‑toxic CO₂, and adequate O₂) would likely demand a complex combination of processes, including mobilization of CO₂, addition of a background gas such as N₂, and active engineering of the atmospheric composition, none of which are modelled here.

On Mars today, O₂ is a minor constituent of the near‑surface atmosphere, with a volume mixing ratio of order 0.1% and corresponding partial pressures of a few 10 ⁻ ³–10 ⁻ ² hPa under present conditions, as constrained by in situ measurements and photochemical modelling of modern Martian atmosphere (e.g., [51,52,56]). The question of interest here is how the O₂ fraction will scale as the CO₂ content of the atmosphere is increased from the present 6 hPa to 100 hPa. If the fraction of O₂ remains constant at 0.13%, then there is not enough O₂ since 0.13% of 100 hPa = 0.13 hPa – well below the level of O₂ needed.

The O₂ concentration in CO₂-dominated atmospheres has been considered in studies of early Mars and in considerations of spectroscopic detection of O₂ as a sign of life on exoplanets. [57] considered O₂ in a CO₂-dominated atmosphere on Mars, and obtained 1hPa of O₂ for a 1000 hPa CO₂ atmosphere. The O₂ dropped to very low levels as CO₂ decreased, becoming less than 0.1 hPa at 100 hPa of CO₂. [58] explicitly considered the O₂ levels in a terraformed Mars, assuming a pressure of CO₂ of 1000 hPa. They found between 0.5 hPa and 20 hPa of O₂ depending on the thermal profile in the stratosphere. The higher O₂ values corresponded to a cold stratosphere with low levels of water (see Table 3 of [58]). Segura et al. [59] criticized the applicability of the [58] results for exoplanets, arguing “that abiotic O₂ buildup is only likely to occur on dry or frozen planets”. This is perhaps not applicable to Earth but would perhaps pertain to Mars. Selsis et al. [58] did not present results for a 100 hPa CO₂ atmosphere but if the mixing ratio persisted down to this level the result would be 2 hPa O₂ in a 100 hPa CO₂ atmosphere -much higher than the results reported in [57]. Recent coupled climate–photochemistry studies of CO₂‑dominated atmospheres on Mars and terrestrial exoplanets provide additional context for our assumptions about oxygen production and retention. For example, [60] modelled the early Martian climate under a denser CO₂ atmosphere and highlighted the strong coupling between atmospheric pressure, temperature, and the water cycle. [54,55] explored the photochemical and radiative behavior of high‑CO₂ atmospheres in the context of exoplanet biosignatures, showing that substantial abiotic O₂ can accumulate under certain climatic and stellar conditions. These studies underscore that O₂ abundances in CO₂‑rich atmospheres are highly sensitive to the thermal structure and water availability, and therefore remain a major uncertainty in assessing the viability of complex plant life on a terraformed Mars.

Thus, we consider that the O₂ level on Mars in a 100 hPa CO₂ atmosphere is not certain, and more work needs to be done including models that limit the CO₂ to <10 hPa with the total pressure set by N₂. However, current models suggest that at least initially when Mars is still cold and dry over most of the planet, O₂ mixing ratios due to photochemical production may be high enough to support the first tree. If not, then increasing the pressure of CO₂ to as high as 500 hPa may be necessary. This would exceed the currently recognized sources of CO₂ on Mars and would also be far above the 10 hPa maximum limit of CO₂ pressure for plant growth.

The discussion of potential O₂ accumulation in terraforming scenarios should be regarded as highly uncertain. Existing photochemical models of CO₂‑dominated atmospheres on Mars and terrestrial exoplanets yield a wide range of possible O₂ mixing ratios, depending sensitively on the thermal structure, water abundance, and escape processes, and thus cannot yet be treated as firm predictions for a terraformed Mars. In this context, our analysis does not rely on any specific O₂ value: the thermal windows we identify are independent of the actual O₂ abundance and merely indicate where temperature and pressure conditions would not preclude tree growth. We refer to O₂ only as an additional constraint that would have to be satisfied, alongside limitations on CO₂ toxicity and total pressure, for real trees to survive, and we do not imply that achieving favorable O₂ levels is likely or guaranteed.

