General Comments

The manuscript by Langer et al. utilizes a numerical model to simulate the evolution of Arctic permafrost for the last three centuries (1750-2000). The response to changes in air temperature of the thermal state of permafrost and active layer thickness are simulated and conclusions have been made regarding the impacts on permafrost distribution. These types of simulations are of interest and can help to provide better understanding future evolution of permafrost conditions. The paper is interesting and is within the scope of “The Cryosphere” and would be of interest to permafrost scientists. I have no major issue with the numerical thermal model that is utilized. However, there are some issues that should be addressed regarding model inputs and validation for the MS to be acceptable for publication.

Values for thermal properties have been provided in Table A.1. Only one value is provided for the mineral component of soil, and it is unclear how this value was chosen – is this considered an average value? There is a large difference between the thermal conductivity of clay minerals and quartz for example (2.92 vs 8.80 Wm^-1K^-1 – values from Williams and Smith 1989) which will be an important factor in the thermal response. It also is not clear what value is used for bedrock and whether it varies with the mineralogy of the rock (the quartz content will be an important factor). There does not appear to be any information provided regarding the source of information on the type of bedrock or inclusion of bedrock stratigraphy in the model.

Validation of the ability of the model to reproduce the ground thermal regime and temperature trends is mainly done through comparison to borehole temperatures at 10 m depth for 2007-2016 extracted from Biskaborn et al. (2019). Deviations of up to 2K are reported which does seem rather large. It is not clear why the 10 m depth was chosen, and it should be noted that the values given in Biskaborn et al. (2019) are only provided for one depth, i.e. zero annual amplitude (ZAA) or the measurement depth closest to it. In some cases ZAA was much deeper than the measurement depth including at some sites where the measurement depth is 10 m. Although temperatures at 10 m depth may show little seasonal variation for some sites (eg. forested warm permafrost sites), for other sites there may be considerable seasonal variation and it may be more difficult to evaluate long-term trends.  Only the trend over a 10-year period has been utilized for validation and it is not clear why other information on trends over longer periods of time has not been utilized or why other evidence of permafrost evolution during earlier time periods has not been considered in the model evaluation.

Trends in permafrost temperature over longer periods, up to 4 decades, are reported for several sites in various publications including the annual State of Climate reports published in BAMS (most recent Smith et al. 2022). Consideration of longer time periods for model validation is important given that rate of permafrost temperature change has varied over time from the latter few decades of the 20^th century to the present as shown in for example Romanovsky et al. (2010, 2017); Smith et al. (2010, 2022). There have also been studies that have compared recent observations of permafrost occurrence and thaw depths to measurements made 4-6 decades earlier (e.g. James et al. 2013; Holloway and Lewkowicz 2020). These observations provide additional information on permafrost evolution, particularly in the southern portion of the permafrost region, that could be compared to model results. There are also studies that use proxy data to consider the evolution of permafrost over the last 6000 years (see for e.g. Treat and Jones 2018). These studies show that permafrost particularly in the current discontinuous zone formed fairly recently, during the Little Ice Age. The latter portion of this cold period overlaps with the 1750-1800 period considered in the results presented in the MS and these proxy data could also be used in the evaluation of model performance. It should also be noted that permafrost that formed during the Little Ice Age persists in peatlands (e.g.  James et al. 2013; Holloway and Lewkowicz 2020).

The authors present estimates regarding loss of permafrost, including loss of continuous permafrost. However, only the extent of near-surface permafrost (upper 3 m) is considered – essentially only considering a change in thaw depth. In the continuous permafrost zone where permafrost is several 10s to 100s of metres thick, loss of permafrost in the upper 3 m does not really provide a characterization of the lateral extent of permafrost. Justification of the loss of continuous permafrost would therefore be rather difficult.

Additional Comments

L5 – Trends in what? Active layer thickness?

L9-12 – See comments above regarding interpretation of results with respect to lateral extent of permafrost.

