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Effects of varying obliquity on Martian sublimation thermokarst landforms
Icarus 281 (2017) 115–120
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Effects of varying obliquity on Martian sublimation thermokarst landforms Colin M. Dundas Astrogeology Science Center, U.S. Geological Survey, 2255 N. Gemini Dr., Flagstaff, AZ 86001, USA
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Article history: Received 16 May 2016 Revised 23 August 2016 Accepted 30 August 2016 Available online 31 August 2016 Keywords: Mars, surface Mars, climate Geological processes Ices
a b s t r a c t Scalloped depressions in the Martian mid-latitudes are likely formed by sublimation of ice-rich ground. The stability of subsurface ice changes with the planetary obliquity, generally becoming less stable at lower axial tilt. As a result, the relative rates of sublimation and creep change over time. A landscape evolution model shows that these variations produce internal structure in scalloped depressions, commonly in the form of arcuate ridges, which emerge as depressions resume growth after pausing or slowing. In other scenarios, the formation of internal structure is minimal. Significant uncertainties in past climate and model parameters permit a range of scenarios. Ridges observed in some Martian scalloped depressions could date from obliquity lows or periods of low ice stability occurring <5 Ma, suggesting that the pits are young features and may be actively evolving. Published by Elsevier Inc.
1. Introduction The distribution of ice on Mars is strongly sensitive to the planetary climate. At one extreme, stacks of thin layers make up the polar layered deposits and record variations in the deposition of ice and dust over time (e.g., Byrne, 2009). At lower latitudes, ice comes and goes as the climate changes (Mellon and Jakosky, 1995; Chamberlain and Boynton, 2007), resulting in a landscape shaped by this repeated emplacement and removal. However, the details of past climates are not known well, and must be inferred from the traces they have left on the modern surface. Scalloped depressions (“scallops”; Fig. 1) are commonly found on Mars in the Utopia Planitia region and around Amphitrites and Peneus Paterae south of Hellas Planitia (e.g., Costard and Kargel, 1995; Plescia, 2003; Morgenstern et al., 2007; Lefort et al., 2009, 2010; Séjourné et al., 2011, 2012; Soare et al., 20 07, 20 08, 2011; Ulrich et al., 2010, 2012; Zanetti et al., 2010). They are typically meters to decameters deep, and range in size from hundred-meterscale to merged structures spanning kilometers. Most workers attribute these pits to sublimation-thermokarst processes under a variety of evolution scenarios, while others have proposed origins as thermokarst lakes. Such origins imply that their formation, evolution, and morphology are potentially useful recorders of climate history, if they can be interpreted correctly. One morphology of particular interest is the occurrence of arcuate ridges in certain scalloped depressions (Fig. 1), which are
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found in many pits in Utopia (e.g., Soare et al., 2007; Lefort et al., 2009), but not in the Amphitrites/Peneus Paterae region (Lefort et al., 2010). Lefort et al. (2009) argued that the ridges arise from several intervals of sublimation and erosion, while Séjourné et al. (2011) proposed that they are exposed shallowly-dipping layers. Soare et al. (20 07, 20 08) suggested an origin as shoreline features, but Lefort et al. (2010) pointed out that these ridges are not level and that scallops occur on slopes that make lake formation improbable. Dundas et al. (2015) used a landscape evolution model to demonstrate that sublimation under the current Martian climate can produce landforms similar to simple scalloped depressions. Here I apply this model with a varying climate in order to understand how this modifies landform evolution. 2. Model This work uses the sublimation-thermokarst model described in Dundas et al. (2015), hereafter referred to as Paper 1. The basis of the model is insolation-driven sublimation of excess ground ice, dependent on slope and aspect, combined with diffusive mass movement of dry regolith. The diffusive mass movement is due to surface creep of the dry lag, which may be caused by factors like thermal cycling, frost loading and sublimation, or seismic shaking. The subsurface initially comprises a surface layer of ice-free regolith above excess ice with low regolith content, and pore-filling ice can develop within the lag during periods of net deposition. Aggradation always fills the pores just above the ice table, although in reality more diffuse deposition can occur, as discussed in Paper
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Time (Ma) Fig. 1. A) Scalloped depressions in Utopia Planitia. Note arcuate ridges paralleling the pole-facing scarp (arrows indicate example). B) Simple scalloped depression in Utopia without distinct ridges. C) Scalloped depressions near Peneus Patera region with irregular interior pits, but not ridges. (A: cutout from HiRISE image ESP_03,6802_2265, 46°N, 90.7°E. B: PSP_0,02,439_2265, 46°N, 92.1°E. C: ESP_02,3077_1225, 57.1°S, 51°E. North is up and illumination from the left in all figures. Images credit: NASA/JPL/University of Arizona.).
