the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 Oct 2025
Modeling the Distribution of Mountain Permafrost in Chile
Abstract. Mountain permafrost is an important feature affecting slope stability and hydrological processes, yet its distribution remains poorly understood in many parts of the world, including Chile. This study develops the first countrywide high-resolution (30 m x 30 m) model of mountain permafrost distribution in mainland Chile, using geomorphological evidence from intact (active and inactive) and relict rock glaciers, along with empirical indicators of permafrost presence/absence primarily derived from borehole temperature records, test pits, and surface temperature measurements. We employ a generalized additive model representing local and regional trends by incorporating mean annual air temperature, potential incoming solar radiation, and latitude as predictors. This model achieved an area under the receiver operating characteristic curve (AUROC) of 0.70 (0.74) in spatial (non-spatial) cross-validation. The model's predictions generate a Permafrost Favorability Index (PFI), which expresses the potential of permafrost occurrence conditional on the predictor variables. Excluding glaciers, rock glaciers and vegetated surfaces, areas with PFI values ≥0.75 were classified as having favorable conditions for permafrost development. Under this criterion, approximately 1.06 % (8,042 km2) of mainland Chile exhibits conditions suitable for mountain permafrost, concentrated in the Atacama, Antofagasta, Coquimbo, and Santiago Metropolitan regions (21–32° S and 33–34° S). In contrast, permafrost is scarce or absent from the Maule to the Magallanes regions (south of ~36° S). The interpretation of PFI values should consider local environmental factors not included in the model, such as snow cover duration, clast size, soil properties, and surface albedo. These variables may influence the presence or absence of permafrost locally and should be accounted for using an interpretative guide. This first version of the permafrost distribution model provides a baseline for understanding its general distribution in Chile, which should be refined as new empirical evidence and improved subsurface temperature records become available in the future.
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Status: final response (author comments only)
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CC1: 'Comment on egusphere-2025-5090', David Boutt, 01 Dec 2025
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AC1: 'Reply on CC1', Alexander Brenning, 03 Dec 2025
Dear David Boutt,
thank you for your comment. I double-checked the validity of the link and did not encounter any problems. The hyperlink in the document links correctly to the resource in the DGA's Digital Library.
The files are hosted in an official government repository and referenced with a link that is identified as a permanent link. We are therefore confident that this is suitable as a persistent identifier.
What happens sometimes when using copy & paste to copy a link into a browser is that a delimiter is accidentally copied along with the link. In this case, there is a period (".") right after the URL (but not included in the URL's hyperlink). Kindly double-check that this is not the cause of the problem.
Alexander Brenning - on behalf of all co-authors
Citation: https://doi.org/10.5194/egusphere-2025-5090-AC1
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AC1: 'Reply on CC1', Alexander Brenning, 03 Dec 2025
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RC1: 'Comment on egusphere-2025-5090', Anonymous Referee #1, 19 Feb 2026
SUMMARY
Brenning et al. present the first countrywide high-resolution (30 m) permafrost favourability model for mainland Chile, spanning approximately 18° S to 56° S. This is no doubt a useful contribution – prior assessments for the Chilean Andes were either coarse-resolution global products (Gruber, 2012) or limited to sub-regions (Azócar et al., 2017). The integration of 238 in-situ observations alongside rock glacier inventories is a great strength of the study. The interpretive guide (Fig. 4) is a particularly practical addition for end-users.
However, I have a number of comments that I think would benefit from being addressed before publication. In particular I think the paper undersells what is most interesting about it (the challenges of scaling this approach across 38 degrees of latitude) while perhaps not fully addressing the mismatch between current-climate predictors and response variables that reflect past climate. I'm happy to see this published in The Cryosphere subject to considering the revisions detailed below.
MAIN COMMENTS
1. The modelling framework here closely follows the Boeckli et al. (2012) method as applied to Chile by Azócar et al. (2017), with relatively modest refinements. I think the paper would benefit from being more clear about this and instead focusing on what was learned from scaling the approach across 38 degrees of latitude. The suppressed 'cold anomaly' at 37–44° S is a case in point — that's an interesting result that deserves more attention.
2. The PFI approach assumes that rock glacier activity status reflects present-day permafrost conditions as characterised by current MAAT. But rock glaciers are geomorphological features that integrate climate signals over centuries to millennia, and I'm not sure this assumption gets quite the scrutiny it deserves here.
An intact rock glacier sitting at +1 °C MAAT today may have formed during the Little Ice Age or earlier and persist due to thermal inertia. The model labels it 'permafrost present' and associates it with current warm temperatures – which could push predictions too warm at marginal temperatures. Azócar et al. (2017) noted this: they found substantial proportions of intact rock glaciers at positive MAAT, particularly in the southern watersheds (31–32° S).
