In situ data used to assess the TTOP model parameters were collected from a variety of Canadian permafrost environments ranging from Subarctic to polar desert, in lowlands and mountains (Fig. 1).

The sampling locations were initially grouped into 21 study areas based on the data source and proximity (Table 1). The latter were then combined into seven main study regions based on similarity in environmental and permafrost conditions and on statistically significant differences in model parameters (Table S1): High Arctic, Northern NWT and NU, Southern NWT, Western Yukon, Eastern Yukon, Southern Yukon-Northern BC, and Labrador.

Air, ground surface and ground temperature at depth measurements were recorded at 1 to 8 h intervals at 330 sites (Table 1). Record lengths ranged from 2 to 16 years. This dataset, spanning over two decades, is the product of long-term federal, territorial, and academic monitoring networks, only possible through funding and support from the Geological Survey of Canada and several Canadian universities.

Air temperatures were generally measured ∼1.5 to ∼2 m above the ground surface with an Onset Hobo U23-002 (±0.25–0.4 °C accuracy, 0.04 °C resolution) thermistors or Vemco loggers (accuracy and precision 0.1 °C) (previously owned by AMIRIX Systems Inc.) housed in a radiation shield (Onset RS1). At newer sites, a Hobo U23-001 (±0.25 °C accuracy, 0.04 °C resolution) was housed in a radiation shield. At all sites except the Southern NWT, ground surface temperature was measured 2–5 cm below the ground surface with the Hobo U23-002 internal thermistor. The slight difference in surface sampling depth (∼3 cm) did not have an impact on the results as the temperature difference is outside the logger accuracy. The Southern NWT ground surface temperatures were measured with Maxim Integrated TM Thermochron iButton temperature loggers (model no. DS1922L; accuracy ±0.5 °C).

For most sites, ground temperature at depth was measured using the Hobo U23-002 or Hobo Pro U12-008 external thermistors, while for the remaining sites, ground temperatures at depth were recorded using multi-sensor cables with RBR loggers. For a majority of sites, the ground depth sensor was positioned close to or at the top of the frost table at the time of installation. For sites with multiple ground temperature observations, the sensor closest to the depth of the frost table was used. However, for less than a quarter of observations (23 %), annual mean ground temperature (AMGT) may not correspond to the temperature at the top of the frost table due to installation depth limitations. These sites are generally confined to coarse grained, dry, rocky sediment where the thermal gradient is typically small (Lewkowicz et al., 2012). Based on estimations of active layer or frost depth and temperature extrapolation (see Sect. S1 in the Supplement), the difference between the true TTOP and the temperature at the monitoring depth was generally less than 0.5 °C (90 % observations, average =0.2 °C). Therefore, at these sites, AMGT was still compared directly to the modelled TTOP value.

The data were assessed for sensor drift, erroneous measurements, and missing intervals. Short data gaps (<3 consecutive days) were filled using linear interpolation, while larger gaps were flagged. Average air, ground surface and ground temperatures were only calculated for years ≥85 % daily data completeness once erroneous values were removed and data gaps were considered.

The TTOP model calculates equilibrium permafrost temperature using air freezing and thawing degree days, n-factors and the thermal conductivity ratio (Table 2). The TTOP model is often used spatially as the meteorological input parameters are commonly able to be estimated from meteorological stations (Juliussen and Humlum, 2007). However, as an equilibrium model, TTOP is not ideal for modelling transient changes in permafrost temperature and distribution. TTOP model errors are often largest near 0 °C due to latent heat effects, which the model does not consider (Riseborough, 2007).

To assess the TTOP model sensitivity to input parameters we first calculated baseline input parameters for the TTOP model and the reference TTOP value (TTOP model output when using values for baseline parameters derived from the measured field data) were calculated for each site.

