Sublimation of terrestrial permafrost and the implications for ice-loss processes on Mars

Sublimation of ice is rate-controlled by vapor transport away from its outer surface and may have generated landforms on Mars. In ice-cemented ground (permafrost), the lag of soil particles remaining after ice loss decreases subsequent sublimation. Varying soil-ice ratios lead to differential lag development. Here we report 52 years of sublimation measurements from a permafrost tunnel near Fairbanks, Alaska, and constrain models of sublimation, diffusion through porous soil, and lag formation. We derive the first long-term in situ effective diffusion coefficient of ice-free loess, a Mars analog soil, of 9.05 × 10−6 m2 s−1, ~5× larger than past theoretical studies. Exposed ice-wedge sublimation proceeds ~4× faster than predicted from analogy to heat loss by buoyant convection, a theory frequently employed in Mars studies. Our results can be used to map near-surface ice-content differences, identify surface processes controlling landform formation and morphology, and identify target landing sites for human exploration of Mars.

compared to the natural variation in properties. Since the measurement is in situ, this might still be worthy of reporting if quantitatively correct but, as the authors note in equation 1, the measured value is the product of D ∆N, where ∆N is the difference in water vapor density at the ice surface and in the tunnel. As a result, referring to steam tables, the same result would be achieved if D were identical to the lab measurement and the ice surface were at -2˚C instead of the assumed -4.1˚C (i.e. in equilibrium with the air conditioned tunnel air). As stated in the manuscript, the Fairbanks area has a mean annual temperature of -3.4˚C as per a cited 2001 study, already nearly a degree warmer than assumed. Considering the influence of climate change since 2001, as well as the fact that mean air temperature and mean ground temperature aren't necessarily the same, -2˚C is a plausible ice surface temperature. Since evidence that the wall temperature is in equilibrium with the air conditioned tunnel air was not provided in the manuscript, the new result would have to be considered as within the error bar of the old. 2) A similar argument applies to the anomalous 4x faster sublimation rate than predicted by theory. In that case, the theoretical rate goes as ∆rho/rho (or, since it is nearly isothermal, ∆p/p where p is partial water vapor pressure). Since RH is maintained at 91% within the tunnel, the measured sublimation rate turns out to be consistent with an ice surface that is only slightly warmer than the air conditioned air in the tunnel. To give a specific example; saturation vapor pressure (SVP) at -4˚C is ~440 Pa, so at 91% RH, ∆p will be ~40 Pa and p will be 400 Pa. If the ice surface is at -1˚C (SVP~560 Pa), ∆p will be 160 Pa, 4x the assumed value. As above, lacking quantitative measurement of the ice surface temperature, the measured rate would seem to fall within the error bars. Thermodiffusion may also contribute to a larger rate if the wall is warmer than the surrounding air.
3) With respect to realistic diffusion constants for Mars, the authors failed to cite the extensive work of Hudson and others (Hudson et al JGR 112 E-5-16 2007;Hudson & Aharonson JGR 113, E09008, 2008 and references therein), which provide more insight than the work here on both the physics of diffusion under martian conditions and the range of expected value.
Reviewer #1 (Remarks to the Author): The manuscript by Douglas and Mellon combines observations and theory to better constrain the magnitude of sublimation on both Earth and Mars. The study is based on observations that were made in a tunnel in the permafrost, thanks to the fact that the tunnel was carved 52 years ago, providing a timescale sufficiently large to be more significant than lab based studies. Their conclusion has strong impact on terrestrial studies on permafrost as well as studies on Mars geology. They observe sublimation rates 4 times higher than predicted.
Overall, I think the paper is well done, the sections with terrain data and measurements are well detailed and the implications well written. I have only minor comments before publications. The paper will be a nice contribution to this topic for multiple communities (Geomorphology, Planetary science, Environmental Science). We thank this Reviewer for their time and constructive comments.
