Seasonal Variations of Soil Thermal Conductivity at the InSight Landing Site

The heat flow and physical properties package measured soil thermal conductivity at the landing site in the 0.03–0.37 m depth range. Six measurements spanning solar longitudes from 8.0° to 210.0° were made and atmospheric pressure at the site was simultaneously measured using InSight's Pressure Sensor. We find that soil thermal conductivity strongly correlates with atmospheric pressure. This trend is compatible with predictions of the pressure dependence of thermal conductivity for unconsolidated soils under martian atmospheric conditions, indicating that heat transport through the pore filling gas is a major contributor to the total heat transport. Therefore, any cementation or induration of the soil sampled by the experiments must be minimal and soil surrounding the mole at depths below the duricrust is likely unconsolidated. Thermal conductivity data presented here are the first direct evidence that the atmosphere interacts with the top most meter of material on Mars.

in unconsolidated material, whereas conduction through the gas phase becomes less important when the soil is cemented or indurated, where conduction mainly occurs through the soil matrix (Piqueux & Christensen, 2009b).
The only in situ thermal measurements of the martian soil using transient heating methods were performed by the thermal and electrical permittivity probe (TECP) during the Phoenix mission (Zent et al., 2010) and those taken by the heat flow and physical properties package (HP 3 ) on the InSight mission (Banerdt et al., 2020;Grott et al., 2019Grott et al., , 2021Spohn et al., 2018). The Phoenix measurements in Vastitas Borealis at 68.22°N 234.25°E, as well as the InSight measurements in Elysium Planitia at 4.50°N, 135.62°E, both showed that the martian soil is a poor thermal conductor. Thermal conductivity at the Phoenix site was determined to be 0.085 W m −1 K −1 in the upper 1.5 cm of the soil (Zent et al., 2010), while an average thermal conductivity of 0.039 ± 0.002 W m −1 K −1 was determined for the upper 37 cm of the soil column at the InSight landing site . As grain sizes at the two landing sites are comparable (Goetz et al., 2010;Grott et al., 2021;Presley & Christensen, 1997), similar thermal conductivities would be expected, and the difference between the two measurements has been attributed to the presence of cementing agents like perchlorate salts , which are abundant at the polar Phoenix landing site (Hecht et al., 2009;. However, perchlorates may also be present at InSight (Navarro-González et al., 2010;Glavin et al., 2013;Kounaves, Chaniotakis, et al., 2014). Therefore, it seems likely that the presence of ground ice near the surface (Mellon et al., 2009) and the resulting atmospheric water vapor interactions (Fischer et al., 2019) may play an important role in increasing soil thermal conductivity at the Phoenix site when compared to the results presented here. To study the relative importance of grain-to-grain as well as gas conduction in the martian soil, measurements at different atmospheric pressures are needed. However, due to the Phoenix mission's limited lifetime, such measurements could not be made. Here we report on the first long term monitoring of soil thermal conductivity as a function of atmospheric pressure as derived from in situ measurements at the InSight landing site.

Probe Emplacement, Data Acquisition, and Inversion
The HP 3 mole is a self penetrating probe with a length of 400 mm and a diameter of 27 mm that uses a hammering mechanism to achieve soil penetration. Heating foils inside the mole allow the probe to be used as a modified line heat source. Following deployment onto the martian surface, HP 3 started its first penetration attempt on Sol 92 of the mission (28 February 2019). However, insufficient friction to compensate for recoil during hammering resulted in an initial failure to penetrate (Spohn, Hudson, Marteau, et al., 2022;Spohn, Hudson, Witte, et al., 2022). Further penetration was only possible after removing the HP 3 support structure and using the lander's robotic arm to provide friction by directly interacting with the HP 3 mole. In this way, it was possible to reach a mole depth of approximately 3 cm below the surface as measured from the mole's back cap. Following penetration, the hole behind the mole was filled with scraped soil which was tamped down to ensure that the mole was fully buried and in contact with soil. A first thermal conductivity measurement with a fully buried mole was conducted on Sol 680 of the mission and a final hammering attempt was conducted on Sol 754. However, no additional depth progress was observed and further penetration attempts were abandoned.
