## Introduction

Warming and thawing (i.e., degradation) of near-surface permafrost can damage infrastructure by reducing substrate strength, increasing mass movement frequency and producing thermokarst activity, making it the greatest threat to infrastructure in cold regions1,2,3,4. Such damage shortens the lifespan of infrastructure and increases maintenance costs, leading to diverse financial risks5. Investments in infrastructure adaptation reduce the engineering damage rate and social inequality6,7 and enhance social-ecosystem resilience in cold regions under a warming climate8. In the Northern Hemisphere, nearly 70% of the current infrastructure is at risk in areas with a high potential for degradation of near-surface permafrost by the middle of this century3. Current infrastructure valued at approximately $21.6 billion could be affected by permafrost degradation, which would require an additional investment of approximately$15.47 billion to maintain the service function of this infrastructure in the circumpolar Arctic by 20609.

The Qinghai-Tibet Plateau (QTP), a dominant part of the Third Pole, has an average altitude of 4000 m above sea level (a.s.l.) and has a developed cryosphere that is characterized by mountain glaciers, snow cover, and permafrost. Most of the Earth’s permafrost in the middle and low latitudes occurs on the QTP, which is warmer than the high Arctic10. Nearly 40% of permafrost in the area is considered to be especially warm and unstable (ground temperature > −0.5 °C)11,12. Warm permafrost is especially vulnerable to climate change and ecosystem disturbances (both natural and human)13,14.

The social and economic development of the vast QTP depends heavily on reliable infrastructure. In past decades, several economically and societally important infrastructure projects have been constructed on the QTP that focus on transportation (e.g., Qinghai-Tibet Highway, Qinghai-Tibet Railway), energy provision (e.g., Qinghai-Tibet DC power transmission line), and structures (e.g., buildings). The expansion of infrastructure has reshaped socioeconomic conditions on the QTP and the surrounding population. More than 10 million people live on the QTP, and hundreds of millions of people rely directly on this infrastructure in the form of food security, energy equality, culture, education, health care, and opportunities for sustainable development15.

In this study, we quantified the future risk of current infrastructure (including major roads, railways, powerlines, and buildings) exposure to permafrost degradation and its additional costs, defined as the difference in net present value for infrastructure replacement over time under the normal case (no permafrost degradation) and under permafrost degradation with and without adaptation on the QTP under four shared socioeconomic pathways (SSP126, SSP245, SSP370, and SSP585) and two global warming (1.5 °C, 2.0 °C above preindustrial levels by the end of this century) conditions in the Paris Agreement (see Methods). A well-trained ensemble statistical/machine learning model was used to project the mean annual ground temperature (MAGT) and active layer thickness (ALT) for the reference period in 2008 (2000–2016) and future periods in 2050 (2040–2060) and 2090 (2080–2100) with a 1 km resolution. A consensus of five hazard indices was used to quantify the potential hazard level of future permafrost degradation. Then, a lifespan replacement model was used to quantify the future cost of the current infrastructure caused by permafrost degradation with and without adaptation. A simplified damage relationship between the potential hazard level of permafrost degradation and the equivalent lifespan of infrastructure was used to parameterize the lifespan replacement model.

Our results demonstrate that approximately 63.3% of the permafrost area will be located in a high-hazard zone under the historical climate scenario (SSP245) by 2090. Correspondingly, approximately 60% of the current infrastructure in the permafrost area will be exposed in the high-hazard zone, and an additional cost of approximately $6.31 billion will be needed to maintain the service functions of the current infrastructure without adaptation measures. However, 20.9% of the potential additional cost can be saved through strategic adaptation measures by 2090. An additional cost of approximately$5.65 billion will be needed, even if the Paris Agreement target (global warming of 2.0 °C) is achieved.