Minor comments: -End of page 8: The effective diffusion coefficient ca be scaled to a value of: 9.9 10^-4 m2/s There is a difference of two orders of magnitude compared to Earth (9 10^-6 m2/s). First, this difference should be better highlighted. Second, what is the main reason of this difference? Is this more P or T? Or both? Or other parameters? Is it at fixed tortuosity. I miss some explanations here. Pressure is the main factor, followed by temperature and gas species. The first two sentences in this paragraphstate: "Based on the kinetic theory of gases, the binary diffusion coefficient scales as T 3/2 and P -1 , as noted above. On Mars, the mean temperature is 205K and atmospheric pressure is 600 Pa." To address this comment we clarified the difference between Earth and Mars and including gas species and modified the remainder of the paragraph to read: "Based on the kinetic theory of gases, the binary diffusion coefficient scales as T 3/2 and P -1 , as noted above. On Mars, the mean temperature is -68°C (205K) and atmospheric pressure is 600 Pa, such that the diffusion coefficient for this same soil would be ~109x larger. However, the difference in diffusion through air (Earth atmosphere) and carbon dioxide (Mars atmosphere) 27 reduces this scaling by a factor of 1.65 to give a Mars effective diffusion coefficient of 5.99 X 10 -4 m 2 /s, ~66x larger. This value is similar to laboratory measurements conducted with glass spheres conducted at Mars 41 . This value is also 4 to 5 times larger than has been utilized previously in Mars theoretical studies 25,26,27,42,3 , which can be mainly attributed to the high porosity and low tortuosity structure of this analog to martian soil." -Middle of page 9: It is mentioned that studies were inconsistent pointing to similar values and up to a factor 4x. Is this really so inconsistent? A factor 4 is not two orders of magnitude different and so it is not that meaningful. Which also lead to the question: What are the implications of the finding of your study, in other words, what differences a factor 4 would make in the understanding of landscapes or processes on Earth or Mars? For instance, given the poor knowledge on tortuosity of Mars ground, would the factor of 4 be so significant compared to the parameters controlling the soil properties? This factor of 4 applies to exposed ice, so tortuosity and other soil parameters do not apply.
To clarify this and directly address this Reviewer's comment we added a brief list of example relevant applications of the 4x difference: "On Mars, this difference is important when linking sublimation to the timing of naturally occurring secular or cyclic changes. For example: i) summertime sublimation from the martian polar caps, which is thought be linked to the global atmospheric humidity 44 ; ii) the rate of evolution of non-polar ice exposures 7 ; iii) determining the concentration of soil in ice exposed by recent impacts 33 ; and iv) the lifetime and instability of transient liquid water 30,31,32 ." -End of page 6, it is written that equation 3 can be fit to the observations on Figure 4. It would be useful to actually show this curve on the plot (for instance by a thin dashed line). We have added the curve to an updated Figure 3. This Figure is also presented here: The caption for Figure 3 has been edited to address this as follows: This manuscript claims the first in situ measurement of the diffusion coefficient of ice-free loess and argues for its relevance to interpretation of features on Mars. The justification for the exclusive nature of the measurement is the unique permafrost tunnel environment, in which sublimation is the dominant erosional process.
The manuscript is well written, of appropriate length, etc. (the only quibble is the repeated use of the word relic where relict is intended). Thank you for identifying this spelling error. We apologize. This has been fixed in both locations in the manuscript in the section titled "Ramifications for sublimation on Mars and Earth," fifth paragraph: "Relict ice (unstable ice left over a past climate state) may persist if a sufficient delay of ice-loss follows the most recent period of stability. Rapid diffusion of sublimated water vapor decreases the potential for relict ice to occur." The highlighted findings are (1) a measured diffusion constant of .0905 cm^2/s compared to previous measurements of .0735 cm^2/s, and (2) a sublimation rate 4x larger than predicted by accepted theory, and (3) implications for interpretation of martian geology. Taking these separately: 1) The 23% discrepancy of D relative to prior laboratory measurements is relatively small compared to the natural variation in properties. Since the measurement is in situ, this might still be worthy of reporting if quantitatively correct but, as the authors note in equation 1, the measured value is the product of D ∆N, where ∆N is the difference in water vapor density at the ice surface and in the tunnel. As a result, referring to steam tables, the same result would be achieved if D were identical to the lab measurement and the ice surface were at -2˚C instead of the assumed -4.1˚C (i.e. in equilibrium with the air conditioned tunnel air). As stated in the manuscript, the Fairbanks area has a mean annual temperature of -3.4˚C as per a cited 2001 study, already nearly a degree warmer than assumed. Considering the influence of climate change since 2001, as well as the fact that mean air temperature and mean ground temperature aren't necessarily the same, -2˚C is a plausible ice surface temperature. Since evidence that the wall temperature is in equilibrium with the air conditioned tunnel air was not provided in the manuscript, the new result would have to be considered as within the error bar of the old. The Reviewer makes a good point here-the temperature information for the Fairbanks area, the ambient air inside the Permafrost Tunnel, and at the wall surface in the Tunnel are all potential variables to consider. We have addressed this in detail here and have clarified the manuscript text as well. While the quantitative scaling the reviewer uses at -2°C is not correct, the point is taken. We have added a discussion of the uncertainty associated with the tunnel wall temperature, the factors that influence it, and the sensitivity of our findings to the wall temperature value.
