1. Introduction

1.1 Planet Formation and Atmospheric Evolution It is widely believed that all planets in our solar system were formed similarly involving the same processes within the proto-planetary disk around the sun (Yung & DeMore, 1999). However, due to the masses of the planets and their individual distance to the sun their development varied strongly leading to eight very different planets, two of which, Earth and Mars, having possibly shared a similar early history.

Earth and Mars possess rocky surfaces with a clear separation to the atmosphere. Their atmospheres have lost most of the originally contained light gases like hydrogen and helium through escape processes and are believed to have formed by outgassing from the planets interior. Therefore it is assumed that Earth and Mars had quite similar atmospheres in the early stages of their development. However, when compared now, the atmospheres of these two neighbour planets show severe differences in composition and density. While Mars has a thin, carbon dioxide (CO₂) dominated atmosphere with only traces of molecular nitrogen (N₂) and molecular oxygen (O₂), Earth developed a thick N₂ dominated atmosphere with a substantial O₂ content (Jacob, 1999).

The reasons for these differences are manifold. The most important ones are the mass difference between the planets, which leaves the atmosphere of the lighter Mars more affected by escape processes (Lammer et al., 2008), and the evolution of life on Earth (Kasting & Siefert, 2002).

1.2 The Evolution of Earth’s Atmosphere The first life forms on Earth were anoxic microorganisms whose metabolism substantially altered the Earth's climate, oceans, and land masses and atmosphere by liberating various minerals, metals, and gasses including oxygen (Joseph 2010). Methane (CH₄) was likely one of the major metabolic products in this process. CH₄ has a 10³ times longer lifetime in the absence of atmospheric oxygen compared to its present residence time of 10 years in the current atmospheric composition of Earth. Due to this longer lifetime the atmospheric content of CH₄ in the early Earth’s development could have risen to over 1000 ppm assuming a biogenic release similar to today’s 535 Tg (CH₄)/year (Kasting & Siefert, 2002).

Following this first transition of the Earth’s atmosphere from a CO₂ dominated to a presumably thick, high CH₄ atmosphere like on Titan, the transition to an atmosphere with a high O₂ content took place (Joseph 2010). This oxygenation of the atmosphere was made possible by the release of O₂ produced by photosynthesis of cyanobacteria, and and increased substantially around 2.45 Ga ago (Farquhar, Bao, & Thiemens, 2000; Holland & Bengtson, 1994); and which made it possible for multi-cellular eukaryotes, equipped with mitochondria, to evolve (Joseph 2010). Evidence for this socalled great oxidation event can be found in geologic records, which show that older sedimentary rocks lost their iron content via weathering rather than via iron oxidation that can be found in rocks after about 2.0 Ga. This lack indicates a lower partial pressure of oxygen in the ancient Earth’s atmosphere (Kasting, 1993). Another way of determining the timing of the great oxidation is the analysis of signature of the degree of mass-independent fractionation (MIF) of sulphur isotopes (Farquhar et al., 2000). Under present atmospheric conditions MIF of sulphur photochemistry is uncommon in the lower atmosphere and is homogenised quickly. In an anaerobic environment however the MIF signature is preserved and can be detected in the geologic record (Kump, 2008). This method indicates that the increase in atmospheric oxygen took place about 2.45Ga ago (Zahnle, Claire, & Catling, 2006). The precise cause of the sudden rise of atmospheric oxygen content is still not fully understood and remains subject to ongoing research (Kump, 2008), though accumulating evidence points to biological activity as a major contributor (Joseph 2010).