## Results

### Projected changes in permafrost thermal state

The simulated results showed that the area of permafrost extent on the QTP was approximately 101×104 km2, and the average MAGT at a depth of zero annual amplitude (10–25 m) and ALT were −1.72 (−2.23 to −1.30) °C and 2.11 (1.75–2.48) m, respectively, for the reference period in 2008 (2000–2016). The average MAGT over the QTP was projected to increase by 1.55 °C in 2050 (2041–2060) under SSP245 and to further increase by 0.82 °C by the end of this century, i.e., 2090 (2081–2100) (Supplementary Table 1). The average ALT was projected to increase by 0.62 m from the reference period to 2050 (2041–2060) (SSP245) and further increase by 0.26 m by the end of this century. Consistent with the change in MAGT, ALT will increase by 1.61 m under SSP585 (rapid and unconstrained growth scenario) from the reference period to 2090 (2081–2100). Controlling global warming below 1.5 °C may reduce permafrost warming by 0.75 °C relative to the 2 °C target.

The fine-resolution projection suggests that there will be substantial but region-specific changes in MAGT and ALT due to climate change in this century (Supplementary Figure 2). The increase in the average MAGT in the western and southern QTP was generally greater than 1.5 °C from the reference period to 2050 (2041–2060) (SSP245). It was significantly larger than that in the eastern and northern QTP, whereas the corresponding increase was approximately 1.2 °C. The pattern of the ALT change was generally consistent with the change in MAGT. For the areas within 10 km of the Qinghai-Tibet Railway from Golmud to Lhasa, the most important engineering corridor on the QTP, the corresponding increase in average MAGT was approximately 1.36 °C (the ALT increased by 0.64 m) from the reference period to 2050 (SSP245) and increased by another 1.83 °C (ALT increased by 0.96 m) by the end of this century. This warming rate is generally consistent with historical measurement data19. The near synchronous warming of permafrost with near-surface air temperature on the QTP is probably due to the weak surface thermal offset of sparse vegetation, dry soil, thin snow cover, and low organic matter content and is thus climate-driven14.

Permafrost degradation can lead to subsequent hazards that threaten engineering infrastructure through the complex interaction of multiple physical processes, including mechanical processes such as loss of foundation bearing capacity and ground subsidence associated with the phase change of pore water and ground ice in the permafrost, thermal processes such as the development of talik and thermokarst, and mass wasting processes on slopes2. This process of degradation may affect the service function of infrastructure and thus increase the infrastructure repair and replacement frequency. The consequence can be expressed as the shortening of useful life and is closely related to hazard levels.

### Trends in the hazard level of permafrost

Associated with the warming of permafrost and the thickening of the active layer, the hazard level of permafrost on the QTP is rising, but there are significant differences among SSPs. By 2050, the proportion of infrastructure in high-hazard zones is predicted to be approximately 28.66 (7.78–52.35)% under SSP245 (Fig. 1) but will increase to 63.25 (23.25–78.70)% under SSP585 by 2050 and further increase to 83.52 (73.85–95.46)% by the end of this century. Accordingly, the areas of medium and low hazard will decrease (Supplementary Table 2). However, the proportion of infrastructure in high-hazard zones is predicted to be approximately 17.62 (5.83–26.13)% under SSP126 (the green scenario) by 2050, which is significantly smaller than those under other SSPs. Regionally, the high-hazard hotspot areas are mainly distributed in the source area of the Yellow River, the Qinghai-Tibet engineering corridor, and the Xinjiang-Tibet highway corridor (Fig. 1), where the infrastructure is relatively concentrated and may be critically damaged.

### Infrastructure in the high-hazard zone

Currently, more than 9,389 km of roads, 580 km of railways, 2,631 km of power lines, and 1,064,590 m2 of buildings are located in the QTP permafrost area. This infrastructure may be affected by the increasing hazard level of permafrost in the future. By 2050, 38.14% (19.92–60.36%) of roads, 38.76% (11.35–71.30%) of railways, 39.41% (14.82–31.28%) of power lines, and 20.94% (14.82–31.28%) of buildings may be threatened by permafrost degradation in high-hazard areas (SSP245) (Fig. 2a, Supplementary Table 3). These proportions may nearly double over the decades following 2050 (Supplementary Figure 3). The global climate warming goals of the Paris Agreement, i.e., to limit warming to well below 2 °C above preindustrial levels, preferably to 1.5 °C, could have a considerably different influences on infrastructure hazards by the end of this century (Fig. 2b). Controlling global warming below 1.5 °C may reduce the infrastructure in high-hazard zones by approximately half relative to the results under the 2 °C target.

