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 The recent results by the Gamma Ray Spectrometer instrument on Mars Odyssey [Boynton et al., 2002] indicate the possibility of ground ice deposits within a few meters of the surface even at low latitudes and midlatitudes. The stability of ground ice deposits at these latitudes is a puzzling question. To address this question, we have developed the Berlin Mars Near-Surface Thermal model (BMST), a model for the thermal behavior of the Martian surface with a special focus on the volatile transport within the subsurface material. Using the BMST, we have performed a case study to derive limits on the burial depth of ground ice deposits stable over annual cycles at the MER landing sites in Isidis Planitia. We have studied the temperature gradient within the subsurface, assuming different structures and thermophysical properties for the surface and subsurface material. While the results derived here will have no immediate consequences for the MER mission because Isidis Planitia has been demoted to a backup landing site, the results show the potential and versatility of the model we have developed and give some results on the surface properties of Isidis Planitia.
 As the result of several Mars missions, the thermal properties of the Martian surface are relatively well known. For our approach of a detailed study of the thermal behavior of the surface we make use of this wealth of information. The model we have developed includes a detailed treatment of the energy transfer into the surface, including energy transported by gas flux and energy used to sublimate and provided by recondensation of volatiles within the surface. We present here a case study for the proposed MER landing sites in Isidis Planitia, discussing different structures of the surface and covering by dust. We have started this study while Isidis Planitia was still a prime landing site for the MER. In subsequent publications we will present results for the Beagle 2 landing site and for the MER landing site in Gusev crater.
2. Berlin Mars Near-Surface Thermal Model
 There is a wide variety of models for the thermal properties of the Martian surface. They range from simplified surface models as a boundary condition for atmospheric models, like the NASA Ames GCM [Haberle et al., 1993], the European Mars Climate Database [Forget et al., 1999; Lewis et al., 1999] or the modeling of the 1 m air temperature at MER landing sites by Martin et al.  to sophisticated models for the global water vapor distribution by Farmer and Doms , for the thermal behavior of the surface as derived by the IRTM measurements on Viking [Paige et al., 1994] or the recently updated model for the global distribution of subsurface ice by Mellon . The latter models study the near-surface layers down to a depth of about 100 m. These models are ideally suited to study the stability of ground ice deposits reachable by future landing missions. However most of these models assume a simplified subsurface structure. They assume that the underlying material has the same thermophysical properties as the surface layer as measured by the IRTM or TES instrument, respectively. In these models usually only the ice content of the subsurface material changes the thermal properties of the material. While all of this models have produced valid results there have been recently concerns, that the simplified assumptions about the subsurface structure might influence the results [Clifford, 2003].
 To address these concerns we have developed a new model for the thermal behavior of the Martian surface. The Berlin Mars Near-Surface Thermal model (BMST) is based on a standard model for cometary surfaces [Benkhoff and Huebner, 1995]. We have adapted this model to the conditions of the Martian surface. Our model is based on a layered structure of the subsurface material, in which each layer can have different physical and thermophysical properties. On the basis of the recent results for the polar layered deposit [Blasius et al., 1982; Howard et al., 1982] (and recently Milkovich and Head ) and from the layering found for example in Maris Vallenaris [Malin and Edgett, 2000; Edgett and Malin, 2003] this seems to be a more realistic representation of the Martian surface. The main features of the BMST are a variable high lateral resolution down to the centimeter range, a realistic treatment of the thermal properties of ice-rock mixtures, a detailed treatment of gas flux within the surface and into the atmosphere and a variable temporal resolution which allows to study daily as well as annual variations.
 For the study presented here we have assumed a 100 m thick surface layer with a lateral resolution of 5 cm. This layer is divided in a dust layer of variable thickness at the surface which is initially ice-free and an underlying layer initially composed of a homogeneous, porous, crystalline ice dust mixture. The underlying layer can contains several components of chemically different ices (usually H2O and CO2). For the modeling presented here we have only included H2O ice as discussed later in this paper. The dust layer and the underlying surface material can have different thermal conductivities. The ice-dust matrix has a thermal conductivity calculated from the weighted mean of the thermal conductivity of the base material and the ice within the pores. The initial porosity is set to 0.5 and can vary during the modeling due to recondensation of ice within the pore space.
