future permafrost conditions and limitations of different modelling approaches, before providing future research priorities and knowledge gaps.
As ground temperatures at depth cannot be observed using satellite or airborne techniques, monitoring changes in the thermal state of permafrost is challenging. However, direct field measurements of ground temperatures at depth and active-layer thickness provide documentation of changing permafrost conditions in many areas, particularly in the Northern Hemisphere.
Observation networks. Temperatures measured in boreholes -typically drilled to depths of 20-30 m, below the DZAA, to represent longer-term climatic changesallow direct, quantitative and comparable observations of permafrost thermal state. Ground temperature monitoring sites typically consist of boreholes instrumented with multi-sensor cables to measure temperature at several depths. The Global Terrestrial Network for Permafrost (GTN-P), an international programme of the Global Climate Observing System, currently includes over 200 boreholes distributed throughout permafrost regions 18,19 , including: the Arctic and sub-Arctic regions of North America, Russia and the Nordic countries; mountain and high-elevation regions of Europe and Asia; and Antarctica 4 . However, large spatial gaps exist in the monitoring network owing to the costly and challenging logistics of borehole installation in remote circumpolar regions and mountain areas with steep and complex topography. Site selection has therefore historically favoured locations near communities, critical infrastructure and areas of specific research interests, but existing sites nevertheless encompass a broad range of geologic and ecoclimatic conditions.
Although some sites in polar areas have been in operation for more than 40 years, most were established during or since the International Polar Year (IPY; 2007-2009). Other regional efforts have focused on nonpolar regions, such as the Permafrost and Climate in Europe project 20 , which established monitoring sites to extend and support ongoing monitoring of European mountain permafrost 8,21 , and other programmes in Antarctica 22 and high-elevation areas of Asia 23 .
To monitor ALT, frost probing in late summer or early autumn, near the time of maximum thaw, is the most frequently used method. These ALT measurements have been collected at many sites since the 1990s, particularly as part of the Circumpolar Active Layer Monitoring (CALM) network in the Arctic, Antarctic and highelevation and mountain permafrost regions 24 , and of other regional programmes 25,26 . Other methods to determine ALT include the use of thaw tubes or interpolation of the 0 °C isotherm from shallow ground temperature measurements 27 , the latter of which is the only practical method in areas dominated by debris and bedrock slopes 28 .
Continuous operation of these monitoring sites has allowed annual updates to ground temperature time series and ALT records, informing key assessments [4][5][6][7][29][30][31][32] . Several early regional and local-scale investigations documented changes in permafrost temperatures in North America [33][34][35][36] , Siberia 37 , Europe and Scandinavia 21,38,39 , and the Tibetan Plateau 40 . However, it was the IPY that spurred the first comprehensive synthesis of the permafrost thermal state at a circum-Arctic scale 19 . A major achievement of this effort was the establishment of a temperature baseline from which to assess future change. Regional syntheses placed the conditions during the IPY in the context of the longer record (where available), providing documentation of changes over time [41][42][43] . These regional syntheses presented evidence of increasing permafrost temperatures, in some cases since the 1970s up to the IPY, for several Arctic areas 19 .
Permafrost temperature changes. Widespread and persistent warming is observed in most contemporary global assessments of permafrost temperatures measured at or near the DZAA 4,29,30 (Fig. 1). However, there is considerable regional variability in the magnitude of this warming owing to differences in the proximity of permafrost temperatures to 0 °C, substrate properties (including ground ice), and snow and vegetation conditions. In particular, temperature changes differ substantially between continuous and discontinuous permafrost domains.
The highest permafrost temperatures in the instrumental record, which spans more than three decades at some sites, were recorded in 2018-2019 at most sites in Arctic and sub-Arctic regions (Fig. 2a,b). Maximum temperature increases are typically evident in the cold Arctic ground of the continuous permafrost region (Figs 1,2a). For instance, warming rates of 0.4-0.8 °C per decade have occurred since the 1980s in northern Alaska and in the northern Mackenzie Valley 30,44 , and up to 0.7 °C per decade in northern Quebec and on Baffin Island 5,31,45 . At the high-latitude Arctic station of Alert on Ellesmere Island, similar increases of 0.4-0.6 °C per decade have been apparent since the 1980s. Here, twenty-first-century warming rates have been greater (0.6-1.1 °C per decade) than for the entire record (which started in 1978), as is also the case with temperature trends further south in the Baffin region 30 . Permafrost temperature increases on the Arctic Svalbard archipelago and Russia are also similar, typically reaching 0.8 °C per decade 8,30 and 0.5 °C per decade 30,46,47 , respectively. However, warming rates of 0.9 °C per decade have been recorded in some Siberian boreholes since 2008 (reF. 4 ).