The final burial of the HP 3 mole is shown in Figure 1a and thermal conductivity was measured in this configuration when energy could be made available on the lander. Six measurements were conducted on Sols 798, 827, 874, 1070Sols 798, 827, 874, , 1160Sols 798, 827, 874, , and 1204 to solar longitudes L s of 8. 0°, 22.0°, 44.2°, 135.3°, 184.0°, and 210.0°, where L s is defined as the aerocentric longitude measured from the northern hemisphere spring equinox where L s = 0°. During the measurements, the mole was used as a modified line heat source (Hammerschmidt & Sabuga, 2000;Spohn et al., 2018) and a specified constant heating power was provided to the mole's outer hull. Thermal conductivity was then determined from the resulting temperature rise of the mole hull as a function of time (Spohn et al., 2018). Before each active heating experiment was started, background temperature drift was monitored for 2 Sols and the average was subtracted from the measurements to obtain the heating-induced temperature rise from which conductivity was determined (see Grott et al. (2021) for details).
A schematic cross section of the soil surrounding the mole, which has been derived based on geologic observations (Golombek, Williams, et al., 2020) and the history of probe emplacement (Spohn, Hudson, Marteau, et al., 2022), is shown in Figure 1b. It includes a layer of unconsolidated surficial dust and sand as well as a hole surrounding the back of the mole, which has been back-filled by scraping unconsolidated material followed by tapping the soil down using the robotic arm's scoop. Furthermore, a duricrust, whose presence is inferred from image and penetration data and that is underlying the unconsolidated material, is indicated. At larger depth, the soil is inferred to be unconsolidated. The soil volume sampled by the experiments is indicated in red shades and the generated heat pulse has a diffusion length scale of = √ ∕ . Assuming a thermal conductivity of k = 0.0385 W m −1 K −1 , density ρ of 1,211 kg m −3 , and heat capacity c p of 630 J kg −1 K −1 , d ϵ ≈ 6.2 cm for the 21 hr 40 min heating experiment. The volume of soil sampled during the experiment extends to 2-3 mol diameters and is thus considerably larger than the region of potentially disrupted soil (also compare Figure 3 in Grott et al. (2021)). Note that the presence of a gravel layer around of the tip of the mole has been hypothesized based on the mole's penetration performance (Spohn, Hudson, Marteau, et al., 2022) but is not shown here. The tilt of the mole with respect to the local gravity vector is close to 30°.
The retrieved temperature rise as a function of time t is shown for all six thermal conductivity measurements in Figure 2 and all measurements were performed in the final mole configuration with no hammering in between. Heating curves followed a similar trend, showing the classical log-linear increase of temperature as a function of log(t) at intermediate heating times between 2 and 10 hr before axial heat flow causes a deviation at later times.
For a classical line heat source, the slope of the heating curve dT/d log(t) is inversely proportional to the thermal conductivity of the medium. Therefore a first qualitative conclusion concerning the pressure dependence of thermal conductivity at the InSight landing site can be already drawn from inspection of the slopes in Figure 2. In the figure, large slopes are associated with Sols of low atmospheric pressure and vice versa (compare Table 1), which implies that soil thermal conductivity and atmospheric pressure are positively correlated. This conclusion is supported by analytical models (Carslaw & Jaeger, 1959;Hammerschmidt & Sabuga, 2000;Jaeger, 1956) and a linear analysis roughly reproduces the trends reported below (see Supporting Information S1). However, using the classical line heat source approach (von Herzen & Maxwell, 1959), thermal conductivities are slightly overestimated due to the fact that axial heat flow cannot be accounted for in these models (Blackwell, 1956). Therefore, we rely on numerical models to invert the heating curves for soil thermal conductivity k. The model accounts for the non-negligible specific heat of the mole, the contact conductance H between mole and regolith as well as the geometry of the problem including axial heat transport. It is described in detail in Spohn et al. (2018) and Grott et al. (2019Grott et al. ( , 2021, and we used a Monte-Carlo approach to find admissible sets of model parameters k and H which fit the observations. While thermal conductivity k as well as contact conductance H change as a function of atmospheric pressure, soil density ρ remains unaffected and we require the numerical model to fit measurements at different seasons using a fixed density. For each model run, modeled temperature T mod (t, k, H) is compared to the measured temperature rise T dat (t) and the root mean square deviation between the two quantities is determined according to here n = 1,000 is the number of measurement points. Following Grott et al. (2021), data were inverted between t 1 = 1 hr and t n = 21 hr 40 min. Admissible parameter sets (k, H) were then determined by requiring the root mean square deviation ΔT rms (k, H) to be smaller than 0.17 K. This threshold takes the observed day-to-day temperature variations as well as other sources  of uncertainty into account (see Grott et al. (2021) for details). As the soil density was not known a priori, we ran two different sets of inversions using the two median densities derived for the InSight landing site by Grott et al. (2019). These are ρ = 1,007 kg m −3 and ρ = 1,211 kg m −3 , where the latter corresponds to an estimate that includes the additional constraint posed by the surface thermal inertia as derived from HP 3 radiometer measurements (N. T. Mueller et al., 2020;N. Mueller et al., 2021). For the soil specific heat capacity, a value of 630 J kg −1 K −1 has been assumed (Morgan et al., 2018). Twenty thousand Monte-Carlo simulations were then run for each of the measurements performed on Sol 798, 827, 874, 1070, 1160, and 1204. In the simulations, thermal conductivity k and contact conductance H were drawn from uniform probability distributions spanning the range 0.034 < k < 0.042 W m −1 K −1 and 3 < H < 250 W m −2 K −1 , respectively.