Comprehensive GCM studies of the Martian water cycle under a significantly thicker atmosphere, while assuming the present‐day obliquity and solar luminosity, remain limited. However there have been simulations of the water cycle in a higher pressure atmosphere on early Mars, with a reduced solar luminosity (e.g., [60,61]). These indicate that a thicker atmosphere would transport water from the poles to equatorial regions more effectively. These models show that increasing atmospheric pressure generally enhances the efficiency of water transport away from the poles, but stable surface liquid water remains difficult to achieve without additional warming [14,53]. However, in these models with reduced solar luminosity, the water that accumulates on the surface remains frozen. Similar results are seen in models of the water cycle of Mars at high obliquity (e.g., [62,63]), including studies with our baseline model [64].Even with the present solar luminosity conditions, Mars remains too cold for this moisture to be a significant source of liquid water [64]. However, these models of early Mars and Mars at high obliquity indicate that as the atmospheric pressure increases, there is more effective transport of water from the polar regions to mid latitudes. In considering the first tree on Mars, we make a qualitative inference that a higher‑pressure atmosphere would lead to warmer conditions and, in turn, to more effective transport of water toward mid‑latitudes and an increased likelihood of transient liquid water, thereby improving the potential for tree growth. However, this remains a conceptual assumption rather than a result of explicit hydrological modelling, and a fully coupled simulation of the Martian water cycle under thick‑atmosphere scenarios is an important avenue for future research.

In our thermal simulations the atmosphere is treated as pure CO₂, with total surface pressures ranging from 10 to 1000 hPa and an externally prescribed grey infrared opacity. This choice is intended as a computational device to span a range of thermal states, rather than as a self‑consistent representation of atmospheres compatible with plant physiology. Laboratory and greenhouse studies indicate that for higher plants the optimal CO₂ partial pressure is of order ~1 hPa, with growth inhibition and toxicity becoming significant above ~10 hPa. Thus, the pure‑CO₂ atmospheres considered here are not directly compatible with these biological thresholds. In any realistic scenario where terrestrial trees could grow on Mars, most of the total pressure would instead have to be provided by an inert background gas such as N₂, with CO₂ restricted to the physiologically acceptable range and O₂ maintained near ~1 hPa for respiration. Under such conditions, similar total pressures and effective longwave opacities could, in principle, be achieved with much lower CO₂ fractions, and our simulations should therefore be interpreted as mapping thermal states as a function of total pressure and τ, not as literal plant‑ready atmospheric compositions.

In addition to temperature and pressure, the surface radiation environment on Mars represents an important independent constraint on complex plant life. Even under low‑pressure or moderately thick CO₂ atmospheres, ultraviolet and ionizing radiation at the Martian surface are expected to remain substantially higher than on present‑day Earth due to the lack of a global magnetosphere and ozone layer. Our model does not attempt to quantify these radiative effects or their biological impact, and they therefore lie outside the scope of the present thermal analysis. Nevertheless, any realistic assessment of the viability of trees or forests on Mars would need to consider radiation mitigation measures – such as partial burial in soil, local topographic shielding, or engineered atmospheric composition – in addition to satisfying the thermal thresholds discussed here.

Surface energy balance model assumptions and limitations

We have developed an energy balance model for Mars [64]. The planet is discretized into 4002 equal-area polygons (3990 hexagons and 12 pentagons; area ≈ 36,000 km² each), providing uniform horizontal resolution and avoiding polar singularities. Vertical structure is treated in bulk: a surface–subsurface layer in thermal contact with the atmosphere, without explicit vertical levels.

In this study, we employ a simplified but spatially explicit surface energy balance model of Mars. The atmosphere is treated as composed of pure CO₂ for the thermal calculations, so that the prescribed CO₂ surface pressure directly sets the background greenhouse contribution; this choice slightly overestimates warming relative to mixed N₂–CO₂ atmospheres at the same total pressure. Additionally, artificial greenhouse forcing is represented by a single grey infrared opacity parameter, which we vary externally rather than computing from detailed radiative transfer or aerosol microphysics. We treat the grey infrared opacity τ as an effective, vertically integrated longwave optical depth that represents the combined impact of additional greenhouse absorbers (for example, engineered gases, aerosols, or enhanced CO₂ columns) on the outgoing thermal radiation. The grey infrared opacity τ is a mathematical construct: it is defined as the value of a uniform grey absorber across the thermal infrared spectrum that yields the same downward infrared flux as obtained from detailed line‑by‑line radiative transfer calculations (e.g., [9]). In this study, τ is therefore used as an abstract sensitivity parameter that controls the strength of the generic greenhouse effect, rather than as a directly measurable physical quantity tied to any specific gas or aerosol species. Increasing τ in our model reduces the effective infrared cooling to space and therefore raises the surface temperature, analogous to an increase in radiative forcing in more detailed radiative–convective or 3‑D GCM studies. This parametrization is intentionally simple and is used to explore the sensitivity of the thermal field to a generic increase in greenhouse effect, rather than to represent any specific engineered greenhouse species.