To allow for direct comparison of model sensitivity in all environments with measured data, the TTOP model equation for permafrost was also applied to sites considered to be seasonally frozen (Way and Lewkowicz, 2018; Obu et al., 2019; Garibaldi et al., 2021). For each year and each site, FDD and TDD were calculated using daily average air (Ta) and ground surface temperatures (Ts) from 1 September to 31 August of the subsequent year. Freezing and thawing n-factors were then calculated for each measurement location (Table 2). The ratio of thawed to frozen thermal conductivity (rk) for sites with a deeper ground temperature measurement was calculated using FDD and TDD for both the ground surface (_s) and the ground temperature observation at or near the frost table (_g) (Table 2). For sites without a depth sensor, rk, was assigned based on vegetation class for the High Arctic and substrate for the Mackenzie Valley (n=38) (Kersten, 1949; Gregory, 2011; Obu et al., 2019; Garibaldi et al., 2021). These sites were included even though rk needed to be assigned as they filled a substantial latitudinal gap in the dataset (Fig. S2). Using the observed thermal offset to determine rk may not necessarily be possible given the materials that are present due to potential disequilibrium. However, for the purposes of this study we assumed equilibrium conditions for each observation.

Once the parameters and reference TTOP values were determined, the sensitivity of the model to changes in each parameter was assessed by iteratively substituting values for one parameter while holding all other inputs constant and then calculating the TTOP value for each substitution. The substituted values used percentiles (minimum, 10th, 25th, 50th, 75th, 90th and maximum) calculated using the parameters across the entire study dataset. We selected percentile-based substitution to test TTOP Model sensitivity as it allowed us to increase and decrease parameter values within observed ranges while avoiding introducing negative values. Additionally, percentile substitution allows for a direct comparison of sensitivity to each parameter across regions as the parameters at all sites were changed to the same value. Each year of data for each site was treated as its own observation and run through the sensitivity analysis resulting in 9100 different TTOP values for each parameter. Sensitivity analysis TTOPs were then compared to the reference (i.e. observed) TTOP values to assess the influence of the TTOP model to changes in each parameter.

Since vegetation is often used when assigning n-factors and rk in regions without observations, the TTOP sensitivity analysis was re-run using the median value for these parameters based on vegetation class and region. These TTOP outputs were then compared to the reference TTOP value for each site.

Algorithm inputs included TTOP model and additional parameters (see Table 2). Samples were randomly split into testing and training data (40 % and 60 % respectively both for the overall dataset and individual regions) with individual years treated as independent observations. Two random forest models were created, one using all the input variables and the other using only the TTOP model parameters (Table 3). The target variable for each random forest model was mean annual ground temperature at TTOP (MAGT). The random forests were generated in R Studio and run using the default settings for the number of variables sampled for splitting at each node (4 and 2 for iterations 1 and 2 respectively) and number of trees (500). For each iteration, the same training and test dataset was used to ensure comparability. The Northern NWT and NU regions were not included in this analysis because they lacked sufficient deeper ground temperature measurements.

Random forest provides variable importance rankings through two methods: permutation accuracy importance (mean square error (MSE) reduction) or Gini importance (Strobl et al., 2008). The former, used here, has been more widely employed in variable importance studies due to biases in Gini importance when predictor parameters vary in number and scale (Díaz-Uriarte and Alvarez de Andrés, 2006; Strobl et al., 2008; Grömping, 2009; Genuer et al., 2010). Reduction in MSE involves the random permutation of each variable individually to simulate its absence in the model prediction. Variable importance is then determined based on the difference in prediction accuracy before and after the permutation. Variable importance plots were created for each random forest model both for the entire dataset (averaged across all sites) and for each region individually (averaged for all sites within each region) (e.g. Colyn et al., 2025).

For sites with measured ground temperature, the performance of the TTOP model was assessed by comparing the calculated TTOP and the measured AMGT at or near the top of permafrost (observed TTOP). For the few sites where the observed AMGT was not near the top of the frost table, the observed AMGT was still compared to TTOP as the thermal offset at these sites was low (Sect. S1 in the Supplement). TTOP model performance was based on model root mean square error (RMSE), r2, and bias compared to measured temperatures for individual years and sites.