### Additional costs to maintain the service function of the current infrastructure

The lifespan of infrastructure will be significantly reduced due to damage from permafrost degradation. The degree of damage is related to the hazard level of permafrost. Long-term observation data for the Qinghai-Tibet Highway over the past 60 years show that the lifespan of the road may be reduced by more than 50% in high-hazard areas26. This change will lead to a substantial increase in costs due to the damaged infrastructure that needs to be repaired, possibly relocated, or completely replaced to maintain its service function27.

Our assessment shows that significant additional costs will be required to maintain the service function of the current infrastructure. From 2008 (reference period) to 2050, the additional cost of $3.98 (3.33–4.75) billion (net present value, 2.85% annual discount rate) will be needed to cover the costs of permafrost degradation under SSP245 (Fig. 3). The transportation infrastructure includes roads and railways that account for most of the costs, i.e., 93% (87% for roads, 6% for railways) (Supplementary Table 4). Other infrastructure includes power lines and buildings, which account for 7%. Under SSP126 (the green scenario), an additional cost of$3.62 (3.01–4.44) billion will be required by 2050, which is a substantial reduction of $0.35 billion compared to the results under SSP245. This reduction could further increase to$1.59 billion by 2090. The adaptation measures for highways (and paved roads), railways, power lines and buildings would greatly reduce this additional cost (the cost of adaptation measures has been deducted, see Methods) (Fig. 3). By 2050, the percentage of potential cost savings from adaptations is approximately 15.36% (SSP245). This savings could reach 21% by the end of the century. For low-grade roads or high-grade roads in low-risk areas, additional adaptation measures may be less economical (i.e., the cost of adaptation measures is greater than the reduction of maintenance costs), so they were excluded from this analysis. The impact of the global warming goals of the Paris Agreement (2.0 °C or 1.5 °C) on these additional costs is also considerable. Controlling global warming below 1.5 °C may save $1.32 billion relative to the costs under the 2 °C target by the end of the century. ### Distribution of additional costs over the Qinghai-Tibet Plateau The distribution of cumulative additional infrastructure costs during this century varied across the prefectural-level regions over the QTP (Fig. 4a, b). Under the SSP585 scenario, the highest additional costs were projected in the central-eastern regions, including Yushu, Golog, Haixi, and Nagqu, while the lowest additional costs were projected in the northern and southeastern prefectures, including Bayingolin, Lhasa, Linzhi, Qamdo, and Garze (Fig. 4b), due to the small proportion of permafrost or small infrastructure inventory in those areas. Almost all prefectures in permafrost regions will need additional investment in infrastructure, but the investment will be lower under SSP245 than under SSP585 (Fig. 4a, b), indicating the benefits of low carbon development at the global scale on the QTP. The largest reductions in the per capita additional costs between SSP245 and SSP585 were projected in Golog and Yushu (Fig. 4c, d). In both the SSP245 or SSP585 scenarios, the additional investment in Ngari is very important because it is a low-cost corridor relative to the Qinghai-Tibet engineering corridor, which helps to enhance the connectivity between the Qinghai-Tibet Plateau and the surrounding area and thus to enhance the social resilience of the Qinghai-Tibet Plateau. ## Discussion Based on the data-driven or knowledge-informed data-driven projection of permafrost thermal degradation, this study quantified the hazard potential of permafrost degradation, its associated effect on current infrastructure and its future additional maintenance costs with and without adaptation. We found that the near-surface permafrost on the QTP warmed nearly synchronously with the air temperature. A high proportion of infrastructure will be exposed in areas with rapid warming associated with permafrost with high hazard potential. Thus, permafrost degradation increases the risk to and future costs of infrastructure on the QTP even under the green scenario (SSP126) and when controlling global warming below 1.5 °C by the end of the century. Sustainable regional planning and highly resilient infrastructure management require information on the costs of maintaining construction under climate change9,28,29,30. Economic damage information from climate change is also critically important for understanding the benefits of social investments for reducing greenhouse gas emissions and climate mitigation25. This information is available for Alaska1,27, Canada31 and Russia32,33,34,35. For example, the costs of permafrost damage to Alaska’s public infrastructure were estimated to be$1.6 billion for representative concentration pathway (RCP) 4.5 by the