Permafrost Thermal Responses to Asymmetrical Climate Changes: An Integrated Perspective

An integrated perspective of permafrost dynamics is a key bridge between permafrost and global socioeconomic assessments. This study investigated the air temperature changes (1976–2020) among permafrost zones in the Northern Hemisphere and their potential impacts on permafrost. We found that continuous permafrost zones experienced faster warming than other regions. The freezing index declined 724°C‐day while the thawing index increased only 166°C‐day over continuous permafrost zones. This may explain why the temperature of cold permafrost increased rapidly but the active layer thickness changed only slightly. Assuming permafrost carbon emissions arise only from thaw processes may miss a significant source of the emissions. An often‐neglected factor is that cold‐season snow amplifies permafrost warming caused by summertime air temperature changes. Due to seasonal effects, using mean‐annual air temperature to depict permafrost evolution under integrated assessment frameworks may lead to significant errors.

for permafrost temperature changes on the Arctic Slope of Alaska has been air temperature changes since at least 1900 and that snow cover changes have had little impact on decadal and longer timescales. A semiphysical permafrost model also shows that air temperature is one of the most important forcings altering the ground thermal regime (Wang et al., 2020). Certainly, if snow thickness showed a significant positive trend, permafrost temperatures may increase more than changes in air temperature (Biskaborn et al., 2019;Osterkamp, 2005;Park et al., 2014;Wang et al., 2018). Although some observational evidence showed that the snow cover may have become thicker (Zhong et al., 2022), there is no robust evidence to support a synchronous change in air temperature and snow cover (i.e., thicker snow in a year with warmer air temperature, and vice versa). Therefore, the influence of snow cover changes to amplify or dampen the air temperature increase on the ground is uncertain (Stieglitz et al., 2003;Zhang, 2005). Recent synthesis studies, which reviewed the permafrost changes in the Arctic and Qinghai-Tibetan Plateau, concluded that cold permafrost warmed more rapidly than warm permafrost due to the latent heat effects during permafrost degradation Zhang et al., 2020).
Mean-annual air temperature (MAAT) provides a common interface bridging permafrost with integrated assessment models (e.g., the Dynamic Integrated Climate-Economy model, e.g., Kessler, 2017). However, MAAT may be insufficient to explain permafrost dynamics at even a low level of complexity. For example, one important condition is the original permafrost thermal state (Lunardini, 1996) because different permafrost temperatures may result from different unfrozen water contents and latent heat during phase change processes (Riseborough, 1990;Wang et al., 2022). On the other hand, physics-based permafrost models may be too complex to interface with integrated assessment models.
Therefore, the aims of this study are to: (a) investigate changes in seasonal and annual air temperatures over different permafrost zones by using gridded near-surface air temperature data sets, and (b) explore their impacts on the permafrost thermal regime in the Arctic and subarctic regions by using a numerical permafrost thermal model. This study provides an integrated perspective for understanding permafrost dynamics in a rapidly changing climate, as well as a potential way to improve land surface and integrated assessment models in the future.