In the warmer ground of the discontinuous permafrost zone, by contrast, temperature increases are typically
• Widespread and persistent warming of permafrost is observed in polar regions and at high elevations since about 1980, at rates that vary regionally. • The highest permafrost temperatures in the instrumental record were recorded in 2018-2019 at most sites in arctic and sub-arctic regions. • Trends in permafrost warming are consistent with trends in air temperature.
However, local conditions including snow cover and vegetation modulate the response of permafrost under a warming climate. • Permafrost is projected to continue to warm and thaw in response to climatic warming, but there is uncertainty with respect to the magnitude and timing of these changes. In Antarctica, permafrost monitoring sites have been established more recently than those in the Northern Hemisphere, and there is a limited number of boreholes that extend beyond the DZAA. While there is some indication of temperature increases at shallower depths since about 2010 (reF. 4 ), longer-term trends are not as evident at greater depths 48 .
The thermal state of permafrost has also been monitored in high-elevation areas of the Northern Hemisphere such as the European Alps and the Tibetan Plateau. In the European Alps, as with the Arctic, warming rates are generally higher for colder permafrost 8,26,29 , with temperature increases comparable to those of the Arctic for ice-poor shaded bedrock sites at high elevations (Figs 1,2c). For example, the longest record, spanning >30 years, is observed in an ice-rich rock glacier in the Swiss Alps, where temperatures have increased by about 0.2 °C per decade, as measured at 20 m depth. On the Tibetan Plateau, where permafrost temperatures are typically higher than -3.0 °C, warming of up to 0.25 °C per decade has been observed since 2000 at depths of 15 m (reF. 32 ). Although permafrost also exists in other mountain ranges, including the Himalayas 49,50 , North America 51,52 , the Andes [53][54][55] and New Zealand 56 , records are not sufficiently long or from great enough depths to allow trends comparable to other areas to be determined.
The thermal characteristics of permafrost include various features and metrics (see the figure, left panel). near-surface ground temperatures generally respond to the annual cycle of air temperature. Temperature variation decreases with depth, becoming negligible at the depth of zero annual amplitude (DZaa), which for practical purposes is where annual fluctuations are <0.1 °C. The DZaa depends on the thermal properties of the ground, influenced by material type, moisture and ice content. For example, the DZaa is greater in bedrock with a high quartz content (>20 m) compared to fine-grained silt or organic material (<10-15 m). Below the DZaa, temperature increases with depth owing to the geothermal gradient. In flat terrain, variations in the geothermal gradient with depth are indicators of climatic fluctuations 169 .
The permafrost layer occurs where temperatures remain ≤0 °C. The active layer is the layer of ground above permafrost that thaws and freezes annually. Differences in the thermal conductivity of frozen and thawed materials in this layer can result in mean annual temperature being higher at the ground surface compared to the top of the permafrost layer. This effect is referred to as the thermal offset 98,100 , the magnitude of which is greater in material with higher moisture contents, although the effects of non-conductive heat transport are also a factor 170 . The thermal offset means that permafrost can exist even in areas where annual mean ground surface temperatures are above 0 °C. The surface offset is defined as the difference between the annual mean ground surface temperature and the annual mean air temperature, and reflects the buffering effect of snow and vegetation cover 98,171 , and the influence of solar radiation on the surface energy balance 51,170 .
