A GAM was implemented to predict the spatial distribution of permafrost in mainland Chile. GAMs extend generalized linear models (GLMs) by allowing nonlinear relationships between predictors and the response variable through the use of smoothing functions . They have been applied successfully to model rock glacier and mountain permafrost distribution as well as other geomorphological processes and landforms . While the use of more flexible models such as random forests has been proposed in the context of permafrost modeling , increases in model performance are often negligible or due to overfitting and may not outweigh the loss of interpretability compared to additive models .

As response variable Y we use an indicator variable for permafrost presence (Y= 1) versus absence (Y= 0) derived from all geomorphological and in-situ evidence described in Sect. . Our predictors are MAAT, CPISR, and latitude. The model, which uses a logistic link function, can therefore be expressed as: 1ln⁡Px1-Px=β0+fMAATMAATx+fCPISRCPISRx+fLATLATx, where P(x) is the probability of permafrost presence at location x, β0 is the intercept, and fMAAT, fCPISR, fLAT are nonlinear smoothing functions for MAAT, CPISR, and latitude, respectively. We impose monotonicity constraints to avoid overfitting and improve geomorphological plausibility by ensuring a monotonic decrease in predicted probabilities for increasing MAAT, CPISR, and latitude. In addition, model adjustments as outlined below are implemented to reduce possible biases.

Model predictions on the probability scale were used to define a permafrost favorability index (PFI), which we interpret as a relative indicator of potential permafrost conditions rather than as a calibrated probability of local permafrost occurrence .

The model was fitted in R using the scam package, which extends the mgcv implementation of spline-based GAMs for model fitting, RSAGA and terra for spatial data processing , and sperrorest for model assessment . Predictor variables were extracted and processed using SAGA GIS (v9.0.2; ). For reproducibility, a revised, fully terra-based implementation of the workflow was released at Zenodo .

The dataset for modeling permafrost distribution consisted of 10 517 observations, including 6187 intact and 4092 relict rock glaciers from multiple inventories, and in-situ evidence (DGA, ). Observations were classified into two categories: presence of permafrost (6279 observations) and absence of permafrost (4238 observations).

MAAT, CPISR and latitude each were negatively associated with permafrost presence (univariate AUROC values: 0.67, 0.62 and 0.52, respectively; Table ). We also evaluated concurvity (a measure of nonlinear dependence among predictors in GAMs). Pairwise Pearson and Spearman correlations of predictors were weak (absolute values below 0.40), indicating no concurvity issues.

In the model of permafrost presence versus absence, all predictor variables (MAAT, CPISR, and latitude) showed a statistically significant association with the response (p-values < 0.001; Table ), using moderately nonlinear smoothing functions with up to 5.7 effective degrees of freedom for each predictor (Fig. ). The monotonicity constraint on latitude eliminated an implausible overshoot or “cold anomaly” in a data-poor region in south-central Chile (37–44° S), which would have been modeled with 8.9 additional degrees of freedom if an unconstrained model had been used. Using spatial CV, the model's AUROC showed “acceptable” discrimination between presence and absence of permafrost, with a mean AUROC of 0.74 for random partitions and 0.70 for spatial blocks. This difference suggests that the model generalizes well from the data.

Model-derived local uncertainty was estimated with the delta method and expressed on the PFI scale. This uncertainty describes the sampling uncertainty of the fitted response surface, conditional on the selected model structure, predictor variables, and training data. It was small over most of the prediction domain: in 75 % of the area, the standard error was below 0.015 and only in 1 % of the area it exceeded 0.05 PFI units. They were lowest (< 0.01 on average) between ∼ 29 and ∼ 48° S and highest (> 0.015) north of (∼ 25° S). These values indicate that the fitted regional-scale response surface is relatively stable. They should not be interpreted as comprehensive local uncertainty bounds for permafrost occurrence, because they do not include uncertainty from response classification, omitted local controls, or predictor errors.

In the interpretation of predictor–response relationships, the odds of permafrost presence were found to be about 4.7 times higher for a 2 °C lower MAAT, when focusing on the -4 to 0 °C range. A CPISR difference of 0.2 was associated with an odds ratio of 3.0, when accounting for the other variables in the model. Latitudinally, the model predicted increased permafrost presence in the northernmost part (odds ratio up to 54 compared to central Chile), indicating more favorable conditions than in central Chile, under otherwise equal conditions.

As a consistency check, the PFI was evaluated against local borehole data, which represent the most reliable, but non-randomly distributed subset of the training evidence for permafrost presence or absence. These borehole sites represent a subset of the in-situ observations described in Sect. . Of 80 borehole sites, 35 indicated permafrost presence, and 45 indicated absence. Agreement between thresholded PFI classes and borehole evidence was summarized using confusion matrices with several PFI thresholds (0.75, 0.85, and 0.90). At a threshold of PFI ≥ 0.75, the model achieved high specificity (96 %), correctly predicting almost all sites without permafrost, but only 40 % sensitivity, or permafrost detection rate (Table ). Reducing the threshold to PFI ≥ 0.50 improved sensitivity to 83 %, with a substantial decrease in specificity to 33 %. In terms of the predictive value of identified permafrost areas, 88 % (49 %) of identified permafrost locations presented borehole evidence of permafrost, when applying a PFI threshold of 0.75 (0.50). Based on these results, a threshold of 0.75 was deemed appropriate for identifying conditions favorable for permafrost existence, while recognizing that alternative thresholds may be chosen depending on the intended application, and permafrost is considered possible for PFIs between 0.50 and 0.75.