1. This may influence the details of landform evolution but is unlikely to alter the general behavior. The lookup tables for ice loss were generated for a latitude of 50ºN, a thermal inertia of 300 J m−2 K−1 s−1/2 and albedo of 0.13, reasonable values for the northern plains. Because the model is optimized for computational efficiency, the precise equilibrium ice depths are not as accurate as in some other models, but the uncertainties due to this factor are likely less than the uncertainties in past climate conditions. Unlike Paper 1, the simulations described in this work use timevarying climate conditions. This is implemented via time variation of the lookup tables used to model sublimation, which are derived from a thermal model and depend on the ice depth, mean atmospheric water content, and the obliquity and orbit of Mars. Melting never occurs in the climate scenario considered here; only the rate and distribution of sublimation varies. The model steps between lookup tables generated for a range of conditions in order to model a variable climate. Mars’ obliquity, eccentricity and longitude of perihelion all vary and influence the stability of ground ice (Mellon and Jakosky, 1995; Chamberlain and Boynton, 2007). However, generating lookup tables for all combinations of these variables experienced in recent history is computationally expensive. This paper focuses on the effect of obliquity, for two reasons. First, obliquity has the most significant effect on mean surface temperature at most latitudes, other than a narrow zone near 60° latitude (Schorghofer, 2008), and has the strongest effect on the distribution of stable ground ice (Chamberlain and Boynton, 2007). Second, the relative evolution of surfaces with different orientations and ice depths controls the morphology of sublimation landforms. Eccentricity and the timing of perihelion affect the distance to the sun as a function of season, but obliquity controls the solar zenith angle. The zenith angle is more relevant for determining the relative heating of different slopes and aspects. Therefore, this paper examines only the variation of obliquity, assuming a circular orbit. The mean annual atmo-
Fig. 2. Recent modeled obliquity history of Mars. Plotted from data provided at http://vo.imcce.fr/insola/earth/online/mars/mars.html and described by Laskar et al. (2004).
spheric water vapor content follows the zero-eccentricity-orbit values of Chamberlain and Boynton (2007). The lookup table changes every 2.5° of obliquity, so I interpolate values intermediate to their estimates (spaced 5°) using the logarithm of the water vapor content. Obliquity variations follow Laskar et al. (2004) (Fig. 2), but the general conclusions below are not sensitive to the details of this evolution. In order to simplify the climate variations (the details of which are subject to significant uncertainty), some factors are not considered. The model does not include surface ice deposition, which is predicted to occur at high obliquity (e.g., Forget et al., 2006; Madeleine et al., 2009, 2014). I discuss the effects of this assumption below. Atmospheric pressure is also held constant in the model, although in reality it does vary over time. There are several other important parameters in the model. Paper 1 used a nominal regolith diffusivity of 10−4 m2 s−1 , but considered this likely to be an upper bound. In baseline cases here I used a value of 3 × 10−5 m2 s−1 , which may still be high; use of too-low regolith diffusivity values can lead to numerical instabilities as discussed in Paper 1. For comparison, Golombek et al. (2014) estimated a value of 10−6 m2 s−1 for Meridiani Planum, although mid-latitude geomorphic evolution is likely faster. Though the regolith diffusivity value is constant in time in the model, it may vary in reality. However, the strength or even the direction of the effect as a function of obliquity are unknown. I also examine different values of the diffusion coefficient for water vapor as it sublimates through the regolith, nominally 3 × 10−4 m2 s−1 . The standard model domain for these model runs is 200 m in the east-west dimension and 500 m north-south, with periodic boundary conditions. The elongated domain accommodates growth along the north-south axis. For most model runs the scallop did not reach the edge of the domain. The spatial resolution was 0.5 m, and higher resolution runs gave negligible differences in trial cases. Scallop growth in each run is initiated by removal of a shallow spherical cap of regolith tangent to the top of the ice table, destabilizing ground ice by reducing the lag thickness. This initiating
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Fig. 3. Development of interior ridges in a depression due to climate variations (see main text). Obliquity history as in Fig. 2. Panels are 200 m wide. In all figures and sub-figures in this paper, shaded-relief images have brightness values stretched to maximize contrast, so visibility of morphological features is enhanced but shading and relief are not comparable between panels.
Fig. 4. Profile of the depression from Fig. 3, shown at 140 ka (360 kyr after the start of the model run). Elevation reference is arbitrary.
factor is arbitrary, but other factors such as small impacts or inhomogeneities in the ice could have similar destabilizing effects. 3. Results Given the number of unknowns in both model parameters and the climate history of Mars, it is difficult to conduct and present a set of simulations that covers the entire parameter space. Instead, I show several model runs as examples, and consider the effects of variations of some parameters. Unlike the stable-climate model runs in Paper 1, internal structures develop in depressions growing under variable conditions. In the baseline case (Fig. 3), a scallop is initiated at 500 ka. The depression grows poleward, especially during an obliquity low around 460 ka, and nearly stabilizes during an obliquity high around 390 ka. Growth accelerates during a period of declining obliquity, with a concentric structure developing and partially migrating within the depression. The scallop again nearly stabilizes during a long but low-amplitude obliquity high starting around 300 ka. Growth resumes as obliquity falls at around 200 ka, with an additional outer concentric structure developing. Fig. 4 shows a profile from this stage of development. The depression again partially stabilizes before beginning a final phase of growth during a
