Preliminary simulation of spatial distribution patterns of soil thermal conductivity in permafrost of the Arctic

ABSTRACT

The Arctic amplification (AA) has exacerbated permafrost degradation, posing a serious threat to infrastructure security and other areas. Therefore, it is crucial to accurately assess the current status and future changes of permafrost, and reliable soil thermal conductivity (STC) is an important prerequisite for permafrost prediction. However, few methods and products are available for regional-scale STC simulations in permafrost of the Arctic, which lead to greater uncertainty in the simulation of land surface temperatures. This study conducted a preliminary STC simulation based on the XGBoost method. The results show that the average STC during the freezing period is between 0.71∼0.73 W·m⁻¹K⁻¹, and around 0.67 W·m⁻¹K⁻¹ during the thawing period; The variation of STC between the thawing and freezing period ranged from −0.34–0.23 W·m⁻¹K⁻¹, with an average value of −0.02 W·m⁻¹K⁻¹; The areas where STC of the thawing period is smaller than that of the freezing period are mainly concentrated in the marginal areas near the sea on the continental side of North America and in the typical areas of plains, lowlands, and plateaus on the continental side of Eurasia. The areas with large STC during the thawing period are concentrated in mountainous areas.

KEYWORDS:

• Permafrost
• soil thermal conductivity
• Arctic
• spatial pattern
• machine learning

Highlights

• Machine learning methods are more reliable than traditional schemes in regional STC simulation.

• The mean STC value during the freezing period is higher than that during the thawing period.

• Spatial distribution patterns of STC in the Arctic permafrost were presented for the first time.

1. Introduction

Permafrost, which occupies about one-fifth of the land surface area of the Northern Hemisphere, is an important component of the cryosphere and a key focus of cryospheric scientific research (Zhang et al. 2008; Obu et al. 2019; Wang et al. 2019; Peng et al. 2020; Wang et al. 2022). The Arctic, which contains large areas of permafrost, is a key area for the ground-air exchange, the surface processes, and the hydrological cycle, and is particularly sensitive to global climate change. It also acts as an early-warning system in global- and regional-scale climate system research (Serikova et al. 2019; You et al. 2021; Hjort et al. 2022). In recent years, the climate system of the Arctic has changed significantly in response to a rapid increase in temperature. The stronger effects of global warming in the Arctic are known as Arctic amplification (AA) (Bowen et al. 2020). Recent studies report that the Arctic is warming at a rate of 0.75°C/10a, which is nearly four times higher than the global average (Chylek et al. 2022; Rantanen et al. 2022). This anomalous warming effect has led to the degradation of the permafrost, which has far-reaching impacts on regional hydrogeological processes, ecosystem functioning, engineering safety, infrastructure, carbon cycle, and interactions between the surface water, soil, air, and living organisms (Peters-Lidard et al. 1998; Cuntz and Haverd 2018; Hjort et al. 2022; Miner et al. 2022; Liu et al. 2023c). Therefore, it is of great significance to strengthen the study of the permafrost in the Arctic under the background of climate warming.

Soil thermal conductivity (STC or λ, measured in W·m⁻¹K⁻¹) is an important physical parameter for describing the heat transfer capacity of the soil. It can directly affect the turbulent flux exchange between the ground and the air, momentum exchange, and long-wave radiation, while also regulating the energy distribution of the surface and the subsurface soil layers. In particular, STC also controls the transport and storage of heat in the active layer and influences processes such as hydrothermal salt coupling, making it an important physical soil characteristic in the permafrost (De Vries 1963; Johansen 1975; Farouki 1981; Côté and Konrad 2005; Lu et al. 2007; Lawrence and Slater 2008; Tarnawski and Leong 2016; He et al. 2020). For these reasons, STC has important applications in many fields of research, such as engineering design, facility safety and operational assurance, and climate change (Peters-Lidard et al. 1998; Cuntz and Haverd 2018; Wang and Yang 2018; Zhao et al. 2018).

The model-based simulation is one of the most important tools in the analysis of hydrothermal processes in the active layer of permafrost (Slater and Lawrence 2013; Wang et al. 2017). In these studies, STC is often widely used in the land-surface models, hydrological models, and soil-vegetation-atmosphere transport (SVAT) models (Wang and Yang 2018; Zhao et al. 2018; Dai et al. 2019; He et al. 2020; He et al. 2021). The accurate measurements of the STC are necessary to improve the accuracy of hydrothermal simulations of the active layer in land-surface process models and to improve the results of earth-system model simulations in the permafrost (Wang and Yang 2018; Dai et al. 2019). However, the complex thermodynamic and hydrodynamic processes and related mechanisms within the Arctic permafrost remain unclear. Meanwhile, there is a lack of STC data available. As a result, the current hydrothermal transport schemes cannot accurately capture dynamic hydrothermal changes during the freeze–thaw cycle of the active layer, and the STC computation schemes are generally inaccurate, which leads to large errors in the simulation of the land-surface processes in permafrost and seriously exaggerates the surface temperature variability (Poutou et al. 2004; Zhang, Gao, and Wei 2012; Su et al. 2013; Guo and Sun 2015; Domine, Barrere, and Morin 2016; Barrere et al. 2017; Kunitski et al. 2019; Davy and Outten 2020; Domine et al. 2021). For example, a comparison of simulated and measured ISBA-Crocus and ISBA-ES coupled snow-land surface models for permafrost on Bylot Island found that the complex heat transfer processes of the freeze–thaw cycle and snow can significantly affect STC simulation results (Barrere et al. 2017). In addition, the overestimation of STC in the Noah LSM model directly contributes to a warm bias in the simulation of summer surface temperatures in the Arctic permafrost, though this bias was reduced by 0.2 W·m⁻¹ K⁻¹ with program improvement (Kim et al. 2019). In addition, parameterization schemes based on single-point and small-scale regions take different forms, with high data collection requirements for the input parameters, weak applicability of large-scale simulations in complex environments, and large uncertainty in the simulation results (Li et al. 2015; Li et al. 2019). Therefore, it is vital to simulate the STC of the permafrost in the Arctic on a regional scale. However, there is still a lack of basic observation data on soil hydrothermal physical properties in the Arctic (Li et al. 2019). In addition, the permafrost in the Arctic region is widely distributed, and the STC of permafrost soils is affected by a variety of complex factors from both inside and outside the soil, so it is difficult to carry out large-scale STC simulations.