To test TTOP model sensitivity, percentile values for each parameter (calculated over the entire dataset) were directly substituted for the measured parameter value (Table 4). As the range of measured values differed for each parameter, the values and range of the substituted percentiles were also different. The potential impact of this on the interpretation of the sensitivity is discussed below.

For a majority (>53 %) of sample points, changes to FDD_a, nt, TDD_a, and rk resulted in < 1 °C difference between the reference and perturbed TTOP output (Fig. 2b–e). However, for nf less than half (< 27 %) remained within 1 °C of the initial TTOP value (Fig. 2a). FDD_a showed more sensitivity than TDD_a, nt, and rk with less than 70 % of sample points remaining within 2 °C of the initial observation value (compared to > 75 %).

Latitudinal trends in sensitivity were observed with the region with the coldest permafrost (High Arctic) showing a much greater response to changes in winter parameters (FDD_a and nf) and muted response to changes in summer parameters (nt) and the thermal conductivity ratio (rk) (Table 5, Fig. 3). However, the High Arctic region was also disproportionately sensitive to changes in TDD_a when compared to more southern regions. Moving from north to south the difference between the reference and perturbed TTOP generally increased for the thawing parameters and decreased for the freezing parameters. In the southernmost regions (Southern Yukon-Northern BC and Labrador) all parameters had similar sensitivity. All sites had the greatest sensitivity to changes in nf or nt and the least sensitivity to changes in FDD_a and rk. The sensitivity to rk was most similar between regions compared to the other parameters.

Using the internal median parameter value (based on measured values for each landcover class within each region) resulted in a lower error than using the external median parameter value for every region and landcover class (Fig. 4). These differences were especially pronounced for nf. For each region the shrub landcover class showed the least difference when using the internal vs. external parameters.

For the random forest iterations 1 and 2 (Table 3), several parameters were consistently ranked as the most and least important by virtue of the percent increase in MSE (Fig. 5). When all variables were used within the entire dataset, TO, rk and FDD_s were ranked as the most important. The least important were NVO, nt and TDD_a. Regionally, freezing season parameters (FDD_s and nf) and MAGST were consistently ranked as the most important parameters. Surprisingly, TDD_s was ranked as highly important only in the High Arctic and Labrador.

When using only the TTOP model parameters, nf was ranked as the most important for every region, while nt, rk, and TDD_a most often ranked lower in importance. TDD_a was the second most important parameter for the High Arctic region but was not deemed to be of high importance for any other region. Overall, the variable importance rankings once again highlight the prominence of freezing season conditions compared to thawing.

The variable importance conclusions from the TTOP sensitivity and random forest using only the TTOP parameters did not match perfectly, but there were commonalities for certain parameters. When comparing parameter rankings between the TTOP sensitivity analysis and random forest all but nt showed strong correlation (Table 6). Both analyses highlighted the importance of the freezing parameters (especially nf) which had the highest (almost perfect) correlation. There were greater discrepancies in parameter importance rankings, particularly for nt and rk which had the lowest correlations, especially nt which was the only parameter to have a weak ranking correlation. Despite the methodological differences between the two analyses, the parameter ranking showed good agreement, capturing the trends in the overall and regional differences in parameter importance.

The TTOP model performed well compared to the observed AMGT overall with an RMSE of 0.2 °C, but with regional differences in model performance (Fig. 6). The model also has a slight warm bias (0.02 °C) and a high r2 (0.99). Model error was low in most regions, except for the High Arctic. However, the Southern NWT region included an outlier with a large error.

Additionally, the model only misclassified permafrost presence (TTOP <0°C) or absence (TTOP >0°C) at 3 of the 612 observations. Two of the three observations were in the Southern Yukon-Northern BC region both of which were false positives for permafrost (no permafrost in observation but negative modelled temperature). The third observation was in the SNWT region where permafrost was observed but the model indicated its absence.