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shallow obliquity low around 50 ka. Some intricate internal structure developing during the final growth stage is likely due to the quantization inherent in the lookup tables. In addition to pit expansion, there is also a general lowering of the surface during lowobliquity phases, when ice becomes unstable under level ground. Several basic patterns appear: scallop growth is most pronounced at low obliquity. Concentric inner ridges appear when growth resumes after pausing or slowing, and migrate within the depression. Although initially concentric, the internal structures evolve to incomplete arcs over time. Migration is due to preferential sublimation under the warm, equator-facing parts of the ridge. A model run with identical starting conditions initiated at 1 Ma displays similar behavior. This model run experiences more, and more pronounced, cycles of instability. The pit initially deepens, and then becomes shallower in the later stages of expansion since the floor sinks more slowly than the surroundings due to a thickened lag. Due to the more varied history, the pit develops a more complex internal structure in the late stages of growth. A longer model run starting at 5 Ma had a shallower starting ice table. This run also followed the same trend, but eventually wrapped through the periodic boundary conditions and interacted with itself (Fig. 5). The late stages of this model run are an irregularly lowered surface with ridges and interference patterns. The latter stages of both of these long model runs showed internal patterns that were more complex than any well-defined landform observed in the scalloped terrain regions. Likely reasons for this are discussed below. Several model runs varied regolith diffusivity and sublimation rate (Fig. 6). A model run with higher regolith diffusivity (10−4 m2 s−1 ) showed the same general effects as the baseline case. In general, the depth of the pit was reduced, but the relief of the interior ridges was greater, and they can approach the level of the surrounding terrain. Both effects are consequences of a larger available thickness of lag material due to mass movement. The interior ridges showed a similar pattern, although different in detail. Lower vapor diffusivity (3 × 10−5 m2 s−1 ) has the effect of slowing sublimation. The same spatial patterns producing ridges can be discerned, but the relief is lower and mass movement can erase the ridges during periods of low sublimation. The pits produced under these conditions are smaller and more circular than the baseline case at any given timestep, since the slope-retreat effect of sublimation is reduced. A combination of high regolith diffusivity and low vapor diffusivity significantly reduced development of both the depression and internal ridges. A long model run starting at 5 Ma with low vapor diffusivity initially developed interior structures, but they were erased over time, and for most of the model run the only interior structure was a central mound that developed because of a thickened lag of material transported into the original depression. Small variations in the time of scallop initiation have visible effects on the morphology. However, after sufficient time (several obliquity cycles) has passed, the basic spatial patterns are similar (Fig. 7). Details differ, but the effects seen in the baseline case remain. 4. Discussion Some basic factors in scallop evolution are clear from the results above. First, in the mid-latitudes, sublimation-thermokarst evolution is most effective at low obliquity and on equator-facing slopes. This is consistent with models indicating that ground ice advances towards the equator at high obliquity (Mellon and Jakosky, 1995; Chamberlain and Boynton, 2007). Second, the interplay between slope retreat and variable rates of sublimation can produce interior structures such as arcuate ridges, consistent with the qualitative model of Lefort et al. (2009). These structures become more complex as the surface is subjected to more cycles of
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Fig. 6. Variations in scallop internal morphology due to variations in sublimation rate and regolith diffusivity, subject to the same climate variations from 500 ka – present. A) Baseline case. B) Higher regolith diffusivity. C) Lower sublimation diffusion coefficient. D) Both high regolith diffusivity and low sublimation diffusivity. The higher sublimation rate cases (A–B) have somewhat similar ridged patterns. At lower sublimation rates, internal structure is faint because depression growth within each obliquity cycle is small. Panels are 200 m wide.
Fig. 5. Complex patterns develop in a long-term model run. This model run began at 5 Ma, and is shown at 4 Ma. This level of complexity is not observed in real scalloped terrain and is regarded as unphysical behavior, due either to poorly constrained parameters or additional processes not included in the model.
variation. The prominence and preservation of internal structures are dependent on both the relative and absolute rates of sublimation and creep, so their expression on Mars may be highly variable. This does suggest that the geomorphology of scallops records information about the climate history of Mars that could be read as knowledge of these parameters is refined. The longer model runs showed very complex internal structures in some cases, resulting from the combined effects of many obliquity cycles. Such patterns are not observed in real scallops. There are several possible reasons for unrealistic behavior: small-scale inhomogeneities such as variable ice content are likely to break up the “memory” of older structures, and real climate variations are probably more complex than modeled here. Additionally, slower landform evolution due to low vapor diffusivity, or climate varia-
tions more conducive to stability, could reduce the development of internal structure, with only the strongest or longest-lasting variations leaving a signature. In general, the scallop-like depressions produced by the model are significantly shallower than well-developed scallops on Mars. A possible reason for this is the nature of the initial disturbance. Trials with various disturbance sizes showed that the length of a scallop is only weakly dependent on the size of the initial disturbance, but the depth and volume show a much stronger dependence. This suggests that the initial triggers for scallop formation on Mars are larger than the shallow depressions modeled here. Possibilities include small impacts and local collapse due to heterogeneities in the ice. Lower regolith diffusivity would also increase the depth of depressions by reducing lag development. The model used here and in Paper 1 is a simplification. The true values of many parameters are not well known, and it is not possible to incorporate all relevant factors. The climate variations modeled here are simplified, and the formation of clean ice is not included, although this may be an ongoing process that interacts with thermokarst growth. Viscous creep of ground ice is also omitted, but may be important in some conditions
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Fig. 7. Effects of different start time. The depression at right was initiated at 450 ka, compared with the baseline 500 ka. Similar, but not identical, internal structures have developed. The older scallop is slightly shorter because it was initiated under more-stable conditions, so regolith diffusion moved some material inwards before it experienced the less-stable climate.