end of this century1. In Russia, the total cost of support and maintenance of road and building infrastructure due to permafrost degradation from 2020 to 2050 could be as high as $34 billion33,34. However, these central estimates are lacking for the QTP, which is the largest permafrost region in the middle and low latitudes of the world. This study found that the amount of infrastructure in the QTP permafrost area is less than that in Alaska27, but its economic damage is much larger1. However, this value is much lower than that in Russia30,33,34, where the amount of infrastructure is much greater than that on the QTP due to Russia’s vast area. The larger economic damage on the QTP than in Alaska is probably due to the higher degradation rate of warm, arid and climate-driven permafrost on the QTP14 and the different infrastructure components, and the methods include permafrost projection, stressor–response relationships, and spatial resolution. The damage caused by permafrost degradation in Alaska1 represented only the cost required for infrastructure replacement. It also distinguished the damage caused by permafrost degradation due to flooding, precipitation, and freeze-thaw cycles. In this study, because permafrost degradation is driven by climate change and closely related to air temperature, precipitation, freeze-thaw cycles, and even flooding36,37, infrastructure damage is difficult to separate from these related factors. Therefore, the damage considered in this study is the apparent damage associated with permafrost degradation. Considering this inherent difference, the economic damage estimation in this paper is comparable to that in Melvin et al. (2017) but smaller than the estimation of Larsen et al. (2008). The large additional costs of infrastructure damaged by permafrost degradation on the QTP provide insights in at least two ways. First, adaptation measures (e.g., shading boards, ventilation ducts, thermosiphons, air-cooled and crushed rock embankments for roads and railways; gravel pads for buildings, thermosiphons, fibreglass-reinforced plastic covering, and excavated and pile foundations for power line towers) are generally economical options to increase infrastructure stability at the regional scale. Compared to no adaptation, the proportion of additional cost saved by taking adaptation measures ranges from 12% (SSP126 by 2050,$0.45 billion) to nearly 24% (SSP585 by 2090, $1.74 billion) (Table 1). The benefit of adaptation increases with an increasing warming rate and analysis period. However, it is likely that a deficit would occur (i.e., the increased cost from adaptation is less than that caused by the reduction of replacement costs due to increased lifespan) for low-grade roads (grade 4 and other roads) when adopting measures under all SSPs unless the ratio of the adaptation cost to the construction cost is greatly reduced to the level of high-grade highways in the future. This result is consistent with engineering practices in which adaptive measures are rarely used in low-grade roads. Thus, the damage relationship between the permafrost hazard level and economic loss used in this study is reasonable. Second, the damage is significantly different among socioeconomic development pathways and warming targets. By 2050, compared to the historical scenario (SSP245), the weak mitigation scenario (SSP370) may place an additional nearly 19% of the current infrastructure at high risk, and the corresponding economic damage would increase by nearly 5% ($0.21 billion without adaptation). This proportion may further increase to more than 40% (13%, $0.53 billion) under the rapid and unconstrained growth scenario (SSP585), while the proportion would decrease by 29% (9%,$0.36 billion) under the green scenario (SSP126). By the end of this century, the differences become greater (Supplementary Table 3, Table 4, Supplementary Figure 4). If global warming is controlled to below 1.5 °C by the end of this century, the quantity of high-risk infrastructure will be nearly 57% less than that under the 2 °C target, and the corresponding additional cost will be reduced by approximately 23% (\$1.32 billion without adaptation). This difference highlights the importance of global green development and reducing greenhouse gas emissions to the vulnerability of infrastructure on the QTP. Additionally, the maintenance/repair of roads in permafrost areas is generally much more expensive than normal maintenance in nonpermafrost areas, reaching a more than 8-fold difference in some cases38. The high infrastructure maintenance cost in permafrost areas combined with the amplification effect of warming16,39 may lead to a more negative consequence of climate change on the QTP and thus exacerbate potential social inequality6. Increasing infrastructure investment, the development of less expensive adoption technologies, and a global coordinated green development policy would help to reduce exposure and to enhance the stability of vulnerable infrastructure and safety, thus reducing this social inequality on the QTP.