Data
Our primary data source was the Climate Research Unit (CRU) monthly mean near-surface air temperature (TAS) data set (Harris et al., 2020); TAS data were usually obtained at the 1.5-2.0 m height. All these data were produced on a 0.5° regular latitude-longitude grid over the Earth's land area, excluding Antarctica, for the period 1901-2020 (CRUTS v4.05). Because permafrost thermal observations were rare prior to the late 1970s (AMAP, 2017) and air temperature observations were sparse in high latitudes and mountain regions before the 1950s (Macias-Fauria et al., 2014), we restricted the use of the CRU TAS data to the period 1976-2020 in our analyses. We calculated the annual mean TAS (i.e., MAAT) and the annual amplitude ((hottest month − coldest month)/2). In addition, we calculated freezing and thawing indices of air temperature (DDF and DDT, respectively) following Nelson and Outcalt (1987). The details can be found in Nelson and Outcalt (1987) or the Perma-Model toolbox . These indices have been widely used in understanding and predicting permafrost distribution and dynamics.
The Canadian Meteorological Center (CMC) Daily Snow Depth Analysis data set (Brown & Mote, 2009) was used to estimate the climatology (1998-2017) of snow depth in different permafrost zones. This data set has a spatial resolution of ∼24 km over the NH and was remapped to 0.5° to be consistent with the TAS gridded data. It should be noted that the reanalysis approach used for this product is based on a simple snow accumulation and melt model driven by air temperature and precipitation (Brown & Mote, 2009). Although it may have some known issues associated with its precipitation inputs, it should be able to provide basic information on seasonal snow cover across the NH.
The permafrost map (Brown et al., 2002;Zhang et al., 1999) compiled by the International Permafrost Association (IPA) was used to define different permafrost zones within the Northern Hemisphere (Figure S1a in Supporting Information S1). Based on the IPA map, continuous, discontinuous, sporadic, and isolated permafrost zones occupy 46. 92%, 19.19%, 17.13%, and 16.77% of the permafrost regions as a whole (Zhang et al., 1999). To avoid large areal divergence, we regrouped discontinuous, sporadic, and isolated zones as noncontinuous permafrost zones. Finally, continuous (considered as cold permafrost, PFC) and noncontinuous (warm permafrost, PFNC) 10.1029/2022GL100327 3 of 11 permafrost zones occupied approximately half of the total permafrost area. The remaining land areas in the NH were defined as nonpermafrost regions. We acknowledged that there are several new permafrost maps (Obu et al., 2019;Ran et al., 2022). However, their periods are generally after the 2000s, which is not suitable to be an approximation of the initial state at the beginning of warming (around the 1970s).

Regional Mean Climate Variable Anomalies
We utilized anomalies to analyze regional changes. Anomalies on the spatial grid were derived by subtracting the long-term (1998-2017) means from the observed data. At a monthly scale, anomalies were similarly calculated using the long-term (1998-2017) means for the corresponding month. Regional average anomalies were weighted by their areas because the data set was on regular latitude-longitude grids. The regional average temperature or freezing/thawing index anomaly of a specific permafrost region (T r ) was calculated for each year following Jones and Hulme (1996) where n is the number of grids in permafrost region r, Area i is the area of grid i in region r, and ΔT ir is the anomaly of the air temperature or freezing/thawing index of grid i in region r.

Nonlinear Trends
Although a linear trend is generally used to quantify the amount or rate of climate change (e.g., IPCC AR5 (2013) report), further analysis demonstrates the nonlinear characteristics of the changing climate (Franzke, 2014;Ji et al., 2014;Wu et al., 2007). Here, we used the ensemble empirical mode decomposition (EEMD) method to estimate the nonlinear trends of the selected variables, including air temperature, thawing, and freezing indices. The most important advantage of this approach is that it does not assume any functional form (e.g., linear, cubic, etc.) for any changes. EEMD reduces potentially large uncertainties in trend estimates due to different selections for an analysis period, particularly the onset and termination times. Details of the EEMD method can be found in Wu and Huang (2009).