 The model solves the time-dependent mass and energy equations for the different volatiles simultaneously. Solar energy input varies due to orbital and rotational motion of the planet. Variation of the solar flux on the surface due to dust opacity of the atmosphere is not yet included. The dust load of the atmosphere attenuates the solar flux and will slightly lower the resulting daytime temperature on the surface. During the nighttime the dust in the atmosphere can reflect heat back to the surface, and will keep the surface warmer as assumed in our model. In the conclusions we will shortly discuss the influence of these effects on the results. Heat is transferred into the interior of the body by solid state heat conduction in the dust-rock-ice mixture (matrix) and by vapor flowing through the porous matrix. The gas flow from the sublimation fronts is driven by vapor pressure gradients. While initially only the dust layer is desiccated, the desiccated layer can grow downward because of inward migration of the sublimation fronts. In our model we assume that the crust is always stable and cannot be destroyed by the escaping gas or impacts. The energy conservation equation for the porous, icy, dusty layer is (for details, see Benkhoff and Huebner  and Fanale and Salvail )
where ΔHi and qi are the enthalpies of sublimation and the intrinsic mass release rate of vapor per unit volume of components i, respectively, κm is the thermal conductivity of the matrix, T is the temperature, t the time, ψ the porosity, ρg the mean density and v the mean velocity of the gas evaporating from deeper layers and streaming through the crust, and c and cg the average specific heats of the matrix and of the gas at constant volume, respectively. The energy conservation equation for the crust is
where κd is the thermal conductivity of the dust matrix. The surface temperature is calculated from the balance between the net incoming solar flux, losses from thermal reradiation, heat needed for sublimation or becoming free during condensation, and heat transport in and out of the shell
 In equation (3), A denotes the albedo, F0 the solar constant, r the heliocentric distance in AU, ζ the local zenith angle of the Sun, ϵ the infrared emissivity, σ the Stefan Boltzmann constant, and Ts the surface temperature, and Q the gas production rate at the surface. The local zenith angle can be expressed as a function of latitude, hour angle, obliquity, the true anomaly, and the angle between the ascending node and the subsolar point at perihelion [see, e.g., Fanale and Salvail, 1984]. The latent heat L = ΔH is calculated from the Clausius Claperon equation
where P is the saturation pressure and R is the universal gas constant. The conservation of mass in an n component system undergoing a phase change is given by the following equations:
where, for each component i, ρg is the density of the porous matrix and j the flux of gas. The internal gas production rate q is given by
with ci the mean thermal velocity of the gas molecules, ρsat the saturation density and a the radius of the pores.
 For the boundary condition at the bottom of the layer we assume a constant and zero mass flux and no heat flux from the interior. We have also computed model runs with an internal heat flux of 25 mW/m2. The net effect on the upper 10 m of the surface is negligible, but the computing time of the model increases dramatically, because stable conditions are only reached after the heat wave from the interior has reached the surface. Under the conditions we have studied in this work this takes far more than 1000 Mars years. For this reason we have run all subsequent models with an initial temperature of the base material of 130 K. We have derived this temperature from test runs assuming internal heat flux which were continued until the heat wave from the lower boundary reached the upper layers and the model had reached an overall stable condition.
3. Proposed MER Landing Sites in Isidis Planitia
 As a first test region for the modeling we had chosen an area around the MER landing ellipses IP84A2 and IP96B2 (4.22N, 87.91E) in Isidis Planitia while it was still a prime landing site. Isidis Planitia is now only a backup landing site, therefore the results derived in this work have no immediate consequences for the MER mission, but they are still valid as a proof of concept for our modeling approach. The results presented here demonstrate the capability and versatility of the modeling. They also give some indications on the subsurface structure and volatile inventory of the Isidis Planitia region.