The key text additions are as follows. In the subsection "Vapor diffusion and lag formation", third paragraph, we have added: "The temperature history of the wall-ice surface (the wedge-ice surface or the interface between dry loess and ice-rich loess) has not been measured. We expect the bulk permafrost at the depth of the tunnel to reflect the local mean surface temperature over the past 30 to 100 years, estimated to be in the range of -5 to -3C 19, 20, 29 . However, the active cooling of air within the tunnel will slowly effect the wall surfaces such that: i) the wall temperatures will gradually warm or cool toward the mean air temperature; ii) large swings in air temperature will be greatly subdued by the large thermal mass of the permafrost, compounded by any insulating dry loess layer; and ii) latent heat of sublimation of wall ice will further cool the walls. As such -4.1C is a reasonable mean wall temperature, but may deviate slightly, the sensitivity of which is discussed below." Further, in the subsection "Ramifications for sublimation on Mars and Earth", we have added a new (now) paragraph 8: "In both cases of diffusion and exposed-ice sublimation a warmer than assumed wall temperature may help to explain some of these differences. Only ¼°C increase in the mean wall temperature would be needed for the diffusion coefficient to match the laboratory measurements of the disturbed loess. A 1°C increase would be needed for observed sublimation to agree with theory. While these temperature increases are small, they are difficult to envision in light of cooler tunnel air temperature and the cooling effect of sublimation itself. What's more, no value of wall temperature provides a simultaneous match to both diffusion through loess and sublimation. Given the parameterized nature and heat-convection-analogy of the model of ice sublimation, a simpler explanation is that this model under predicts sublimation." 2) A similar argument applies to the anomalous 4x faster sublimation rate than predicted by theory. In that case, the theoretical rate goes as ∆rho/rho (or, since it is nearly isothermal, ∆p/p where p is partial water vapor pressure). Since RH is maintained at 91% within the tunnel, the measured sublimation rate turns out to be consistent with an ice surface that is only slightly warmer than the air conditioned air in the tunnel. To give a specific example; saturation vapor pressure (SVP) at -4˚C is ~440 Pa, so at 91% RH, ∆p will be ~40 Pa and p will be 400 Pa. If the ice surface is at -1˚C (SVP~560 Pa), ∆p will be 160 Pa, 4x the assumed value. As above, lacking quantitative measurement of the ice surface temperature, the measured rate would seem to fall within the error bars. Thermodiffusion may also contribute to a larger rate if the wall is warmer than the surrounding air. Our response to point #1 and the added/edited text in the manuscript also applies to and addresses this comment.
3) With respect to realistic diffusion constants for Mars, the authors failed to cite the extensive work of Hudson and others (Hudson et al JGR 112 E-5-16 2007;Hudson & Aharonson JGR 113, E09008, 2008 and references therein), which provide more insight than the work here on both the physics of diffusion under martian conditions and the range of expected value. We added reference to Hudson et al 2007 (now reference #41), who report diffusion coefficients measured for glass spheres at Mars pressures that can be compared to our findings. In which case their results are supportively similar, which we now note. However, a precise quantitative comparison is not useful due to various differences, grain size and pore size distributions, packing densities, and atmospheric pressures and gas species, such that this comparison with take a path through theoretical modeling containing a number of assumptions we do not feel confident to make from our measurements. Neither of these papers measured the properties of Fox tunnel loess and so their data is of limited application toward our study.