The sensitivity of the TTOP model to changes in specific parameters is affected by the structure of the model and the values of the parameters. The model across all regions was most sensitive to changes in nf, due to the higher number of FDD_a (compared to TDD_a), which amplified the response to changes (Smith and Riseborough, 1996, 2002; Bevington and Lewkowicz, 2015). Additionally, nf represents the impact of freezing season air temperature and snow depth which has an important influence on the ground thermal regime and therefore permafrost occurrence in the discontinuous zone (Riseborough and Smith ,1998; Smith and Riseborough, 2002, Gisnås et al., 2014; Way and Lapalme, 2021; Tutton et al., 2021; von Oppen et al., 2022). Therefore, it is unsurprising that it was consistently ranked as an important parameter.

Regionally, the sensitivity of the model to changes in the thawing parameters, especially TDD_a and nt increased southward as the difference between FDD_a and TDD_a decreased. The exception to this was the High Arctic, where the model was disproportionately sensitive to changes in TDD_a despite the large contrast in the number of FDD_a and TDD_a in this region (up to five times as many FDD_a as TDD_a). The increased sensitivity to changes in TDD_a likely results from the high values of nt and rk, with values regularly approaching or exceeding 1.0. As a result, changes in TDD_a were amplified in this region. This also potentially highlights the sensitivity of this region to changes in summer climate as the lack of tall vegetation reduces the potential buffering effect of warmer temperatures on the ground thermal regime compared to other regions with more well-developed surface cover (Shur and Jorgenson, 2007; Throop et al., 2012; Smith et al., 2022).

It is also important to note this study perturbed TTOP model parameters using the entire measured dataset. Therefore, sensitivity to certain parameters may be higher than for studies with altered parameters based on values measured within a region which may have limited variability (Way and Lewkowicz, 2018). As a result, our results may highlight relatively higher sensitivity for different parameters such as nt compared to nf in Labrador (Way and Lewkowicz, 2018). However, the sensitivity and random forest analysis results also agreed with variable importance rankings overall across northern Canada, especially regarding the importance of nf (Bevington and Lewkowicz, 2015; Colyn et al., 2025).

The sensitivity analysis also showed that TTOP model parameters are not necessarily transferable between regions with the same landcover class. This is especially true for nf and nt as using the median values for the same landcover class from a different region resulted in a significantly greater error than using the median value corresponding to the site's actual region. This could be a result of the large range of environments sampled in this analysis as previous studies have shown transferability of nt between rock and forest landcovers of Labrador and Southern Yukon (Way and Lewkowicz, 2018). However, utilizing nf from Southern Yukon in Labrador increased TTOP model errors (Way and Lewkowicz, 2016), which supports our findings. The lack of transferability of nf likely stems from differences in snow depth and density across Canada (Bormann et al., 2013; Way and Lewkowicz, 2016; Simpson et al., 2022). As a result, utilizing snow redistribution algorithms are likely a more viable way to accurately capture permafrost presence and temperature on national and circumpolar scales (Gisnås et al., 2014; L'Hérault et al., 2017; Obu et al., 2019). However, using landcover as a proxy even when parameter values were outside of the region still resulted in a smaller error range than when values from the entire dataset (regardless of landcover type) were used.

Rk appears to be generally more transferable, especially for the limited number of tundra sites which might be the result of restricted soil (and organic) development and moisture in this landcover (Throop et al., 2012). Additionally, rk may have a smaller influence on ground temperature in certain environments (Karjalainen et al., 2019) and therefore the importance (or lack of transferability) may be masked by the large dataset. These results demonstrate the need for caution in assuming the regional transferability of parameters, especially in environments where values may differ substantially.

The variable importance rankings for the overall and regional datasets were a product of differences in values of the measured field inputs. TO and rk were ranked as the most important parameters when all variables were used. TO has previously been suggested as the most important parameter for determining the southern extent of permafrost, under equilibrium conditions, as a high TO can protect permafrost from higher air temperatures (Smith and Riseborough, 2002). However, neither were ranked as the most important parameters in any of the regional analyses. TO and rk had lower correlation with the other parameters (0.06–0.49), which may have artificially elevated their importance, but they are highly correlated with each other (0.93) which may explain why both have elevated importance (Fig. S4).