The local permafrost evidence indicates that the global PZI may be comparatively restrictive in the Chilean Andes. Using a threshold of PZI ≥ 0.50, only 16 % of all positive field observations and 37 % of the borehole-based permafrost observations would be identified as potential permafrost locations, indicating low sensitivity even at this relatively low threshold. Similar discrepancies between the global PZI and regional permafrost evidence in the Chilean Andes have previously been reported by . These results suggest that the global PZI underestimates the extent of conditions favorable for mountain permafrost in the Chilean Andes when compared with locally calibrated empirical models.

The predicted PFI's generalized lati-altitudinal distribution is summarized in Fig. , showing that the transition from relict to intact rock glaciers takes place mostly within a 500 m elevation band above the ZIA, or between about -3 and 0 °C MAAT. In the southern part and especially in the extreme north, this transition occurs at somewhat higher MAAT, around 0 °C and even above, respectively. This transition band generally corresponds to the 0.50–0.75 PFI range. Nevertheless, favorable conditions can be shifted about 500 m downward where incoming solar radiation is low (dashed line in Fig. ).

Assuming PFI ≥ 0.75 indicates conditions highly favorable for permafrost, approximately 1.06 % (8042 km²) of mainland Chile may support permafrost, excluding glaciated and vegetated areas (Table ; Fig. ). Considering that the PFI may not be reliable in exposed bedrock areas, which can be approximated by having slope angles 30° , this reduces to 6378 km².

Regions with the highest concentrations of favorable permafrost conditions are located in Atacama, Antofagasta, Coquimbo (21–32° S), and the Santiago Metropolitan Region (33–34° S), where extensive mountain areas exceed the critical elevation thresholds (Fig. ). In contrast, regions south of Maule (∼ 36° S) exhibit only isolated or no favorable conditions for permafrost due to higher temperatures and generally lower elevations. Statistics for the main catchments with likely permafrost presence are included in the Appendix in Table . This allows for a comparison with results of an earlier study in the semi-arid Andes (Huasco to Choapa basins), which obtained very similar estimates using a similar methodology (1051 km² in vs. 1118 km² in this study, both for PFI ≥ 0.75 and limited to slope < 35°).

A qualitative interpretation guide was developed based on a similar document by to aid governmental and public use of PFI maps (Fig. ). In particular, the consideration of snow cover duration, surface material properties and climatic conditions need to be considered in practical applications (see Sect. ). Figure shows a sample PFI map from central Chile, and additional maps are included in the Appendix (Figs. and ), illustrating representative areas in the northern and southern Andes. The complete PFI raster dataset and the corresponding technical report is publicly available through Zenodo and Dirección General de Aguas repositories (DGA, ; ); PFI map sheets covering the entire study region are published in a separate repository .

Rock glaciers are widely recognized as indicators of the lower limit of permafrost distribution, as evidenced by studies across various mountain regions globally . However, their use as a proxy for permafrost conditions requires bias adjustments and careful interpretation, particularly when considering local environmental variability . In this study, glaciers and areas with (even sparse) vegetation cover were excluded, although they may locally present permafrost. More importantly, only root-zone locations of rock glaciers were considered as permafrost evidence to exclude permafrost evidence from rock glacier tongues and lobes, which may have crept into non-permafrost terrain. Where only rock glacier toe locations were available, a bias adjustment was applied that accounts for the average altitudinal extent of rock glaciers . Nevertheless, we point out that permafrost near the lower limit of its modeled potential distribution may be sporadic in extent consisting of remnants that may not be preserved under present and future climatic conditions.

Also, the classification of rock glacier activity used in this study is subject to uncertainties and subjectivity. Recent advances in remote sensing allow their dynamics to be quantified using satellite-based kinematic observations (e.g., InSAR-derived velocity fields), which may provide an additional basis for distinguishing active from inactive landforms in future studies .

The incorporation of additional in-situ permafrost evidence, including borehole measurements, enriches the empirical basis for model training and assessment. This is particularly relevant in regions where rock glaciers are scarce or inexistent, as in parts of southern Chile or the most arid parts of the Atacama desert . Future studies should prioritize expanding ground-truth observations across diverse environmental contexts, especially in non-rock glacier debris-covered terrain. Such studies would greatly benefit from targeted study designs rather than circumstantial evidence from various research or industrial activities.

The statistical performance of the model indicates that MAAT, CPISR, and latitude emerge as key predictors of permafrost distribution at the regional scale, consistent with previous studies e.g.,. Our AUROC values (0.70 in spatial CV) are consistent with regional-scale permafrost modeling efforts in the Andes and Alps (∼ 0.75–0.80). Higher AUROC values in some studies (≥ 0.9) often result from more restrictive definitions of permafrost indicators, which reduce data heterogeneity but may artificially inflate model performance. This happens when inactive rock glaciers are excluded as indicators or where low-elevation non-rock glacier areas are conceptualized as non-permafrost areas .