Both the classical parameterization schemes and the latest machine learning schemes have been used in STC simulation in recent years (De Vries 1963; Johansen 1975; Farouki 1981; Côté and Konrad 2005; Lu et al. 2007; Zhang et al. 2018; Wen, Bi, and Guo 2020; Bayat, Ebrahimzadeh, and Mohanty 2021; Liu et al. 2023a; 2023b), but there is no research to compare which scheme is more suitable for regional-scale simulation of STC in the Arctic. In addition, the spatial distribution of STC in Arctic permafrost and its response to freeze–thaw processes have not been systematically reported. It is very important to master these simulations and characteristics for the future study of hydrothermal processes in the active layer of permafrost in the Arctic. Therefore, this study intends to carry out research for STC of permafrost in the Arctic in the following aspects: a) construct a scheme more suitable for regional-scale STC simulation; b) reveal the distribution characteristics of STC; c) compare the distribution and changing characteristics of STC between the freezing period and thawing period.

2. Data and methods

2.1. Key data

1. Boundaries of the Arctic. There is currently no clear definition of the Arctic within the academic community. As adopted by the Arctic Monitoring and Assessment Program (AMAP) in 2017 in its assessment report Snow, Water, Ice, and Perennial Frozen Soils in the Arctic, the Arctic is defined as the land and sea within the Arctic Circle, the northern part of the Eurasian continent (north of 62° N), the sea to the north of the Aleutian Islands, Hudson Bay, parts of the North Atlantic Ocean region, and the northern part of the North American continent (north of 60° N), a range that has been widely employed in many studies. Therefore, this was also used in the present study for the analysis.

2. SoilGrids data. In 2020, the ISRIC released the SoilGrids V.2.0, a global soil texture map with a medium spatial resolution, which has been used in several soil studies because of its high accuracy and high resolution (Xu et al. 2023; Sekiyama et al. 2023; Duarte et al. 2022). In order to better serve terrestrial and earth system modeling tasks, which typically operate at coarse resolutions of 250 m or more in 2020, ISRIC released the composite SoilGrids products with a resolution of 1000 and 5000 m for the water pH, soil texture, coarse components, bulk density, total nitrogen, and organic carbon concentration. Considering the simulation needs of the present study, clay, chalk, and sand percent data at a depth of 5 cm at a resolution of 1000 m were used from this dataset.

3. Soil moisture data. Because SoilGrids 2.0 does not provide monthly comparisons for moisture data, the present study employed a reanalyzed dataset from ERA5-Land for Arctic precipitation data. Yang et al. (2020) systematically evaluated the accuracy of soil moisture data from four reanalyzed sources (CFSv2, ERA-Interim, ERA5, and GLDAS-Noah) based on in-situ measurements and found that ERA-Interim and ERA5 were the best-performing datasets. The present study used the ERA5-Land dataset because it provides consistent data on the change in land variables over decades at a higher resolution than the ERA5. Because this study focused on the characterization of shallow STC, soil moisture data for a depth of 0–7 cm from this dataset were used. The data were processed via cropping and resampling to ensure consistency with other data sources in terms of range and resolution.

4. Permafrost data. The High-Resolution Northern Hemisphere Multi-Year Permafrost Dataset (2000–2016) published by Ran et al. (2022) was used for the permafrost data in the present study. This dataset integrates the largest number of surface observations of the annual mean ground temperature (1002) and active layer thickness (452) in the Northern Hemisphere at present. The annual mean ground temperature, active layer thickness, probability of permafrost occurrence, and permafrost hydrothermal zonation for the Northern Hemisphere from 2000 to 2016 were simulated with a spatial resolution of 1 km, which has been shown to have a higher accuracy.

5. Global STC measurement dataset

A systematic STC dataset from 35 published research papers for a total of 270 soils from many parts of the world was compiled and systematically analyzed in two previous studies by the author (Liu et al. 2023a; 2023b) (Table 1). The dataset contained 10 attributes: Clay%, Silt%, Sand%, quartz Q_tz%, percent content of different fractions, solid thermal conductivity (λ_s), soil grain density (ρ_s), bulk weight (ρ_b), porosity (n), water content (θ_w) and saturation (S_r).