NVO has also been highlighted in the literature as an important parameter, determining the northern and southern limit of discontinuous permafrost and influencing permafrost existence within the discontinuous zone (Nicholson and Granberg, 1973; Smith and Riseborough, 2002). However, in this study NVO ranked as middle to low importance overall and for every region, even those spanning the continuous to discontinuous permafrost transition. Finally, overall and regionally, MAGST was deemed to be an important parameter for accurate predictions of MAGT. While this may be true for sites with a negligible thermal offset (Luo et al., 2019; Garibaldi et al., 2021), MAGST alone cannot accurately predict the thermal state of permafrost without additional information on the thermal properties, especially at sites with larger thermal offsets (James et al., 2013; Guo et al., 2024; Brown and Gruber, 2025). Therefore, the elevated importance of this parameter may indicate that sites with small thermal offsets are over-represented in the dataset (Fig. S3c).

The TTOP model generally performed well compared to observed AMGT, resulting in minimal errors in predicted TTOP even at seasonally frozen sites. The RMSE for the TTOP model for this study was similar to or smaller than those from previous TTOP modelling results in the same region (Obu et al., 2019; Garibaldi et al., 2021). This is likely a product of the use of directly measured and calculated input parameters rather than the characterization of parameters from environmental variables such as vegetation or spatial interpolation. This highlights the importance of in situ data for validation of parameters for accurate predictions of permafrost and ground temperatures.

The TTOP model did not perform as well in the High Arctic for certain observations, especially those from Cape Bounty during 2016–2017, when the predicted TTOP was higher than the observed values. The AMGST for 2016–2017 was substantially higher than those from the previous years. Although the AMAT showed only a slight deviation, nf at these sites decreased substantially, indicating greater snow depths. As a result, the TTOP model parameters were not in equilibrium with ground temperature for this year, yielding a larger discrepancy. Additionally, one year at one site in the Southern NWT region was also an outlier. At this site the relatively warm ground conditions during the freezing season led to a low nf (0.1) during this year compared to the other 12 years (0.46 on average). However, despite the warm winter conditions the annual mean ground temperature remained comparable to the other years, only increasing slightly. As a result, the TTOP model produced a larger error for this site during this year but produced low error at this location for the remaining years.

The TTOP model using measured parameters performed surprisingly well in locations of warmer, more marginal permafrost or locations with seasonal frost, despite these locations potentially being in disequilibrium with the current climate. However, these regions, also showed slightly increased error and more outliers (Fig. 6a, b) reflecting a lack of consistency in model performance. These results may indicate sites with more ecosystem-protected permafrost and high apparent TOs or disequilibrium conditions (Shur and Jorgenson, 2007; James et al., 2013; Vegter et al., 2024). It should be noted that even small temperature errors can result in the misclassification of permafrost presence where ground temperatures are close to 0 °C (Daly et al., 2022; Vegter et al., 2024) whereas the classification would be unaffected even with a larger temperature error in the High Arctic. However, the model accurately predicted permafrost presence or absence for the vast majority of observations (> 98 %) in this study even though 38 % of observations were within -1 to +1 °C.

The methods used to rank the importance of variables have their own uncertainties that could affect the reliability of the results. First, since the percentiles were derived from the observed data the range of values for each parameter differed and would vary if a different dataset was used. Second, although random forest is able to cope with highly correlated variables for prediction (Boulesteix et al., 2012), there are conflicting conclusions on the reliability of variable importance rankings (Strobl and Zeileis, 2008; Nicodemus et al., 2010; Tolosi and Lengauer, 2011; Gregorutti et al., 2017). For this study, a majority of the input parameters are highly correlated with at least one other parameter as some parameters are used to derive others (Figs. S4–6). This may have led the variable importance rankings of the random forest to be unreliable when all parameters where used. Additionally, although the random forest model using all variables performed relatively well (MSE 0.2 °C; variance explained 98 %), the regional models had lower percentages of variance explained (43 %–93 %) even though MSE was similar (0.2–0.8 °C). This may have impacted the reliability of the variable importance rankings for these models, as they may have accurately predicted ground temperature. Finally, it is important to note that due to the nature of random forest, the variable importance rankings are not perfectly repeatable. However, in several random forest runs the most important and least important parameters were consistent even if they were not in the exact same order each time. Despite the possible errors and uncertainty in the results of this, the variable importance analyses were in general agreement for the two methods and supported findings from previous studies.