L18 – Models presented in Chadburn and Obu are equilibrium models, so the permafrost distribution determined is not necessarily representative of current conditions.

L22-23 – There are other references regarding the link between deeper temperatures and past climate. One of the earliest is Lachenbruch and Marshall (1986).

L23-33 – Another paper that considers permafrost that has survived over glacial-interglacial cycles is Froese et al. (2008). It should also be noted that the glacial history is not only important from a climatic perspective with respect to permafrost evolution, it also an important factor in ground ice conditions (see for example O’Neill et al. 2019) including the occurrence of buried ice. It is also related to sea level changes which influence ground ice conditions and evolution of permafrost thermal state in coastal areas and regions below the marine limit.

L62 – What about uncertainties in bedrock properties?

L75 – Is there a bedrock module?

L101 – Is excess ice considered or only pore ice?

L122 – Snow cover exhibits much local variability due to for example topography, vegetation, exposure to wind. Is this considered?

L148 – Does the observational data support setting snow depth to zero in August?

L149 – Ground stratigraphy section 2.2 – Not much information is provided on bedrock stratigraphy, only soil stratigraphy – see earlier comments.

L213 – What is used for the water/ice content of bedrock?

L251-254 – See earlier comment regarding depth of temperatures included in Biskaborn et al. (2019). Have only the boreholes that have temperatures reported at 10 m depth been utilized in the model evaluation. This would reduce the amount of information available that could be utilized for model validation and also means that some regions are not represented.

L256 – Deviation of up to 2K seems rather large. There is no real consideration of vegetation which is an important factor influencing the ground thermal regime. This could be a key factor responsible for the deviation.

L265-269 – The other thing that may be important in mountainous terrain is that there may be little soil and organic material. This along with bedrock conditions means ground temperatures will closely track air temperature.

Figure 2 – Some clarifications are required. Be clear what the reference period is for the anomaly calculation. If I understand correctly, the map (a) only shows the mean MAGT calculated over a decadal period although the way the caption is written it may imply the map shows trends. The graph in (c) compares observed and simulated trends in MAGT, I assume between 2007-16 and this should be clear in the caption in the description of (c).

Figure 3 – Similar clarifications are required as mentioned for Figure 2. Does the map show average values for ALT? What is the period over which averages and trends are determined?

L280- 282 – You might consider comparison of tundra, shrub dominated and forested sites as the response of the shallow ground thermal regime and therefore ALT will be influenced by vegetation conditions.

L285 – 291 – Note that at some CALM sites, probing is done on grids as large as 1 km² so there are average ALT values available over larger area. Since ALT for most CALM sites is determined through probing, the thaw depth that can be determined is limited to less than 2 m and there is some bias in the data set with respect to the subsurface materials as probing can not be done in coarser material.

L291-292 – In the southern fringes of the permafrost regions, permafrost is largely limited to organic terrain. As mentioned in earlier comment the permafrost that formed during colder periods during the Little Ice Age in these areas continues to persist due to the thermal properties of the peat.

L305-308 – See earlier comments – The beginning of the period considered in the analysis overlaps with the latter part of the Little Ice Age so that the colder permafrost temperatures in the 18^th-19^th century would be a legacy of this period.

L322-325 – The results (including 1970-1990 warming) for northern Quebec do not appear to agree with observations. Observed permafrost temperatures in the eastern Canadian Arctic, including sites in northern Quebec and the high Arctic (e.g. Alert) show that both air temperatures and ground temperatures cooled into the 1980s - 1990s with most of the warming occurring post about 1995 (see for example, Allard et al. 1995; Smith et al. 2010). Reconstructions of ground surface temperature form borehole records also show this later initiation of warming in the Canadian High Arctic (Taylor et al. 2006) and northern Quebec (Chouinard et al. 2007).

L331-333 – The way this part is written it implies this conclusion is based on observational evidence. It would be better to say that “Simulations suggest that during the last decades, permafrost warming has occurred…” (see previous comment that this conclusion isn’t fully supported by observations).