1.3 The Evolution of the Martian Atmosphere It is believed that long ago Mars was a warmer and wetter planets; conditions conducive to the origin and evolution of complex life (Yung et al., 2010). But because of changing geochemical forces which effected energy flow it became impossible for complex life to dwell upon the surface or to continue to evolve. In contrast to Earth, Mars presumably never harboured complex life. Although there is substantial debate about the possibility of microbial life (Houtkooper and Schulze-Makuch 2010; Levin 2010; Sephton 2010; Yung et al., 2010), if extant, they are not in sufficient numbers to significantly alter or to maintain the atmosphere. Whatever atmosphere the planet had was lost after the initial outgassing from its crust. The high atmospheric loss was most likely caused by the comparably smaller mass of the planet and the missing magnetic field that would have protected the Martian atmosphere from powerful solar winds and the impact of loss processes through, for instance, sputtering and ion pickup at the top of the atmosphere (Lammer et al., 2008). The remaining thin atmosphere, the resulting lack of significant greenhouse warming on Mars (which is only 5% of Earth) and the absence of shielding against high energetic ionizing radiation, are conditions that would most likely inhibit the evolution of life on the planet’s surface. Therefore, it is highly unlikely that, unlike Earth, Mars has ever developed a biologically engineered atmosphere. Martian geological history remains however subject to substantial speculation and large uncertainties due to the limited amount of data (Levine et al., 2010a,b).

1.4 The Concept of "Terraforming" In 1971, a publication by Sagan triggered a still ongoing discussion about the deliberate alteration of the Martian climate with the aim to make the planet habitable. Sagan published the theory of the Long Winter Model (LWM), suggesting that the Martian climate alters between an icy state in which most atmospheric components are stored frozen on the surface and a state where the atmosphere is thick and sufficient to allow a warm and wet surface (Sagan, 1971). Even though today this hypothesis is contested, it was the beginning of the discussion about what is usually referred to as "terraforming", a term first coined in science fiction literature, and inspired a variety of subsequent implementation proposals.

Amongst the first ones, Burns and Harwit (1973) proposed to modify the planet’s precession cycle in order to provoke the transition between the cold state of the Martian climate to the warm summer state. First proposed implementation options include changing the orbit of the Martian moon Phobos and introducing material from the asteroid belt into the Martian system (Burns & Harwit, 1973). With further insight, such a Burns-Harwit manoeuvre is widely considered as ineffective, especially since the Long Winter Model no longer seems to be an accurate description of the Martian climate system.

Sagan (1973) suggested a less drastic modification of the Martian climate: changing the polar cap albedo to warm Mars' surface and thus triggering the release of CO₂ into the atmosphere leading to a runaway greenhouse effect (Sagan, 1973). Even though Mars would not be fully habitable after this process the planet would possess a denser CO₂ atmosphere, which could provide enough greenhouse warming to heat the Martian surface to the point where liquid water can exist, fulfilling the prerequisites for ecopoiesis, i.e. the fabrication of an uncontained, anaerobic biosphere on the surface of a sterile planet (Fogg, 1995).

However, modern observational data show that it is rather unlikely that the amount of CO₂ stored in the Martian polar caps will be sufficient to trigger the necessary runaway greenhouse effect. Even if the polar caps did contain a sufficient amount of CO₂, a sufficient change of the polar cap’s albedo seems currently out of reach: calculations show that the amount of material with the albedo of black carbon necessary to change the albedo sufficiently would be approx. 10⁸ tonnes. The transport of such masses from Earth to Mars does not seem feasible in any foreseeable future. Alternative suggestions are therefore to use Martian soil or plants or material from asteroids. Even if such processes were feasible, ensuring a long-enough change in the albedo might prove difficult due to weathering and the harsh Martian climatic conditions (Fogg, 1995; Levine et al., 2010c).

Following these first proposals a variety of other partially even more ambitious concepts to terraform Mars were published. The include (1) changing the orbital eccentricity of Mars’ orbit around the Sun and (2) changing the obliquity of Mars’s spin, (3) channelling of volatile-roch cometary nuclei into the Martian atmosphere, (4) seeding of Martian atmosphere with heat-absorbing, cloud-forming particles, (5) heating the polar caps using large spaceborne mirrors, (6) devolatising of the carbon within the Martian crust, (7) inducing large-scale drainages of potential Martian aquifiers, (8) the introduction of microbes, bioengineered to survive the harsh environment on the Martian surface, (9) the addition of bioengineered plants to lower the surface albedo and (10.) the introduction of super-greenhouse gases (GHGs). An overview of many of these methods has recently been published by Beech (Beech, 2009).