The vulnerability of infrastructure on the QTP associated with the fragility of social–ecosystem interactions highlights the need for investment in the adaptation and maintenance of infrastructure for sustainable development on the QTP and the surrounding areas. This study provides quantitative information on the additional economic costs and benefits of technological adaptation and global green development of QTP infrastructure. The ultimate investment may be potentially much higher than the conservative and preliminary estimates, depending on future technological, social and economic development and the global socioeconomic pathways.

## Materials and methods

The exposure and risk of the current infrastructure and its future additional costs caused by permafrost degradation were evaluated by integrating a statistical/machine learning model-based ensemble projection, multihazard index, and lifespan replacement model (Supplementary Figure 1). First, based on the MAGT at a depth of zero annual amplitude (10–25 m) and ALT measurements (253 MAGT boreholes and 157 ALT sites) during 2000–2016 (Supplementary Figure 2)10, a well-trained ensemble statistical/machine learning model was used to predict the MAGT and ALT for the reference period in 2008 (2000–2016) and future projections in 2050 (2040–2060) and 2090 (2080–2100) with a 1 km resolution. The downscaled and bias-corrected climate model output, i.e., WorldClim (https://worldclim.org)42, under four shared socioeconomic pathways (SSPs), i.e., green scenario (SSP126), historical scenario (SSP245), weak mitigation scenario (SSP370), and rapid and unconstrained growth scenario (SSP585), and two global warming (1.5 °C, 2.0 °C above preindustrial levels by the end of this century) conditions outlined in the Paris Agreement were used as climate predictor variables together with soil and terrain variables. Second, a consensus of five hazard indices was developed based on the simulated MAGT and ALT and other environmental factors to identify the potential hazard level of permafrost degradation. Finally, a lifespan replacement model was used to quantify the future cost to current infrastructure caused by permafrost degradation with and without adaptation measures based on an infrastructure database and the potential hazard level of permafrost degradation. A simplified damage relationship between the potential hazard level and the useful life of infrastructure was used to parameterize the lifespan replacement model.

### Projection of ground temperature and active layer thickness

MAGT was projected based on an ensemble mean of five statistical/machine learning models (GLM: generalized linear model; GAM: generalized additive model; SVR: support vector regression; RF: random forest; GWR: geographically weighted regression)12. A distance-blocked (3000 m) resampling training dataset with 200 repetitions was used by relating the in situ measurement with eight predictor variables. These variables included the freezing degree-days and thawing degree-days (i.e., the annual degree-day totals below and above 0 °C, respectively), solid precipitation (T ≤ 0 °C), liquid precipitation (T > 0 °C), soil bulk density, soil organic content, solar radiation, and elevation. The uncertainty ranges of the MAGT and ALT predictions quantified using the 97.5th and 2.5th percentiles of the ensemble results with 200 runs. A 10-fold cross-validation showed that the acceptable accuracy of MAGT (RMSE = 0.93 °C, bias = −0.02 °C) was achieved.

The ALT was estimated using the simplified Stefan equation40:

$$ALT=E\sqrt{TDD}$$
(1)

where TDD is thawing degree-days, E is a scaling parameter (E-factor) influenced by local characteristics, including vegetation, snow cover, and local soil texture. The E-factor was estimated based on an ensemble mean of five statistical/machine learning models based on the E-factor apparent measurement at 157 sites for the baseline, and it remained constant in the future periods. Although the E-factor may change with the change in vegetation and snow cover in the future, the effect of vegetation and snow cover on permafrost is small due to the low snow cover, arid climate, and sparse vegetation on the QTP. Compared with the simulation error level of ALT itself, the error caused by the constant E-factor is ignored here43.

A 10-fold cross-validation showed an acceptable accuracy of the E-factor (RMSE=18.7, bias=−0.05).