Numerical Simulations of Permafrost Thermal State
To disentangle the impacts of various climatic factors on different permafrost thermal regimes, we conducted experiments with a 1-D numerical heat-transfer model developed for permafrost by the Geophysical Institute Permafrost Lab (GIPL) (Jafarov et al., 2012;Marchenko et al., 2008). The simple model setup is briefly introduced and configurations are described in Supporting Information S1 (Numerical Model Configuration).
The upper boundary condition was set to the snow (or ground) surface temperature, which was assumed to be the air temperature. A constant 50 mW m −2 geothermal heat flux was assumed to exist 100 m below the ground surface, similar to that found at Prudhoe Bay, Alaska (Lachenbruch et al., 1982). The soil vertical column (0-100 m) was divided using 180 nodes with a layer thickness of 0.01 m near the ground surface, increasing to 1 m close to the lower boundary. Time steps were 1 day (86,400 s) with 365 days (nonleap) in an annual cycle. Snow depth in an annual cycle was described by the simple function suggested by Zhang et al. (1996). One of the key parameters in this simple function is the maximum snow depth, which was set to 30 and 40 cm for the cold and warm permafrost cases ( Figure S1c in Supporting Information S1), respectively. The thermal conductivity of snow was set to 0.33 W m −1 K −1 and did not change with time, ignoring the depth hoar, wind slab, and other microstructures. We know that snow conductivity varies with local specific conditions (e.g., different vegetations), which could have lower thermal conductivity than 0.33 W m −1 K −1 . Thus, we also tested another snow thermal conductivity of 0.25 W m −1 K −1 for cold permafrost cases as a cross reference (because under this set, warm permafrost may disappear using the air temperature condition in Figure S1b in Supporting Information S1). We realized it was difficult to consider all possible soil properties because of the different combinations of soil water content, density, and many other features. We used the soil vertical profile at Barrow, Alaska (Table  S1 in Supporting Information S1). It was tested at several different sites (Section S1.4 in Supporting Information S1). Meanwhile, using the results in Table 1, the inferred changes in permafrost temperature were found 10.1029/2022GL100327 4 of 11 to be comparable with Biskaborn et al. (2019). Therefore, we assumed the model results can capture the main characteristics of permafrost thermal dynamics.
To consider different original permafrost thermal states, we generated two baselines of permafrost thermal state based on the air temperature conditions from the CRU data set. To represent cold permafrost (Baseline-PFC), the baseline seasonal air temperature curve was set using a MAAT of −11.0°C and an annual amplitude of 21.0°C ( Figure S1b in Supporting Information S1). A MAAT of −4.0°C and an annual amplitude of 18.0°C were used to represent warm permafrost (Baseline-PFNC). For the warm permafrost baseline, we set the MAAT to −4.0°C rather than −3.0°C (as indicated by the CRU TAS data) because the warmer temperature results in extremely warm permafrost using the parameters in Table 1 and any additional climate warming will convert the permafrost to seasonally frozen ground, which is a substantial change beyond the scope of this study.
We then simulated the effects of warming during different seasons (summarized in Table 1). The cold season was taken to be that portion of the year when daily mean air temperature <0°C while the warm season was defined by daily mean air temperature >0°C. Air temperatures for the cold-season simulations were increased by 7.62% for cold permafrost (TW-PFC) and by 12.70% for warm permafrost (TW-PFNC), both equivalent to an increase of 1°C in MAAT, while the warm season remained unchanged. Similarly, for warm-season simulations the air temperatures were increased by 47.07% (cold permafrost, TS-PFC) and 25.83% (warm permafrost, TS-PFNC), which was also equivalent to an increase of 1°C in MAAT.
For each case, the model was run until the soil temperature profiles reached thermal equilibrium, that is, the maximum difference in ground temperatures at all levels between two successive time steps was <0.01°C. In other words, these simulations represent long-term thermal responses.
10.1029/2022GL100327 5 of 11 The climatology of MAAT (i.e., long-term mean from 1998 to 2017) was approximately −11.1 ± 4.0°C (mean ± standard deviation) in the continuous permafrost zones of the NH ( Figure S1b in Supporting Information S1). In noncontinuous permafrost zones, the climatology of the MAAT was approximately −2.7 ± 2.8°C. Annual amplitudes of TAS were approximately 21.9 ± 4.4°C and 18.2 ± 4.4°C in the continuous and noncontinuous permafrost zones, respectively.
The CMC snow depth product showed that the annual maximum snow depth was 32 and 42 cm in the continuous and noncontinuous permafrost zones, respectively (Figure S1c in Supporting Information S1). Peak snow depth was generally found to occur during March-April. The length of the snow season was 10 and 8 months in the continuous and noncontinuous permafrost zones, respectively, which was mainly dependent on the annual air temperature cycle.