A discussion of measurement uncertainty associated with the determination of thermal conductivity from HP 3 measurements is given in Grott et al. (2019) and Grott et al. (2021). However, for the present analysis, we are searching for relative changes in thermal conductivity only, such that systematic sources of uncertainty which are identical for all measurements can be neglected. These include the uncertainties associated with determining the heat input into the TEM-A foils, the uncertainty associated with the imperfections of the finite element model, as well as the uncertainty of the reference method . Only the contribution stemming from the allowable spread of models determined using the Monte-Carlo simulations needs to be considered, and error bars stated below refer to the 1-σ standard deviations of the admissible model parameters.
Atmospheric pressure at the InSight Landing site has been measured at a cadence of 20 Hz by the Pressure Sensor (PS) of the InSight Auxiliary Payload Sensor Suite (APSS) (Banfield et al., 2019Spiga et al., 2018), and we here use the most recent recalibrated data set as provided by Lange et al. (2022). Diurnal average surface atmospheric pressure P can be approximated by  Note.The mission Sol number, the corresponding martian solar longitude (L s ), soil temperature at the beginning of the experiment T 0 , average (P avr ), minimum (P min ) and maximum (P max ) atmospheric pressure during the measurement, as well as the assumed soil density ρ are given together with the determined thermal conductivity k. Chosen densities of 1,211 and 1,007 kg m −3 correspond to estimates that include and do not include an additional constraint posed by the surface thermal inertia , respectively. Stated error bars represent 1-σ confidence intervals.
Soil thermal conductivity corresponding to the above atmospheric pressures can be estimated using the model of Morgan et al. (2018), which is based on a parameterization of laboratory experiments on unconsolidated soil performed by Presley and Christensen (1997). Given the soil thermal conductivity k 0 (P) at atmospheric pressure P, thermal conductivity at pressure P + ΔP can be calculated from where ΔP is the atmospheric pressure deviation with respect to P in mbar. The fitting constants A and B are given by 5.173 mbar −1 and −0.2416 mbar −2 , respectively (Morgan et al., 2018).

Results
Results of the simulations are summarized in Table 1, where the Sol number, martian solar longitude L s , soil temperature at the beginning of the experiment T 0 , average (P avr ), minimum (P min ) and maximum (P max ) atmospheric pressure during the measurement, as well as soil density ρ are given together with the derived thermal conductivity k. A clear correlation between atmospheric pressure and soil thermal conductivity is evident. Results are insensitive to the chosen soil density, and derived soil thermal conductivities for the two sets of simulations using ρ = 1,007 kg m −3 and ρ = 1,211 kg m −3 are indistinguishable within their respective error bars. Note that in principle the temperature dependence of heat capacity and soil matrix thermal conductivity could account for some of the seasonal variations observed in the inverted thermal conductivities. However, because there is no correlation between soil temperature T 0 and thermal conductivity k in Table 1, such an effect can be ruled out. Also, a direct influence of the observed seasonal trend on the variations of seismic velocities as reported by Compaire et al. (2022) is unlikely for the same reason.