as air and ground surface temperatures rise, increases in ground temperature will occur in the near-surface and gradually propagate to greater depths. The ground acts as a filter with higher-frequency variability in temperature reduced at greater depths, such that only longer-term changes in temperature are preserved at depths beyond the DZaa. Temperature changes at depth lag behind those at the surface, with the lag increasing with depth (see the figure, right panel). Therefore, deeper ground temperatures can provide a record of temperature changes over past decades or centuries or longer 149,172 , and can be used to reconstruct the past history of surface temperatures 75,173,174 . ALTs have increased in some regions of the Arctic since the 1990s, although with marked variability (Fig. 3; TaBle 1). ALT trends are most evident in the Russian Arctic 57 (Fig. 3a,b; TaBle 1). Indeed, some of the greatest increases since the late 1990s have been recorded in the Russian European north and western Siberia 30 (Fig. 3a), where average ALT values increased by up to 0.4 m between 1999 and 2019. In North America, some regions have also exhibited substantial changes, but at a lesser magnitude than observed in Russia. In particular, ALT increased by >0.2 m from 1996 to 2019 in the Alaskan interior 30 (Fig. 3c). By contrast, on the Alaskan North Slope (Fig. 3d) and in the Mackenzie Valley (Fig. 3e), ALT decreased following a 1998 peak, and underwent a slight increase since the mid-2000s 25,30 ; however, present-day ALTs remain relatively unchanged from those measured before 1998. At sites in southern Norway, northern Sweden, northeast Greenland and central Svalbard, ALT has generally increased since the 1990s at an average rate similar to the Russian Arctic (Fig. 3f; TaBle 1), but with considerable inter-annual variation 8,58 .
Decreases in seasonal freezing depths and increases in seasonal thaw depths have also been observed. The ground above permafrost did not completely refreeze in winter 2017-2018 and 2018-2019 at several sites in the Alaskan interior and on Seward Peninsula, indicating formation of a suprapermafrost talik 30 , a zone of unfrozen ground above permafrost 59 . Similarly, refreezing above permafrost has not occurred over the past several winters at sites in the Russian European north and in west Siberia 30 .
In the ice-free regions of Antarctica, ALT has been monitored at 16 sites since 2006. Here, inter-annual variability is high, with no evidence of longer-term increasing trends 60 (Fig. 3g; TaBle 1). In fact, a decrease in ALT was observed on the western Antarctic Peninsula 61 .
Pronounced increases in ALT have been observed in the European Alps since the 1990s (Fig. 3h; TaBle 1). Present-day ALTs are typically >10% above the mean for the entire period 8 . Moreover, ALT has doubled since about 2000 at several sites in the Swiss Alps, increasing by up to several metres 26 . These changes have generally been lower at sites with ice-rich permafrost, such as in rock glaciers, than in bedrock sites. On the Tibetan Plateau, ALT has tended to increase at a rate of about 0.2 m per decade since 1980 (reF. Challenges in interpreting trends. Although ground temperatures and ALT have been used to assess changes in permafrost conditions, it is important to be aware of some of the challenges in interpreting the trends from these records. One such challenge is that temperature records from warm permafrost areas can obscure important physical processes active during permafrost degradation. Increases in permafrost temperature have generally been smaller in warmer permafrost close to 0 °C, particularly in ice-rich fine-grained material 7 (Fig. 2b). As permafrost temperatures approach 0 °C, ground ice melts over a range of sub-zero temperatures. Latent heat is required in this phase change, leading to a lower apparent thermal diffusivity and less energy directed at raising ground temperatures 19,43,[62][63][64] . Decreases in resistivity measured by long-term electrical resistivity tomography surveys can elucidate this reduction in ground ice content during permafrost degradation as temperatures rise slowly 8,26,65 . Although temperature changes in warm, ice-rich permafrost can be slow, melt of ground ice can induce substantial geomorphic changes, including ground surface subsidence and subsequent inundation, or hillslope failures 7,10 . Therefore, temperature records from warm permafrost areas do not always represent the longer-term heat flux into the permafrost and the associated geomorphic effects of climate change 62 .
As discussed, there is also indication of little change in ALT at some locations despite progression of thaw deeper into the ground. This absence of ALT variability can be explained by ground surface subsidence and soil consolidation, which accompany the thaw of ice-rich permafrost. Permafrost thaw at ice-rich sites is obscured by traditional ALT measurements, which are usually made using the ground surface as the reference datum each year [66][67][68][69] . However, ground surface settlement in the range 0.2-0.8 cm per year has been observed in ice-rich terrain using differential GPS in Alaska and ground surface elevations from thaw tube measurements in the northern Mackenzie Valley 67,69 . Traditional ALT measurements therefore underestimate permafrost degradation in these regions, as lowering of the permafrost table is accompanied by subsidence of the ground surface 67 . Thus, in some situations, using ALT as an indicator of 1 for number of sites included in regional averages. Note the contrasting y axes. ALT is increasing in some regions, with change most evident at Russian, Nordic and Swiss sites.
climate change can be problematic, highlighting the need for monitoring of ground surface elevation where repeat ALT measurements are collected.