Table 1. STC dataset and its sources.

NO.	Data Size	Data sources
NO.1-80	80	(Chen 2008)
NO.81-88	8	(Hopmans and Dane 1986)
NO.89-113	25	(Kasubuchi et al. 2007)
NO.114-245	132	(Lu et al. 2007)
NO.246-257	12	(McCombie et al. 2017)
NO.258-333	76	(McInnes 1981)
NO.334-381	48	(Tarnawski et al. 2013)
NO.382-621	240	(Tarnawski et al. 2015)
NO.622-669	48	(Zhao et al. 2019)
NO.670-755	86	(Barry-Macaulay et al. 2015)
NO.756-1017	262	(Chen et al. 2012)
NO.1018-1023	6	(Gori and Corasaniti 2013)
NO.1024-1041	18	(Hiraiwa and Kasubuchi 2000)
NO.1041-1153	23	(Nikolaev, Leong, and Rosen 2013)
NO.1042-1074	7	(Kahr and Müller-Vonmoos 1982; Tang, Cui, and Le 2008)
NO.1075-1130	1	(Lu et al. 2018)
NO.1031-1153	2	(Nikolaev, Leong, and Rosen 2013)
NO.1154-1284	131	(Singh and Devid 2000)
NO.1285-1389	105	(Yamasaki and Kawamura 2009)
NO.1390-1489	100	(Zhang et al. 2017)
NO.1490-1510	21	(Mochizuki, Mizoguchi, and Miyazaki 2008)
NO.1511-1591	81	(Campbell et al. 1994)
NO.1592-1601	10	(Du et al. 2022)
NO.1602-1815	214	(Tarnawski et al., 2019)
NO.1816-1836	21	(Alrtimi, Rouainia, and Haigh 2016)
NO.1837-1866	30	(Tokoro et al., 2016)
NO.1867-1906	40	(Zhang et al. 2020)
NO.1907-1979	73	(Go et al. 2014)
NO.1980-2007	27	(Bristow 1998)
NO.2008-2629	623	(Zhao et al. 2018)
NO.2630-2638	9	(Xu et al. 2023)
NO.2639-2710	72	(Bachmann, Horton, and Van der Ploeg 2001)
NO.2711-2716	6	(Al-Shammary et al. 2022)
NO.2717-2972	256	(Kersten 1949)
Total	2972	-

2.2. Simulation methodology

Although STC can be directly obtained via in-suit measurements, steady-state and transient methods are widely used. However, these methods inevitably have some limitations in practical applications and are often affected by a variety of factors (Woodside and Messmer 1961; He et al. 2021), such as the testing environment, instrumentation, and operation, especially in the Arctic, which has a harsh natural environment. These tests are also time-consuming, costly, and heavily dependent on the instrument and field literacy of the researchers (Zhang and Wang 2017; He et al. 2021; Malek, Malek, and Khanmohammadi 2021). Direct measurement of STC also has a variety of constraints, because it is difficult to fully control all variables, and large-scale STC measurement campaigns are challenging. For these reasons, various parameterization schemes have been developed to incorporate empirical data, including theoretical/physical-based approaches, linear/nonlinear regression, normalization, methods based on the soil matrix potential, and many other types of empirical/semi-empirical strategies (Zhang and Wang 2017; He et al. 2020; Wang et al. 2021). However, several evaluation studies have found that there is still no single parameterized scheme suiting the STC simulation for all soil types (Dai et al. 2019; Yang et al. 2021).

In recent years, many studies have been carried out to simulate the STC of various soil types based on machine learning methods (Zhang et al. 2018; Rizvi et al. 2020a; 2020b; Wen, Bi, and Guo 2020; Zhang et al. 2020; Bayat, Ebrahimzadeh, and Mohanty 2021; Fei, Narsilio, and Disfani 2021; Liu et al. 2023a; b), including artificial neural networks (ANNs), linear regression (MLR), multiple linear regression (MLR), deep neural networks (DNNs), support vector machine (SVM), and the group method of data handling (GMDH). These machine-learning methods can effectively improve the simulation accuracy for STC while also being portable, fast, and stable. Thus, STC can be simulated at the regional scale and for different types of soil. The present study aimed to select the optimal simulation scheme for the STC in Arctic permafrost based on a comparison of conventional parameterized schemes and machine learning methods.

In this study, the four widely used conventional parameterized schemes proposed by Johansen (1975), Côté and Konrad (2005), Lu et al. (2007), and Barry-Macaulay et al. (2015) were employed on the constructed STC dataset. To determine the optimal schemes for use in the present study, their performance in the simulation of the STC of Arctic permafrost was compared with that of six machine learning methods: an ANN, SVM, K-nearest neighbor (KNN), extreme learning machine (ELM), random forest (RF), and eXtreme Gradient Boosting (XGBoost). The features of these schemes and their associated parameters have been described in past studies (Li et al. 2022a; 2022b; Liu et al. 2023a; 2023b), so they are not repeated in the present study. The STC dataset above was randomly divided into a training set (70%) and a test set (30%) to evaluate the generalizability of the machine learning schemes. Five performance parameters were used to evaluate the effectiveness of the training and test results (Table 2). The summary of the research design for this study is presented in Figure 1.