L340 – In warmer permafrost especially with higher moisture/ice content, ground temperature profiles indicate isothermal conditions exist (e.g. Romanovsky et al. 2010; Smith et al. 2010) due to the phase change that is occurring. This should be mentioned to help explain this sharp change in ALT.

L349 – Section 3.4 (see also earlier comments) – The zonation of permafrost such as that presented on Brown et al. (1998) map, is not based on the depth of the permafrost table being less than a critical depth (e.g. 3m) which is essentially is being used in the analysis presented here. It is not really correct to say that a grid cell contains permafrost if the ALT is < 3m (L352-353). In bedrock ALT can be >3 m (see for e.g. figure 7 in Smith et al. 2010 and also Christiansen et al. 2010) and permafrost is still present.

L386 – What is meant by “active thaw height”?

L391-392 – From the information presented, excess ice does not appear to have been considered.

L405-409 – Excess ice does not appear to be considered, only pore ice. There are also other factors related to surface water to consider. Changes in surface water distribution including lake drainage or shifting of rivers may also lead to permafrost formation. In coastal regions that have been undergoing and continue to undergo post-glacial uplift, permafrost is also forming.

L410-415 – This lack of consideration of vegetation conditions is probably one of the most important limitations of the model both for simulations of current permafrost conditions and also the evolution of permafrost over longer periods. Just as snow is an important factor influencing the ground surface temperature, so is vegetation cover including forests, shrubs and mosses.

L431-432 – Vegetation may also be a key factor here as well.

L440-443 – See earlier comments about basing permafrost occurrence on depth of permafrost table.

References

Allard M, Wang B, Pilon JA (1995) Recent cooling along the southern shore of Hudson Strait Quebec, Canada, documented from permafrost temperature measurements. Arctic and Alpine Research 27:157-166

Chouinard C, Fortier R, Mareschal JC (2007) Recent climate variations in the subarctic inferred from three borehole temperature profiles in northern Quebec, Canada. Earth and Planetary Science Letters 263:355-369

Christiansen HH, Etzelmuller B, Isaken K, Juliussen H, Farbot H, Humlum O, Johansson M, Ingeman-Neilsen T, Kristensen L, Hjort J, Holmlund P, Sannel ABK, Sigsgaard C, Akerman J, Foged N, Blikra LH, Pernosky MA, Odegard R (2010) Thermal state of permafrost in the Nordic area during the IPY 2007-2009. Permafrost and Periglacial Processes 21:156-181

Froese DG, Westgate JA, Reyes AV, Enkin RJ, Preece SJ (2008) Ancient permafrost and a future, warmer Arctic. Science 321:1648

Holloway JE, Lewkowicz AG (2020) Half a century of discontinuous permafrost persistence and degradation in western Canada. Permafrost and Periglacial Processes 31:85-96. doi:10.1002/ppp.2017

James M, Lewkowicz AG, Smith SL, Miceli CM (2013) Multi-decadal degradation and persistence of permafrost in the Alaska Highway corridor, northwest Canada. Environmental Research Letters 8 045013:10. doi:10.1088/1748-9326/8/4/045013

Lachenbruch AH, Marshall BV (1986) Changing climate: geothermal evidence from permafrost in the Alaskan Arctic. In:  Science, vol v. 234. pp p.689- 696

Romanovsky V, Isaksen K, Drozdov D, Anisimov O, Instanes A, Leibman M, McGuire AD, Shiklomanov N, Smith SL, Walker D (2017) Chapter 4, Changing permafrost and its impacts. In:  Snow, Water, Ice and Permafrost in the Arctic (SWIPA) 2017. Arctic Monitoring and Assessment Program (AMAP) Oslo, Norway, pp 65-102

Romanovsky VE, Smith SL, Christiansen HH (2010) Permafrost thermal state in the polar Northern Hemisphere during the International Polar Year 2007-2009: a synthesis. Permafrost and Periglacial Processes 21:106-116