In this framework, we explicitly neglect several processes that are known to be important for the Martian climate system. In particular, the model does not resolve the hydrological cycle of H₂O, including cloud formation, atmospheric moisture transport, and phase changes of water, nor does it contain a full three‑dimensional dynamical core capable of representing baroclinic waves, transient eddies, and detailed Hadley circulation structure. As a result, our simulations do not address the stability or spatial distribution of surface or near‑surface liquid water, nor do they capture feedbacks involving water clouds or water vapor. The model should therefore be regarded as a first‑order thermal framework that isolates the radiative–conductive response of the surface–atmosphere system under prescribed CO₂ pressures and infrared opacities, rather than as a full general circulation model suitable for comprehensive climate or hydrological predictions.

The model does not include a fully coupled water cycle: water vapor, clouds, and phase changes of H₂O are not prognostic variables, and any effects of water on radiative transfer or latent heat are therefore neglected. Large‑scale atmospheric circulation and lateral heat transport are represented in a parameterized form using eddy diffusion between neighboring cells and a zonally averaged Hadley‑cell‑like heat flux calibrated against outputs from modern Mars GCMs, rather than being resolved explicitly by a full three‑dimensional dynamical core. Our framework is therefore not a full three‑dimensional general circulation model: it does not explicitly resolve atmospheric dynamics, cloud and dust microphysics, or photochemical processes, and should be viewed as a first‑order thermal model that isolates the radiative–conductive response of the surface–atmosphere system under prescribed CO₂ pressures and infrared opacities.

In the thermal calculations presented here we treat the Martian atmosphere as composed of pure CO₂. This simplification is motivated by the fact that, at the relatively low surface pressures considered (~100 hPa), the direct greenhouse contribution of CO₂ alone is modest and most of the additional warming in our scenarios is produced by the prescribed grey infrared opacity. Replacing part of the CO₂ with radiatively inert N₂ or with O₂ at fixed total pressure would slightly reduce the baseline CO₂ greenhouse effect but would leave the imposed grey forcing unchanged. Consequently, within the conceptual framework of this study, the location and extent of the “thermal windows” identified for potential tree growth are only weakly sensitive to the detailed atmospheric mixture at a given total pressure and τ. A more realistic treatment of N₂–CO₂–O₂ mixtures, and of specific engineered greenhouse species, could be achieved in future work by coupling our surface energy balance model to more detailed radiative transfer calculations.

In our model, the temperature of a cell n on sol t + 1, , is determined from the temperature on sol t, , by an energy balance calculation:

(1)

Where is the mass per unit area of the subsurface and lower atmosphere of the cell , is the specific heat per unit mass, is the solar flux which is a function of latitude, of the cell , and the time of year and specific time of a day h, and depends on the orbital parameters of Mars especially the obliquity. is the albedo of the cell, is a reduction in solar flux due to dust, which depends on latitude and season. is downward greenhouse flux in cell , ε is the emissivity of the surface, σ is the Stefan Boltzman constant, is the net convective heating carried into the cell from adjacent cells by eddy convection accounting for elevation differences in cells. is the latent heat in the cell , released due to the condensation of atmospheric CO₂ or removed due to the evaporation of solid CO₂ in the cell. is the heat flow into the cell from the large scale circulation. is the downward flux to the subsurface ground layer. All fluxes on the right hand side of Eq. 1 are per unit area per unit time. is a time step of simulation, equal to one sol (88,775 sec.) for the baseline, sol-averaged, model and half a Martian hour (1/48 sol, approx. 1850 sec.) for the diurnal model which resolves the sol in 48 timesteps. To compute the greenhouse flux, we assume an atmospheric temperature profile that is in radiative equilibrium, that connects the surface temperature to the effective temperature at the top of the atmosphere, and a gray infrared opacity. The total exchangeable CO₂ is set as a model parameter. This amount, less any CO₂ condensate, determines the mean pressure of CO₂ on the planet. The CO₂ pressure in an individual cell is set with respect to this mean assuming hydrostatic equilibrium. To reproduce the observed asymmetry in seasonal CO₂ cap persistence between the poles, we introduce a dust-related shading parameter R that reduces absorbed solar flux more strongly over selected high-latitude cells. The model is computationally efficient (one Martian year in <10 minutes on a standard desktop), enabling multi-decadal integrations and parameter sweeps. Baseline simulations are evaluated against Viking 1 and 2 lander records and two 3-D GCMs (MCD and the NASA Ames model v3.1). Although our model omits explicit vertical resolution, its high and uniform horizontal resolution yields global-mean surface temperatures within ~2–3 K of the GCMs (with the baseline and MCD solutions ≈2.3 K warmer than the NASA model).