(e.g., Dombard and NOE Dobrea, 2016). Hence, the model results should be taken to illustrate the nature of sublimation-thermokarst processes rather than as detailed predictions of Martian surface morphology. These model results should be used as an aid to interpretation rather than the sole solution. For instance, variable sublimation can produce arcuate ridges, but it is not necessarily true that all arcuate ridges are due to this process, and some depressions do appear to expose layers. Additional processes are needed to explain some other anomalies, such as non-pole-oriented scallops discussed in Paper 1. However, a consequence of this model is that if scallops grow significantly on the timescale of climate variability, this should be reflected in the geomorphology. If the arcuate ridges in Utopia Planitia are due to this process, what does this tell us about the scalloped depressions? In general, this suggests that ridges provide evidence for episodes of ice stability and instability. At one location in Utopia, it is common to observe three sub-parallel ridges within a given depression (Fig. 1a). The most straightforward interpretation of the results above would be that these were produced during the three most recent obliquity lows, within the past ∼500 ka, and that this is the approximate age of the scallops. It would perhaps be surprising for these ridges to be expressed so clearly when periods of greater instability occurred a short time before, but this might be explained by snow deposition at the obliquity highs. An alternative possibility is that scallop evolution is slower than modeled in the baseline case, and that the ridges represent the combined effects of three clusters of obliquity lows centered around 0.8, 1.8 and 3.1 Ma (Fig. 2), rather than the individual lows. Such an effect could occur if, for instance, the sublimation rate is lower than the baseline case; this could arise due to a lower diffusion coefficient for water vapor loss, or lower mean temperatures. More generally, the ridges suggest that these scallops record three major periods of ice instability. Given the model uncertainties, a definitive association between individual ridges and particular climate episodes is not currently possible. Scalloped depressions south of Hellas Planitia (Fig. 1c), which generally lack such arcuate ridges (Lefort et al., 2010), could be younger, or could grow more slowly due to their higher latitude. The variations in ice stability due to change in the longitude of
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perihelion are also less pronounced in the southern hemisphere (Chamberlain and Boynton, 2007), so the cycle of instability may not be as strong. A final reason for this difference could be differing elevation and wind regimes in Hellas and Utopia Planitiae. Eolian processes are not included in the model but may affect landform evolution (e.g., Lefort et al., 2009). Between 5–20 Ma, the mean obliquity of Mars was higher, generally varying between 25°–45° (Laskar et al., 2004). There is no single value separating stable and unstable situations—stability is a function of the slope, aspect, and depth to ice, as well as latitude and thermophysical properties. With sufficiently thin regolith cover, sublimation can proceed at high obliquity, and a thinner lag is likely because of the shallower stability depth. If all other factors are constant it is generally the case that ice becomes less stable as obliquity decreases, and a thermokarst landform that was growing at high obliquity will experience even more sublimation during the transition to low obliquity. A partial exception to this is that at the highest obliquity values considered, the atmospheric water content falls and the stability depth increases slightly (Chamberlain and Boynton, 2007). However, in the mid-latitudes this effect is small compared with the change at low obliquity, which can completely destabilize ice, and is dependent on the particular water vapor model used. Overall, if the model of Laskar et al. (2004) is correct, the last 5 Ma have probably been the most favorable in recent history for sublimation-thermokarst growth. A transition from higher to lower mean obliquity may be particularly favorable for initiating sublimation thermokarst due to the overall reduction in mid-latitude ice stability. The climate variations used in this paper are simple, comprising only variations in the atmospheric water content as a function of obliquity. This is a major aspect of Martian climate history, but it omits at least one factor that may be important for thermokarst. Surface ice deposition by precipitation is thought to occur in various locations at high obliquity (e.g., Forget et al., 2006; Madeleine et al., 2009, 2014), and this would alter the boundary conditions experienced by ice-covered regolith, supplying water vapor to the subsurface. This only enhances the basic result that sublimationthermokarst evolution is most effective at low obliquity, and could supply an additional armor of pore-filling ice that would temporarily protect underlying clean ice during unstable periods. Thus, this effect probably influences landform evolution rates (perhaps strongly) but is unlikely to affect the style of growth, or the trend with obliquity. Ice deposition could also provide the clean ice within which scallops grow, rather than (or in addition to) being superposed above them. The source of clean ice is not addressed by this model, as the surface of Utopia has some morphological characteristics suggesting an atmospheric mantling deposit, but is boulder-rich. The scallop-forming material south of Hellas has fewer boulders, reducing this problem (Lefort et al., 2010). Episodic formation of new clean ice from the atmosphere or in the subsurface (e.g., Fisher, 2005; Sizemore et al., 2015) would add another layer of complexity to sublimation-thermokarst landform evolution. 5. Conclusions A simple model for climate variation with obliquity provides several insights into the development of scalloped depressions as examples of sublimation-thermokarst landforms. In the midlatitudes, scallop expansion is favored at low obliquity, and interior structures like arcuate ridges can develop due to the interplay between sublimation and mass movement. The prominence of such ridges is governed by the relative importance of these processes. Because mean obliquity has been lower in the last 5 Ma, scalloped depressions may date to within this timeframe. Depending on the details of climate history, expansion of some scalloped depressions
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could be proceeding in the current climate, although likely at a rate too low to be detectable with current instruments. Acknowledgements This work was funded by Mars Fundamental Research Program grant NNH13AV59I. I thank Tim Haltigin, Jim Skinner, Michael Bland, and an anonymous reviewer for helpful comments. References Byrne, S., 2009. The polar deposits of mars. Ann. Rev. Earth Planet. Sci. 37, 535–560. Chamberlain, M.A., Boynton, W.V., 2007. Response of martian ground ice to orbit-induced climate change. J. Geophys. Res. 112, E06009. doi:10.1029/ 20 06JE0 02801. Costard, F.M., Kargel, J.S., 1995. Outwash plains and thermokarst on mars. Icarus 114, 93–112. Dombard, A.J., NOE Dobrea, E.Z., 2016. Relaxation of small craters at phoenix landing site latitudes on mars. Lunar Planet. Sci. Conf., 47 abstract #1766. Dundas, C.M., Byrne, S., McEwen, A.S., 2015. Modeling the development of martian sublimation thermokarst landforms. Icarus 262, 154–169. Fisher, D.A., 2005. A process to make massive ice in the martian regolith using long-term diffusion and thermal cracking. Icarus 179, 387–397. Forget, F., Haberle, R.M., Montmessin, F., Levrard, B., Head, J.W., 2006. Formation of glaciers on mars by atmospheric precipitation at high obliquity. Science 311, 368–371. Golombek, M.P., Warner, N.H., Ganti, V., Lamb, M.P., Parker, T.J., Fergason, R.L., Sullivan, R., 2014. Small crater modification on meridiani planum and implications for erosion rates and climate change on mars. J. Geophys. Res. 119, 2522–2547. doi:10.10 02/2014JE0 04658. Laskar, J., Correia, A.C.M., Gastineau, M., Joutel, F., Levrard, B., Robutel, P., 2004. Long term evolution and chaotic diffusion of the insolation quantities of mars. Icarus 170, 343–364. Lefort, A., Russell, P.S., Thomas, N., McEwen, A.S., Dundas, C.M., Kirk, R.L., 2009. Observations of periglacial landforms in utopia planitia with the high resolution imaging science experiment (HiRISE). J. Geophys. Res. 114, E04005. doi:10.1029/ 20 08JE0 03264. Lefort, A., Russell, P.S., Thomas, N., 2010. Scalloped terrains in the peneus and amphitrites paterae region of mars as observed by HiRISE. Icarus 205, 259–268.