The CHELSA data represent a 1979–2019 mean, during which the study region warmed on the order of a degree – comparable to the altitudinal offset applied to correct for rock glacier creep. So the spatial displacement is carefully corrected, but a temporal displacement of similar or larger magnitude doesn't seem to be addressed.
I'm curious why a partial remedy that's already cited in the paper wasn't explored: InSAR-derived rock glacier kinematics from Cusicanqui et al. (2025) could distinguish truly active rock glaciers from inactive ones. Even a discussion of whether restricting the training set to rock glaciers with confirmed present-day movement would sharpen the response variable would be useful.
3. The model is trained on rock glacier inventories plus 238 in-situ observations, and then validated against 80 borehole sites. Are these 80 boreholes a subset of the 238 in-situ observations, or are they entirely independent? This isn't clear to me from the text. If there's overlap, that would affect how the performance metrics should be interpreted. Can the authors clarify?
Assuming the validation is independent, the model at PFI ≥ 0.75 is very conservative: when it detects permafrost, it's usually right (88% positive predictive value), but it only catches 40% of actual permafrost sites. For a planning tool, it might be preferable to have some false alarms rather than miss 60% of permafrost occurrence.
Lowering the threshold to PFI ≥ 0.50 improves sensitivity to 83% but specificity drops to 33%. There doesn't seem to be a threshold that works well on both counts, which suggests the model may need more information to discriminate – whether that's additional predictors, or addressing the temporal mismatch discussed above.
4. The model uses only three predictors: MAAT, centred PISR, and latitude. The authors acknowledge that local factors like snow cover and ground material aren't included but it would be helpful to understand why additional predictors that are available at high resolution weren't tried. Snow cover duration proxies can be derived from remote sensing. Precipitation was a significant predictor in Boeckli et al. (2012) for the Alps, and even in drier settings snow albedo affects the surface energy balance — worth exploring given that PISR is already a key predictor.
The study domain spans from near-zero precipitation in the Atacama to several thousand mm/yr in western Patagonia. In the hyper-arid north, snow is essentially absent and permafrost is primarily a radiation–temperature problem. Further south, snow insulation, duration, and melt infiltration become increasingly important controls on the ground thermal regime. The relative importance of the processes driving permafrost distribution shifts fundamentally across this domain, and with only three additive predictors — none of which capture snow processes — it's not clear the model can express that.
5. The in-situ evidence is heavily concentrated between 26–28° S (181 of 238 observations), with only 6 south of 34° S, and the rock glacier inventories have gaps at 24–26° S and 36.5–43.5° S. The model is extrapolating into large regions with little ground truth, yet the PFI maps cover all of mainland Chile without spatial uncertainty quantification. For a planning tool product, this seems worth flagging – at minimum, which regions are extrapolations vs. validated predictions?
6. I'd like to see a single map showing the entire model domain (18–56° S) with the PFI output. Figure 1 is useful for the detail but it's hard to get a sense of the full extent of the predictions — particularly how the model behaves in the south, where training data are sparse and conditions are very different from the core study area. Even at a coarse scale this would help the reader judge the spatial coverage. The boreholes and rock glaciers could be additionally added to this map, so the reader quickly grasps the setup. That said, Figure 1 is a really informative graphic and should be kept.
7. The activity classification of 10,517 rock glaciers is based on visual interpretation of ESRI World Imagery – a composite mosaic with spatially variable and unspecified acquisition dates, not a time series. Several criteria in Table 1 seem to imply dynamic assessment (e.g. "fresh" debris) that would be difficult from a single undated image. What date range does the imagery represent? This adds to the temporal mismatch discussed in Main Comment 2. Also, visually classifying this many rock glaciers is a large manual undertaking and intact vs. relict can be quite subjective. It's not clear how this was done in practice – how many operators, was reliability tested, were existing classifications re-assessed by the same person(s)? Some clarification would be helpful on this task.
TECHNICAL DETAILS
1. l.74: "prevalant" → "prevalent."
2. l.93: "potential incoming solar radation" → "radiation."
3. l.311: "significanctly" → "significantly."
4. l.200: "concurvity" is technically correct but likely unfamiliar to most readers. A brief description might help.
5. CHELSA downscaling achieves R²_adj = 0.893 with residual SD of 1.09 °C. This seems non-negligible relative to the MAAT range critical for permafrost (−4 to 0 °C). How much does this propagate into PFI uncertainty?