Variation in variable importance rankings between the two methods may also have resulted from the difference in approaches. As the TTOP model utilized multiplicative factors, the importance of the parameters was elevated by nature of the model equation. For example, changes to FDD_a may be elevated through multiplication with nf. The random forest variable importance ranking was not dependent on this equation and as a result, the importance was potentially different based on the predictive method alone. Additionally, the TTOP model sensitivity analysis was determined through perturbation of the model parameters, thereby ranking the parameters' importance based on the response. Contrastingly, the random forest variable importance ranking was determined based on the current thermal conditions. This may also have resulted in some discrepancy in the rankings. However, both methods showed similar rankings and regional trends overall. Lastly, parameters sensitivity rankings do not inherently relate to statistical importance. TTOP model sensitivity to changes in a parameter value may not be statistically different from the sensitivity to changes in another (Table 5). This is especially true for certain regions (N NWT and NU and the more southern regions), where there are few statistically different sensitivities between parameters.

Since the TTOP model was deemed more sensitive to certain model parameters in the entire dataset and in certain regions, accurate parameterization of the most important variables for the study location is vital. Overall, the freezing season parameters were generally deemed the most important; therefore, adequate characterization is essential for accurate predictions of TTOP at national or circumpolar scales. This is especially true for nf which is typically the most difficult to parameterize since it is dependent on a wide range of conditions including timing, depth, and morphology of snow and substrate conditions including soil moisture and is not necessarily transferable between regions (Smith and Riseborough, 2002; Zhang, 2005; Throop et al., 2012; Way and Lewkowicz, 2016).

Regionally, in locations where FDD_a ≫ TDD_a, the impact of inadequate characterization of nt and rk, was shown to be minimal. Therefore, more general assumptions and classifications will not result in a substantial increase in uncertainty and greater focus should be put on accurate characterization of FDD_a and nf. In locations where FDD_a and TDD_a are similar (i.e., AMAT is close to 0 °C), the sensitivity of the model to changes in thawing parameters is elevated and accurate characterization of nt and rk becomes more important. For several continental and circumpolar modelling studies, a uniform value of 1.0 was utilized as the input for nt across the study area (Henry and Smith, 2001; Obu et al., 2019). While this assumption is unlikely to increase uncertainty in areas above treeline and tundra it is likely to result in errors in boreal forested areas due to the elevated importance of nt in this landcover. Additionally, nf and to some extent nt varied regionally even within the same landcover type due to microclimatic differences, vegetation and wind exposure, which influence both summer and winter conditions (Smith and Riseborough, 2002). As such regional transferability of these parameters between regions may be limited especially over large geographic and climatological gradients.

Finally, many studies that determine TTOP characterize rk using vegetation, assigning values between 0.0 and 1.0 (Smith and Riseborough, 1996; Riseborough and Smith, 1998; Way and Lewkowicz, 2016; Obu et al., 2019; Garibaldi et al., 2021). However, recent studies (including the data analyzed for this study) have shown rk values exceeding 1.0 (Bevington and Lewkowicz, 2015; Lin et al., 2015; Zou et al., 2017). This likely occurs as a product of extremely dry conditions in winter and higher soil moisture during summer, resulting in greater thermal conductivity in the warm season. This is typically observed at sites with rocky or bedrock substrates and limited vegetation cover and soil moisture (Lin et al., 2015; Luo et al., 2018). In southern permafrost environments, the assumption of rk < 1 at these sites (such as high elevation rocky slopes, Fig. 2b) likely results in mischaracterization of the permafrost condition. The varying sensitivity of the TTOP model to specific parameters in different environments demonstrates the need for accurate parameterization and validation of TTOP model parameters to ensure valid outputs. This highlights the need for in situ parameter data to increase the accuracy of future TTOP modelling studies to validate remotely-derived parameter values.