Finally, some of the variability observed in ALT records can be related to the timing of frost probe measurements. Specifically, frost probing is often performed in late summer, and thus does not always capture the period of maximum thaw, which might not occur until late October, November, or later. In addition, the length of the thaw season and timing of maximum thaw can vary from year to year. Later active-layer freeze-back due to warming and the potential for suprapermafrost talik formation also present challenges to ALT monitoring that employs probing in late summer 70 . The issue of measurement timing can be avoided by deriving ALT from continuous borehole temperature measurements, but accuracy depends on the sensor spacing and methods of interpolation or extrapolation 71 .
The response of ground temperature to changes in atmospheric conditions is modulated by the interrelated effects of vegetation, snow cover, organic layer thickness and the thermal properties of Earth material (Fig. 4), as now discussed.
Air temperature. Observed changes in permafrost thermal conditions (Figs 1,2) are generally consistent with increases in air temperature owing to polar and high-elevation amplification 2,4,7,31,37,72 . Indeed, regional variations in the temporal patterns of air temperature are reflected in permafrost temperature records. For example, rapid warming of Canadian high-latitude Arctic permafrost since about 2000 (Fig. 2a) aligns with the rapid amplification of atmospheric temperatures that began in the late twentieth century 31,43 . By contrast, lower rates of permafrost temperature warming in the Mackenzie Valley (Fig. 2b) can be linked to smaller increases in air temperature 31,43 .
Although the general patterns of air and permafrost temperature changes are coincident, local conditions prevent significant correlations (at the 95% confidence level) between the two variables 4 . For example, increases in permafrost temperature are greater at sites in bedrock, where the ground thermal conductivity is high, compared to sites underlain by unconsolidated sediments containing appreciable ground ice 8,9,19,26 , where ice must thaw as temperatures rise 62 ; latent heat effects in ice-rich, fine-grained sediments reduce the apparent coupling between air and ground temperatures. These effects are demonstrated at sites underlain by bedrock in Alert and Svalbard, where rates of warming are larger than those underlain by unconsolidated sediments in northwestern North America (Figs 1,2). Similarly, in the Swiss Alps, contemporary warming is larger in ice-poor bedrock than in unconsolidated material (Fig. 2c).
The annual air temperature amplitude (difference between the warmest and the coldest months of the year), which reflects the continentality of the climate, has an important influence on ALT. For locations with the same mean annual air temperature and similar surface and soil conditions, ALT is larger in regions with a more continental climate and larger amplitude of seasonal air temperature variation 19 .
The seasonality of air temperature increases is also an important factor controlling the evolution of the permafrost thermal state. In polar regions such as Alaska and northern Canada, as well as mountain regions such as the Tibetan Plateau, warming of permafrost is mainly associated with increases in winter air temperatures [72][73][74] . These effects are particularly marked at sites with thin snow cover 74 , related to a limited buffering effect between the air and ground surface (Fig. 4). There is evidence that winter warming impacts on ALT interannual variability is also larger at Nordic sites with thin snow cover 58 , although the connection with ALT is more difficult to constrain owing to the dominant impact of summer conditions on this variable.
Temporal variability in snow cover is an additional driver of permafrost thermal state changes owing to its insulating effect, which limits winter heat loss from the ground and modulates the influence of air temperature changes on the ground thermal regime 75 . In near-vertical bedrock slopes in the European Alps, for example, ground temperatures closely follow air temperature owing to the absence of snow cover 26,76 . The net result of an increase in snow cover is an increase in the ground surface temperature (Fig. 5a). For example, permafrost temperatures increased during periods of enhanced snow cover at monitoring sites in Alaska, even as air temperature decreased 33,73 . Late 1980s to early 1990s permafrost warming in the Alaskan interior (Fig. 2b) is further attributed to increases in both snow cover thickness and higher air temperatures 33,73 . The same factors have also been linked to permafrost warming in Norway during 1999-2009 (reF. 64 ).