 The dust coverage index [Ruff and Christensen, 2001] indicates that this region has a fairly low dust coverage. This seems to be confirmed by the first THEMIS infrared day- and night-time images of this area [Christensen and Rice, 2002]. For the modeling we assume a thin dust layer of not more than 100 cm covering a homogeneous base material. For the mean density of the base material we assume a value of 1750 kg m−3. This is a typical value for coarse sand. Judging from the MOC images, which show a general smoothness of the area, and the blandness of the THEMIS daytime infrared images of the region [Christensen and Rice, 2002], it is valid to assume that the upper 50 m have a composition somewhere between coarse sand and sandstone. For the albedo we have used a value of 22%, as a mean value for the studied area. Figure 1 shows the surface albedo as measured by the TES instrument on MGS [Christensen et al., 2001]. Within the area of the landing ellipse, the albedo shows little variation, therefore a constant value is a valid assumption. For the dust a infrared emissivity of 96% was assumed [Burgdorf et al., 2000].
 The Thermal Emission Spectrometer (TES) on Mars Global Surveyor has returned a map of thermal inertia values with a good global coverage for the midlatitude regions [Mellon et al., 2000]. These thermal inertias I have been converted to thermal conductivities k using the relation
where ρ is the mean density of the material and c is the specific heat capacity.
 The thermal conductivity as derived from the TES thermal inertia measurements are shown in Figure 2 as a map for the area surrounding the landing ellipses with a resolution of 8 km. For the conversion we used ρ = 1750 kg m−3 and c = 795 J kg−1 K−1 which are typical values for coarse sand assuming a basaltic mineral composition. The center and the lateral extension of the ellipses are marked. From the map we have derived a mean value of for the area studied here.
 From data of the Infrared Thermal Mapper (IRTM) on board the Viking spacecraft, Christensen  derived for the same region a thermal inertia of I = 384 Jm−2 s−0.5 K−1 for the fine component on the surface. This value has been converted to a thermal conductivity of using a value of ρ = 1500 kg m−3 and c = 795 Jkg−1 K−1, typical values for fine sand.
4. Case Studies
 We have performed a number of case studies to analyze the effect of a layered surface structure on the burial depth of ground ice deposits. Four of the cases we have studied will be presented here. Most models for the Martian surface assume a homogeneous structure of the near-surface layer. Therefore this is our first test case. For this case we have assumed a thermal conductivity of 0.17 WK−1 m−1 as derived from the TES instrument for the surface down to a depth of 100 m. As a slight variation of this case we have assumed a second case in which the surface is covered by a 5 cm thick layer of dust with a thermal conductivity of 0.123 WK−1 m−1 as derived from the IRTM measurements on the Viking mission. As discussed above it seems more likely that the near-surface material is not homogeneous, but shows a layered structure. To investigate the effect of this assumption, including the influence of the thickness of the dust layer, we have study two more cases. In these cases the dust layer has a thermal conductivity of 0.17 WK−1 m−1 as derived from the TES measurements and the underlying base material has a thermal conductivity of 0.5 WK−1 m−1. With these four cases we cover the range of thermal conductivities which are most likely to be expected for the surface material at Isidis Planitia. While the low values for the dust cover are measured values the higher value for the base material is typical for sedimentary material or loose sandstone. On the basis of the images we have so far from the region it is unlikely to expect rock outcrops close to the surface which would have an even higher thermal conductivity. This case study will present the effects on maximum and minimum surface temperatures and the burial depth for ice deposits stable over annual cycles for these extreme cases. The real values will most likely fall somewhere within the limits derived here. A summary of the parameters used for the different cases is given in Table 1.