Land Surface Air Temperature Changes Over Different Regions
The change in MAAT during 1976-2020 was 1.81°C over all NH permafrost regions (Figure 1a), which was 26.4% higher than the corresponding warming (1.44°C) for the entire land area of the NH. Permafrost regions account for approximately 24.0% of the NH land area but contributed approximately 30.0% to the warming over the entire NH. In contrast, nonpermafrost regions showed a slower warming rate than either the NH land area or the aggregate of NH permafrost regions (Figure 1a). These results indicate that the lower atmosphere over permafrost regions experienced faster warming than the entire NH land area. Within permafrost regions, the MAAT increase in continuous permafrost zones was much greater than that in the other permafrost zones. MAAT increased by 2.46°C or at a rate of 0.54°C/decade during 1976-2020 in continuous permafrost zones (Figure 1a), which was approximately 70.0% higher than for the NH land area. Continuous permafrost contributed approximately 18.2% to the changes in NH MAAT, although it accounted for only 10.7% of the NH land area. This feature is similar to the Arctic amplification because most continuous permafrost occurs at high latitudes. Over the other permafrost zones (i.e., discontinuous, sporadic, isolated permafrost zones), the changes in MAAT were 46% lower than those in the continuous permafrost zones, but they were close to those occurring in nonpermafrost regions.
As an integral metric of cold-season air temperature, the freezing index DDF decreased 723.4°C-day in the continuous permafrost zones during 1976-2020, or at a rate of −161°C-day/decade (Figure 1c). This was 4 times greater than the corresponding increase in the warm-season air temperature metric DDT (165.9°C-day or 37.0°C-day/decade) during this period (Figure 1b). Noncontinuous permafrost zones and permafrost regions as a whole experienced similar behavior (i.e., DDF declines were larger than DDT increases). In contrast, warm-season DDT changes in nonpermafrost regions were larger than those for the cold-season DDF.
Furthermore, we confirmed that strong increases in air temperature occurred during cold months in the continuous permafrost zones ( Figure S2 in Supporting Information S1). The fastest TAS warming occurred during October-April, which ranged 2.73-4.41°C, or 0.61-0.98°C/decade, in the continuous permafrost zones during 1976-2020 ( Figure S2 in Supporting Information S1). TAS increased at a much smaller rate during the summer months in the continuous permafrost zones (e.g., August: 1.39°C or 0.31°C/decade). This warming was slightly lower than the NH average trend (1.44°C). In the noncontinuous permafrost zones, changes in monthly TAS ranged from 0.32 to 3.15°C, which were much lower than the continuous permafrost zones.

Potential Responses of Permafrost to Air Temperature Changes
We used a simple one-dimensional heat-transfer model (GIPL) to investigate how permafrost potentially responds to asymmetric warming during cold and warm seasons. All discussions are based on the typical soil column described in Table S1 in Supporting Information S1.

Cold Permafrost (PFC) Scenarios
We first examine the long-term response of cold continuous permafrost to a prolonged 7.62% air temperature warming during cold seasons (TW-PFC, Table 1); the commensurate mean-annual air temperature MAAT increase is 1°C. In this scenario, we find that both the mean-annual soil surface temperature (MAST) and the mean-annual permafrost temperature (T PF ) below the depth of seasonal effects (15 m) increases 0.93°C. Thus, the ground surface and permafrost thermal response almost equals (93%) the change in air temperature. The thermal offset at the surface (Offset S = MAST − MAAT) declines only slightly (0.07°C). The freezing index calculated from the air temperature DDF decreases 365°C-day while that calculated from the soil surface temperature DDF S decreases 338°C-day, again indicating that the thermal response of the ground is 93% of that in the air. In the baseline and cold-season simulations, the freezing n-factor n f = DDT S /DDT (an indicator of the snow cover thermal insulating effect) was found to be 0.72-0.73, consistent with the value (0.75) found by Way et al. (2016) with a similar cold-season averaged snow depth (0.2 m). Compared with the baseline case, the n-factor changed very little (∼0.016) when substantially warming the cold-season air while holding the snowpack thickness constant. In terms of lingering effects the following summer, we found that the cold-season warming has only a limited effect on the annual maximum active layer thickness (ALT) (∼2 cm).
The long-term response of cold continuous permafrost to a 47% increase in warm-season air temperatures is investigated in scenario TS-PFC (Table 1); again, the associated mean-annual air temperature increase is 1°C. With this scenario, MAST increased 1.53°C, substantially more than the MAAT, while the warming of permafrost at the 15-m depth was comparable to that of the MAAT (0.98°C). The thawing index calculated from the air and ground surface temperatures, DDT and DDT S , both increased 365°C-day. Perhaps more interesting is that the freezing index calculated from the cold-season soil temperatures DDF S decreased by 193°C-day in this scenario, suggesting that the additional heat flux into the ground during the warm season is stored at shallow depths (<15 m) until the winter where it is partially trapped by the insulating snow cover (Kudryavtsev et al., 1977). This leads to the enhanced MAST and associated 0.53°C strengthening of the mean-annual thermal offset (Offset S ).
To further investigate the direct impact of the warm-season warming on cold permafrost, we repeated the simulation but removed the cold-season snow cover. The resulting warming of permafrost at the 15-m depth was only ∼0.2°C, implying the warm-season warming will only have a limited impact on cold permafrost without the presence of wintertime snow. Finally, we found that the warm-season warming of cold permafrost (TS-PFC) increased ALT by ∼20 cm, a substantial amount for this environment.