Figure 1. The technical roadmap of this study.

Table 2. Performance parameters used in this study.

Performance Parameters		formulas
R^2	Coefficient of determination	${\mathrm{R}}^2={\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{({\lambda }_{\mathrm{i}}-{\lambda }_{\mathrm{imean}})}^2-{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{({\lambda }_{\mathrm{i}}-{\hat{\lambda }}_{\mathrm{i}})}^2}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{({\lambda }_{\mathrm{i}}-{\lambda }_{\mathrm{i}\mathrm{mean}})}^2}}$
R	Correlation coefficient	$R={\displaystyle \frac{{\sum }_{i=1}^n({\lambda }_i-{\lambda }_{\mathrm{i}\mathrm{mean}})({\hat{\lambda }}_{\mathrm{i}}-{\hat{\lambda }}_{\mathrm{i}\mathrm{mean}})}{\sqrt{{\sum }_{i=1}^n({\lambda }_i-{\lambda }_{\mathrm{i}\mathrm{mean}})({\hat{\lambda }}_{\mathrm{i}}-{\hat{\lambda }}_{\mathrm{i}\mathrm{mean}})}}}$
MAE	Mean absolute error	$\mathrm{MAE}={\displaystyle \frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}|{\hat{\lambda }}_{\mathrm{i}}-{\lambda }_{\mathrm{i}}|}$
MSE	Mean square error	$\mathrm{MSE}={\displaystyle \frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}({\lambda }_{\mathrm{i}}-{\hat{\lambda }}_{\mathrm{i}}{)}^2}$
RMSE	Root Mean Square Error	$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}{({\lambda }_{\mathrm{i}}-{\hat{\lambda }}_{\mathrm{i}})}^2}}$

Note: The table shows measured values (${\lambda }_{\mathrm{i}}$), predicted values (${\hat{\lambda }}_{\mathrm{i}}$), and mean values (${\lambda }_{\mathrm{i}\mathrm{mean}}$).

3. Results and discussion

3.1. Optimal methodology for regional-scale STC simulations

A total of 10 schemes (four parameterized schemes and six machine learning methods) were simulated and compared based on the STC dataset constructed for the present study. Figures 2 and 3 present regression plots for the training and testing results of these six machine learning schemes, and Figure 4 compares the simulation results of the 10 methods.

Figure 2. Training simulation results for the six machine learning schemes.

Figure 3. Testing simulation results for the six machine learning schemes.

Figure 4. Comparison of the simulation performance of the 10 simulation schemes.

The training regression results for the six machine learning schemes based on 2080 data points had R values of more than 0.9, with XGBoost and RF the most reliable at R > 0.99, while the distribution of the XGBoost scatterplot was more convergent. In contrast, the simulation results for the SVM and ELM schemes were less accurate (R = 0.91). Similarly, the test results for 892 test data points revealed that the highest R values were obtained by the XGBoost and RF methods (R = 0.96), followed by the ANN, while the ELM, SVM, and KNN schemes were relatively low at 0.90–0.91. Therefore, of the six machine learning schemes, XGBoost and RF produced the best performance overall.

The simulation results for the parameterized and machine learning schemes were macroscopically compared using four metrics, including R², RMSE, MAE, and MSE (Figure 4). The RMSE, MAE, and MSE are all negative indicators of these models’ performance, thus larger values indicate lower model performance, while R² is a positive indicator, meaning larger values are preferred. The present study also employed the metric of Sum Error, which is the sum of the RMSE, MAE, and MSE.

The simulation results of the machine learning schemes all exceeded the parameterized schemes in terms of R²; the ELM scheme produced the weakest simulation of all these machine learning methods (R² = 0.80), but this still outperformed the parameterized schemes. The parameterized schemes proposed by Côté and Konrad (2005) and Lu et al. (2007) had the highest R² values, while that proposed by Johansen (1975) had the lowest (0.63). XGBoost had the highest R² value, RF had an R² of more than 0.90, while the other four machine learning methods had R² values ranging from 0.80–0.86.

The RMSE, MAE, and MSE results varied among the 10 schemes, but the RF and XGBoost tended to have low values (e.g. RMSE = 0.18 and 0.17; MAE = 0.12 and 0.11). In terms of the Sum Error, the Johansen (1975) scheme had a value of 0.85, indicating a large simulation error, followed by Barry-Macaulay et al. (2015), with a value of 0.75. In contrast, the overall Sum Error values for the machine learning methods were relatively low, with the largest value for ELM (0.61) and the lowest for XGBoost (0.31). The RF had a sum error of 0.33, indicating that XGBoost produced the more accurate simulation results. Overall, based on these results, XGBoost proved to be the optimal model for the simulation of STC in various soils on a regional scale. Therefore, this method was selected for the simulation of STC in the Arctic permafrost.

3.2. Reliability of the preliminary simulation results

The XGBoost scheme was combined with soil moisture and texture input data from permafrost areas in the Arctic region and related ArcGIS modules to generate preliminary simulation products for the STC of permafrost soils in the Arctic region. Before the analysis of these products, their reliability was verified against measured data obtained from Romanovsky and Osterkamp (1997) (Figure 5a), O'Connor et al. (2020) (Figure 5b), and Langer et al. (2011a; b) (Figure 5c). In the figure, the data beginning with ‘P’ are simulated values, and the others are measured values.