The magnitude of the warming effect depends on snow cover depth, timing of accumulation and melt 77 , and snow density, all of which control the snow cover thermal properties 33 . Later accumulation can lead to enhanced cooling of the ground as air temperatures decline 77 . Thus, in the European Alps, a temporary cooling of permafrost down to depths of 20 m (Fig. 2c) was attributed to very late snow cover accumulation in two consecutive winters 26,29 . By contrast, earlier snow accumulation can delay ground cooling and freeze-back of the active layer during winter. Indeed, in the Mackenzie Delta, early snow cover accumulation led to active-layer freeze-back delays of several weeks, elevating ground temperatures compared to years in which snow accumulation occurred later 78,79 . This delay in active-layer freeze-back is larger in substrates with higher moisture content owing to latent heat release during freezing 63,79 . Timing of snow melt in spring can also influence the onset of seasonal ground warming and thaw 33,73 , which will occur after the snow is gone. The warming effect also depends on the thermal properties and moisture content of the underlying soils; the greater the thermal conductivity and the higher the soil water content (and latent heat effects accompanying freezing), the larger the warming effect of the same layer of snow 63,80 .
Vegetation. Vegetation also has a strong role in influencing changes in the thermal characteristics of permafrost. Yet these influences are complex owing to the interlocking effects of shading, snow accumulation and the formation of an insulating surface organic layer 73,81 (Fig. 4).
The vegetation canopy reduces the amount of solar radiation reaching the surface, decreasing summertime ground temperatures 82 . However, ground shading is spatially and temporally variable, and so the total effect on permafrost temperature is difficult to predict. For areas with dense canopies in the boreal forest, shading effects and interception of snow cover contribute to an overall cooling effect, influencing the distribution of permafrost in the discontinuous zone 81 . By contrast, enhanced snow accumulation in areas with open canopies near the treeline lead to warmer winter ground conditions 78,81 . In mid-latitude mountain regions, permafrost generally exists above the tree-line, and so vegetation is typically considered an indicator of permafrost absence 83 . Furthermore, sites with thicker organic layers are generally less responsive to changes in air temperature owing to the buffering between the air and ground surface. For example, increases in permafrost temperatures at forested sites in the central Mackenzie Valley are much lower than observed at high-latitude Arctic polar desert sites 63 (Fig. 1).
The contemporary expansion of shrubs in tundra has also been a topic of interest in regards to permafrost thermal characteristics, owing to their impact on snow cover depth. Generally, shrub presence results in warmer ground conditions compared to tundra with shorter vegetation species 78,84,85 . For example, in northwestern Canada, minimum annual near-surface ground temperatures were up to 5 °C higher at sites with tall shrubs than at sites with short shrubs 86 . While the observed expansion of shrub cover in tundra areas could therefore result in increases in permafrost temperature [85][86][87][88] , direct observations of these impacts are limited.
Rainfall and soil moisture. The presence of water further has a strong impact on permafrost. Inundation leads to increases in permafrost temperature beneath the water body 89,90 because the freezing of water delays winter heat loss from the underlying ground. Taliks can form if freezing does not reach the bottom of the water body 59 . Heat advection from moving surface water (rivers, creeks, fens) can also warm the ground, resulting in permafrost degradation, particularly where the permafrost was discontinuous, warm and thin 81,91 associated with water flow through gullies in ice-wedge networks also leads to ground warming and increases in ALT 92 . By contrast, ground cooling occurs with emergence of the surface following pond drainage, channel migration or uplift in coastal regions 90,93,94 .