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Effects of varying obliquity on Martian sublimation thermokarst landforms Colin M. Dundas Astrogeology Science Center, U.S. Geological Survey, 2255 N. Gemini Dr., Flagstaff, AZ 86001, USA
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Article history: Received 16 May 2016 Revised 23 August 2016 Accepted 30 August 2016 Available online 31 August 2016 Keywords: Mars, surface Mars, climate Geological processes Ices
a b s t r a c t Scalloped depressions in the Martian mid-latitudes are likely formed by sublimation of ice-rich ground. The stability of subsurface ice changes with the planetary obliquity, generally becoming less stable at lower axial tilt. As a result, the relative rates of sublimation and creep change over time. A landscape evolution model shows that these variations produce internal structure in scalloped depressions, commonly in the form of arcuate ridges, which emerge as depressions resume growth after pausing or slowing. In other scenarios, the formation of internal structure is minimal. Significant uncertainties in past climate and model parameters permit a range of scenarios. Ridges observed in some Martian scalloped depressions could date from obliquity lows or periods of low ice stability occurring <5 Ma, suggesting that the pits are young features and may be actively evolving. Published by Elsevier Inc.
1. Introduction The distribution of ice on Mars is strongly sensitive to the planetary climate. At one extreme, stacks of thin layers make up the polar layered deposits and record variations in the deposition of ice and dust over time (e.g., Byrne, 2009). At lower latitudes, ice comes and goes as the climate changes (Mellon and Jakosky, 1995; Chamberlain and Boynton, 2007), resulting in a landscape shaped by this repeated emplacement and removal. However, the details of past climates are not known well, and must be inferred from the traces they have left on the modern surface. Scalloped depressions (“scallops”; Fig. 1) are commonly found on Mars in the Utopia Planitia region and around Amphitrites and Peneus Paterae south of Hellas Planitia (e.g., Costard and Kargel, 1995; Plescia, 2003; Morgenstern et al., 2007; Lefort et al., 2009, 2010; Séjourné et al., 2011, 2012; Soare et al., 20 07, 20 08, 2011; Ulrich et al., 2010, 2012; Zanetti et al., 2010). They are typically meters to decameters deep, and range in size from hundred-meterscale to merged structures spanning kilometers. Most workers attribute these pits to sublimation-thermokarst processes under a variety of evolution scenarios, while others have proposed origins as thermokarst lakes. Such origins imply that their formation, evolution, and morphology are potentially useful recorders of climate history, if they can be interpreted correctly. One morphology of particular interest is the occurrence of arcuate ridges in certain scalloped depressions (Fig. 1), which are
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found in many pits in Utopia (e.g., Soare et al., 2007; Lefort et al., 2009), but not in the Amphitrites/Peneus Paterae region (Lefort et al., 2010). Lefort et al. (2009) argued that the ridges arise from several intervals of sublimation and erosion, while Séjourné et al. (2011) proposed that they are exposed shallowly-dipping layers. Soare et al. (20 07, 20 08) suggested an origin as shoreline features, but Lefort et al. (2010) pointed out that these ridges are not level and that scallops occur on slopes that make lake formation improbable. Dundas et al. (2015) used a landscape evolution model to demonstrate that sublimation under the current Martian climate can produce landforms similar to simple scalloped depressions. Here I apply this model with a varying climate in order to understand how this modifies landform evolution. 2. Model This work uses the sublimation-thermokarst model described in Dundas et al. (2015), hereafter referred to as Paper 1. The basis of the model is insolation-driven sublimation of excess ground ice, dependent on slope and aspect, combined with diffusive mass movement of dry regolith. The diffusive mass movement is due to surface creep of the dry lag, which may be caused by factors like thermal cycling, frost loading and sublimation, or seismic shaking. The subsurface initially comprises a surface layer of ice-free regolith above excess ice with low regolith content, and pore-filling ice can develop within the lag during periods of net deposition. Aggradation always fills the pores just above the ice table, although in reality more diffuse deposition can occur, as discussed in Paper
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Time (Ma) Fig. 1. A) Scalloped depressions in Utopia Planitia. Note arcuate ridges paralleling the pole-facing scarp (arrows indicate example). B) Simple scalloped depression in Utopia without distinct ridges. C) Scalloped depressions near Peneus Patera region with irregular interior pits, but not ridges. (A: cutout from HiRISE image ESP_03,6802_2265, 46°N, 90.7°E. B: PSP_0,02,439_2265, 46°N, 92.1°E. C: ESP_02,3077_1225, 57.1°S, 51°E. North is up and illumination from the left in all figures. Images credit: NASA/JPL/University of Arizona.).