Smith SL, Romanovsky VE, Isaksen K, Nyland KE, Kholodov AL, Shiklomanov NI, Streletskiy DA, Drozdov DS, Malkova GV, Christiansen HH (2022) [Arctic] Permafrost [in "State of the Climate in 2021"]. Bulletin of the American Meteorological Society 103 (8):S286-S290. doi:10.1175/BAMS-D-22-0082.1

Smith SL, Romanovsky VE, Lewkowicz AG, Burn CR, Allard M, Clow GD, Yoshikawa K, Throop J (2010) Thermal state of permafrost in North America - A contribution to the International Polar Year. Permafrost and Periglacial Processes 21:117-135. doi:10.1002/ppp.690

Treat CC, Jones MC (2018) Near-surface permafrost aggradation in Northern Hemisphere peatlands shows regional and global trends during the past 6000 years. The Holocene 28 (6):1000-1010. doi:10.1177/0959683617752858

Williams PJ, Smith MW (1989) The Frozen Earth: fundamentals of geocryology. Cambridge University Press, Cambridge, U.K.

General comments

The article describes a new permafrost model, labelled CryoGridLitle, focused on minimizing the computational and forcing resources required to be executed while achieving a realistic representation of permafrost areas. Furthermore, the analysis presents a comprehensive estimate of the uncertainties associated to the model, with the only exception of the uncertainties due to the external forcing and the model itself. The paper is clearly written and structured but I have concerns about the suitability of the model evaluation process followed by the authors, as it is limited in scope. I think that the topic is adequate for the journal, and that the development of a permafrost model able to perform multi-century simulations is relevant for the climate and cryosphere communities. I recommend publication after major revisions.

Major points

M1- The authors cite in the Introduction a series of works in which permafrost models are used in paleoclimate studies. Nevertheless, the performance of the CryoGridLitle is not compared to that from other models applied at paleoclimate scales. Is the CryoGridLitle framework performing better? What are the advantages of this new model in comparison with previous models used in paleoclimate studies? What are the disadvantages? The answer to these questions should appear in an article introducing a new modelling framework when other models are already available.

M2- The ERA Interim reanalysis and the MK3Lv.1.2 model are now outdated. ERA5 and ERA5-Land are state-of-the-art reanalyses with better spatial resolution. And the same can be said about paleosimulations included in the PMIP4/CMIP6 projects. Why were these old products selected as forcings of the simulations? As the authors indicate in the manuscript, the spatial resolution of the forcings is one of the aspects affecting the performance of the CryoGridLite model, and those forcings need to be interpolated before running the model. Would not make more sense to use new, high resolution renalyses and paleosimulations for this study?

M3- After reading the two first sections, it is clear that the main advantage of the CryoGridLitle is the speed of execution in comparison with more comprehensive permafrost medelling schemes. To this end, many important processes are not in cluded in the model, such as water advection or runoff. Nevertheless, there is no estimate about the performance gain of CryoGridLitle in comparison with other schemes. Comparing the time required to simulate the 1400 years of this study in the CryiGridLitle and in another scheme (maybe CryoGrid3?) would allow the reader to assess if the gains in execution time really compensate for the absent processes.

M4- The authors should consider the possibility of adding some theoretical tests to evaluate the ability of the model to simulate physical processes, such as propagation of heat with different thawing conditions. I am aware that the CryoGrid3 model is able to successfully reproduce such processes, but since the formulation for heat propagation in the CryoGridLitle model has been modified, there should be some proof that the model is able to correctly reproduce phase change and basic heat diffusion though the ground.