Groundwater additionally affects ground temperature and ALT, specifically through the relation between soil moisture content and the thermal properties of the active layer, including thermal conductivity, heat capacity and the latent heat of freezing/thawing. Increases in water content lead to better heat conduction into the ground 95 , particularly in organic soils, which combined with advective heat transfer from enhanced groundwater flow, leads to a substantial deepening of the active layer and the rapid expansion of taliks 70,82,96,97 . For organic material, the influence of moisture content on thermal conductivity is particularly apparent when comparing seasons 81,82,98,99 : drying of peat in the summer leads to lower thermal conductivity, limiting ground warming and reducing thaw penetration, whereas in autumn and winter, enhanced moisture content resulting from autumn rainfall, and its subsequent freezing, increases thermal conductivity, promoting cooling. Latent heat effects associated with evaporation from wet soils and associated surface cooling can counter the effect of increased thermal conductivity, but it is unclear whether this impact outweighs that of increased heat flow 81,95 . Moreover, latent heat effects associated with freezing of wet soils can delay freeze-back of the active layer in the autumn 81 and thaw in the spring 95 . The relation between the moisture content in the active layer and permafrost temperature is less straightforward, depending on seasonal changes to the soil's frozen and unfrozen thermal conductivity, which control the thermal offset 98,100 (Box 1).
The infiltration of summer rainfall also influences the ground thermal regime. The magnitude of this effect depends on the difference between the soil temperature and the rain temperature, which generally approximates the air temperature 101 . Summer infiltration of water from the ground surface into the unsaturated soil of the active layer increases both ground temperature and the ALT if the rainwater is warmer than the soil [102][103][104] , whereas rapid cooling occurs following rain events on cooler summer days or in the autumn 101 . However, knowledge of this effect comes largely from modelling, with limited field evidence of impacts of changing precipitation on the ground thermal regime 99,105 . For example, while there is some observational evidence of soil warming and accelerated spring thaw following the infiltration of rainfall 99,101,105 , an insignificant correlation (at 95% confidence level) between total summer precipitation and ALT has also been observed 95 . Additional empirical evidence is required to better understand these effects, particularly the extent and significance of the process, and the direct impact of the additional energy brought by summer precipitation into the active layer 105 . Environmental disturbances. Finally, environmental disturbances, including wildfire, human activities and thermokarst all influence thermal properties. Wildfire is a normal occurrence in high-latitude permafrost regions, particularly in the boreal forest. However, larger and more severe fires have been observed in response to warmer and drier conditions, and fire activity is projected to increase further with continued warming 106,107 . These fires damage the protective surface organic layer that insulates the ground from warm summer air temperatures, decrease the amount of snow interception by trees, decrease the albedo at the ground surface, and decrease cooling by evapotranspiration [107][108][109][110] . Thus, ground temperatures and ALT increase following fires, with greater effects where burning is more severe and the reduction in the surface organic layer more pronounced 107,[111][112][113][114][115] . In permafrost regions of North America, Siberia, Mongolia and northeast China 107 , for example, mean annual ground surface temperatures at burned sites were 1-7 °C higher than at unburned sites.
Landscape change caused by the thaw of ice-rich permafrost (thermokarst) also influences the ground thermal regime. For example, in retrogressive thaw slumps, a type of slope failure in ice-rich permafrost, ground temperatures increase. As the vegetation mat is disturbed, ice-rich mineral soils are exposed and deep snow accumulates in the depression formed by the failure. The resulting warmer ground conditions can further enhance permafrost thaw and slumping activity 116 . Ground surface subsidence and pond formation also results in further warming of permafrost and promotion of thaw 10,117,118 .
Moreover, local disturbances related to human activity disturb the ground thermal regime by altering surface conditions 118 . Structures including road, railway, runway and building embankments enhance snow accumulation, resulting in overall increases in ground temperature, ALT and permafrost degradation 77,[119][120][121] (Fig. 5a). Clearing of vegetation and damage to the organic layer along infrastructure corridors also leads to permafrost warming beneath the cleared area (Fig. 5b) and in the adjacent undisturbed terrain due to lateral heat transfer 122,123 .
Thus, several interacting drivers influence the thermal state of permafrost (Fig. 4). Air temperature and snow cover are often the dominant drivers of permafrost change, but at regional and local scales, other factors become important. Knowledge regarding the effects of some drivers, however, largely comes from modelling, motivating field-based investigations to fully understand how the permafrost thermal state will evolve in response to environmental change.
Given that anthropogenic warming is projected to progress, continued, or even accelerated, permafrost warming and thawing are anticipated 5,6 . The rate and pattern of these future changes will vary depending on regional climate, local environmental factors and their complex interactions 124 . As such, there is substantial uncertainty in predicting the magnitude and timing of future changes, in part, related to limitations and advantages of different modelling approaches 125 .