Figure 5. Comparison of the measured STC for Arctic soils from previous studies with the simulation results from the products in the present study.

Romanovsky and Osterkamp (1997) analyzed the thawing characteristics of the active layer on the Arctic Coastal Plain of Alaska and simulated the STC of the shallow peatlands between 0 and 10 cm in three areas (West Dock, Deadhorse, and Franklin). They proposed that the three-point thresholds of the STC of peatland during the thawing and freezing periods should be in the range of 0.6–1.2 W·m⁻¹K^−1. In the present study, the STC of the products for the thawing and freezing periods in 2020 were extracted and compared. UN and F in Figure 5a are the thresholds given in the literature, and P_UN and P_F are the simulation results of the present study, which were within the range of the thresholds given by Romanovsky and Osterkamp (1997), indicating that the simulation results accurately reflect the actual STC of the local soil. It should be noted that the simulation results of the present study had an error of ±0.19 W·m⁻¹K⁻¹, with the STC during the freezing period somewhat underestimated.

O'Connor et al. (2020) investigated the STC of shallow soils in a study area of about 7,500 km² in Alaska, suggesting that differences in the hydraulic and thermal properties of each soil layer can be predicted from the capacitance weight alone. The STC in their dataset at a depth of about 5 cm was extracted and analyzed, and the STC of saturated and dry soils (Saturated_STC and Dry_STC, respectively) at the three points eligible for comparison were obtained (some points only reflected the STC of either dry or saturated soils, which were not considered) and compared with the simulation results of this study in the region (Figure 5b). The average STC in 2020 from the present study (P_STC) was very close to that of the saturated soil in O'Connor et al. (2020). In this case, there was a gap at point SAR18_503, but this was still within the margin of error.

Langer et al. (2011a; b) studied the surface energy balance of a polygonal tundra site on Samoylov Island in northern Siberia, and measured the STC for the region. The measured STC for dry and wet peatlands during the freezing and thawing periods at the site were compiled and compared with the simulation results of the present study (Figure 5c). The simulation results of this study for the freezing period (P_F) and thawing period (P_UN) were in good agreement with the results of Langer et al. (2011a; 2011b). The STC for dry peat soil (F_Dry peat) and wet peat soil (F_Wet peat) during the freezing period ranged from 0.46–0.95 W·m⁻¹K⁻¹, with an error of around 0.23–0.25 W·m⁻¹K⁻¹, respectively, while the simulated products of the present study had values of 0.60 W·m⁻¹K⁻¹, with an error of around 0.20 W·m⁻¹K^−1. During the thawing period, the simulation was relatively accurate for wet peat soil (UN_Wet peat), but the error was more significant for dry peat (UN_Dry peat).

Collectively, these comparisons suggest that, although the simulation of the STC in the Arctic region in the present study has some errors, the proposed approach still reflects the basic STC distributions for different regions and soil textures. Considering the measured data often contain errors, and the dry and wet conditions, moisture content, soil texture, and depth of the soil all differed from the data used in the simulation products, the products used for verification in the present study have shortcomings such as a large scale, moderate accuracy, and low-resolution moisture and soil texture data. However, the present study provides a reference dataset and an effective, relatively accurate, and credible set of first-generation STC products for the regional scale STC distribution patterns in the Arctic, thus allowing the macroscopic characterization and numerical comparison of different regions.

3.3. Monthly spatial distribution characteristics of STC

To demonstrate the spatial variation and changes in the shallow (5 cm) STC in the Arctic permafrost, this study uses products from January to December in 2020 to assess the monthly mean and maximum STC. The freezing and thawing periods in the Arctic considered in this study are based on the Qinghai-Tibet Plateau (Liu et al. 2023a), with January–April and October–December classified as the freezing periods and May- September classified as the thawing period. In reality, the thawing period does not start until May in many parts of the Arctic, and there is a lag in the freezing period. However, different regions exhibit temporal variability, so the timing of the freezing and thawing periods was standardized across all regions in the present study for ease of comparison.

1. Characteristics of the monthly STC

Based on an analysis of the monthly mean value of STC, the Arctic permafrost generally had a lower STC in the thawing period and a higher STC in the freezing period (Figure 6). For example, in January–April, the STC was about 0.71 W·m⁻¹K⁻¹ (with an error of 0.18), but in May, it rose to 0.77 W·m⁻¹K⁻¹ (with an error of 0.17). This change may be because parts of the Arctic remained frozen or fluctuated in their freeze–thaw cycle characteristics in May, resulting in changes to the soil water content, especially unfrozen water. Subsequently, a slight decrease and then an increase in the STC was observed in June–September, with an average STC in July and August of around 0.67 W·m⁻¹K⁻¹ (with an error of 0.19–0.20), which represented the smallest value of the year. This is also a distinctive feature of the thawing period across the entire Arctic region. The STC rose to 0.72 W·m⁻¹K⁻¹ in September and remained between 0.71 and 0.73 W·m⁻¹K⁻¹ in October and after times, which was slightly higher than in the warm season.