The model provides a horizontally high-resolution, energetically consistent framework for simulating the coupled evolution of surface temperature, CO₂ frost, and pressure on Mars under prescribed orbital, radiative, and dust conditions, suitable both for baseline present-day climate and sensitivity experiments.

Compared to the baseline model [64], the model described in this article has been extended in two ways (Fig 1):

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Fig 1. Diagram of the calculation process.

https://doi.org/10.1371/journal.pone.0349588.g001

• The temporal resolution was increased by an order of magnitude (computational step of 1/48 sol compared to 1 sol in the baseline model), the spatial resolution remained the same (4002 cells – Goldberg polygons). This was done to resolve the diurnal cycle in order to determine daily maximum and minimum temperatures, which are part of the criteria for tree growth.
• Larger values of CO₂ and and artificial warming leading to much larger values of the infrared opacity were included in the greenhouse effect. The methodology for the computation of the greenhouse flux was not changed and was as described in the Baseline model.
• Modification of the subsurface flux calculation in the diurnal application of the model to account for the dependency of the damping depth on period. Instead of a damping depth corresponding to the Martian year in the diurnal model we use a damping depth corresponding to the Martian sol.

The methodology of computations assumes two main steps (Fig 1):

1. (i). calculation of daily average energy balance Martian model for each sol (Martian day) and for each cell;
2. (ii). (ii) calculation of diurnal energy balance Martian model for every sol and cell.

Both models are based on the equation for energy balance.

The model initializes with a total exchangeable CO₂ pressure, including atmospheric CO₂, polar cap CO₂, and surface frost. As the simulation progresses through seasonal cycles, CO₂ condenses or sublimates based on the balance between atmospheric pressure and local saturation pressure. The CO₂ mass flux between phases adjusts dynamically, influencing planetary pressure and thermal balance. The model determines the insolation in every cell for a specific sol. The insolation is computed using a standard orbital equation incorporating Mars’ eccentricity, axial tilt, and the areocentric longitude. The result is the solar insolation at the top of the Martian atmosphere, influencing surface energy dynamics. Latent heat is computed assuming the relation between atmospheric and local saturation pressure. The condensation takes place when atmospheric CO₂ pressure exceeds saturation pressure, leading to latent heat release and pressure reduction. On the contrary, sublimation occurs when condensed CO₂ is present, and the overlying atmospheric CO₂ pressure is below saturation pressure, cooling the cell and increasing atmospheric CO₂ mass. The iterative approach ensures that the CO₂ flux stabilizes within model constraints. Heat transport is modelled using a convection-diffusion equation, incorporating the Laplacian operator over cells in the Goldberg polygonal representation of a Mars surface. Hadley cell-driven heat transport redistributes energy from equatorial to polar regions. The model estimates heat flux convergence using zonal wind and temperature gradients, parameterized based on NASA Ames Research Center GCM model. A Fourier series approximation is used to represent seasonal variations. Heat conduction into the subsurface is computed based on thermal conductivity, depth-dependent temperature variation, and the Carslaw-Jaeger solution for periodic surface temperature fluctuations. The damping depth is set according to annual temperature penetration depth estimates. The model calculates the downward infrared flux based on surface temperature and infrared opacity, primarily influenced by CO₂ and atmospheric dust. This summarized methodology ensures computational efficiency while maintaining physical accuracy in Martian climate modeling.

The diurnal energy balance Martian model is computed using the results of the average daily energy balance Martian model for each sol separately. It takes into consideration average daily surface temperature, subsurface temperature, atmospheric pressure, greenhouse flux, radiation flux, eddy diffusion, Hadley diffusion, latent flux, frozen temp, season, and coordinates. Moreover, it takes into account the sun’s position over the horizon, calculating the insolation for every half an hour (48 times a sol), assuming sunrise and sunset, day and night. At night, the insolation is zero. The model calculates the exact energy from insolation, and exact exchange of energy with subsurface. Remaining energy components are taken as constants calculated in the baseline model [64].