Empirically based, equilibrium models typically rely on statistical relations between the main factors driving permafrost conditions, and are thus relatively simple and require limited data input 125 . For example, models based on the frost index and temperature at the top of permafrost have been used to estimate potential future permafrost distribution at regional-to-global scales [126][127][128][129][130] . However, these models do not consider transient effects and cannot accurately predict the timing of permafrost loss based on imposed warming scenarios. Rather, they indicate a possible eventual (or committed) permafrost loss 127 , which can lag substantially behind imposed changes in air temperature.
Estimates of eventual reductions in Northern Hemisphere permafrost area from such models range from 4.8 ± 2.0 million km 2 to 6.6 ± 2.0 million km 2 for air temperature warming scenarios of 1.5 and 2.0 °C above pre-industrial levels, respectively 127 . For the 2.0 °C scenario, the loss is equivalent to a 40% reduction of the area currently underlain by permafrost, and for the 1.5 °C scenario the reduction is 30%. Reductions >30% are similarly predicted by other simulations 129,130 , with greater losses anticipated for more extreme warming scenarios. Although these results cannot accurately predict the timing of permafrost loss, they provide an estimate of areas that could undergo permafrost degradation.
In high mountain areas, permafrost distribution is highly variable and strongly driven by topography, the effect of which has been incorporated into models. The statistical relation between solar radiation (or aspect) and air temperature (or elevation) is the approach most often applied 76,[131][132][133] and is most suitable for steep and snow-free bedrock areas. For unconsolidated material, such approaches are typically complemented by information derived from rock glacier inventories and ice-rich debris slopes 83,134 . Similar empirical approaches have been utilized to determine the future permafrost distribution in mountainous terrain in the southern Yukon, Canada 135 , projecting an eventual reduction of about 50% in the area underlain by permafrost area for a 2 °C air temperature increase in the region.
Transient numerical models. Transient numerical models simulate the ground thermal regime over time 125 , thus requiring detailed, site-specific input data so that heat transfer between the ground and atmosphere are accurately represented. Such models can be integrated with climate models, or incorporated in land surface or Earth System Models, to predict future ground temperatures and permafrost distribution 62,[136][137][138][139][140][141][142][143] . The application of downscaled climate model outputs to drive numerical permafrost models is challenging, particularly in areas of complex topography 142,144,145 . Some simulations only focus on near-surface permafrost conditions 6,138,146,147 , partly because of the computational requirements of implementing numerical models at large spatial scales to greater depths. These shallow simulations might not accurately represent changes in the thermal state in areas of thicker, colder permafrost 148 , and simulations with greater depth domains better represent the thermal response of permafrost to warming 62,140,143 .
Most global-scale projections by transient models focus only on permafrost occurrence and degradation in the upper 2-3 m, rather than reductions in the total extent of permafrost 6 . From these models, predictions indicate that thaw depths will exceed 3 m in 24 ± 16% to 70 ± 20% of the current permafrost region by 2100, depending on the warming scenario 6 . Other simulations of permafrost volume change project a loss of 3.0-5.3 × 10 3 km 3 frozen material per °C atmospheric warming; thaw below 2 m depth is not considered 136 .
Many models do not include representation of important subsurface properties, including excess ice content. Ground ice in excess of the soil pore space has important latent heat effects and causes ground surface subsidence upon thawing, which can strongly influence the ground thermal regime 7,149 . Neglecting such conditions is a limitation to modelling permafrost response to climate change 150 , though some simulations have begun to incorporate representations of excess ice 117,[151][152][153][154] . Ground ice conditions remain poorly defined in many areas, and further modelling progress will depend largely on improvements in field knowledge of ground ice conditions and improved spatial data products 155 .
Realistic representation of snow cover is necessary for accurate modelling of permafrost temperatures owing to its strong insulating effect 147,156 . Snow distribution and timing have pronounced effects on ground temperatures at small spatial scales that are typically not resolved by land surface models 121,147,157 . Recent modelling shows promise in simulating snow redistribution and associated effects on ground surface temperature 158 , and constitutes a novel approach for investigating climate change impacts on permafrost.