6. Comparison with Gruber (2012): the authors note that the global PZI is "too restrictive" in the Chilean Andes but don't really explore why. Is it resolution, input data, or the modelling approach? A more nuanced comparison would be helpful.
7. Code and data availability: only the PFI raster is shared. The R code, training data, and rock glacier inventory should also be made available. Consider Zenodo or similar.Citation: https://doi.org/10.5194/egusphere-2025-5090-RC1 -
RC2: 'Comment on egusphere-2025-5090', Anonymous Referee #2, 23 Feb 2026
Brenning et al. present a manuscript on a high‑resolution statistical model of mountain permafrost distribution across mainland Chile. The authors integrate geomorphological indicators (intact and relict rock glaciers), in‑situ permafrost evidence (boreholes, test pits, and surface temperature data), and topoclimatic predictors within a shape‑constrained generalized additive modeling framework. The resulting Permafrost Favourability Index (PFI) provides a spatially explicit and interpretable estimate of conditions favourable for permafrost occurrence. The model is validated against available field data.
The study represents an interesting contribution to Andean cryosphere research. It advances previous regional and global assessments by incorporating locally derived empirical evidence and by offering a consistent national‑scale baseline that is directly relevant for scientific research, environmental management, and high-level infrastructure planning in Chile. Despite inherent data limitations, the work clearly improves the current state of knowledge and provides a strong foundation for future refinements.
The manuscript is generally well written and logically structured. The methodology is clearly described, figures and tables are informative, and the discussion places the results in the context of existing literature. It is appreciated that the authors are transparent about uncertainties and limitations, which strengthens the credibility of the study.
Prior to acceptance for publication some aspects should be addressed by the authors:
The authors claim that they presented the first countrywide high-resolution model of mountain permafrost distribution model for Chile. This is not accurate. In 2020 a high-resolution model using similar resolution was developed for SERNAGEOMIN. It is, however, understood that this model may not be easily accessible, but it could be requested from SERNAGEOMIN. Unfortunately, no journal publication was prepared that introduced the model, but it was presented at RCOP in 2021 (Arenson et al., 2021) and at a SOCHICRI meeting in 2022 (Pino et al., 2022).
The model uses current mean annual air temperature (MAAT) as a parameter to identify potential presence of permafrost. There are two issues that must be addressed which typically result in current climate not being used as a parameter to determine the potential presence and absence of permafrost. First, permafrost is not the result of current climatic conditions, but the result of historic climatic conditions, dating back hundreds to thousands of years (as you also clearly state in the paper, e.g. L260). Using current climate will result in a significant underestimation as in many areas permafrost could not form today. Remember, for many cases permafrost exists because permafrost exists. Using modern climate information doesn’t provide valuable input. In addition, and more importantly, the impact of air temperature on permafrost is complex and the impact of summer and winter temperatures are different. The ground thermal regimes at a location where air temperatures vary between -6 and +4 degrees (MAAT = -1°C), and -30 and +28 degrees (MAAT = -1°C) is very different. Hence the value of using MAAT is very questionable. As such the claim that the ZIA (notable, today’s ZIA) is a key parameter that controls permafrost distribution (L70) is extremely questionable and must be supported by references. Similarely, no reference is provided that would support the claim that rock glacier patterns are more closely related to the ZIA than to the ELA of glaciers (L84).
The authors mention that they are only using intact rock glaciers in the development of the model and that they reviewed every rock glacier in the inventory > 6000. Additional details should be provided on how they have reviewed the rock glacier activity and a confirmation provided that they have in fact reviewed every single rock glacier that is in the inventory. Based on my personal review of some rock glaciers that are inventoried, some polygons should have been deleted as they would not qualify as rock glaciers, or the polygons changed as many rock glacier polygons in the DGA inventory include areas upslope that are part of the source zone and not the actual rock glacier. The level of detail completed by the authors during the review is unknown.
The model is using the latitude as a parameter that controls the permafrost distribution. Can the authors confirm that no east-west trend was identified? It seems reasonable with such a narrow mountain range, but it would be useful if the authors confirmed that they have checked the absence of such a trend.
In Figure 3 it is noted that there seems to be relatively little permafrost in the most southern region of Chile. It is understood that Gruber (2012) has similar findings. However, based on some observation in Argentina, I’m wondering if the model isn’t underestimating the extent of permafrost in that region. It would be good if the authors had a close look at their results and some of the landforms that can be found in the area, confirming the confidence in their model results.
The reviewer appreciates Figure 4 as those are very useful, specifically for the general public.