Table 1. Parameters Used for the Modeling of the Cases Studied in This Work
kDust cover, W/km
kBase material, W/km
Dust Cover, cm
Homogeneous surface layer
Thin dust cover on homogeneous surface layer
5 cm dust cover on porous sediment material
100 cm dust cover on porous sediment material
 For all cases we started with a temperature of 130 K for the surface and base material, a water ice content of 40% and no other ices. We have not included CO2 ice for this study. It is unlikely to find CO2 ice at shallow depth (e.g., less than 100 m) at the latitudes of Isidis Planitia. We have performed some test runs all showing that CO2 ice sublimates quickly from the upper layer. After only 50 Mars orbits the surface was down to a depth of 50 m free of CO2 ice.
 With these starting conditions the model needs approximately 600 Mars orbits to reach a stable temperature distribution. The surface temperature and in general temperatures down to a depth of about 20 cm show after only 60 Mars orbits little transient effects with a long term variation of less than 0.01 K per orbit with strong seasonal effects superimposed. For greater depth the temperature distribution and especially the ice content shows transient effects for the first few hundred cycles. Only after this time the temperatures below 2 m remain stable and show only slight annual variations. In this stable state the temperatures below 2 m depth show long term trends of less than 0.01 K per orbit. The volatile transport within the subsurface has reached an equilibrium marked by the fact that the gas density at the sublimation front shows no variations and equals the saturation pressure. While we show in the plots of this paper only two orbits, the modeling itself has been run for several hundred orbits. All results presented in the following have been obtain after the model has reached stable conditions.
 The first result of the modeling is the temperature distribution in the subsurface with a lateral resolution of 5 cm. As described above the model calculates the volatile transport within the surface and yields as one output the ice content as a function of depth. On the basis of this a minimal burial depth for ground ice deposits can be derived. Only below this depth ice remains stable over annual cycles. Above this depth all ice deposits are sublimated over time. Since the model in this configuration uses time steps of a few Mars days, we are not modeling daily ice deposits on or close to the surface. Theses are not topic of this paper, however test runs with higher temporal resolution show this diurnal ice deposits at shallow depth.
Figure 3 shows the temperature distributions over two Mars years for the cases 1 and 2 down to a depth of 50 cm; Figure 4 shows them for the first 10 m below the surface. The seasonal effects dominate in both cases the upper 10 cm. This surface layer endures thermal difference of over 30 K over an annual cycle. The material in this layer is each year thermally stressed and will therefore most likely show signs of thermal erosion. We have derived a maximum mean daytime surface temperature of 286 K for case 1 and 292 K for case 2, and a minimum mean nighttime temperature of 255 K for case 1 and 259 K for case 2 (see Table 2). The differences are small but measurable given accurate instruments like the TES instrument on MGS or the Planetary Fourier Spectrometer (PFS) on Mars Express. The annual heat wave has a noticeable effect down to a depth of about 2 m. Below this the temperature gradient over the whole year has a gentle slope of not more 2 K/m.
Table 2. Results for Maximum tmax and Minimum tmin Surface Temperatures and Burial Depth dice of Stable Ice Deposits
Homogeneous surface layer
Thin dust cover on homogeneous surface layer
5 cm dust cover on porous sediment material
100 cm dust cover on porous sediment material
Figure 5 shows a depth profile of the ice content in weight percentage. We started both cases with an ice content of 40% for the material below a depth of 5 cm. After about 200 orbits all water ice in the first 5 m below the surface is sublimated. For case 1 we have derived a minimal burial depth of 6.0 m and for case 2 we have derived a minimal burial depth of 5.55 m. The thin dust cover on the surface hinders the heat transport into the surface, which leads to the small difference in the minimal burial depth for ice. The small difference in the thermal conductivity of the dust cover results in a difference of 45 cm for the stability region of water ice. For both cases Figure 4 shows an enrichment of ice near the sublimation front. The enrichment extends for more than 2 m below the sublimation front. This effect can be observed to some extend in all cases we have studied. When ice is sublimated, the water vapor can diffuse upward and downward in the pores. Water vapor diffusing downward refreezes in the colder areas. This increases the ice content in these layers and at the same time the pores are closed by ice. We will discuss in the conclusions which consequences this enrichment might have for the interpretation of the hydrogen abundance as derived from the Gamma Ray Spectrometer (GRS) instruments suite on Mars Odyssey.