The freezing degree-days, thawing degree-days, solid precipitation, and liquid precipitation were recalculated based on the downscaled and bias-corrected monthly temperature and precipitation data, i.e., WorldClim version 2.1 (https://worldclim.org)42. Following ref. 44, the WorldClim climate data for 1970–2000 were temporally adjusted to the reference period in 2008 (2000–2016) using the locally smoothed (3×3 pixels) difference between the 2.5-minute WorldClim weather data and the WorldClim climate data. For future periods, i.e., 2050 (2040–2060) and 2090 (2080–2100), the downscaled climate projections from WorldClim, including monthly mean temperature and precipitation, were derived from eight downscaled General Circulation Model outputs of Coupled Model Intercomparison Project phase 6 for four SSPs (126, 245, 370, and 585) with a 0.05° resolution but adjusted to a 1 km resolution using the locally smoothed (3×3 pixels) difference between the SSPs and downscaled Coupled Model Intercomparison Project phase 5 data for 2070 with a 1 km resolution. For the two global warming scenarios, following ref. 45, the mean WorldClim climate data from eleven downscaled General Circulation Model outputs of Coupled Model Intercomparison Project phase 5 for 2061–2080 under RCP2.6 were used for the 1.5 °C global warming condition, and those under RCP4.5 for 2061–2080 were used for the 2.0 °C global warming condition. The soil bulk density, soil organic content, and two terrain-related factors were considered to be unchanged in future periods. The soil bulk density (kg m − 3) and soil organic content (g kg−1) were derived from global SoilGrids250 datasets (https://soilgrids.org)46. Solar radiation (kJ m-2 day-1) data derived from WorldClim version 2.1 and the NASA Shuttle Radar Topography Mission digital elevation model at a 30 arc-second spatial resolution were used.

### Identification of the potential hazard level

Several indices have been developed to evaluate the potential hazard level of permafrost degradation. In this study, to reduce the uncertainty of a single index, a composite index was used to identify the hazard level (high, medium and low) of permafrost degradation that integrated the thermal index (It), settlement index (Is), bearing capacity index (Ib), risk zone index (Ir), and expert-based index (Ia) with surface conditions. The five indices were defined and produced as follows.

First, the thermal index (It) was represented by the relative change in MAGT, which is one of the most direct and reliable indicators for permafrost occurrence and is closely related to bearing capacity and permafrost distress47,48. Following the altitude permafrost classification system for the QTP12 and embankment distress characteristics with varying MAGT26, we classified the permafrost into three types: cold (<−3.0 °C), cool (−1.5 to −3.0 °C), and warm (0 to −1.5 °C). The type transitions during the baseline period and future conditions were used to determine the hazard level (permafrost disappearance or change from cold to warm=high, cold to cool or cool to warm=medium, no type transition=low)1,3.

Second, the settlement index (Is)17 was calculated as follows:

$${I}_{s}=\Delta {{{{{\rm{ALT}}}}}}\times {V}_{ice}$$
(2)

where ΔALT is the relative increase in ALT and Vice is the volumetric proportion of excess ground ice. Ground ice content data with a 1 km resolution estimated based on 164 borehole measurement data and a map of Quaternary sedimentary type over the QTP were used in this study49. Following ref. 3, class-specific values (5, 15 and 35%) were assigned, and the Is values were reclassified into three classes using a nested means procedure50 with the two lower classes combined for a conservative estimate.

Third, the bearing capacity index (Ib) was represented by the relative change in allowable bearing capacity. Bearing capacity was computed using a linear statistical model47 that varied among different soil texture types based on laboratory measurements, but only two soil types were used, which were limited by soil data. The two soil groups were derived from a weighted dominant soil texture class of SoilGrids 1 km data according to coarse and fine sediments (fine=silt and finer class, coarse=sand and coarser class).

$${I}_{b}=\left\{\begin{array}{c}-0.3339 \times {{{{{\rm{MAGT}}}}}}+0.4659,\quad {{{{{\rm{for}}}}}}\,{{{{{\rm{coarse}}}}}}\,{{{{{\rm{class}}}}}}\\ -0.1979\times {{{{{\rm{MAGT}}}}}}+0.3046,\quad {{{{{\rm{for}}}}}}\,{{{{{\rm{fine}}}}}}\,{{{{{\rm{class}}}}}}\end{array}\right.$$
(3)

The resulting Ib values were reclassified into three classes using a nested means procedure.

Fourth, the risk zone index (Ir)51,52 was developed based on a multilevel decision flow diagram by combining the surface condition, soil grain size, ice content, and permafrost thaw potential. First, the SoilGrids 250 m absolute depth to bedrock (cm)46 was used to determine exposed bedrock areas that were directly assigned to the low hazard level51. The soil grain size groups were derived from a weighted dominant soil texture class of SoilGrids 1 km data according to coarse and fine sediments (fine=silt and finer class, coarse=sand and coarser class). A ground ice content with a 1 km resolution49 was used to determine areas of high (>20%) and low (≤20%) ground ice content. The thaw potential of permafrost was defined based on the simulated MAGT (high potential=permafrost thaw; low potential=permafrost remaining).