1. This may influence the details of landform evolution but is unlikely to alter the general behavior. The lookup tables for ice loss were generated for a latitude of 50ºN, a thermal inertia of 300 J m−2 K−1 s−1/2 and albedo of 0.13, reasonable values for the northern plains. Because the model is optimized for computational efficiency, the precise equilibrium ice depths are not as accurate as in some other models, but the uncertainties due to this factor are likely less than the uncertainties in past climate conditions. Unlike Paper 1, the simulations described in this work use timevarying climate conditions. This is implemented via time variation of the lookup tables used to model sublimation, which are derived from a thermal model and depend on the ice depth, mean atmospheric water content, and the obliquity and orbit of Mars. Melting never occurs in the climate scenario considered here; only the rate and distribution of sublimation varies. The model steps between lookup tables generated for a range of conditions in order to model a variable climate. Mars’ obliquity, eccentricity and longitude of perihelion all vary and influence the stability of ground ice (Mellon and Jakosky, 1995; Chamberlain and Boynton, 2007). However, generating lookup tables for all combinations of these variables experienced in recent history is computationally expensive. This paper focuses on the effect of obliquity, for two reasons. First, obliquity has the most significant effect on mean surface temperature at most latitudes, other than a narrow zone near 60° latitude (Schorghofer, 2008), and has the strongest effect on the distribution of stable ground ice (Chamberlain and Boynton, 2007). Second, the relative evolution of surfaces with different orientations and ice depths controls the morphology of sublimation landforms. Eccentricity and the timing of perihelion affect the distance to the sun as a function of season, but obliquity controls the solar zenith angle. The zenith angle is more relevant for determining the relative heating of different slopes and aspects. Therefore, this paper examines only the variation of obliquity, assuming a circular orbit. The mean annual atmo-
Fig. 2. Recent modeled obliquity history of Mars. Plotted from data provided at http://vo.imcce.fr/insola/earth/online/mars/mars.html and described by Laskar et al. (2004).
spheric water vapor content follows the zero-eccentricity-orbit values of Chamberlain and Boynton (2007). The lookup table changes every 2.5° of obliquity, so I interpolate values intermediate to their estimates (spaced 5°) using the logarithm of the water vapor content. Obliquity variations follow Laskar et al. (2004) (Fig. 2), but the general conclusions below are not sensitive to the details of this evolution. In order to simplify the climate variations (the details of which are subject to significant uncertainty), some factors are not considered. The model does not include surface ice deposition, which is predicted to occur at high obliquity (e.g., Forget et al., 2006; Madeleine et al., 2009, 2014). I discuss the effects of this assumption below. Atmospheric pressure is also held constant in the model, although in reality it does vary over time. There are several other important parameters in the model. Paper 1 used a nominal regolith diffusivity of 10−4 m2 s−1 , but considered this likely to be an upper bound. In baseline cases here I used a value of 3 × 10−5 m2 s−1 , which may still be high; use of too-low regolith diffusivity values can lead to numerical instabilities as discussed in Paper 1. For comparison, Golombek et al. (2014) estimated a value of 10−6 m2 s−1 for Meridiani Planum, although mid-latitude geomorphic evolution is likely faster. Though the regolith diffusivity value is constant in time in the model, it may vary in reality. However, the strength or even the direction of the effect as a function of obliquity are unknown. I also examine different values of the diffusion coefficient for water vapor as it sublimates through the regolith, nominally 3 × 10−4 m2 s−1 . The standard model domain for these model runs is 200 m in the east-west dimension and 500 m north-south, with periodic boundary conditions. The elongated domain accommodates growth along the north-south axis. For most model runs the scallop did not reach the edge of the domain. The spatial resolution was 0.5 m, and higher resolution runs gave negligible differences in trial cases. Scallop growth in each run is initiated by removal of a shallow spherical cap of regolith tangent to the top of the ice table, destabilizing ground ice by reducing the lag thickness. This initiating
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Fig. 3. Development of interior ridges in a depression due to climate variations (see main text). Obliquity history as in Fig. 2. Panels are 200 m wide. In all figures and sub-figures in this paper, shaded-relief images have brightness values stretched to maximize contrast, so visibility of morphological features is enhanced but shading and relief are not comparable between panels.
Fig. 4. Profile of the depression from Fig. 3, shown at 140 ka (360 kyr after the start of the model run). Elevation reference is arbitrary.