Soil thermal conductivity for the case ρ = 1,211 kg m −3 is shown in Figure 3 as a function of martian solar longitude L s for the measurements taken on sols 798, 827, 874, 1070, 1160 and 1204, corresponding to L s = 8.0°, 22.0°, 44.2°, 135.3° 184.0°, and 210.0°, respectively. Measurements roughly span ∼60% of a martian year while covering ∼85% of the encountered pressures. To compare the obtained results with conductivities expected for unconsolidated soils, we have converted average diurnal atmospheric pressure for each measurement to a thermal conductivity estimate using Equation 3. Choosing the thermal conductivity derived for Sol 798 to fix k 0 (P), soil thermal conductivity can be estimated as a function of L s by first calculating the average diurnal atmospheric pressure using Equation 2, and then calculating the expected conductivity change with respect to k 0 (P) using Equation 3. The result of this calculation is shown as the solid line in Figure 3 (Morgan et al., 2018). In addition, the gray-shaded area corresponds to the range of conductivities predicted including the diurnal pressure fluctuations. As is evident from the figure, the measured soil thermal conductivities closely follow model predictions, indicating that there is a clear positive correlation of thermal conductivity and atmospheric pressure, that is, increased atmospheric pressure results in increased soil thermal conductivity and vice versa.

Discussion
We have conducted the first long-term in situ monitoring of martian soil thermal conductivity using the HP 3 mole as a modified line heat source. We find that soil thermal conductivity at the InSight landing site correlates with atmospheric pressure and follows the trend predicted by laboratory experiments for unconsolidated soils (Presley & Christensen, 1997). For the conducted experiments, pressure variations of 1.2 mbar resulted in conductivity changes of close to 8%, corresponding to approximately 6.5% mbar −1 . These changes are consistent with model predictions and indicate that a significant fraction of heat transport occurs through the pore-filling gas. Note, that although relative humidity follows a trend similar to the annual pressure fluctuations discussed here (Pal & Kereszturi, 2020), the very low partial pressure of water vapor is unlikely to have a noticeable effect on our measurements. While water capillary bridges can dominate the heat transfer in granular material (Persson, 2023), these are not expected to be present for extended periods of time at the InSight landing site (Pal & Kereszturi, 2020).
Any cementation or induration of the soil would have a significant influence on thermal properties by increasing the contact area between individual grains (Piqueux & Christensen, 2009a) and this does not seem to be the case for the soil sampled by the HP 3 mole. Even small amounts of cement would result in a significant increase of heat transport through the grain matrix and the pressure dependence of thermal conductivity would be minimal (Piqueux & Christensen, 2009b). Therefore, thermal measurements indicate that the sampled soil is unconsolidated.
Some support for the conclusion that soil cementation should be minimal is provided by the analysis of seismic velocities in the shallow subsurface. Using the HP 3 hammering mechanism as a seismic source, Brinkman et al. (2022) determined P-wave v P and S-wave v S velocities in the upper few tens of centimeters of the soil. They found velocities of = 119 +45 −21 and = 63 +11 −7 m s −1 , consistent with values typically encountered in low-density unconsolidated sands. Furthermore, Wright et al. (2022) suggested that any cement at grain contacts within sediment layers at the InSight landing site may have been broken up by impacts or marsquakes, although this may be more relevant for deeper soil layers not probed by the HP 3 mole. Nagihara et al. (2022) studied the dependence of thermal conductivity on atmospheric pressure in the lab using the low-cohesion Mojave Mars simulant (Peters et al., 2008) as an analogue for the martian soil. The simulant is made from crushed basalt with grain sizes ranging from 0.05 to 1 mm and a median grain size of 0.2 mm, slightly larger but comparable to the values derived for the landing site . Cohesion of the simulant is low and smaller than 2 kPa. Experiments were conducted at two different soil densities of 1,540 and 1,660 kg m −3 and atmospheric pressure was varied between 2 and 10 mbar. While absolute thermal conductivity of the simulant was larger than that determined for the soil at the InSight landing site, which may be attributed to the larger grain sizes and larger density of the simulant when compared to the in situ measurements, Nagihara et al. (2022) found the pressure dependence of thermal conductivity to be similar to the one reported here. Over a pressure range of 6-10 mbar, the simulant's thermal conductivity increased by 20%, corresponding to 5% mbar −1 and thus being comparable to the 6.5% mbar −1 observed here.