Fifth, the expert-based index (Ia) was produced using multicriteria decision-making by integrating the relative increase in ALT and MAGT, ground ice content, fine-grained soil content, and slope gradient. All of these criteria were first classified into three classes. For MAGT, the thermal index was used. The original range classes (≤10%, 10–20%, and >20%) of ground ice content were reclassified into three value-specific classes (5, 15 and 35%). The relative increases in ALT, fine-grained sediment, and slope criterion were reclassified using the nested-means approach. The weight coefficients sourced from Hjort et al. (2018)3 were determined based on the analytic hierarchy process.

$${I}_{a}= \; 0.525\times \Delta {{{{{\rm{MAGT}}}}}}+0.248\times {V}_{ice}+0.122\times \Delta {{{{{\rm{ALT}}}}}}+0.071 \\ \times {{{{{\rm{fine}}}}}}\,{{{{{\rm{soil}}}}}}\,{{{{{\rm{content}}}}}}+0.035\times {{{{{\rm{slope}}}}}}\,{{{{{\rm{gradient}}}}}}$$
(4)

The five indices were combined using a majority vote procedure based on ArcMap’s cell statistics tool to represent the potential hazard level of permafrost degradation. In draw situations, i.e., a value had the same number of votes (for example, 2 high hazard vs. 2 low hazard votes, 1 moderate hazard), a moderate hazard level was forced manually. As a result, the high-hazard zone comprised 63.3%, the medium-hazard zone comprised 34.7%, and the low-hazard zone comprised 2% of the study area under the historical scenario (SSP245) for 2090 (2081–2100). The proportions of high-hazard zones, medium-hazard zones, and low-hazard zones were 16.9%, 71%, and 12.1%, respectively, under the green scenario (SSP126) for 2090 (2081–2100).

The uncertainty range of the hazard level corresponding to the uncertainty of the projected MAGT and ALT was also calculated. This uncertainty range will affect the statistics of infrastructure distribution at different hazard levels and ultimately affect the cost calculation.

### Lifespan replacement model

The additional costs of current infrastructure in the future caused by permafrost degradation were assessed using an equivalent lifespan replacement model proposed by Larsen et al. (2008)27 that was improved to allow the calculation of the net present value (PV) of infrastructure economic damage by combining the potential hazard level of permafrost degradation with the equivalent lifespan of infrastructure. This value is based on the assumption that a reduction in the lifespan of infrastructure caused by permafrost degradation leads to higher costs due to the impacted infrastructure that needs to be repaired, relocated, completely replaced more frequently or adapted to the built environment to maintain its service function27. The relationship between the potential hazard level and lifespan of infrastructure is more direct than that of temperature and precipitation in the original model. The equivalent lifespan replacement model is characterized by a clear structure and is easy to understand and has been successfully applied to the economic damage assessment of infrastructure caused by climate change in Alaska and Russia. The additional costs (Φ) are computed as the cost difference under the conditions between permafrost degradation and the normal case:

$$\Phi ={{PV}}_{{Permafrost}{degradation}}-{{PV}}_{{normal}}$$
(5)
$${{PV}}_{{normal}}=\mathop{\sum }\limits_{j}^{8}\mathop{\sum }\limits_{{{{{{\rm{i}}}}}}=2008}^{2050\,{or}\,2090}\frac{{L}_{{{{{{\rm{j}}}}}}}{{RC}}_{j}}{{{{UL}}_{j}(1+r)}^{i-2008}}$$
(6)
$${{PV}}_{{Permafrost}{degradation}}=\mathop{\sum }\limits_{j}^{8}\mathop{\sum }\limits_{h=1}^{3}\mathop{\sum }\limits_{{{{{{\rm{i}}}}}}=2008}^{2050\,{or}\,2090}\frac{{L}_{{{{{{\rm{j}}}}}}}{{RC}}_{j}}{{{{AUL}}_{{hj}}(1+r)}^{i-2008}}$$
(7)