The entire concept of active interference in the planet of another planet raises also a series of ethical, philosophical, economic and legal questions (Arnould, 2005; Pompidou & Audouze, 2000; Reiman, 2010). These issues are not addressed in the present paper. The authors are fully aware that concepts related to the deliberate introduction of terrestrial life forms would raise currently insurmountable difficulties related to planetary protection requirements (Rummel et al., 2010). The reader is referred to the Planetary Protection Policy of the Committee on Space Research (COSPAR) as well as recent publications in the field (Arnould, 2010; Conley & Rummel, 2010; COSPAR, 2005; Guarnieri, Lobascio, Saverino, Amerio, & Giuliani, 2009; Kminek et al., 2010; C. P McKay, 2009; Nicholson, Schuerger, & Race, 2009; Rummel et al., 2010).

For the purpose of this paper, the term Martian "climate engineering" is preferred to "terraforming".

1.5 Feasibility of Martian Climate Engineering Concepts While some of the afore mentioned proposals seem completely out of reach for foreseeable futures considering contemporary technological capabilities, their assessment and especially the potential effects on Mars and its atmosphere are often scientifically interesting, such as e.g. if the alteration of the Martian orbit as proposed by Burns and Harwit would introduce a substantial perturbation of the equilibrium of the solar system (Beech, 2009). The deliberate introduction of bioengineered plants and microbes as well as space borne mirrors to melt the ice caps seem to be also out of reach at this stage of the technological development. Proposals dealing with the devolatization of the Martian crust or the drainage of aquifers are problematic as they require a sufficient abundance of the respective material in order to introduce enough greenhouse warming to allow ecopoiesis. Considering the lack of evidence about their existence from recent measurements by Mars missions such as ESA’s Mars Express and NASA’s Mars Odyssey, it is not clear if these proposals could ever be realised (Picardi et al., 2005).

One of the proposals considered as potentially feasible in a far but foreseeable future is the introduction of GHGs into the Martian atmosphere as suggested by Lovelock and Allaby (1984). Lovelock and Allaby originally suggested the injection of chlorofluorocarbons (CFCs) into the Martina atmosphere to increase the planet’s greenhouse effect. However, the use of CFCs as GHGs to warm Mars would be limited based on the lack of a shield to protect the lower Martian atmosphere from high energetic radiation. The lower atmosphere of Earth, i.e. the troposphere, is protected through the ozone layer, which reaches from approx. 15 km to 40 km. On Mars such a layer is missing hence CFCs are photolysed at a high rate, which would make it necessary to produce them continuously. Furthermore, the dissolving of CFCs produces ozone-depleting species, e.g. highly reactive chlorine, which prevent the production of an effective shield against ionizing radiation similar to the one on Earth (Fogg, 1995).

A possible way to prevent the release of O3 depleting gases was presented in the study by Marinova et al. in 2005 who analysed a set of four fluorine based GHGs in regards to their warming potential in the Martian atmosphere by introducing these into a one-dimensional radiative convective model of the Martian atmosphere (Marinova, Christopher P. McKay, & Hashimoto, 2005). This assessment is of special interest as it shows the ability of these gases to warm the Martian surface significantly without the release of ozone depleting products that would prevent the development of an UV-radiation shield (Table 1).

Even though some bacteria and higher life forms are known to be able to withstand high radiation levels, the shielding from excessive natural radiation would likely be one key question to be to support the introduction of life forms like bacteria that can pursue the transformation of the Martian climate.