Figure 6. Monthly characteristics of the STC in the Arctic permafrost.

This variation of the STC in the Arctic permafrost had a strong similarity to that in the soil moisture content. In the present study, EAR5-Land 7-cm moisture data were used instead of shallow Arctic 5-cm moisture data, but the monthly mean moisture was relatively high during the freezing period and gradually decreased during the thawing period (Figure 6). This indicates that moisture is a key factor in determining the numerical characteristics of the shallow STC in the Arctic permafrost.

(2)	Characteristics of the monthly spatial distribution of STC

The monthly spatial distribution pattern shows that the STC in the Arctic permafrost varied markedly between months, though there was some regularity in the distribution of relatively high and low values (Figure 7).

Figure 7. Monthly spatial distribution and characteristics of changes in the STC in the Arctic permafrost in 2020.

In January, on the North American side, high values of the STC were concentrated in the central region, the low values occurred in the Yukon Plateau near Brooks Ridge, and there was a continuous region of STC values in the range of 0.12–0.49 W·m⁻¹K⁻¹. In the marginal zone of Greenland, the STC had a range of 0.64–0.82 W·m⁻¹K⁻¹, and in Iceland, the STC distribution was relatively complex, with an STC of 0.64–0.82 W·m⁻¹K⁻¹ in some areas and of 0.82–1.76 W·m⁻¹K⁻¹ in others. In contrast, on the continental side of Asia and Europe, the STC was relatively high, particularly on the eastern edge of the Central Siberian Plateau (0.64–1.80 W·m⁻¹K⁻¹). In the southern part of the northern Kolyma Lowland, STC ranged from 0.82–1.10 W·m⁻¹K⁻¹, and in the Chukchi Peninsula, the range was 0.49–0.82 W·m⁻¹K^−1. In February, the overall characteristics remained generally similar to those of January. However, in the northern part of the Preliminary Plateau, the distribution of low values widened and, in several areas, the STC decreased from more than 0.58 W·m⁻¹K⁻¹ to between 0.12 and 0.58 W·m⁻¹K⁻¹. This was also observed for the Chukotka Peninsula, where the STC decreased to below 0.58 W·m⁻¹K⁻¹ in some areas. The STC of the Taimyr Peninsula, which is located in the middle of the right-hand side, slowly increased in February, with values of 0.49–0.64 W·m⁻¹K⁻¹, or even 0.64–0.82 W·m⁻¹K⁻¹. The overall pattern in March–April was very similar to that in January–February, which indicates that the overall STC of the Arctic permafrost is very similar to that of the Arctic region during the freezing period of January–April. The overall STC of the permafrost remained relatively stable throughout the January–April freezing period, indicating that key elements, such as vegetation and soil hydrothermal processes, were relatively stable in the Arctic during this period. Subsequently, in May, many areas slowly entered a transition period in the freeze–thaw changes, and the spatial patterns for the STC also changed considerably. Firstly, the area of low STC values in the Yukon Plateau retracted rapidly, with the STC generally increasing to 0.49–0.82 W·m⁻¹K⁻¹, while the Chukchi Peninsula also experienced an increase in the STC. The southern part of the Central Siberian Plateau on the western side also demonstrated a large-scale rapid increase in the STC to 0.82 W·m⁻¹K⁻¹ or more. In June, with the thawing of the underground ice in many areas, the STC fell again. In particular, a decrease in the STC was observed in most areas of Brooks Ridge (0.12–0.49 W·m⁻¹K⁻¹) and on the Chukotka Peninsula. In addition, on the Central Siberian Plateau and in most of the southern regions, a rapid decrease in STC was observed over a wider area, with several regions decreasing from 0.82–1.80 W·m⁻¹K⁻¹–0.49–1.82 W·m⁻¹K⁻¹. In the lowland regions of Northern Siberia, the STC was relatively stable, but the range of 0.49–0.64 W·m⁻¹K⁻¹ still expanded. In July, a wider thawing period in many parts of the Arctic led to a more significant change in the spatial STC patterns, particularly in several island regions in western Greenland, where a significant decrease in the STC was observed. In addition, in the West Siberian lowlands and the surrounding Gyda Peninsula, the STC also appeared to fall sporadically. In August, the distribution of the low value of the region still continuously expanded, and in the Taimyr Peninsula, the southern North Siberian lowlands, and the Putorana Plateau, there was a rapid decline in the STC. In September, some regions entered the freezing period early, leading to a transition between freeze–thaw phenomena, including the emergence of subterranean ice conductivity in some areas. However, in October, the total soil moisture decreased in some areas, leading to a fall in the STC, such as on the Yukon Plateau of North America and the hinterland of Brooks Ridge. In addition, the decrease in the STC was significant in the North Siberian lowland areas. In general, the STC was lowest in the Arctic region during October. In November and December, with an increase in the freezing intensity, the STC rebounded significantly in some areas from 0.12–0.49 W·m⁻¹K⁻¹–0.49–0.82 W·m⁻¹K⁻¹ and some areas even increased to 0.82–1.10 W·m⁻¹K⁻¹.