factor is arbitrary, but other factors such as small impacts or inhomogeneities in the ice could have similar destabilizing effects. 3. Results Given the number of unknowns in both model parameters and the climate history of Mars, it is difficult to conduct and present a set of simulations that covers the entire parameter space. Instead, I show several model runs as examples, and consider the effects of variations of some parameters. Unlike the stable-climate model runs in Paper 1, internal structures develop in depressions growing under variable conditions. In the baseline case (Fig. 3), a scallop is initiated at 500 ka. The depression grows poleward, especially during an obliquity low around 460 ka, and nearly stabilizes during an obliquity high around 390 ka. Growth accelerates during a period of declining obliquity, with a concentric structure developing and partially migrating within the depression. The scallop again nearly stabilizes during a long but low-amplitude obliquity high starting around 300 ka. Growth resumes as obliquity falls at around 200 ka, with an additional outer concentric structure developing. Fig. 4 shows a profile from this stage of development. The depression again partially stabilizes before beginning a final phase of growth during a
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shallow obliquity low around 50 ka. Some intricate internal structure developing during the final growth stage is likely due to the quantization inherent in the lookup tables. In addition to pit expansion, there is also a general lowering of the surface during lowobliquity phases, when ice becomes unstable under level ground. Several basic patterns appear: scallop growth is most pronounced at low obliquity. Concentric inner ridges appear when growth resumes after pausing or slowing, and migrate within the depression. Although initially concentric, the internal structures evolve to incomplete arcs over time. Migration is due to preferential sublimation under the warm, equator-facing parts of the ridge. A model run with identical starting conditions initiated at 1 Ma displays similar behavior. This model run experiences more, and more pronounced, cycles of instability. The pit initially deepens, and then becomes shallower in the later stages of expansion since the floor sinks more slowly than the surroundings due to a thickened lag. Due to the more varied history, the pit develops a more complex internal structure in the late stages of growth. A longer model run starting at 5 Ma had a shallower starting ice table. This run also followed the same trend, but eventually wrapped through the periodic boundary conditions and interacted with itself (Fig. 5). The late stages of this model run are an irregularly lowered surface with ridges and interference patterns. The latter stages of both of these long model runs showed internal patterns that were more complex than any well-defined landform observed in the scalloped terrain regions. Likely reasons for this are discussed below. Several model runs varied regolith diffusivity and sublimation rate (Fig. 6). A model run with higher regolith diffusivity (10−4 m2 s−1 ) showed the same general effects as the baseline case. In general, the depth of the pit was reduced, but the relief of the interior ridges was greater, and they can approach the level of the surrounding terrain. Both effects are consequences of a larger available thickness of lag material due to mass movement. The interior ridges showed a similar pattern, although different in detail. Lower vapor diffusivity (3 × 10−5 m2 s−1 ) has the effect of slowing sublimation. The same spatial patterns producing ridges can be discerned, but the relief is lower and mass movement can erase the ridges during periods of low sublimation. The pits produced under these conditions are smaller and more circular than the baseline case at any given timestep, since the slope-retreat effect of sublimation is reduced. A combination of high regolith diffusivity and low vapor diffusivity significantly reduced development of both the depression and internal ridges. A long model run starting at 5 Ma with low vapor diffusivity initially developed interior structures, but they were erased over time, and for most of the model run the only interior structure was a central mound that developed because of a thickened lag of material transported into the original depression. Small variations in the time of scallop initiation have visible effects on the morphology. However, after sufficient time (several obliquity cycles) has passed, the basic spatial patterns are similar (Fig. 7). Details differ, but the effects seen in the baseline case remain. 4. Discussion Some basic factors in scallop evolution are clear from the results above. First, in the mid-latitudes, sublimation-thermokarst evolution is most effective at low obliquity and on equator-facing slopes. This is consistent with models indicating that ground ice advances towards the equator at high obliquity (Mellon and Jakosky, 1995; Chamberlain and Boynton, 2007). Second, the interplay between slope retreat and variable rates of sublimation can produce interior structures such as arcuate ridges, consistent with the qualitative model of Lefort et al. (2009). These structures become more complex as the surface is subjected to more cycles of
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Fig. 6. Variations in scallop internal morphology due to variations in sublimation rate and regolith diffusivity, subject to the same climate variations from 500 ka – present. A) Baseline case. B) Higher regolith diffusivity. C) Lower sublimation diffusion coefficient. D) Both high regolith diffusivity and low sublimation diffusivity. The higher sublimation rate cases (A–B) have somewhat similar ridged patterns. At lower sublimation rates, internal structure is faint because depression growth within each obliquity cycle is small. Panels are 200 m wide.
Fig. 5. Complex patterns develop in a long-term model run. This model run began at 5 Ma, and is shown at 4 Ma. This level of complexity is not observed in real scalloped terrain and is regarded as unphysical behavior, due either to poorly constrained parameters or additional processes not included in the model.
variation. The prominence and preservation of internal structures are dependent on both the relative and absolute rates of sublimation and creep, so their expression on Mars may be highly variable. This does suggest that the geomorphology of scallops records information about the climate history of Mars that could be read as knowledge of these parameters is refined. The longer model runs showed very complex internal structures in some cases, resulting from the combined effects of many obliquity cycles. Such patterns are not observed in real scallops. There are several possible reasons for unrealistic behavior: small-scale inhomogeneities such as variable ice content are likely to break up the “memory” of older structures, and real climate variations are probably more complex than modeled here. Additionally, slower landform evolution due to low vapor diffusivity, or climate varia-
tions more conducive to stability, could reduce the development of internal structure, with only the strongest or longest-lasting variations leaving a signature. In general, the scallop-like depressions produced by the model are significantly shallower than well-developed scallops on Mars. A possible reason for this is the nature of the initial disturbance. Trials with various disturbance sizes showed that the length of a scallop is only weakly dependent on the size of the initial disturbance, but the depth and volume show a much stronger dependence. This suggests that the initial triggers for scallop formation on Mars are larger than the shallow depressions modeled here. Possibilities include small impacts and local collapse due to heterogeneities in the ice. Lower regolith diffusivity would also increase the depth of depressions by reducing lag development. The model used here and in Paper 1 is a simplification. The true values of many parameters are not well known, and it is not possible to incorporate all relevant factors. The climate variations modeled here are simplified, and the formation of clean ice is not included, although this may be an ongoing process that interacts with thermokarst growth. Viscous creep of ground ice is also omitted, but may be important in some conditions
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Fig. 7. Effects of different start time. The depression at right was initiated at 450 ka, compared with the baseline 500 ka. Similar, but not identical, internal structures have developed. The older scallop is slightly shorter because it was initiated under more-stable conditions, so regolith diffusion moved some material inwards before it experienced the less-stable climate.