1.6 The Assessment of Martian Climate Engineering Proposals using Numerical Climate Models The assessment of all Martina climate engineering proposals in regards to their warming potential relies on the numerical description of the Martian climate system. Over the last decades the quality and accuracy of these numerical climate models has increased significantly. The high variety of models with different dimensions and resolutions increased accordingly and has allowed new insights into the climate of Mars in a way that has not been possible before (Wordsworth et al., 2010). Especially highly sophisticated global circulation models (GCM), which are also used for simulating Earth’s climate support this new view on our neighbour planet. These continuously improved GCMs allow the assessment of past, present and future climates on Mars in more detail than ever before. Despite this development, scientific assessment of Martian climate engineering proposals has been scarce up until recent times. However with the tools to perform such assessments in a scientifically rigorous way matured sufficiently to allow such research questions to be addressed in a scientific sound way. This paper reports on the assessment of the effects of the four fluorine-based gases used by Marinova et al. (2005) on the Martian climate, by using for the first time a three-dimensional GCM. The method and first results of this study are presented.

The study used the model developed at the Laboratoire Météorologie Dynamique (LMD) (Forget et al., 1999, 2007; Spiga & Forget, 2009). The results aim to provide new insights into the reaction of the Martian climate system to artificially introduced gases in the atmosphere. In contrast to the study of Marinova et al. (2005), the present study not only gives information about the global temperature in the new balanced climate state, but also monitors the progress and typical timescales of these climate adjustments. The main aim of this paper is to give an overview of the applied method, the approach and discuss the preliminary results obtained during the continuing work on this project.

Section 2 summarizes the model that is used. Section 3 gives a detailed description of the changes to the radiative scheme of the model to account for the greenhouse warming of the injected gases; section 4 describes the first simulations that were performed in this study and the preliminary results. An outlook to future work on this ongoing project and other work in this area is given in section 5.

2. The Model

The present study uses the LMD GCM described by Spiga and Forget (2009). This model is continuously improved and regularly updated. Its horizontal resolution can vary over a broad range, including a few hundreds of kilometres to only a few meters, which makes it applicable to global and locally targeted simulations.

The model has been validated using measured data (e.g. from Viking and Pathfinder missions, from the Miniature Thermal Emission Spectrometer (Mini-TES)) and is reported to represent well a number of observed phenomena in the Martian atmosphere, such as wind patterns, regional / daily temperature patterns, dynamic phenomena such as convective motions, overlying gravity waves, and dust devil–like vortices (Spiga & Forget, 2009).

2.1. Model Structure The model calculates the temporal evolution of atmospheric and surface temperature, surface pressure, wind and tracer concentrations, i.e. variables that control or describe the Martian meteorology and climate, on a 3D grid (Forget et al., 2007). The dependencies and interactions between the different variables are parameterized based on physical phenomena and integrated over time. The LMD GCM consists of two parts, a fully compressible non-hydrostatic dynamical core and the physical part to incorporate parameterizations for the Martian dust, CO₂, water, and photochemistry cycles. The operations of the two parts are as follows:

2.2. Radiative Transfer The radiative scheme is embedded in the physical part of the model. The radiative scheme of the LMD GCM is a classical molecular band model in which the infrared spectrum is divided into four spectral intervals. The strong CO₂ 15 μm band, extending from 11.5 to 20 μm, is divided into two wide bands representing the central strongly absorbing part (14.2-15.7 μm) and the wings. The rest of the spectrum is divided into the CO₂ 9 μm band (5-11.5 μm) and a far infrared band (20-200 μm). Upward and downward heat fluxes are calculated and the radiative cooling rates of the vertical layers are derived from the flux divergence. For each spectral interval, the upward and downward fluxes (both oriented upward) are computed by

where B_Δν is the spectral-band-averaged Planck function, τ_Δν is the spectral-band-averaged transmission function, T_z is the temperature at level z, and F_Δν(s) is the flux emitted or reflected by the surface. The transmission τ_Δν is a function of the absorber amount, evaluated with the Padé approximant (Dufresne, et al. 1974).