 In the second part of this case study we present results for a layered surface structure. We have studied 2 cases with a thickness of the dust cover of 5 cm and 100 cm respectively. The dust cover has a thermal conductivity as derived from the TES measurements and for the base material we have assumed sedimentary material with a typical thermal conductivity of 0.5 WK−1 m−1 (see Table 1). In both cases we have assumed that the upper dust layer was desiccated, in the starting conditions ice was placed only in the base material. Figures 6 and 7show the results for our models with a layered surface structure. Figure 6 shows temperature for the first 50 cm below the surface; Figure 7 shows it for a depth up to 10 m. The thickness of the upper layer increases in Figures 6 and 7 from left to right.
 The layered structure has little influence on the temperature distribution within the first meter below the surface. A comparison of Figures 3 and 6 shows that especially the first 20 cm below the surface are not affected by the change in the thermal conductivity below this layer. For the cases 3 and 4 we have derived slightly lower surface temperatures. For the maximum daytime surface temperature we get 287 K for case 3 and 288 K for case 4, and for the minimum nighttime temperature we obtain 252 K for case 3 and 254 K for case 4 (see Table 2). Looking at Table 2 it is interesting to note, that even the case of a only 5 cm thick layer of dust covering the base material with a higher thermal conductivity (case 3) results in a change of only about 1 K in the surface temperature compared to the homogeneous surface material (case 1). For the 100 cm thick dust layer the differences are even smaller. This indicates, that in this situation the measurement of the surface temperature can give only little information the subsurface structure. Comparison of Figures 4 and 7 shows that the temperature distribution at greater depth shows some differences. The higher thermal conductivity of the sedimentary base material in the cases 3 and 4 allows a deeper penetration of the annual heat wave. During the modeling run we observed differences in the transient effects, the heat wave penetrates in case 3 faster into greater depth. But after the models for both cases have reached stable conditions there are little differences left for the temperature distribution at greater depth as can be seen from Figure 8.
Figure 8 presents the depth profiles of the ice content (in weight percentage) for the three cases with a layered subsurface structure. Interestingly there are little difference between the two test cases, which is due to the similar temperature distribution for the material at greater depth. For both cases we have derived a minimal burial depth of 7.40 m, any differences are below the 5 cm depth resolution of our modeling.
 Looking at Table 2, it is worth noting that for instruments like TES the surface for cases 1, 3 and 4 will return the same results for the thermal inertia. The difference in the subsurface structure, however, results in a difference of more than 1 m for the burial depth of stable ground ice deposits. The surface temperatures can provide only limited information on the subsurface structure because the resulting differences are small. The difference might be masked by atmospheric effects especially the dust load of the atmosphere. On the basis of a first estimate the effect on the surface temperature can be in the same order of magnitude as the influence of the subsurface structure. The comparison of modeled surface temperatures with measured brightness temperature is further complicated by uncertainty in the surface emissivity necessary for the conversion.
5. Conclusions for the Isidis Planitia Region
 The results of our case study show that the absolute values of the surface temperature on annual cycles are varied only slightly by the structure of the subsurface or the assumed values for the thermal conductivity of the base material. It is mainly influenced by the assumed thermal conductivity of the dust cover. The differences are on average not larger than 4 K for the maximum temperature and 6 K for the minimum temperature. Therefore it seems that the surface temperature is not a very sensitive indicator for the subsurface structure. Independent of the assumed thermophysical properties we find for all test cases a strong temperature gradient within the first 10 cm below the surface which also varies strongly over the annual cycle. The material which can be accessed by MER, even using the Rock Abrasion Tool or by forming trenches spinning the wheels, will be thoroughly thermally stressed and therefore altered. It is unfortunate that the rovers are not equipped with digging or drilling equipment, because in a depth of about 1.5 m most of the annual heat wave is dampened and the material endures only slight variations in temperature over the annual cycles.