With regards to the model output, the reviewer would encourage the authors to have a close look and apply some filtering. The small, isolated areas are very unrealistic. Figure 5 and Figure A2 do show several small outlines with a PFI. These areas maker no sense in a periglacial / permafrost context, but are simple modelling artefacts. It would be easy to apply a filter and eliminate such areas as it is not realistic to find permafrost in such small areas. In these locations, permafrost often only can exists because it is ice-rich and consists of a critical mass. Permafrost does not grow and shrink like glaciers in the dry Andes. The model should reflect that.
The figures also highlight that rock glaciers are often outside areas with a PFI. This seems to be the result of using rock glacier source zones in the model. It seems very illogical to me to use that approach as it underestimates the extent of permafrost significantly. Rock glaciers are permafrost features and part of the periglacial environment. As such they must be included and the model. The reviewer also wants to remind the authors of their own definition of a PFI of 0,75: “Permafrost only present in cold conditions and depending on material.” This is exactly where rock glaciers would fall under. The area should be highlighted as an area where permafrost is typically absent but may, under special conditions, be present. It is therefore recommended that the authors have another closer look at their model and make the necessary adjustments.
In the discussion, it would be good if the authors would also look at Mathys et al. (2022) and how their model results matches this publication.
The reviewer generally agrees with the discussion and conclusion, would, however, also like to see the mentioning of InSAR as it is a important parameter in rock glacier monitoring.
Model access remains unavailable online despite repeated attempts to download it from different computers, as the connection consistently times out. This issue must be fixed before publication.
Some additional observations:
- L10: “SantiagoMetropolitan” → Santiago Metropolitan (missing space).
- L15: “should be accounted for using an interpretative guide” → consider accounted for through an interpretative guide.
- L23–24: “There are currently no regulations…” → sentence could be streamlined for clarity.
- L31: “specific region” → specific regions.
- L65: “tenfold differences” → ten‑fold differences (hyphenation).
- L72: “Zero Isotherm Altitud” → Zero Isotherm Altitude.
- L74: “prevelant” → prevalent.
- L95: “solar radation” → solar radiation.
- L130: “NASADEMproduct” → NASADEM product.
- L135: “R 2 adj” → adjusted R² (formatting).
- L155: “use an indicator variable of presence” → use an indicator variable for presence.
- L175: Extra closing parenthesis in “PFI ≥ 0.75)”.
- L210: “2 K” do you mean 2°C as you use centigrade as the main unit.
- L230: “0 ◦ CMAAT” → 0 °C MAAT.
- L305: “substantiallymore” → substantially more.
- L310: “significanctly” → significantly.
Editorial / Clarity Suggestions
- General: Terms such as important, significant, or crucial would benefit from brief contextual justification or rephrasing to avoid subjective emphasis.
- Model interpretation (Results & Discussion): Clarify that low PFI values do not imply absence of permafrost everywhere, particularly in data‑poor southern regions.
In conclusion, this manuscript represents a valuable contribution to Andean and global permafrost research. However, the current model is likely underestimating the extent of permafrost in Chile, which is believed to be the result of incorporating modern MAAT and using rock glacier source zones as attributes. Nevertheless, the core methodology and results are acceptable in principle, and the study clearly improves upon existing large‑scale assessments. The manuscript does require some revisions, primarily to improve clarity, address conceptual misconstructions, refine interpretation, and correct minor editorial issues. With these revisions, the paper could be recommended for publication.
References:
Arenson, L. U., Pino, C., Schimnowsky, M., Wainstein, P. A., & Cecioni R., A. (2021). A Continental Permafrost Distribution Model for the South American Andes Regional Conference on Permafrost and 19th International Conference on Cold Regions Engineering. Virtual meeting, Octobre 2021.
Pino, C., Arenson, L. U., Wainstein, P. A., & Schimnowsky, M. (2022). Modelo de Distribución de Permafrost en los Andes Sudamericanos IV Congreso de la Sociedad Chilena de la Criósfera, Pucón, Chile, Mayo 2022.
Mathys, T., Hilbich, C., Arenson, L. U., Wainstein, P. A., & Hauck, C. (2022). Towards accurate quantification of ice content in permafrost of the Central Andes – Part 2: An upscaling strategy of geophysical measurements to the catchment scale at two study sites. The Cryosphere, 16(6), 2595-2615. https://doi.org/10.5194/tc-16-2595-2022
Citation: https://doi.org/10.5194/egusphere-2025-5090-RC2
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The link to the digital repository do not work.
https://snia.mop.gob.cl/PIA/handle/20.500.13000/126863