In summary, although there is annual variation in the STC, the intra-annual analysis of the monthly variation in the STC still provides some useful information. For example, the STC was high across the Arctic permafrost in the freezing period, while the STC was low during the thawing period in several locations. May and September represented transitional periods between these two periods, leading to distinctive changes in the STC. In terms of spatial distribution, the Yukon Plateau in North America, the northern Siberian lowlands, and the archipelago west of Greenland were more likely to have a low STC, while high values were concentrated in the southern part of the Central Siberian Plateau in the Asian region.

3.4. Distribution characteristics of the STC during the freeze–thaw periods

To investigate the spatial distribution characteristics of the STC in the permafrost in more detail during the thawing and freezing periods, this study calculated the mean STC for the corresponding periods and investigated the distribution characteristics of the STC (Figure 8). UN denotes the thawing period and F denotes the freezing period.

Figure 8. Spatial distribution of STC during thawing and freezing periods in the Arctic permafrost in 2020.

During the thawing period, the overall spatial pattern was characterized by a low STC on the North American side and a high STC on the Eurasian side. Specifically, in North America, the STC values had a range of 0.15–0.69 W·m⁻¹K⁻¹, with a certain range of high values only observed in the eastern portion of the Marmot Mountains in the northern section of the Rocky Mountains and the Great Bear Lake region. Within the Yukon Highlands, Brooks Ridge, and much of the Alaska Range, the STC was low (0.15–0.56 W·m⁻¹K⁻¹). In contrast, on the Eurasian side, the STC was predominantly in the 0.69–110 W·m⁻¹K⁻¹ range, with high values in the Central Siberian Plateau and relatively low values near the North Siberian Lowlands. The Kola Peninsula STC, on the other hand, was in the range of 0.56–0.69 W·m⁻¹K^−1.

During the freezing period, the STC distribution pattern was similar to that of the thawing period, though there were some notable changes. For example, during the freezing period, the STC in about 50% of the Brooks Ridge region increased from 0.15–0.56 W·m⁻¹K⁻¹–0.56–0.69 W·m⁻¹K⁻¹. In addition, large archipelagic areas near Greenland also increased from 0.15–0.56 W·m⁻¹K⁻¹–0.69–0.81 W·m⁻¹K⁻¹.

3.5. Variables and spatial distribution characteristics of STC between the thawing and the freezing periods

This study analyzed the variables and spatial characteristics of the STC between the thawing and the freezing periods in the Arctic permafrost (Figure 9).

Figure 9. Spatial distribution of STC variables between the thawing and freezing periods in the Arctic permafrost in 2020.

The mean value of the variables between the thawing and freezing periods was –0.02 W·m⁻¹K⁻¹, confirming that the mean STC during the thawing period was lower than during the freezing period. The variables varied from –0.34–0.23 W·m⁻¹K⁻¹, which indicates that the values of STC in this region during the freezing and thawing periods were generally comparable, and there were no extreme variations. In terms of the spatial distribution, the variables of STC on the North American side was 0–0.04 W·m⁻¹K⁻¹, which accounts for about 50–60% of the whole area, while the Eurasian continent side exhibited a change in the STC from–0.34–0 W·m⁻¹K⁻¹, which is about 60–70%. This suggests that, during the thawing and freezing periods, the variables in the STC on the North American side were very small, while variables on the Eurasian continent side were low during the thawing period and high during the freezing period.

The STC variables between the thawing and freezing periods were 0.04–0.23 W·m⁻¹K⁻¹ in the Marmara Mountains and parts of the Yukon Plateau, and there were also scattered positive areas in Scandinavia and localized areas of the North Siberian lowlands. Smaller regions with variations from 0 to 0.04 W·m⁻¹K⁻¹ were concentrated in North America, in the central regions of the Chukchi Peninsula and the Korema lowlands, in parts of northern Central Siberia, and most of Scandinavia. In contrast, areas of high STC during the freezing period were concentrated in the Melville Peninsula and surrounding islands, the northern part of the Brooks Ridge, and most of the Eurasian side of the continent. Therefore, it can be assumed that the Arctic permafrost STC for the thawing period is lower than during the freezing period on the North American continental side near the sea and the Eurasian continental side in the plains, lowlands, plateaus, and other typical areas. Areas where the thawing period STC was higher than the freezing period were primarily mountainous.

3.6. Discussion and outlook on future work

1. The spatial distribution of STC is a comprehensive result of multiple factors.

As we mentioned above, STC is an important physical metric that describes the heat transfer capacity of the soil. This heat conduction process includes seven different forms such as conduction in particles, conduction in air, and conduction in liquid (De Vries 1963; Johansen 1975; Farouki 1981; Côté and Konrad 2005; Lu et al. 2007). All conduction processes actually occur within the soil, and this process is affected by a variety of factors including soil composition, soil particles, and volume fractions of water and air. In the vast Arctic region, the growth and development of soil are strongly affected by regional characteristics (Alrtimi, Rouainia, and Haigh 2016). Regional climate, landforms, sedimentation, weathering, precipitation, vegetation, freeze–thaw processes, and other factors will have differential effects on soil development. All these processes directly lead to regional differences and temporal changes in the internal and external characteristics of the soil. Therefore, the present paper believes that STC, as one of the most critical physical properties of soil, is a comprehensive response to these characteristics and is comprehensively affected by these factors.

(2)	Moisture factors are drivers of changes in STC during the freeze–thaw cycle in permafrost.