(e.g., Dombard and NOE Dobrea, 2016). Hence, the model results should be taken to illustrate the nature of sublimation-thermokarst processes rather than as detailed predictions of Martian surface morphology. These model results should be used as an aid to interpretation rather than the sole solution. For instance, variable sublimation can produce arcuate ridges, but it is not necessarily true that all arcuate ridges are due to this process, and some depressions do appear to expose layers. Additional processes are needed to explain some other anomalies, such as non-pole-oriented scallops discussed in Paper 1. However, a consequence of this model is that if scallops grow significantly on the timescale of climate variability, this should be reflected in the geomorphology. If the arcuate ridges in Utopia Planitia are due to this process, what does this tell us about the scalloped depressions? In general, this suggests that ridges provide evidence for episodes of ice stability and instability. At one location in Utopia, it is common to observe three sub-parallel ridges within a given depression (Fig. 1a). The most straightforward interpretation of the results above would be that these were produced during the three most recent obliquity lows, within the past ∼500 ka, and that this is the approximate age of the scallops. It would perhaps be surprising for these ridges to be expressed so clearly when periods of greater instability occurred a short time before, but this might be explained by snow deposition at the obliquity highs. An alternative possibility is that scallop evolution is slower than modeled in the baseline case, and that the ridges represent the combined effects of three clusters of obliquity lows centered around 0.8, 1.8 and 3.1 Ma (Fig. 2), rather than the individual lows. Such an effect could occur if, for instance, the sublimation rate is lower than the baseline case; this could arise due to a lower diffusion coefficient for water vapor loss, or lower mean temperatures. More generally, the ridges suggest that these scallops record three major periods of ice instability. Given the model uncertainties, a definitive association between individual ridges and particular climate episodes is not currently possible. Scalloped depressions south of Hellas Planitia (Fig. 1c), which generally lack such arcuate ridges (Lefort et al., 2010), could be younger, or could grow more slowly due to their higher latitude. The variations in ice stability due to change in the longitude of
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perihelion are also less pronounced in the southern hemisphere (Chamberlain and Boynton, 2007), so the cycle of instability may not be as strong. A final reason for this difference could be differing elevation and wind regimes in Hellas and Utopia Planitiae. Eolian processes are not included in the model but may affect landform evolution (e.g., Lefort et al., 2009). Between 5–20 Ma, the mean obliquity of Mars was higher, generally varying between 25°–45° (Laskar et al., 2004). There is no single value separating stable and unstable situations—stability is a function of the slope, aspect, and depth to ice, as well as latitude and thermophysical properties. With sufficiently thin regolith cover, sublimation can proceed at high obliquity, and a thinner lag is likely because of the shallower stability depth. If all other factors are constant it is generally the case that ice becomes less stable as obliquity decreases, and a thermokarst landform that was growing at high obliquity will experience even more sublimation during the transition to low obliquity. A partial exception to this is that at the highest obliquity values considered, the atmospheric water content falls and the stability depth increases slightly (Chamberlain and Boynton, 2007). However, in the mid-latitudes this effect is small compared with the change at low obliquity, which can completely destabilize ice, and is dependent on the particular water vapor model used. Overall, if the model of Laskar et al. (2004) is correct, the last 5 Ma have probably been the most favorable in recent history for sublimation-thermokarst growth. A transition from higher to lower mean obliquity may be particularly favorable for initiating sublimation thermokarst due to the overall reduction in mid-latitude ice stability. The climate variations used in this paper are simple, comprising only variations in the atmospheric water content as a function of obliquity. This is a major aspect of Martian climate history, but it omits at least one factor that may be important for thermokarst. Surface ice deposition by precipitation is thought to occur in various locations at high obliquity (e.g., Forget et al., 2006; Madeleine et al., 2009, 2014), and this would alter the boundary conditions experienced by ice-covered regolith, supplying water vapor to the subsurface. This only enhances the basic result that sublimationthermokarst evolution is most effective at low obliquity, and could supply an additional armor of pore-filling ice that would temporarily protect underlying clean ice during unstable periods. Thus, this effect probably influences landform evolution rates (perhaps strongly) but is unlikely to affect the style of growth, or the trend with obliquity. Ice deposition could also provide the clean ice within which scallops grow, rather than (or in addition to) being superposed above them. The source of clean ice is not addressed by this model, as the surface of Utopia has some morphological characteristics suggesting an atmospheric mantling deposit, but is boulder-rich. The scallop-forming material south of Hellas has fewer boulders, reducing this problem (Lefort et al., 2010). Episodic formation of new clean ice from the atmosphere or in the subsurface (e.g., Fisher, 2005; Sizemore et al., 2015) would add another layer of complexity to sublimation-thermokarst landform evolution. 5. Conclusions A simple model for climate variation with obliquity provides several insights into the development of scalloped depressions as examples of sublimation-thermokarst landforms. In the midlatitudes, scallop expansion is favored at low obliquity, and interior structures like arcuate ridges can develop due to the interplay between sublimation and mass movement. The prominence of such ridges is governed by the relative importance of these processes. Because mean obliquity has been lower in the last 5 Ma, scalloped depressions may date to within this timeframe. Depending on the details of climate history, expansion of some scalloped depressions
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