Although the model provides a useful regional-scale understanding of permafrost distribution, it does not fully account for critical local factors, such as snow redistribution by wind and avalanches or variations in soil and surface material properties, because spatially consistent datasets describing these processes are currently not available across the full extent of mainland Chile. These factors are known to influence ground thermal regimes . For example, coarse blocky materials favor permafrost by enhancing ventilation and reducing heat retention, while fine-grained sediments tend to create warmer ground conditions . showed that in the Andes of Santiago (33.5° S), openwork boulder terrain was associated with ∼ 0.6–0.8 °C lower mean annual ground surface temperatures (MAGST). Moreover, surfaces with 30 d of additional snow cover had a MAGST depression by 0.1–0.6 °C. In the semi-arid Andes at 30° S, areas with long-lasting snow cover had a ∼ 0.4 °C cooler MAGST .

Geophysical studies in the Central Andes have also highlighted the large variability in ground-ice contents between different permafrost landforms and the presence of substantial ground ice outside rock glaciers . This is consistent with interpreting intermediate PFI values as areas where permafrost may occur with lower or more heterogeneous ice contents.

The magnitude of these local modifications of ground thermal regimes shows that these effects should be incorporated in future modeling efforts. Field investigations of local-scale permafrost patterns outside of rock glaciers are now required to fill this gap, enabling future models to integrate regional and local patterns and thereby reduce uncertainties. In addition to ground temperature monitoring, geophysical methods can help elucidate spatial patterns as well as characteristics such as ice content and thickness, which influence the sensitivity of mountain permafrost to climate change . Our model can help guide future sampling and monitoring campaigns as it identifies areas with particularly high uncertainties, close to the proposed PFI thresholds.

The scarcity of permafrost observations in some regions of the Chilean Andes introduces additional uncertainty into the modeled distribution. This is particularly evident in south-central (37–44° S) and southernmost Chile (∼ 54° S), where comparatively low mountain elevations and glacier-dominated cryospheric conditions limit the occurrence of rock glaciers. In such data-poor regions, statistical models may produce unstable or geomorphologically implausible patterns unless appropriate constraints are imposed. The shape-constrained GAM applied in this study helps enforce physically plausible relationships between predictors and permafrost occurrence, thereby reducing the risk of unrealistic spatial predictions in poorly constrained regions, but predictions in these areas should still be interpreted cautiously. Targeted field investigations and monitoring programs in these regions would help improve the empirical basis of future permafrost distribution models, and data from across the border may further help to stabilize models.

In the meantime, the PFI offers a semi-quantitative rating of permafrost potential based on statistical relationships between predictors and observed permafrost evidence. As in similar modeling efforts (e.g., ), the interpretation of PFI scores must consider the local environmental context as this is not incorporated in the current model in sufficient detail. We propose that PFI values greater than 0.9 should be interpreted as permafrost being very likely present regardless of local conditions. In PFI zones between 0.75 and 0.90, permafrost may be present primarily under cold local conditions (with shading or long-lasting snow cover) and dependent on surface materials. In areas with PFI values between 0.50 and 0.75, we conclude that permafrost presence is limited to favorable local conditions. In areas with lower PFI scores, permafrost is unlikely under most conditions.

The model predicts that more than 8000 km² of mainland Chile may have favorable conditions for permafrost occurrence (PFI ≥ 0.75). These areas are predominantly concentrated in high-altitude zones within the Atacama, Antofagasta, Coquimbo and Santiago Metropolitan regions, with minimal to no favorable conditions observed in southern regions (i.e., Maule to Magallanes). This pattern reflects the interplay between altitude, solar radiation, and latitude as first-order controls of permafrost occurrence. Being driven by local permafrost evidence, our model not only provides more detail but also eliminates biases detected in the too restrictive global permafrost index, PZI .

This research provides the first countrywide empirically calibrated assessment of mountain permafrost distribution in Chile based on local geomorphological and in-situ evidence, offering a baseline for future monitoring, environmental assessment, and infrastructure planning in high-mountain regions. It furthermore refines previous models with new in-situ data from various sites and monitoring contexts, and it provides a generalized, synoptic vision across multiple rock glacier inventories.

This study also highlights the need for enhanced ground-truthing efforts to improve the calibration and validation of permafrost distribution models. A systematic approach to sampling ground temperatures across varied landforms and environmental conditions, coupled with expanded geophysical surveys, would strengthen the empirical foundation for future permafrost studies. At present, studies on local patterns are limited to near-surface ground temperatures , which provide limited insights into thermal conditions at relevant depths . Additionally, the integration of remotely-sensed information with higher spatial and temporal resolution could refine the representation of local environmental factors, such as surface roughness, snow cover and vegetation dynamics , and confirm the activity status of rock glaciers .

Although the PFI can suggest areas with cold ground conditions, it should not be used as a direct indicator of ground ice content. The presence of ground ice in permafrost may depend on local environmental conditions and the general climate setting .