Warm Permafrost (PFNC) Scenarios
For the purposes of this study, we consider warm permafrost to be any permafrost other than cold continuous permafrost (i.e., discontinuous, sporadic, and isolated permafrost). The baseline case for warm permafrost (Baseline-PFNC) shows that MAST for this category is ∼1.2°C while the 15-m deep permafrost temperature (T PF ) is about −0.87°C (Table 1), implying a large amount of unfrozen water may exist even if the deep soils are still frozen. In addition, the n-factor n f (0.34) is much lower and the surface thermal offset (Offset S ) much higher than for the cold permafrost baseline case. This is because of more heat during the warm season and thicker snowpack during the winter that results in greater thermal insulation by the snow cover. Again, both the cold-season and warm-season warming scenarios are designed to produce a 1°C increase in MAAT.
We find that the thermal response of warm permafrost to a cold-season warming (TW-PFNC, Table 1) is much less (MAST increases 0.68°C, T PF increases 0.55°C) than was the case for cold continuous permafrost (0.93°C). As a result, the soil freezing index DDF S is only reduced by 248°C-day in this scenario although the air temperature freezing index drops by 365°C-day. Although typically large for warm permafrost, the surface thermal offset (Offset S ) is reduced by 0.32°C in the cold-season warming scenario and the n-factor n f is also reduced by 0.049. As with cold permafrost, the thermal response of warm permafrost to a warm-season warming is amplified in the soil but to a somewhat smaller degree (MAST increases 1.24°C rather than 1.53°C). One possible reason for this is that warm-season warming has weaker indirect impacts during the cold season at a warm permafrost site since the DDF is much lower than for cold permafrost. Thus, a reduction of n f may only provide a decrease in the freezing index DDF S of ∼87°C-day. Although MAST increases 1.24°C in the warm-season warming scenario, the permafrost temperature T PF only increases by 0.57°C, indicating 0.67°C is damped between the ground surface and the ∼15-m depth. In cold permafrost, this damping effect is only 0.26°C. This is mainly because of the thicker active layer and higher unfrozen water content in warm permafrost. Warm-season (TS-PFNC) and cold-season (TW-PFNC) warming of warm permafrost resulted in a deepening of the active layer by 37 and 12 cm, respectively (Table 1).