The water in the freezing and thawing periods in the soil is the greatest difference between permafrost and other types of soils. The freeze–thaw process is characterized by changes in soil moisture content and phase changes. Therefore, research of the STC in permafrost must pay attention to the key processes of freeze–thaw cycle processes. Across the Arctic region, there is variability in the scope, extent, and duration of freeze–thaw processes. The most critical driver of this difference is moisture. It has been shown that when the water content is small (less than the maximum molecular water content), there is gas with weak thermal conductivity in the soil pores. As the moisture content increases and the gas content decreases, the water increases the connection between the soil particle skeleton. The contact thermal resistance between particles is reduced, and the thermal conductivity of water is greater than that of gas. Therefore, the STC increases rapidly with the increase of moisture content. When the soil moisture content is between the maximum molecular moisture content and the liquid limit moisture content, the domination of STC gradually changes from solid particle thermal conductivity to the thermal conductivity of water, and the connection between the soil particle skeletons becomes a secondary effect. The increase rate of STC slows down; when the soil moisture content is greater than the liquid limit, water gradually plays a dominant role in the thermal conductivity of the soil, and the increase rate of the STC gradually approaches a certain fixed value. At this time, the value of the STC is related to the proportion of soil moisture content and solid particles (Jame and Norum 1980; Tao and Zhang 1983; Li et al. 2003; Lu et al. 2007). Therefore, it can be considered that this change process of moisture content drives the STC changes in Arctic permafrost during the freeze–thaw period, shaping the spatio-temporal differences of STC in different regions between the freezing and thawing periods.

(3)	The patterns STC of the permafrost in the Arctic and the Qinghai-Tibet Plateau are differences between the thawing and freezing periods.

The Qinghai-Tibet Plateau (QTP) and the Arctic are typical representative areas of ‘high altitude and high latitude’ permafrost, with complex natural environments, diverse underlying surface types, and large differences in soil characteristics. Combined with our research on the QTP (Liu et al. 2023b), we found that the STC distribution characteristics of these two regions have obvious regional differences, which is manifested in the fact that the regional mean values of STC between the freezing and thawing periods in the two regions have opposite modes. On the QTP, the simulation results of shallow (5 cm) STC of the permafrost in 2018 show that the variables between the thawing period and freezing period range from −0.48–1.56 W·m⁻¹K⁻¹, and most areas are positive, ranging from 0 to 0.59 W·m⁻¹K⁻¹, presenting the feature that the mean value of the STC during the freezing period is smaller than that during the thawing period. However, the results of this study show that the variables in STC between the thawing and freezing period in permafrost on the Arctic have a range of −0.34–0.23 W·m⁻¹K⁻¹, and the average STC variables are −0.02 W·m⁻¹K^-, which means that the mean value of the STC in the thawing period is smaller than that in the freezing period. Although we have not yet investigated the specific reasons for this difference, we still believe that differences in moisture and soil texture are the main reasons for this modal difference. As a next step, we will carry out a detailed study to reveal the internal mechanism of this phenomenon.

(4)	Prospect of further research

It should be pointed out that the accuracy of the products in this study was not consistent between regions, and in general, there was an underestimation of the STC. However, given that many of the influencing mechanisms are still to be refined and that the accuracy of the data and other factors can be improved, the results from the proposed large-scale simulation still provide a macroscopic characterization of the STC in the Arctic permafrost and represent a valuable first-generation STC product for Arctic permafrost that can be used for future analysis. In the future, we are planning follow-up studies to improve the accuracy of the product and the quality of the data in order to provide more reliable STC simulation models and data products.

4. Conclusion

In the present study, the preliminary simulation and analysis of the STC in the Arctic permafrost were conducted using the XGBoost method. The following preliminary conclusions were obtained: (1) XGBoost is the optimal method for the regional scale STC simulation for permafrost in the Arctic; (2) High values of the STC in the Arctic permafrost occurred in the freezing period, with an average of 0.71–0.73 W·m⁻¹K⁻¹, while a low STC was observed in the thawing period, with an average of 0.67 W·m⁻¹K⁻¹. May and September represented transition periods between the thawing and freezing periods. The spatial distribution is characterized by a low STC in the Yukon Plateau of North America, the northern Siberian lowlands, and the archipelago on the west side of Greenland, while high values were concentrated in the southern part of the Central Siberian Plateau in Asia; (3) The STC variables between the thawing and freezing periods ranged from –0.34–0.23 W·m⁻¹K⁻¹, with an average of –0.02 W·m⁻¹K⁻¹. During the thawing period, the overall spatial pattern was characterized by a low STC on the North American side and a high STC on the Eurasian continent side. The distribution pattern for the STC in the freezing period was similar but, in some areas, there were changes in the value of high and low.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Key Research and Development Program of China: [grant no 2020YFA0608502]; National Natural Science Foundation of China [grant no 42071093]; The State Key Laboratory of Cryospheric Science [grant no SKLCSZZ-2023]. The National Natural Science Foundation of China [grant no 41961144021, 41941015, 32061143032, 41671070]; Youth Science and Technology Fund Plan of Gansu Province [grant no 21JR7RA063]; Gansu Province Science and Technology Plan Project [grant no 22JR5RA061].