M5- Another concern is the evaluation of the model against measurements of soil temperature and active layer thickness (ALT) at CALM sites. I wonder if evaluating soil temperatures and ALT from CALM is enough to “validate” the model. The CALM network is indeed a very valuable resource for model assessment, but it is also limited geographically and in time. Otherwise, there are several estimates of near-surface permafrost area in the present, some of the relevant articles have been cited in the manuscript, and several indices have been developed in order to use meteorological data as a benchmark for evaluating permafrost models (e.g., 1-2). Then, why is the evaluation of CryoGridLitle restricted to comparing with CALM stations? At the very least, a comparison with estimates of permafrost area during recent times should appear in the article, as this is a relevant factor to evaluate the quality of the simulations.

M6- Lines 309-319: There are some works providing ground surface temperature histories from inversions of deep subsurface temperature profiles in the North American part of the Arctic (e.g., 3-6). Nevertheless, the authors choose proxy-based paleoreconstructions of surface air temperature to compare with permafrost temperature changes in Alaska. Inversions of subsurface temperature profiles are more adequate for this comparison, since these are estimates of changes in ground surface temperature.

Minor points

m1- The title should be changed to reflect the model evaluation part of the study. Something like “The evolution of Arctic permafrost over the last three centuries using a new, fast permafrost model”.

m2- Lines 103-106: It is not clear how the model can produce deviations  larger than the threshold and still conserve energy. Could you please give more detail about this point?

m3- The definition of 1850-1900 as preindustrial period is not consistent with the consensus in paleoclimate publications. Indeed, the period 1750-1800 is a better option for preindustrial times (3). Please, consider a change of labelling, perhaps with 1850-1900 as later 19th century (L19C).

m4- I am unable to see the mentioned short-term changes in permafrost area due to volcanic eruptions in Figure 6. Is there any other way of presenting the results of Figure 6 that shows more clearly the effect of the eruptions?

References

1- Koven, C. D., Riley, W. J., and Stern, A.: Analysis of Permafrost Thermal Dynamics and Response to Climate Change in the CMIP5 Earth System Models, Journal of Climate, 26, 1877–1900, https://doi.org/10.1175/JCLI-D-12-00228.1, 2012/10/01.

2- Burke, E. J., Zhang, Y., and Krinner, G.: Evaluating permafrost physics in the Coupled Model Intercomparison Project 6 (CMIP6) models and their sensitivity to climate change, The Cryosphere, 14, 3155–3174, https://doi.org/10.5194/tc-14-3155-2020, 2020.

3- Majorowicz, J. A., Skinner, W. R., and Šafanda, J.: Large ground warming in the Canadian Arctic inferred from inversions of temperature logs, Earth and Planetary Science Letters, 221, 15–25, https://doi.org/https://doi.org/10.1016/S0012-821X(04)00106-2, 2004.

4- Taylor, A. E., Wang, K., Smith, S. L., Burgess, M. M., and Judge, A. S.: Canadian Arctic Permafrost Observatories: Detecting contemporary climate change through inversion of subsurface temperature time series, Journal of Geophysical Research: Solid Earth, 111, https://doi.org/https://doi.org/10.1029/2004JB003208, 2006.

5- Taylor, A. E. and Wang, K.: Geothermal inversion of Canadian Arctic ground temperatures and effect of permafrost aggradation at emergent shorelines, Geochemistry, Geophysics, Geosystems, 9, https://doi.org/https://doi.org/10.1029/2008GC002064, 2008.

6- Jaume-Santero, F., Pickler, C., Beltrami, H., and Mareschal, J.-C.: North American regional climate reconstruction from ground surface temperature histories, Climate of the Past, 12, 2181–2194, https://doi.org/10.5194/cp-12-2181-2016, 2016.

7- Hawkins, E., Ortega, P., Suckling, E., Schurer, A., Hegerl, G., Jones, P., Joshi, M., Osborn, T. J., Masson-Delmotte, V., Mignot, J., Thorne, P., and van Oldenborgh, G. J.: Estimating Changes in Global Temperature since the Preindustrial Period, Bulletin of the American Meteorological Society, 98, 1841–1856, https://doi.org/10.1175/BAMS-D-16-0007.1, 2017.