 The temperature gradient within the surface for depth greater than about 1 m is strongly influenced by the thermal and physical properties of the base material. This results in differences of more than 1 m for the minimal burial depth of water ice deposits stable over annual cycles. The Mars Odyssey measurements of the global distribution of neutrons from Mars [Boynton et al., 2002; Feldman et al., 2002] show a low flux of epithermal neutrons and a normal to high flux of thermal neutrons from this region. On the basis of the analysis given by Feldman et al.  and Boynton et al.  Isidis Planitia is a “dry spot” on the Martian surface. Unfortunately the GRS instruments can provide information on the hydrogen abundance only to depth of about 2 m. Therefore the comparison with our results can only be quantitative. Our modeling indicates that water ice can not be stable on annual scales within 2 m below the surface, in agreement with the results of the GRS measurements.
 On the basis of our modeling it is difficult to decide whether the surface material at the MER landing sites in Isidis Planitia is homogenous down to a depth of 10 m or more or if the TES instrument measured only the thermal properties of a fine sand or dust crust on top of a sedimentary base material. With the case study we have covered the extreme ranges of thermal conductivities likely for the material at Isidis Planitia. The temperature differences can give some indications on the structure, given accurate measurements of the surface brightness temperature and a good determination of the surface emissivity needed to convert these values to kinetic temperatures. The hydrogen abundance values derived by the GRS instrument can contribute little because for all cases studied here we expected ice deposits deeper than 2 m below the surface.
 With the in situ measurements of the dust structure, especially the size distribution, porosity and composition of the dust, and the thermal mapping provided by the Mini-TES instrument at the MER landing sites it would have been possible to improve the modeling for Isidis Planitia. Since this is not an option anymore we have to turn to Beagle 2. Beagle 2 will also land in Isidis Planitia about 5° north of the proposed MER landing sites. We will use their measurements to improve our modeling of the region studied here and compare the results with our studies of the Beagle 2 landing site.
6. General Conclusions
 The GRS instruments suite on Mars Odyssey is capable of detecting hydrogen within the first 2 m below the surface. This hydrogen abundance has been converted by Boynton et al.  and Feldman et al.  to obtain estimates on the ice content of the surface to a depth of about 2 m. Some authors have estimated the global ice inventory using the derived ice content for the upper 2 m and assuming that this content will continue to greater depths. The enrichment effect we have found in our modeling may lead to a significant overestimation of the real ice content and should be taken into account when giving global or large scale estimates based on GRS data.
 The modeling does not include an atmospheric model in the current version. This affects to some extend our results, especially on the surface temperature. As discussed in the model description the dust in the atmosphere will have an effect on the day- and nighttime temperatures. Both effects have little influence on the burial depth of water ice deposits and will change the results by a few centimeters at most. The influence on the surface temperature can however be on the same order of magnitude as the influence of the subsurface structure. We are currently working on a microscale atmospheric model based on a simple radiative-convective model for the atmosphere layer to a height of about 100 m. The upper boundary condition for the microscale atmospheric model will be derived from the “European Mars climate database” [Forget et al., 1999], which will also be used to calculated an attenuated solar flux taking into account the dust load of the atmosphere.
 Global measurements of the thermal properties of the surface in combination with in situ measurements will provide the input parameters needed to allow an investigation of the upper layers of the surface regarding structure and composition. Combining the modeling presented here with the surface brightness nighttime temperatures as derived from measurements by TES or the Planetary Fourier Spectrometer (PFS) on Mars Express will allow to give even further constraints. A detailed modeling of the surface layers is of special interest for the volatility inventory of the surface layers. The selection of future landing sites, especially for missions with a strong exobiology focus, will concentrate on sites which show moderate subsurface temperatures and high volatility contents.
 This work was funded by the German Research Council under grant number BE 1630/2. We would like to thank the two anonymous referees for their constructive and supportive comments.