Representation of topographic effects and the spatial variability of snow cover and other important physical parameters in high-relief landscapes is an additional challenge in modelling mountain permafrost 11,83,143,159 . Numerical simulation of lateral heat fluxes in threedimensional temperature fields are important to address changes at greater depth in steep mountain terrain 143,160 . Differential heating of mountain slopes can also substantially increase warming rates at depth in high mountain peaks or ridges 149 .
Empirical and transient modelling approaches have different advantages and limitations, and it is critical to understand these capabilities to meaningfully interpret results on the extent and timing of permafrost loss. While there is high confidence that thaw depth will increase and permafrost extent will decrease, there is lower confidence in the magnitude and timing of the changes 6 . Thus, it is clear that a considerable portion of the area currently underlain by permafrost will experience varying degrees of thaw under warming.
Monitoring of permafrost thermal state since about 1980 provides clear evidence of warming and thawing of permafrost throughout permafrost regions. Permafrost temperatures have typically increased at a rate of around 0.2-0.8 °C per decade, with changes particularly pronounced within colder permafrost regions, including those of the continuous permafrost zone of the Arctic, and in bedrock such as at sites in the European Alps. ALT has correspondingly increased in many regions, particularly in the Russian Arctic where increases of 0.4 m are apparent over a 20-year time frame. Although changes in air temperature are a primary driver of these changes in permafrost thermal state, several other factors including snow cover and vegetation are also important. These observed trends are projected to continue in response to climate warming, albeit with large uncertainties in the magnitude and timing of changes. Indeed, although our understanding of the thermal characteristics of permafrost has developed, progress is needed in many aspects.
Permafrost is a subsurface phenomenon, meaning that monitoring relies on in situ measurements, unlike other cryospheric variables that can be measured using remote-sensing techniques. Considerable spatial gaps in monitoring networks exist, particularly in remote, less accessible areas. Additional monitoring sites in these remote areas, including in the Arctic and mountain ranges outside of Europe, are thus needed to reduce uncertainties in the characterization of permafrost thermal state worldwide. These additional ground thermal monitoring sites could benefit from robust construction and automatic data transmission 28,161 . High-quality and accessible archives with complete metadata and site information on vegetation and subsurface materials, including ground ice content, are critical for climate-related monitoring and analysis. Development of such standards will benefit from the establishment of best practices 28,161 , such as those under development by Global Cryosphere Watch, to ensure standardized and comparable data sets of sufficient quality.
Remote-sensing methods could potentially also address gaps in the in situ monitoring network. Opportunities to better utilize satellite imagery for permafrost characterization have been explored 162 , but available applications cannot directly monitor permafrost thermal state or ALT. However, satellite imagery analysis has been used extensively to map landscape change and ground movements associated with thawing permafrost [163][164][165][166] . These approaches provide evidence of physical changes from larger areas and complement information from ground temperature and ALT monitoring sites. Further development of applications that provide more direct measurements of important permafrost characteristics are required. For example, improved quantification of ground surface elevation and subsidence, in conjunction with thermal measurements at long-term field monitoring sites, would help to establish the extent of permafrost degradation and to reconcile measurements of subsidence with displacement measurements from satellite imagery analyses.
Simulations of future permafrost conditions predict continued warming and permafrost degradation, although there are considerable uncertainties on the magnitude and timing of changes. The relation between permafrost thermal state and climate is complex and depends on local conditions above and below the ground surface. A greater understanding of longer-term interactions between permafrost and climate, vegetation and snow cover is required to reduce uncertainty in responses of the ground thermal regime to climate change. One example is the role of non-conductive heat transfer and the effect of summer precipitation infiltration to the active layer. Most of the knowledge related to this process has been acquired through modelling, and empirical studies are required to better assess the overall impact on permafrost temperatures. Enhancing existing permafrost monitoring sites to include additional types of observations such as air temperature, precipitation, snow cover, soil moisture and vegetation conditions would help to further elucidate relations between the various drivers as the climate changes.
The field-based research suggested here would contribute to improved model representation of interactions between hydrologic processes and geomorphic (landscape) and permafrost conditions, and would reduce uncertainties in projections. Updated information on ground ice conditions is required for model input, and validation with field measurements is needed to ensure reasonable process representation in simulations.
Published online 11 January 2022
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