The absorber amount is computed at each time step and point on the grid by integrating the density over the depth of the considered layer. In the original model, pressure and Doppler broadening of spectral lines are taken into account for CO₂., following Rodgers and Walshaw (Berman et al., 1976; Dufresne et al., 2005).

3. Adjusting the Radiative Transfer

In the version of the LMD GCM described in Forget et al. (1999) the radiative transfer through the Martian atmosphere can be affected by the presence of CO₂ gas, mineral dust, water vapour, water ice particles and CO₂ ice particles (Forget et al., 1999, 2007). In addition to the absorption coefficients of the species already present in the model, the absorption coefficients of the four fluorine based GHGs CF₄, C₂F₆, C₃F₈ and SF₆, are introduced into the radiative scheme of the model. The absorption of these gases is a function of wavelength (see e.g. Fig. 1 for the wavelength-dependent absorption of the most potent of these gases, C₃F₈).

To implement the absorption of the four artificial GHGs, the transmission function of the atmosphere is adjusted. The new atmospheric transmission value is computed by following the approach of Marinova et al. who identified different absorption bands for each gas and fitted the band-averaged transmission data (based on laboratory measurements) to a sum of exponential functions of the column density N of the absorbing gas (in molecules m^-2) (Dufresne et al., 2005)

where T is the transmission averaged over the spectral interval, a_i is a weighing factor, k_i is the absorption coefficient (in m² per molecule) and n varies between 1 and 3, depending on what order exponential fit is needed to produce a good fit. N is a measure for the absorber amounts of the absorbing gas, expressed in column density (molecules m^-2). In the present study these fits for 68 different absorption bands are used to compute the new opacity of the atmosphere. In the model N is derived from the partial pressure, which is computed by taking a specified percentage of the total atmospheric pressure.

After computing the transmission of the 68 narrow bands, these numbers are translated into the new widebandaveraged transmission (τ_Δν in Eq. (1) and Eq. (2)). τΔν is derived from the spectrally averaged results of the narrow band transmission ( nb in Eq. (4)) weighted by the Planck function and the width of the narrow spectral bands (Dufresne et al., 2005).

where (B_Δν )_i is the Planck function averaged over narrow spectral band i and n is the number of narrow bands that make up the considered wide spectral band. In this approach, the Doppler and Lorentz broadenings are not taken into account.

4. Simulations

In order to test the adjustments in the radiative scheme and of the adapted model, a preliminary short-duration simulation is performed in which the climate evolution is modelled over four Martian years. In this simulation the greenhouse gasses are introduced at concentrations of 0.2% (CF₄), 0.2% (C₂F₆), 0.4% (C₃F₈) and 0.2% (SF₄) of the total atmospheric pressure (so that in total these gases sum up to 1% of the atmospheric pressure). These partial pressures are taken constant in time.

4.1 Spatial and temporal resolution The tendencies in the radiation were calculated at a temporal resolution of 12 times a day, which is relatively coarse compared with the default setting of twice per hour. The atmospheric dynamical tendencies were calculated at the default frequency of 480 times a day. The applied horizontal spatial resolution is 32x24 and the Martian atmosphere is subdivided into 25 layers in the vertical.

4.2 Settings of the model parameters The model has been run with the "default" settings as suggested in the User Manual for the LMD GCM (Forget et al, 2007), except for the following parameters:

4.3 Computation Details The simulation was performed using a single processor on a Intel Xeon x5355 2.6 GHz 8 processor computer with 8 GB RAM. The simulation of the evolution of one Martian year takes about 10 hours of calculation time. The code has not yet been optimised for speed and further improvements in the simulation speed can therefore be expected.

5. Discussion and Conclusions

5.1 Discussion of Results The Martian surface temperature profile as used by the model is shown in Fig. 2. This profile is typical for the Northern Hemisphere spring, at zero solar longitude. Temperatures vary between 150K at the poles and 280K at some regions at the equator.