At the InSight landing site, the thermally dominant grain size as derived from a comparison of soil thermal conductivity with results of laboratory experiments (Presley & Christensen, 1997) is close to 125 μm. As the largest particles dominate bulk thermal conductivity (Presley & Craddock, 2006), up to 95% of all particles in the soil sampled by the HP 3 experiment could be smaller than 125 μm. In particular, dust sized particles could be intermixed with larger grains. These small particles could add significant cohesion to the soil, which would help to explain the presence of steep sided pits in image data (Golombek, Warner, et al., 2020) as well as the lack of friction on the mole's outer hull during penetration (Spohn, Hudson, Witte, et al., 2022).
While thermal conductivity measurements thus clearly indicate that soil cementation or induration should be minimal, minimal cementation is difficult to reconcile with image data that show clods in the pits and on the surface (Golombek, Warner, et al., 2020) as well as with cohesion estimates that have been derived using the lander's robotic arm (Marteau et al., 2021). These data strongly suggest a duricrust to be present, which could have been generated by the deposition of salts due to soil-atmosphere interactions (Banin et al., 1992;Ditteon, 1982;Haskin et al., 2005;Hurowitz et al., 2006;Moore et al., 1999;Mutch et al., 1977). However, experimental studies have shown that granular materials behave more cohesively when tested under vacuum (Bromwell, 1966;Grossman et al., 1970;Salisbury et al., 1964) and reduced-gravity conditions (Elekes & Parteli, 2021;Kleinhans et al., 2011;Walton et al., 2007;White & Klein, 1990), which suggests an enhanced cohesive behavior of the soil under Martian atmospheric pressure and gravity. The penetration data gathered by the HP 3 mole also indicates significant penetration resistance of the soil (Spohn, Hudson, Marteau, et al., 2022).
This discrepancy may be resolved when considering the history of probe emplacement. During the initial penetration attempts, the soil was significantly disrupted and a hole up to 7 cm deep was created around the mole. This was later back-filled by loose material, but the duricrust in this depth range has been disaggregated into sand (Spohn, Hudson, Marteau, et al., 2022). At larger depth, some soil may also have been disrupted, but the amount of modified material is estimated to be minor when compared to the volume sampled by the heat pulse generated in the thermal conductivity experiments, which extends to approximately 2-3 mol diameters (see above). Therefore, the soil properties derived here should correspond to the unconsolidated soil layers surrounding the mole at larger depths rather than the duricrust closer to the surface.
The existence of gas exchange between soil and the martian atmosphere has been inferred from models of the martian climate (e.g., Martínez et al. (2017); Buhler and Piqueux (2021)), models for regolith-water exchange (e.g., Savijärvi et al. (2016)), models for the transport of trace gases (e.g., Bullock et al. (1994)), as well as models for barometric pumping (de Beule et al., 2014). Furthermore, the exchange and adsorption of gases has been studied in the lab (e.g., Fanale, Banerdt, et al. (1982); Fanale, Salvail, et al. (1982); Rannou et al. (2001)). However, to our knowledge, the thermal conductivity data presented here is the first direct evidence that the atmosphere interacts with the top most meter of material on Mars.

Conclusions
Soil thermal conductivity at the InSight landing site strongly correlates with atmospheric pressure and conductivities vary by 6.5% mbar −1 . This is within the range predicted by models of thermal conductivity as a function of pressure for unconsolidated soils (Morgan et al., 2018) and consistent with the results of laboratory experiments under martian atmospheric conditions (Nagihara et al., 2022;Presley & Christensen, 1997). Furthermore, the observed strong correlation between thermal conductivity and atmospheric pressure indicates that pore spaces may be filled with dust sized particles, which could result in significant soil cohesion.
Both the rather low absolute value of thermal conductivity of around 0.038 W m −1 K −1 as well as the observed strong pressure dependence of 6.5% mbar −1 indicate that the soil probed by the HP 3 experiment is unconsolidated. Cementation or induration would significantly increase grain-to-grain contacts and thus increase the absolute conductivity by a large factor while at the same time removing the pressure dependence (Piqueux & Christensen, 2009b). We conclude that the thermal properties derived here are representative for the deeper, unconsolidated soil layers rather than the undisturbed duricrust observed in image data.

Data Availability Statement
Calibrated HP 3 heating experiment data are archived in NASA's Planetary Data System (InSight HP3 Science Team, 2021). The numerical code and data necessary to reproduce the results and figures of this paper have been made publicly available in Grott (2022).