Implications and Limitations
Using We realize that similar magnitudes of climate warming during the cold and warm seasons may play an equivalent role in permafrost thermal evolution when the permafrost was originally cold (T PF < − 2°C, depending on unfrozen water content). However, the direct impact of warm-season air temperature warming on permafrost may be limited. Using numerical modeling, we demonstrated that interseasonal effects (mainly thermal storage or thermal memory) due to snow cover plays a critical role in enhancing the impacts of warm-season warming on permafrost, particularly for cold continuous permafrost. Warm permafrost is less responsive to air temperature changes due to the damping effects of latent heat and reduced warming during the cold season. A recent study in the Russian Arctic also found a similar phenomenon (Wang et al., 2021), that is, soil temperatures increased at a higher rate in colder basins than in warmer basins, although the mean-annual air temperature changes were similar.
Our findings are important for understanding permafrost carbon cycles. More than 45% of permafrost carbon is stored in the upper 1 m of soils and the carbon density in continuous permafrost is generally higher than other permafrost zones (Hugelius et al., 2013). Our study demonstrates that considering all permafrost regions as a whole may be insufficient to capture the major features of permafrost carbon cycles because of the different responses of cold and warm permafrost to climate warming. Furthermore, potentially the largest influence in continuous permafrost zones may be permafrost warming rather than deepening thaw depth because of asymmetrical changes in cold and warm seasons. Thus, assuming permafrost carbon emissions arise only from thaw processes may miss a significant source of the emissions. It is necessary to give more attention to carbon cycles during cold seasons due to permafrost temperature warming. There are several studies that already have reported this phenomenon (e.g., Natali et al., 2019).
In addition, this study raises some important issues when considering permafrost thermal processes: (a) Climate warming may alter the thermal insulation effect of snow, which is especially important for cold permafrost. Snow cover can potentially enhance the warming of permafrost even if its timing and thickness do not change. (b) Some empirical models should be used with caution when predicting permafrost temperature evolution, particularly in warm permafrost because of unaccounted for unfrozen water content (Romanovsky & Osterkamp, 2000). In addition, we find that the n-factor found in some empirical models does not remain constant even if the snow condition does not change but rather responds to the increased heat flux into the ground resulting from climate change.
Without doubt, uncertainties in this complexity-reduced study still need further investigation. (a) Soil properties are so complex that we were unable to investigate all combinations of soil properties. One significant issue is that soil properties strongly influence the thermal conditions in permafrost during the initialization stage of a simulation using the same climate forcing. There exist several gridded soil databases, but they contain little original information for permafrost regions because of sparse soil profiles. In this study, we created 15 soil types according to Goodrich (1982) (Table S2 in Supporting Information S1). We then implemented a series of simulations as described in Section 2.2.3. The results of these simulations confirm our previous findings (Table  S3 and Figure S3 in Supporting Information S1). (b) Snow is one of the important sources of uncertainty. For example, in comparison with a snowpack using our reference thermal conductivity (Table 1), a snow with lower thermal conductivity could dampen more of the permafrost response to changes in atmospheric temperature changes during the winter while amplifying the response in summer (Table S4 in Supporting Information S1, similar to Table 1 with different magnitudes). (c) The model in this study only considered subsurface heat-transfer processes, that is, other physics (convection, surface energy balance, disturbances, etc.) are not considered, which could lead to accelerated permafrost degradation.

Conclusions
We investigated the seasonal and annual land surface air temperature changes from 1976 to 2020 over different permafrost regions of the NH and explored the potential responses of permafrost temperature to climate warming. We found that continuous permafrost zones experienced faster warming than the entire NH, permafrost regions as a whole, and noncontinuous permafrost zones. Particularly for the cold season, continuous permafrost zones warmed rapidly, showing a 724°C-day decrease of the freezing index DDF during 1976-2020. Over nonpermafrost zones and noncontinuous permafrost (discontinuous, sporadic, isolated permafrost zones), the changes were much smaller. Overall, permafrost temperature changes during this period were primarily controlled by changes in cold-season air temperature (or DDF). However, it should be noted that the effects of summer warming could be amplified when there is cold-season snow cover. For the same magnitude of mean-annual air temperature change, the response of permafrost thermal regime and active layer thickness may differ substantially depending on the primary season during which the change occurs. The asymmetrical responses in cold and warm permafrost are critical for assessing permafrost carbon cycles and feedbacks due to the differences in permafrost carbon density among permafrost zones. This lower complexity study provides an integrated perspective for understanding permafrost thermal evolution during the past few decades. To predict more detailed permafrost dynamics due to climate change, we need to know the original thermal state of permafrost, thermal properties of snow and soils, geothermal heat flux, and the magnitude and seasonality of climate warming.

Conflict of Interest
The authors declare no conflicts of interest relevant to this study.