Modelled changes in the Martian surface temperature due to the implemented radiative effects of the GHGs after 5, 10 and 15 Martian years are plotted in Figure 3, 4 and 5 respectively. The figures show temperature changes averaged over the 5th, 10th and 15th simulated Martian year respectively. Positive values indicate regional warming in the simulation with the implemented greenhouse gases compared with the default run, whereas negative values show a cooling. The figures show that regional changes in the order of 0.01 K to 0.2 K start to evolve after only a few years of simulation. The alterations appear regionally grouped and are concentrated around the poles. There effect of the implemented greenhouse gasses does not clearly increase in time.

The evolution of the global surface temperatures in a climate with and without greenhouse gases are plotted in figure 6. The effects of the GHGs are small relative to the absolute value of the temperature and are not visible in this figure. Figure 7 shows the evolution of the temperature differences. The figure shows that the surface temperature changes are fluctuating in time at a scale of -0.05 K to 0.2 K around a value of about 0.05 K. There is no trend observed in the evolution of the climate system under the influence of the implemented GHGs. It might well be the considered time scale is too short to distinguish a clear trend. At this timescale the expected trend is small and could be masked by the observed fluctuations in the effect of the greenhouse gases.

5.2. Ongoing Project and Next Steps The subsequent step is to perform long-term simulations in which the Martian climate is able to converge towards a new equilibrium. When a new balance is reached, the warming potentials of the different GHGs can be determined and compared with and validated against the results obtained with the one-dimensional model by Marinova et al. In order to be able to perform longer simulations of at least at a temporal scale of about 100 years, the model’s computational time needs to be optimised, which likely involves also a parallelisation of part of the code. Following a full three-dimensional simulation of the atmospheric concentrations of the injected GHGs used in the assessment by Marinova et al. (2005) (Table 1), these will then be used as open optimisation parameters to determine their relative concentrations for the optimal warming potential. The adopted approach is to start with the assessment of the temperature increase caused by one GHG at a time. Both, the global temperature increase and the spatial pattern of the changes need to be considered. Following this, an assessment of mixtures of GHGs is performed including, but not limited to, those given in Marinova et al. (2005). The final step is the inclusion of atmospheric chemistry and the lifetimes of the chemicals in the model simulations.

6. Summary and Concluding Remarks

The state of the art LMD GCM model has been modified to allow for the assessment of the effects of the introduction of four different strong artificial greenhouse gases, CF₄, C₂F₆, C₃F₈ and SF₆, in the Martian atmosphere. Short-term simulations have been performed to validate the modifications in the adapted model. These simulations show small temperature changes (in the order of 0.01 to 0.6 K) after a few Martian years following their introduction into the Martian atmosphere. The magnitudes and the spatial distribution of the temperature differences agree with expectations, which indicates that the adjusted model is a good representation of the chosen scenario. First simulations in the order of decades allowed obtaining insight into short to medium term trends and evolution of the Martian climate under such conditions. The changes are as expected relatively small within the studied timeframe and centered around the poles. The introduction of the four species at a total of 1% of the atmospheric pressure results in localized surface temperature changes in an order of 0.05 K within only a few Martian days. The respective concentrations of the four gases have been kept constant at 0.2% (CF₄), 0.2% (C₂F₆), 0.4% (C₃F₈) and 0.2% (SF₄) of the total atmospheric pressure and assumed homogenously distributed. The different model runs were started at solar longitude Ls=0 (Northern Hemisphere spring) and lasted for 15 Martian years.

Despite of the rather basic implementation of the radiative effects of the GHGs and assumptions such as a fixed lifetimes for all species, a uniform mixture of the GHGs within the atmosphere and the neglect of chemical reactions with other atmospheric species, the results of this study give first indications about the reaction of the Martian climate system to such an interference. Though conclusions about the long term changes of the climatic state of the Martian atmosphere cannot be deduced from the limited runtime of the model, this study contributes to the understanding of the sensitivity of the Martian climate to external interferences and intends to build a foundation for more detailed and increasingly realistic studies.